Average Error: 0.1 → 0.0
Time: 13.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(\left(1 + \frac{x}{y}\right) - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r233559 = 1.0;
        double r233560 = 4.0;
        double r233561 = x;
        double r233562 = y;
        double r233563 = 0.75;
        double r233564 = r233562 * r233563;
        double r233565 = r233561 + r233564;
        double r233566 = z;
        double r233567 = r233565 - r233566;
        double r233568 = r233560 * r233567;
        double r233569 = r233568 / r233562;
        double r233570 = r233559 + r233569;
        return r233570;
}
↓
double f(double x, double y, double z) {
        double r233571 = 4.0;
        double r233572 = 1.0;
        double r233573 = x;
        double r233574 = y;
        double r233575 = r233573 / r233574;
        double r233576 = r233572 + r233575;
        double r233577 = z;
        double r233578 = r233577 / r233574;
        double r233579 = r233576 - r233578;
        double r233580 = r233571 * r233579;
        return r233580;
}

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

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

  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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(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)))