Average Error: 0.2 → 0.0
Time: 14.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right) + 4
double f(double x, double y, double z) {
        double r54547617 = 1.0;
        double r54547618 = 4.0;
        double r54547619 = x;
        double r54547620 = y;
        double r54547621 = 0.75;
        double r54547622 = r54547620 * r54547621;
        double r54547623 = r54547619 + r54547622;
        double r54547624 = z;
        double r54547625 = r54547623 - r54547624;
        double r54547626 = r54547618 * r54547625;
        double r54547627 = r54547626 / r54547620;
        double r54547628 = r54547617 + r54547627;
        return r54547628;
}
↓
double f(double x, double y, double z) {
        double r54547629 = 4.0;
        double r54547630 = x;
        double r54547631 = y;
        double r54547632 = r54547630 / r54547631;
        double r54547633 = z;
        double r54547634 = r54547633 / r54547631;
        double r54547635 = r54547632 - r54547634;
        double r54547636 = r54547629 * r54547635;
        double r54547637 = r54547636 + r54547629;
        return r54547637;
}

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

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

  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

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

Reproduce

herbie shell --seed 2019173 
(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)))