Average Error: 0.1 → 0.0
Time: 9.2s
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 r791337 = 4.0;
        double r791338 = x;
        double r791339 = y;
        double r791340 = r791338 - r791339;
        double r791341 = z;
        double r791342 = 0.5;
        double r791343 = r791341 * r791342;
        double r791344 = r791340 - r791343;
        double r791345 = r791337 * r791344;
        double r791346 = r791345 / r791341;
        return r791346;
}
↓
double f(double x, double y, double z) {
        double r791347 = 4.0;
        double r791348 = x;
        double r791349 = y;
        double r791350 = r791348 - r791349;
        double r791351 = z;
        double r791352 = r791350 / r791351;
        double r791353 = 0.5;
        double r791354 = r791352 - r791353;
        double r791355 = r791347 * r791354;
        return r791355;
}

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 2020047 +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))