Average Error: 0.2 → 0.0
Time: 1.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + 4 \cdot \left(\frac{x}{y} - \frac{z}{y}\right)
double f(double x, double y, double z) {
        double r240498 = 1.0;
        double r240499 = 4.0;
        double r240500 = x;
        double r240501 = y;
        double r240502 = 0.75;
        double r240503 = r240501 * r240502;
        double r240504 = r240500 + r240503;
        double r240505 = z;
        double r240506 = r240504 - r240505;
        double r240507 = r240499 * r240506;
        double r240508 = r240507 / r240501;
        double r240509 = r240498 + r240508;
        return r240509;
}
↓
double f(double x, double y, double z) {
        double r240510 = 1.0;
        double r240511 = 0.75;
        double r240512 = 4.0;
        double r240513 = r240511 * r240512;
        double r240514 = r240510 + r240513;
        double r240515 = x;
        double r240516 = y;
        double r240517 = r240515 / r240516;
        double r240518 = z;
        double r240519 = r240518 / r240516;
        double r240520 = r240517 - r240519;
        double r240521 = r240512 * r240520;
        double r240522 = r240514 + r240521;
        return r240522;
}

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. Using strategy rm

  4. Applied distribute-lft-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Simplified0.0

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

  8. Applied div-sub0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020056 
(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)))