Average Error: 0.1 → 0.0
Time: 1.6s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) + \left(-2\right)
double f(double x, double y, double z) {
        double r882862 = 4.0;
        double r882863 = x;
        double r882864 = y;
        double r882865 = r882863 - r882864;
        double r882866 = z;
        double r882867 = 0.5;
        double r882868 = r882866 * r882867;
        double r882869 = r882865 - r882868;
        double r882870 = r882862 * r882869;
        double r882871 = r882870 / r882866;
        return r882871;
}
↓
double f(double x, double y, double z) {
        double r882872 = 4.0;
        double r882873 = x;
        double r882874 = z;
        double r882875 = r882873 / r882874;
        double r882876 = y;
        double r882877 = r882876 / r882874;
        double r882878 = r882875 - r882877;
        double r882879 = r882872 * r882878;
        double r882880 = 2.0;
        double r882881 = -r882880;
        double r882882 = r882879 + r882881;
        return r882882;
}

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

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

  5. Applied div-sub0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 
(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))