Average Error: 0.1 → 0.0
Time: 12.4s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x - y}{z} - 0.5\right)
double f(double x, double y, double z) {
        double r531108 = 4.0;
        double r531109 = x;
        double r531110 = y;
        double r531111 = r531109 - r531110;
        double r531112 = z;
        double r531113 = 0.5;
        double r531114 = r531112 * r531113;
        double r531115 = r531111 - r531114;
        double r531116 = r531108 * r531115;
        double r531117 = r531116 / r531112;
        return r531117;
}
↓
double f(double x, double y, double z) {
        double r531118 = 4.0;
        double r531119 = x;
        double r531120 = y;
        double r531121 = r531119 - r531120;
        double r531122 = z;
        double r531123 = r531121 / r531122;
        double r531124 = 0.5;
        double r531125 = r531123 - r531124;
        double r531126 = r531118 * r531125;
        return r531126;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(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))