Average Error: 0.1 → 0.0
Time: 1.6s
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 r937323 = 4.0;
        double r937324 = x;
        double r937325 = y;
        double r937326 = r937324 - r937325;
        double r937327 = z;
        double r937328 = 0.5;
        double r937329 = r937327 * r937328;
        double r937330 = r937326 - r937329;
        double r937331 = r937323 * r937330;
        double r937332 = r937331 / r937327;
        return r937332;
}
↓
double f(double x, double y, double z) {
        double r937333 = 4.0;
        double r937334 = x;
        double r937335 = y;
        double r937336 = r937334 - r937335;
        double r937337 = z;
        double r937338 = r937336 / r937337;
        double r937339 = r937333 * r937338;
        double r937340 = 2.0;
        double r937341 = -r937340;
        double r937342 = r937339 + r937341;
        return r937342;
}

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 2020060 
(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))