Average Error: 0.2 → 0.0
Time: 13.8s
Precision: 64
\[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r15460430 = 1.0;
        double r15460431 = 4.0;
        double r15460432 = x;
        double r15460433 = y;
        double r15460434 = 0.75;
        double r15460435 = r15460433 * r15460434;
        double r15460436 = r15460432 + r15460435;
        double r15460437 = z;
        double r15460438 = r15460436 - r15460437;
        double r15460439 = r15460431 * r15460438;
        double r15460440 = r15460439 / r15460433;
        double r15460441 = r15460430 + r15460440;
        return r15460441;
}
↓
double f(double x, double y, double z) {
        double r15460442 = 4.0;
        double r15460443 = x;
        double r15460444 = y;
        double r15460445 = r15460443 / r15460444;
        double r15460446 = z;
        double r15460447 = r15460446 / r15460444;
        double r15460448 = r15460445 - r15460447;
        double r15460449 = r15460442 * r15460448;
        double r15460450 = r15460442 + r15460449;
        return r15460450;
}

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

    \[1.0 + \frac{4.0 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{4.0 \cdot \left(0.75 - \frac{z - x}{y}\right) + 1.0}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4.0 \cdot \frac{x}{y} + 4.0\right) - 4.0 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)}\]

  5. Final simplification0.0

    \[\leadsto 4.0 + 4.0 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]

Reproduce

herbie shell --seed 2019162 
(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)))