Average Error: 0.2 → 0.0
Time: 23.0s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[2 + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
2 + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r165125 = 1.0;
        double r165126 = 4.0;
        double r165127 = x;
        double r165128 = y;
        double r165129 = 0.25;
        double r165130 = r165128 * r165129;
        double r165131 = r165127 + r165130;
        double r165132 = z;
        double r165133 = r165131 - r165132;
        double r165134 = r165126 * r165133;
        double r165135 = r165134 / r165128;
        double r165136 = r165125 + r165135;
        return r165136;
}
↓
double f(double x, double y, double z) {
        double r165137 = 2.0;
        double r165138 = x;
        double r165139 = z;
        double r165140 = r165138 - r165139;
        double r165141 = y;
        double r165142 = r165140 / r165141;
        double r165143 = 4.0;
        double r165144 = r165142 * r165143;
        double r165145 = r165137 + r165144;
        return r165145;
}

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

    \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 + \left(\frac{x - z}{y} + 0.25\right) \cdot 4}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\left(4 \cdot \frac{x}{y} + 2\right) - 4 \cdot \frac{z}{y}}\]

  4. Simplified0.0

    \[\leadsto \color{blue}{2 + \frac{x - z}{y} \cdot 4}\]

  5. Final simplification0.0

    \[\leadsto 2 + \frac{x - z}{y} \cdot 4\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, C"
  :precision binary64
  (+ 1 (/ (* 4 (- (+ x (* y 0.25)) z)) y)))