Average Error: 0.2 → 0.2
Time: 18.0s
Precision: 64
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[4.0 \cdot \left(\frac{1}{\frac{z}{x - y}} - 0.5\right)\]
\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
4.0 \cdot \left(\frac{1}{\frac{z}{x - y}} - 0.5\right)
double f(double x, double y, double z) {
        double r28838319 = 4.0;
        double r28838320 = x;
        double r28838321 = y;
        double r28838322 = r28838320 - r28838321;
        double r28838323 = z;
        double r28838324 = 0.5;
        double r28838325 = r28838323 * r28838324;
        double r28838326 = r28838322 - r28838325;
        double r28838327 = r28838319 * r28838326;
        double r28838328 = r28838327 / r28838323;
        return r28838328;
}
↓
double f(double x, double y, double z) {
        double r28838329 = 4.0;
        double r28838330 = 1.0;
        double r28838331 = z;
        double r28838332 = x;
        double r28838333 = y;
        double r28838334 = r28838332 - r28838333;
        double r28838335 = r28838331 / r28838334;
        double r28838336 = r28838330 / r28838335;
        double r28838337 = 0.5;
        double r28838338 = r28838336 - r28838337;
        double r28838339 = r28838329 * r28838338;
        return r28838339;
}

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

Original0.2
Target0.0
Herbie0.2
\[4.0 \cdot \frac{x}{z} - \left(2.0 + 4.0 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.2

    \[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\frac{x - y}{z} - 0.5\right) \cdot 4.0}\]
  3. Using strategy rm

  4. Applied clear-num0.2

    \[\leadsto \left(\color{blue}{\frac{1}{\frac{z}{x - y}}} - 0.5\right) \cdot 4.0\]

  5. Final simplification0.2

    \[\leadsto 4.0 \cdot \left(\frac{1}{\frac{z}{x - y}} - 0.5\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(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))