Average Error: 0.1 → 0.2
Time: 7.9s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\frac{4}{z} \cdot \left(x - y\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\frac{4}{z} \cdot \left(x - y\right) - 2
double f(double x, double y, double z) {
        double r572439 = 4.0;
        double r572440 = x;
        double r572441 = y;
        double r572442 = r572440 - r572441;
        double r572443 = z;
        double r572444 = 0.5;
        double r572445 = r572443 * r572444;
        double r572446 = r572442 - r572445;
        double r572447 = r572439 * r572446;
        double r572448 = r572447 / r572443;
        return r572448;
}
↓
double f(double x, double y, double z) {
        double r572449 = 4.0;
        double r572450 = z;
        double r572451 = r572449 / r572450;
        double r572452 = x;
        double r572453 = y;
        double r572454 = r572452 - r572453;
        double r572455 = r572451 * r572454;
        double r572456 = 2.0;
        double r572457 = r572455 - r572456;
        return r572457;
}

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
Herbie0.2
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Final simplification0.2

    \[\leadsto \frac{4}{z} \cdot \left(x - y\right) - 2\]

Reproduce

herbie shell --seed 2019291 
(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))