Average Error: 0.1 → 0.0
Time: 13.8s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x - y}{z} - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\frac{x - y}{z} - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r887148 = 4.0;
        double r887149 = x;
        double r887150 = y;
        double r887151 = r887149 - r887150;
        double r887152 = z;
        double r887153 = 0.5;
        double r887154 = r887152 * r887153;
        double r887155 = r887151 - r887154;
        double r887156 = r887148 * r887155;
        double r887157 = r887156 / r887152;
        return r887157;
}
↓
double f(double x, double y, double z) {
        double r887158 = x;
        double r887159 = y;
        double r887160 = r887158 - r887159;
        double r887161 = z;
        double r887162 = r887160 / r887161;
        double r887163 = 0.5;
        double r887164 = r887162 - r887163;
        double r887165 = 4.0;
        double r887166 = r887164 * r887165;
        return r887166;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +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))