Average Error: 0.2 → 0.0
Time: 8.8s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r44250732 = 4.0;
        double r44250733 = x;
        double r44250734 = y;
        double r44250735 = r44250733 - r44250734;
        double r44250736 = z;
        double r44250737 = 0.5;
        double r44250738 = r44250736 * r44250737;
        double r44250739 = r44250735 - r44250738;
        double r44250740 = r44250732 * r44250739;
        double r44250741 = r44250740 / r44250736;
        return r44250741;
}
↓
double f(double x, double y, double z) {
        double r44250742 = x;
        double r44250743 = z;
        double r44250744 = r44250742 / r44250743;
        double r44250745 = y;
        double r44250746 = r44250745 / r44250743;
        double r44250747 = r44250744 - r44250746;
        double r44250748 = 0.5;
        double r44250749 = r44250747 - r44250748;
        double r44250750 = 4.0;
        double r44250751 = r44250749 * r44250750;
        return r44250751;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original0.2
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.2

    \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x - y}{z} - 0.5\right) \cdot 4}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0.5\right) \cdot 4\]

  5. Final simplification0.0

    \[\leadsto \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))