Average Error: 0.1 → 0.0
Time: 12.9s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x - y}{z} - 0.5\right)\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x - y}{z} - 0.5\right)
double f(double x, double y, double z) {
        double r644364 = 4.0;
        double r644365 = x;
        double r644366 = y;
        double r644367 = r644365 - r644366;
        double r644368 = z;
        double r644369 = 0.5;
        double r644370 = r644368 * r644369;
        double r644371 = r644367 - r644370;
        double r644372 = r644364 * r644371;
        double r644373 = r644372 / r644368;
        return r644373;
}
↓
double f(double x, double y, double z) {
        double r644374 = 4.0;
        double r644375 = x;
        double r644376 = y;
        double r644377 = r644375 - r644376;
        double r644378 = z;
        double r644379 = r644377 / r644378;
        double r644380 = 0.5;
        double r644381 = r644379 - r644380;
        double r644382 = r644374 * r644381;
        return r644382;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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))