Average Error: 0.2 → 0.0
Time: 6.6s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[4 \cdot \left(1 + \frac{x - z}{y}\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
4 \cdot \left(1 + \frac{x - z}{y}\right)
double f(double x, double y, double z) {
        double r176111 = 1.0;
        double r176112 = 4.0;
        double r176113 = x;
        double r176114 = y;
        double r176115 = 0.75;
        double r176116 = r176114 * r176115;
        double r176117 = r176113 + r176116;
        double r176118 = z;
        double r176119 = r176117 - r176118;
        double r176120 = r176112 * r176119;
        double r176121 = r176120 / r176114;
        double r176122 = r176111 + r176121;
        return r176122;
}
↓
double f(double x, double y, double z) {
        double r176123 = 4.0;
        double r176124 = 1.0;
        double r176125 = x;
        double r176126 = z;
        double r176127 = r176125 - r176126;
        double r176128 = y;
        double r176129 = r176127 / r176128;
        double r176130 = r176124 + r176129;
        double r176131 = r176123 * r176130;
        return r176131;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

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)))