diff --git a/apps/shared/continuous_function_cache.cpp b/apps/shared/continuous_function_cache.cpp
index df24141a9..a2fac0c01 100644
--- a/apps/shared/continuous_function_cache.cpp
+++ b/apps/shared/continuous_function_cache.cpp
@@ -19,6 +19,14 @@ void ContinuousFunctionCache::PrepareForCaching(void * fun, ContinuousFunctionCa
   }
 
   ContinuousFunction * function = static_cast<ContinuousFunction *>(fun);
+  if (tStep < 3 * k_cacheHitTolerance) {
+    /* If tStep is lower than twice the tolerance, we risk shifting the index
+     * by 1 for cache hits. As an added safety, we add another buffer of
+     * k_cacheHitTolerance, raising the threshold for caching to three times
+     * the tolerance. */
+    function->clearCache();
+    return;
+  }
   if (function->cache() != cache) {
     cache->clear();
     function->setCache(cache);
diff --git a/apps/shared/continuous_function_cache.h b/apps/shared/continuous_function_cache.h
index ee5bf598d..60faca9b8 100644
--- a/apps/shared/continuous_function_cache.h
+++ b/apps/shared/continuous_function_cache.h
@@ -27,7 +27,15 @@ public:
   void clear();
   Poincare::Coordinate2D<float> valueForParameter(const ContinuousFunction * function, Poincare::Context * context, float t);
 private:
-  static constexpr float k_cacheHitTolerance = 1e-3;
+  /* We need a certain amount of tolerance since we try to evaluate the
+   * equality of floats. But the value has to be chosen carefully. Too high of
+   * a tolerance causes false positives, which lead to errors in curves
+   * (ex : 1/x with a vertical line at 0). Too low of a tolerance causes false
+   * negatives, which slows down the drawing.
+   *
+   * The value 128*FLT_EPSILON has been found to be the lowest for which all
+   * indices verify indexForParameter(tMin + index * tStep) = index. */
+  static constexpr float k_cacheHitTolerance = 128 * FLT_EPSILON;
 
   void invalidateBetween(int iInf, int iSup);
   void setRange(ContinuousFunction * function, float tMin, float tStep);