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 r225556 = 1.0;
        double r225557 = 4.0;
        double r225558 = x;
        double r225559 = y;
        double r225560 = 0.25;
        double r225561 = r225559 * r225560;
        double r225562 = r225558 + r225561;
        double r225563 = z;
        double r225564 = r225562 - r225563;
        double r225565 = r225557 * r225564;
        double r225566 = r225565 / r225559;
        double r225567 = r225556 + r225566;
        return r225567;
}
↓
double f(double x, double y, double z) {
        double r225568 = 1.0;
        double r225569 = 0.25;
        double r225570 = 4.0;
        double r225571 = r225569 * r225570;
        double r225572 = r225568 + r225571;
        double r225573 = x;
        double r225574 = z;
        double r225575 = r225573 - r225574;
        double r225576 = y;
        double r225577 = r225575 / r225576;
        double r225578 = r225577 * r225570;
        double r225579 = r225572 + r225578;
        return r225579;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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 2020024 
(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)))