Average Error: 0.2 → 0.0
Time: 9.6s
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 r36170106 = 4.0;
        double r36170107 = x;
        double r36170108 = y;
        double r36170109 = r36170107 - r36170108;
        double r36170110 = z;
        double r36170111 = 0.5;
        double r36170112 = r36170110 * r36170111;
        double r36170113 = r36170109 - r36170112;
        double r36170114 = r36170106 * r36170113;
        double r36170115 = r36170114 / r36170110;
        return r36170115;
}
↓
double f(double x, double y, double z) {
        double r36170116 = 4.0;
        double r36170117 = x;
        double r36170118 = y;
        double r36170119 = r36170117 - r36170118;
        double r36170120 = z;
        double r36170121 = r36170119 / r36170120;
        double r36170122 = 0.5;
        double r36170123 = r36170121 - r36170122;
        double r36170124 = r36170116 * r36170123;
        return r36170124;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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))