Average Error: 0.1 → 0.0
Time: 7.8s
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 r931260 = 4.0;
        double r931261 = x;
        double r931262 = y;
        double r931263 = r931261 - r931262;
        double r931264 = z;
        double r931265 = 0.5;
        double r931266 = r931264 * r931265;
        double r931267 = r931263 - r931266;
        double r931268 = r931260 * r931267;
        double r931269 = r931268 / r931264;
        return r931269;
}
↓
double f(double x, double y, double z) {
        double r931270 = x;
        double r931271 = y;
        double r931272 = r931270 - r931271;
        double r931273 = z;
        double r931274 = r931272 / r931273;
        double r931275 = 0.5;
        double r931276 = r931274 - r931275;
        double r931277 = 4.0;
        double r931278 = r931276 * r931277;
        return r931278;
}

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 +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))