Average Error: 0.2 → 0.0
Time: 1.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + 4 \cdot \frac{x - z}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + 4 \cdot \frac{x - z}{y}
double f(double x, double y, double z) {
        double r276662 = 1.0;
        double r276663 = 4.0;
        double r276664 = x;
        double r276665 = y;
        double r276666 = 0.75;
        double r276667 = r276665 * r276666;
        double r276668 = r276664 + r276667;
        double r276669 = z;
        double r276670 = r276668 - r276669;
        double r276671 = r276663 * r276670;
        double r276672 = r276671 / r276665;
        double r276673 = r276662 + r276672;
        return r276673;
}
↓
double f(double x, double y, double z) {
        double r276674 = 1.0;
        double r276675 = 0.75;
        double r276676 = 4.0;
        double r276677 = r276675 * r276676;
        double r276678 = r276674 + r276677;
        double r276679 = x;
        double r276680 = z;
        double r276681 = r276679 - r276680;
        double r276682 = y;
        double r276683 = r276681 / r276682;
        double r276684 = r276676 * r276683;
        double r276685 = r276678 + r276684;
        return r276685;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020034 
(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)))