Average Error: 0.2 → 0.0
Time: 8.6s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2
double f(double x, double y, double z) {
        double r41408008 = 4.0;
        double r41408009 = x;
        double r41408010 = y;
        double r41408011 = r41408009 - r41408010;
        double r41408012 = z;
        double r41408013 = 0.5;
        double r41408014 = r41408012 * r41408013;
        double r41408015 = r41408011 - r41408014;
        double r41408016 = r41408008 * r41408015;
        double r41408017 = r41408016 / r41408012;
        return r41408017;
}
↓
double f(double x, double y, double z) {
        double r41408018 = 4.0;
        double r41408019 = x;
        double r41408020 = z;
        double r41408021 = r41408019 / r41408020;
        double r41408022 = y;
        double r41408023 = r41408022 / r41408020;
        double r41408024 = r41408021 - r41408023;
        double r41408025 = r41408018 * r41408024;
        double r41408026 = 2.0;
        double r41408027 = r41408025 - r41408026;
        return r41408027;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 2\]

  6. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]

Reproduce

herbie shell --seed 2019192 
(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))