Average Error: 0.2 → 0.0
Time: 10.5s
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 r13601820 = 1.0;
        double r13601821 = 4.0;
        double r13601822 = x;
        double r13601823 = y;
        double r13601824 = 0.75;
        double r13601825 = r13601823 * r13601824;
        double r13601826 = r13601822 + r13601825;
        double r13601827 = z;
        double r13601828 = r13601826 - r13601827;
        double r13601829 = r13601821 * r13601828;
        double r13601830 = r13601829 / r13601823;
        double r13601831 = r13601820 + r13601830;
        return r13601831;
}
↓
double f(double x, double y, double z) {
        double r13601832 = 4.0;
        double r13601833 = x;
        double r13601834 = y;
        double r13601835 = r13601833 / r13601834;
        double r13601836 = z;
        double r13601837 = r13601836 / r13601834;
        double r13601838 = r13601835 - r13601837;
        double r13601839 = r13601832 * r13601838;
        double r13601840 = r13601832 + r13601839;
        return r13601840;
}

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 0.2

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

  2. Simplified0.0

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

  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 2019172 
(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)))