Average Error: 0.1 → 0.0
Time: 1.3s
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 r882315 = 4.0;
        double r882316 = x;
        double r882317 = y;
        double r882318 = r882316 - r882317;
        double r882319 = z;
        double r882320 = 0.5;
        double r882321 = r882319 * r882320;
        double r882322 = r882318 - r882321;
        double r882323 = r882315 * r882322;
        double r882324 = r882323 / r882319;
        return r882324;
}
↓
double f(double x, double y, double z) {
        double r882325 = 4.0;
        double r882326 = x;
        double r882327 = y;
        double r882328 = r882326 - r882327;
        double r882329 = z;
        double r882330 = r882328 / r882329;
        double r882331 = r882325 * r882330;
        double r882332 = 2.0;
        double r882333 = -r882332;
        double r882334 = r882331 + r882333;
        return r882334;
}

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

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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))