Average Error: 0.2 → 0.0
Time: 2.3s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)
double f(double x, double y, double z) {
        double r215464 = 1.0;
        double r215465 = 4.0;
        double r215466 = x;
        double r215467 = y;
        double r215468 = 0.75;
        double r215469 = r215467 * r215468;
        double r215470 = r215466 + r215469;
        double r215471 = z;
        double r215472 = r215470 - r215471;
        double r215473 = r215465 * r215472;
        double r215474 = r215473 / r215467;
        double r215475 = r215464 + r215474;
        return r215475;
}
↓
double f(double x, double y, double z) {
        double r215476 = 1.0;
        double r215477 = 4.0;
        double r215478 = 0.75;
        double r215479 = x;
        double r215480 = y;
        double r215481 = r215479 / r215480;
        double r215482 = z;
        double r215483 = r215482 / r215480;
        double r215484 = r215481 - r215483;
        double r215485 = r215478 + r215484;
        double r215486 = r215477 * r215485;
        double r215487 = r215476 + r215486;
        return r215487;
}

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 0.2

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + 4 \cdot \left(0.75 + \frac{x - z}{y}\right)}\]
  3. Using strategy rm

  4. Applied div-sub0.0

    \[\leadsto 1 + 4 \cdot \left(0.75 + \color{blue}{\left(\frac{x}{y} - \frac{z}{y}\right)}\right)\]

  5. Final simplification0.0

    \[\leadsto 1 + 4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right)\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))