Average Error: 0.2 → 0.0
Time: 13.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r228790 = 1.0;
        double r228791 = 4.0;
        double r228792 = x;
        double r228793 = y;
        double r228794 = 0.75;
        double r228795 = r228793 * r228794;
        double r228796 = r228792 + r228795;
        double r228797 = z;
        double r228798 = r228796 - r228797;
        double r228799 = r228791 * r228798;
        double r228800 = r228799 / r228793;
        double r228801 = r228790 + r228800;
        return r228801;
}
↓
double f(double x, double y, double z) {
        double r228802 = 4.0;
        double r228803 = x;
        double r228804 = z;
        double r228805 = r228803 - r228804;
        double r228806 = y;
        double r228807 = r228805 / r228806;
        double r228808 = r228807 * r228802;
        double r228809 = r228802 + r228808;
        return r228809;
}

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

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

  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

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

  5. Final simplification0.0

    \[\leadsto 4 + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2019303 
(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)))