Average Error: 0.4 → 0.2
Time: 1.9s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{\frac{x + y}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{\frac{x + y}{100}}
double f(double x, double y) {
        double r912918 = x;
        double r912919 = 100.0;
        double r912920 = r912918 * r912919;
        double r912921 = y;
        double r912922 = r912918 + r912921;
        double r912923 = r912920 / r912922;
        return r912923;
}
↓
double f(double x, double y) {
        double r912924 = x;
        double r912925 = y;
        double r912926 = r912924 + r912925;
        double r912927 = 100.0;
        double r912928 = r912926 / r912927;
        double r912929 = r912924 / r912928;
        return r912929;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.4

    \[\frac{x \cdot 100}{x + y}\]
  2. Using strategy rm

  3. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}}\]

  4. Final simplification0.2

    \[\leadsto \frac{x}{\frac{x + y}{100}}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"
  :precision binary64

  :herbie-target
  (* (/ x 1) (/ 100 (+ x y)))

  (/ (* x 100) (+ x y)))