Average Error: 0.1 → 0.0
Time: 9.5s
Precision: 64
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4.0 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)\]
\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4.0 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)
double f(double x, double y, double z) {
        double r36119911 = 4.0;
        double r36119912 = x;
        double r36119913 = y;
        double r36119914 = r36119912 - r36119913;
        double r36119915 = z;
        double r36119916 = 0.5;
        double r36119917 = r36119915 * r36119916;
        double r36119918 = r36119914 - r36119917;
        double r36119919 = r36119911 * r36119918;
        double r36119920 = r36119919 / r36119915;
        return r36119920;
}
↓
double f(double x, double y, double z) {
        double r36119921 = 4.0;
        double r36119922 = x;
        double r36119923 = z;
        double r36119924 = r36119922 / r36119923;
        double r36119925 = y;
        double r36119926 = r36119925 / r36119923;
        double r36119927 = 0.5;
        double r36119928 = r36119926 + r36119927;
        double r36119929 = r36119924 - r36119928;
        double r36119930 = r36119921 * r36119929;
        return r36119930;
}

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
\[4.0 \cdot \frac{x}{z} - \left(2.0 + 4.0 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

    \[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(\frac{x - y}{z} - 0.5\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 4.0 \cdot \left(\color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 0.5\right)\]

  5. Applied associate--l-0.0

    \[\leadsto 4.0 \cdot \color{blue}{\left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)}\]

  6. Final simplification0.0

    \[\leadsto 4.0 \cdot \left(\frac{x}{z} - \left(\frac{y}{z} + 0.5\right)\right)\]

Reproduce

herbie shell --seed 2019163 
(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))