Average Error: 0.2 → 0.0
Time: 1.4s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \frac{x - y}{z} + \left(-2\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \frac{x - y}{z} + \left(-2\right)
double f(double x, double y, double z) {
        double r893533 = 4.0;
        double r893534 = x;
        double r893535 = y;
        double r893536 = r893534 - r893535;
        double r893537 = z;
        double r893538 = 0.5;
        double r893539 = r893537 * r893538;
        double r893540 = r893536 - r893539;
        double r893541 = r893533 * r893540;
        double r893542 = r893541 / r893537;
        return r893542;
}
↓
double f(double x, double y, double z) {
        double r893543 = 4.0;
        double r893544 = x;
        double r893545 = y;
        double r893546 = r893544 - r893545;
        double r893547 = z;
        double r893548 = r893546 / r893547;
        double r893549 = r893543 * r893548;
        double r893550 = 2.0;
        double r893551 = -r893550;
        double r893552 = r893549 + r893551;
        return r893552;
}

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

Original0.2
Target0.0
Herbie0.0
\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.2

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

  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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 
(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))