Average Error: 0.1 → 0.0
Time: 11.1s
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 r27228912 = 4.0;
        double r27228913 = x;
        double r27228914 = y;
        double r27228915 = r27228913 - r27228914;
        double r27228916 = z;
        double r27228917 = 0.5;
        double r27228918 = r27228916 * r27228917;
        double r27228919 = r27228915 - r27228918;
        double r27228920 = r27228912 * r27228919;
        double r27228921 = r27228920 / r27228916;
        return r27228921;
}
↓
double f(double x, double y, double z) {
        double r27228922 = 4.0;
        double r27228923 = x;
        double r27228924 = z;
        double r27228925 = r27228923 / r27228924;
        double r27228926 = y;
        double r27228927 = r27228926 / r27228924;
        double r27228928 = r27228925 - r27228927;
        double r27228929 = r27228922 * r27228928;
        double r27228930 = 2.0;
        double r27228931 = r27228929 - r27228930;
        return r27228931;
}

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. 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 2019179 
(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))