Average Error: 0.2 → 0.0
Time: 9.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(0.75 + \frac{x - z}{y}\right) \cdot 4 + 1\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(0.75 + \frac{x - z}{y}\right) \cdot 4 + 1
double f(double x, double y, double z) {
        double r308833 = 1.0;
        double r308834 = 4.0;
        double r308835 = x;
        double r308836 = y;
        double r308837 = 0.75;
        double r308838 = r308836 * r308837;
        double r308839 = r308835 + r308838;
        double r308840 = z;
        double r308841 = r308839 - r308840;
        double r308842 = r308834 * r308841;
        double r308843 = r308842 / r308836;
        double r308844 = r308833 + r308843;
        return r308844;
}
↓
double f(double x, double y, double z) {
        double r308845 = 0.75;
        double r308846 = x;
        double r308847 = z;
        double r308848 = r308846 - r308847;
        double r308849 = y;
        double r308850 = r308848 / r308849;
        double r308851 = r308845 + r308850;
        double r308852 = 4.0;
        double r308853 = r308851 * r308852;
        double r308854 = 1.0;
        double r308855 = r308853 + r308854;
        return r308855;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(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)))