Average Error: 0.2 → 0.0
Time: 8.5s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(0.75 + \left(\frac{x}{y} - \frac{z}{y}\right)\right) + 1
double f(double x, double y, double z) {
        double r296797 = 1.0;
        double r296798 = 4.0;
        double r296799 = x;
        double r296800 = y;
        double r296801 = 0.75;
        double r296802 = r296800 * r296801;
        double r296803 = r296799 + r296802;
        double r296804 = z;
        double r296805 = r296803 - r296804;
        double r296806 = r296798 * r296805;
        double r296807 = r296806 / r296800;
        double r296808 = r296797 + r296807;
        return r296808;
}
↓
double f(double x, double y, double z) {
        double r296809 = 4.0;
        double r296810 = 0.75;
        double r296811 = x;
        double r296812 = y;
        double r296813 = r296811 / r296812;
        double r296814 = z;
        double r296815 = r296814 / r296812;
        double r296816 = r296813 - r296815;
        double r296817 = r296810 + r296816;
        double r296818 = r296809 * r296817;
        double r296819 = 1.0;
        double r296820 = r296818 + r296819;
        return r296820;
}

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

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

  4. Applied div-sub0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(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)))