Average Error: 0.1 → 0.0
Time: 7.4s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\frac{x - y}{z} - 0.5\right) \cdot 4\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\frac{x - y}{z} - 0.5\right) \cdot 4
double f(double x, double y, double z) {
        double r968412 = 4.0;
        double r968413 = x;
        double r968414 = y;
        double r968415 = r968413 - r968414;
        double r968416 = z;
        double r968417 = 0.5;
        double r968418 = r968416 * r968417;
        double r968419 = r968415 - r968418;
        double r968420 = r968412 * r968419;
        double r968421 = r968420 / r968416;
        return r968421;
}
↓
double f(double x, double y, double z) {
        double r968422 = x;
        double r968423 = y;
        double r968424 = r968422 - r968423;
        double r968425 = z;
        double r968426 = r968424 / r968425;
        double r968427 = 0.5;
        double r968428 = r968426 - r968427;
        double r968429 = 4.0;
        double r968430 = r968428 * r968429;
        return r968430;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

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))