Average Error: 0.2 → 0.0
Time: 1.9s
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 r869517 = 4.0;
        double r869518 = x;
        double r869519 = y;
        double r869520 = r869518 - r869519;
        double r869521 = z;
        double r869522 = 0.5;
        double r869523 = r869521 * r869522;
        double r869524 = r869520 - r869523;
        double r869525 = r869517 * r869524;
        double r869526 = r869525 / r869521;
        return r869526;
}
↓
double f(double x, double y, double z) {
        double r869527 = 4.0;
        double r869528 = x;
        double r869529 = y;
        double r869530 = r869528 - r869529;
        double r869531 = z;
        double r869532 = r869530 / r869531;
        double r869533 = r869527 * r869532;
        double r869534 = 2.0;
        double r869535 = -r869534;
        double r869536 = r869533 + r869535;
        return r869536;
}

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 2020064 
(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))