Average Error: 0.2 → 0.0
Time: 13.8s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right)
double f(double x, double y, double z) {
        double r620097 = 4.0;
        double r620098 = x;
        double r620099 = y;
        double r620100 = r620098 - r620099;
        double r620101 = z;
        double r620102 = 0.5;
        double r620103 = r620101 * r620102;
        double r620104 = r620100 - r620103;
        double r620105 = r620097 * r620104;
        double r620106 = r620105 / r620101;
        return r620106;
}
↓
double f(double x, double y, double z) {
        double r620107 = 4.0;
        double r620108 = x;
        double r620109 = z;
        double r620110 = r620108 / r620109;
        double r620111 = y;
        double r620112 = r620111 / r620109;
        double r620113 = r620110 - r620112;
        double r620114 = 0.5;
        double r620115 = r620113 - r620114;
        double r620116 = r620107 * r620115;
        return r620116;
}

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. 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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(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))