Average Error: 0.2 → 0.2
Time: 8.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 - \frac{4}{y} \cdot \left(z - x\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 - \frac{4}{y} \cdot \left(z - x\right)
double f(double x, double y, double z) {
        double r197492 = 1.0;
        double r197493 = 4.0;
        double r197494 = x;
        double r197495 = y;
        double r197496 = 0.75;
        double r197497 = r197495 * r197496;
        double r197498 = r197494 + r197497;
        double r197499 = z;
        double r197500 = r197498 - r197499;
        double r197501 = r197493 * r197500;
        double r197502 = r197501 / r197495;
        double r197503 = r197492 + r197502;
        return r197503;
}
↓
double f(double x, double y, double z) {
        double r197504 = 4.0;
        double r197505 = y;
        double r197506 = r197504 / r197505;
        double r197507 = z;
        double r197508 = x;
        double r197509 = r197507 - r197508;
        double r197510 = r197506 * r197509;
        double r197511 = r197504 - r197510;
        return r197511;
}

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

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

  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

    \[\leadsto \color{blue}{4 + 4 \cdot \frac{x - z}{y}}\]
  5. Using strategy rm

  6. Applied div-sub0.0

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019291 
(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)))