Average Error: 0.1 → 0.0
Time: 13.3s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)
double f(double x, double y, double z) {
        double r525906 = 4.0;
        double r525907 = x;
        double r525908 = y;
        double r525909 = r525907 - r525908;
        double r525910 = z;
        double r525911 = 0.5;
        double r525912 = r525910 * r525911;
        double r525913 = r525909 - r525912;
        double r525914 = r525906 * r525913;
        double r525915 = r525914 / r525910;
        return r525915;
}
↓
double f(double x, double y, double z) {
        double r525916 = 4.0;
        double r525917 = x;
        double r525918 = z;
        double r525919 = r525917 / r525918;
        double r525920 = y;
        double r525921 = r525920 / r525918;
        double r525922 = 0.5;
        double r525923 = r525921 + r525922;
        double r525924 = r525919 - r525923;
        double r525925 = r525916 * r525924;
        return r525925;
}

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

Original0.1
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. Applied associate--l-0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(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))