Average Error: 0.3 → 0.2
Time: 2.9s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\frac{4}{y} \cdot \left(x - z\right) + 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\frac{4}{y} \cdot \left(x - z\right) + 4
double f(double x, double y, double z) {
        double r209469 = 1.0;
        double r209470 = 4.0;
        double r209471 = x;
        double r209472 = y;
        double r209473 = 0.75;
        double r209474 = r209472 * r209473;
        double r209475 = r209471 + r209474;
        double r209476 = z;
        double r209477 = r209475 - r209476;
        double r209478 = r209470 * r209477;
        double r209479 = r209478 / r209472;
        double r209480 = r209469 + r209479;
        return r209480;
}
↓
double f(double x, double y, double z) {
        double r209481 = 4.0;
        double r209482 = y;
        double r209483 = r209481 / r209482;
        double r209484 = x;
        double r209485 = z;
        double r209486 = r209484 - r209485;
        double r209487 = r209483 * r209486;
        double r209488 = r209487 + r209481;
        return r209488;
}

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 0.3

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

  2. Simplified0.0

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

  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

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.75)) z)) y)))