Average Error: 0.1 → 0.0
Time: 1.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[\left(1 + 0.25 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
\left(1 + 0.25 \cdot 4\right) + \left(\frac{x}{y} - \frac{z}{y}\right) \cdot 4
double f(double x, double y, double z) {
        double r317816 = 1.0;
        double r317817 = 4.0;
        double r317818 = x;
        double r317819 = y;
        double r317820 = 0.25;
        double r317821 = r317819 * r317820;
        double r317822 = r317818 + r317821;
        double r317823 = z;
        double r317824 = r317822 - r317823;
        double r317825 = r317817 * r317824;
        double r317826 = r317825 / r317819;
        double r317827 = r317816 + r317826;
        return r317827;
}
↓
double f(double x, double y, double z) {
        double r317828 = 1.0;
        double r317829 = 0.25;
        double r317830 = 4.0;
        double r317831 = r317829 * r317830;
        double r317832 = r317828 + r317831;
        double r317833 = x;
        double r317834 = y;
        double r317835 = r317833 / r317834;
        double r317836 = z;
        double r317837 = r317836 / r317834;
        double r317838 = r317835 - r317837;
        double r317839 = r317838 * r317830;
        double r317840 = r317832 + r317839;
        return r317840;
}

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. Using strategy rm

  7. Applied div-sub0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 
(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)))