Average Error: 0.1 → 0.0
Time: 8.0s
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 r22921663 = 4.0;
        double r22921664 = x;
        double r22921665 = y;
        double r22921666 = r22921664 - r22921665;
        double r22921667 = z;
        double r22921668 = 0.5;
        double r22921669 = r22921667 * r22921668;
        double r22921670 = r22921666 - r22921669;
        double r22921671 = r22921663 * r22921670;
        double r22921672 = r22921671 / r22921667;
        return r22921672;
}
↓
double f(double x, double y, double z) {
        double r22921673 = 4.0;
        double r22921674 = x;
        double r22921675 = y;
        double r22921676 = r22921674 - r22921675;
        double r22921677 = z;
        double r22921678 = r22921676 / r22921677;
        double r22921679 = 0.5;
        double r22921680 = r22921678 - r22921679;
        double r22921681 = r22921673 * r22921680;
        return r22921681;
}

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

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

Reproduce

herbie shell --seed 2019172 +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))