Average Error: 0.1 → 0.0
Time: 10.0s
Precision: 64
\[\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}\]
↓
\[\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4.0\]
\frac{4.0 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z}
↓
\left(\left(\frac{x}{z} - \frac{y}{z}\right) - 0.5\right) \cdot 4.0
double f(double x, double y, double z) {
        double r42383415 = 4.0;
        double r42383416 = x;
        double r42383417 = y;
        double r42383418 = r42383416 - r42383417;
        double r42383419 = z;
        double r42383420 = 0.5;
        double r42383421 = r42383419 * r42383420;
        double r42383422 = r42383418 - r42383421;
        double r42383423 = r42383415 * r42383422;
        double r42383424 = r42383423 / r42383419;
        return r42383424;
}
↓
double f(double x, double y, double z) {
        double r42383425 = x;
        double r42383426 = z;
        double r42383427 = r42383425 / r42383426;
        double r42383428 = y;
        double r42383429 = r42383428 / r42383426;
        double r42383430 = r42383427 - r42383429;
        double r42383431 = 0.5;
        double r42383432 = r42383430 - r42383431;
        double r42383433 = 4.0;
        double r42383434 = r42383432 * r42383433;
        return r42383434;
}

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
\[4.0 \cdot \frac{x}{z} - \left(2.0 + 4.0 \cdot \frac{y}{z}\right)\]

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019163 
(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))