Average Error: 0.1 → 0.1
Time: 13.7s
Precision: 64
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
↓
\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}\]
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
↓
1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y}
double f(double x, double y, double z) {
        double r247928 = 1.0;
        double r247929 = 4.0;
        double r247930 = x;
        double r247931 = y;
        double r247932 = 0.25;
        double r247933 = r247931 * r247932;
        double r247934 = r247930 + r247933;
        double r247935 = z;
        double r247936 = r247934 - r247935;
        double r247937 = r247929 * r247936;
        double r247938 = r247937 / r247931;
        double r247939 = r247928 + r247938;
        return r247939;
}
↓
double f(double x, double y, double z) {
        double r247940 = 1.0;
        double r247941 = 4.0;
        double r247942 = x;
        double r247943 = y;
        double r247944 = 0.25;
        double r247945 = r247943 * r247944;
        double r247946 = r247942 + r247945;
        double r247947 = z;
        double r247948 = r247946 - r247947;
        double r247949 = r247941 * r247948;
        double r247950 = r247949 / r247943;
        double r247951 = r247940 + r247950;
        return r247951;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(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)))