Average Error: 0.2 → 0.0
Time: 10.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r13431564 = 1.0;
        double r13431565 = 4.0;
        double r13431566 = x;
        double r13431567 = y;
        double r13431568 = 0.75;
        double r13431569 = r13431567 * r13431568;
        double r13431570 = r13431566 + r13431569;
        double r13431571 = z;
        double r13431572 = r13431570 - r13431571;
        double r13431573 = r13431565 * r13431572;
        double r13431574 = r13431573 / r13431567;
        double r13431575 = r13431564 + r13431574;
        return r13431575;
}
↓
double f(double x, double y, double z) {
        double r13431576 = 4.0;
        double r13431577 = x;
        double r13431578 = y;
        double r13431579 = r13431577 / r13431578;
        double r13431580 = z;
        double r13431581 = r13431580 / r13431578;
        double r13431582 = r13431579 - r13431581;
        double r13431583 = r13431576 * r13431582;
        double r13431584 = r13431576 + r13431583;
        return r13431584;
}

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 0.2

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

  2. Simplified0.0

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

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))