Average Error: 0.1 → 0.0
Time: 12.5s
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 r81154 = 4.0;
        double r81155 = x;
        double r81156 = y;
        double r81157 = r81155 - r81156;
        double r81158 = z;
        double r81159 = 0.5;
        double r81160 = r81158 * r81159;
        double r81161 = r81157 - r81160;
        double r81162 = r81154 * r81161;
        double r81163 = r81162 / r81158;
        return r81163;
}
↓
double f(double x, double y, double z) {
        double r81164 = 4.0;
        double r81165 = x;
        double r81166 = y;
        double r81167 = r81165 - r81166;
        double r81168 = z;
        double r81169 = r81167 / r81168;
        double r81170 = 0.5;
        double r81171 = r81169 - r81170;
        double r81172 = r81164 * r81171;
        return r81172;
}

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 2019310 
(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))