Average Error: 0.1 → 0.0
Time: 11.3s
Precision: 64
\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]
\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2
double f(double x, double y, double z) {
        double r630261 = 4.0;
        double r630262 = x;
        double r630263 = y;
        double r630264 = r630262 - r630263;
        double r630265 = z;
        double r630266 = 0.5;
        double r630267 = r630265 * r630266;
        double r630268 = r630264 - r630267;
        double r630269 = r630261 * r630268;
        double r630270 = r630269 / r630265;
        return r630270;
}
↓
double f(double x, double y, double z) {
        double r630271 = 4.0;
        double r630272 = x;
        double r630273 = z;
        double r630274 = r630272 / r630273;
        double r630275 = y;
        double r630276 = r630275 / r630273;
        double r630277 = r630274 - r630276;
        double r630278 = r630271 * r630277;
        double r630279 = 2.0;
        double r630280 = r630278 - r630279;
        return r630280;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x}{z} - \left(4 \cdot \frac{y}{z} + 2\right)}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto 4 \cdot \color{blue}{\left(\frac{x}{z} - \frac{y}{z}\right)} - 2\]

  6. Final simplification0.0

    \[\leadsto 4 \cdot \left(\frac{x}{z} - \frac{y}{z}\right) - 2\]

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))