Average Error: 0.1 → 0.2
Time: 7.2s
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 r471369 = 4.0;
        double r471370 = x;
        double r471371 = y;
        double r471372 = r471370 - r471371;
        double r471373 = z;
        double r471374 = 0.5;
        double r471375 = r471373 * r471374;
        double r471376 = r471372 - r471375;
        double r471377 = r471369 * r471376;
        double r471378 = r471377 / r471373;
        return r471378;
}
↓
double f(double x, double y, double z) {
        double r471379 = 4.0;
        double r471380 = z;
        double r471381 = r471379 / r471380;
        double r471382 = x;
        double r471383 = y;
        double r471384 = r471382 - r471383;
        double r471385 = r471381 * r471384;
        double r471386 = 2.0;
        double r471387 = r471385 - r471386;
        return r471387;
}

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. Simplified0.0

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

  5. Applied div-sub0.0

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019298 
(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))