Average Error: 0.1 → 0.0
Time: 9.1s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[4 \cdot \frac{x - z}{y} + \left(4 \cdot 0.25 + 1\right)\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
4 \cdot \frac{x - z}{y} + \left(4 \cdot 0.25 + 1\right)
double f(double x, double y, double z) {
        double r191803 = 1.0;
        double r191804 = 4.0;
        double r191805 = x;
        double r191806 = y;
        double r191807 = 0.25;
        double r191808 = r191806 * r191807;
        double r191809 = r191805 + r191808;
        double r191810 = z;
        double r191811 = r191809 - r191810;
        double r191812 = r191804 * r191811;
        double r191813 = r191812 / r191806;
        double r191814 = r191803 + r191813;
        return r191814;
}
↓
double f(double x, double y, double z) {
        double r191815 = 4.0;
        double r191816 = x;
        double r191817 = z;
        double r191818 = r191816 - r191817;
        double r191819 = y;
        double r191820 = r191818 / r191819;
        double r191821 = r191815 * r191820;
        double r191822 = 0.25;
        double r191823 = r191815 * r191822;
        double r191824 = 1.0;
        double r191825 = r191823 + r191824;
        double r191826 = r191821 + r191825;
        return r191826;
}

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 0.1

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

  2. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Applied associate-+l+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(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)))