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 r96341 = 4.0;
        double r96342 = x;
        double r96343 = y;
        double r96344 = r96342 - r96343;
        double r96345 = z;
        double r96346 = 0.5;
        double r96347 = r96345 * r96346;
        double r96348 = r96344 - r96347;
        double r96349 = r96341 * r96348;
        double r96350 = r96349 / r96345;
        return r96350;
}
↓
double f(double x, double y, double z) {
        double r96351 = 4.0;
        double r96352 = x;
        double r96353 = y;
        double r96354 = r96352 - r96353;
        double r96355 = z;
        double r96356 = r96354 / r96355;
        double r96357 = 0.5;
        double r96358 = r96356 - r96357;
        double r96359 = r96351 * r96358;
        return r96359;
}

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 2019310 +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))