Average Error: 0.1 → 0.0
Time: 6.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \left(0.25 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1
double f(double x, double y, double z) {
        double r314487 = 1.0;
        double r314488 = 4.0;
        double r314489 = x;
        double r314490 = y;
        double r314491 = 0.25;
        double r314492 = r314490 * r314491;
        double r314493 = r314489 + r314492;
        double r314494 = z;
        double r314495 = r314493 - r314494;
        double r314496 = r314488 * r314495;
        double r314497 = r314496 / r314490;
        double r314498 = r314487 + r314497;
        return r314498;
}
↓
double f(double x, double y, double z) {
        double r314499 = 4.0;
        double r314500 = 0.25;
        double r314501 = x;
        double r314502 = y;
        double r314503 = r314501 / r314502;
        double r314504 = z;
        double r314505 = r314504 / r314502;
        double r314506 = r314503 - r314505;
        double r314507 = r314500 + r314506;
        double r314508 = r314499 * r314507;
        double r314509 = 1.0;
        double r314510 = r314508 + r314509;
        return r314510;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))