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 r857479 = 4.0;
        double r857480 = x;
        double r857481 = y;
        double r857482 = r857480 - r857481;
        double r857483 = z;
        double r857484 = 0.5;
        double r857485 = r857483 * r857484;
        double r857486 = r857482 - r857485;
        double r857487 = r857479 * r857486;
        double r857488 = r857487 / r857483;
        return r857488;
}
↓
double f(double x, double y, double z) {
        double r857489 = 4.0;
        double r857490 = x;
        double r857491 = y;
        double r857492 = r857490 - r857491;
        double r857493 = z;
        double r857494 = r857492 / r857493;
        double r857495 = r857489 * r857494;
        double r857496 = 2.0;
        double r857497 = -r857496;
        double r857498 = r857495 + r857497;
        return r857498;
}

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 2020035 
(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))