Average Error: 0.1 → 0.0
Time: 1.8s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}\]
↓
\[\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y}
↓
\left(1 + 0.75 \cdot 4\right) + \frac{x - z}{y} \cdot 4
double f(double x, double y, double z) {
        double r310793 = 1.0;
        double r310794 = 4.0;
        double r310795 = x;
        double r310796 = y;
        double r310797 = 0.75;
        double r310798 = r310796 * r310797;
        double r310799 = r310795 + r310798;
        double r310800 = z;
        double r310801 = r310799 - r310800;
        double r310802 = r310794 * r310801;
        double r310803 = r310802 / r310796;
        double r310804 = r310793 + r310803;
        return r310804;
}
↓
double f(double x, double y, double z) {
        double r310805 = 1.0;
        double r310806 = 0.75;
        double r310807 = 4.0;
        double r310808 = r310806 * r310807;
        double r310809 = r310805 + r310808;
        double r310810 = x;
        double r310811 = z;
        double r310812 = r310810 - r310811;
        double r310813 = y;
        double r310814 = r310812 / r310813;
        double r310815 = r310814 * r310807;
        double r310816 = r310809 + r310815;
        return r310816;
}

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

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Applied associate-+r+0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(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)))