Average Error: 0.1 → 0.0
Time: 5.1s
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 r949187 = 4.0;
        double r949188 = x;
        double r949189 = y;
        double r949190 = r949188 - r949189;
        double r949191 = z;
        double r949192 = 0.5;
        double r949193 = r949191 * r949192;
        double r949194 = r949190 - r949193;
        double r949195 = r949187 * r949194;
        double r949196 = r949195 / r949191;
        return r949196;
}
↓
double f(double x, double y, double z) {
        double r949197 = x;
        double r949198 = y;
        double r949199 = r949197 - r949198;
        double r949200 = z;
        double r949201 = r949199 / r949200;
        double r949202 = 0.5;
        double r949203 = r949201 - r949202;
        double r949204 = 4.0;
        double r949205 = r949203 * r949204;
        return r949205;
}

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 2020046 
(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))