Average Error: 0.1 → 0.0
Time: 18.1s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)
double f(double x, double y, double z) {
        double r570709 = 4.0;
        double r570710 = x;
        double r570711 = y;
        double r570712 = r570710 - r570711;
        double r570713 = z;
        double r570714 = 0.5;
        double r570715 = r570713 * r570714;
        double r570716 = r570712 - r570715;
        double r570717 = r570709 * r570716;
        double r570718 = r570717 / r570713;
        return r570718;
}
↓
double f(double x, double y, double z) {
        double r570719 = 4.0;
        double r570720 = x;
        double r570721 = z;
        double r570722 = r570720 / r570721;
        double r570723 = y;
        double r570724 = r570723 / r570721;
        double r570725 = r570722 - r570724;
        double r570726 = 0.5;
        double r570727 = r570725 - r570726;
        double r570728 = r570719 * r570727;
        return r570728;
}

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

Original0.1
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4 (/ x z)) (+ 2 (* 4 (/ y z))))

  (/ (* 4 (- (- x y) (* z 0.5))) z))