Average Error: 0.1 → 0.0
Time: 2.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r234352 = 1.0;
        double r234353 = 4.0;
        double r234354 = x;
        double r234355 = y;
        double r234356 = 0.25;
        double r234357 = r234355 * r234356;
        double r234358 = r234354 + r234357;
        double r234359 = z;
        double r234360 = r234358 - r234359;
        double r234361 = r234353 * r234360;
        double r234362 = r234361 / r234355;
        double r234363 = r234352 + r234362;
        return r234363;
}
↓
double f(double x, double y, double z) {
        double r234364 = 1.0;
        double r234365 = 0.25;
        double r234366 = 4.0;
        double r234367 = r234365 * r234366;
        double r234368 = r234364 + r234367;
        double r234369 = x;
        double r234370 = z;
        double r234371 = r234369 - r234370;
        double r234372 = y;
        double r234373 = r234371 / r234372;
        double r234374 = r234373 * r234366;
        double r234375 = r234368 + r234374;
        return r234375;
}

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

Derivation

  1. Initial program 0.1

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + 4 \cdot \left(0.25 + \frac{x - z}{y}\right)}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in0.0

    \[\leadsto 1 + \color{blue}{\left(0.25 \cdot 4 + \frac{x - z}{y} \cdot 4\right)}\]

  5. Applied associate-+r+0.0

    \[\leadsto \color{blue}{\left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4}\]

  6. Final simplification0.0

    \[\leadsto \left(1 + 0.25 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))