Average Error: 0.3 → 0.2
Time: 14.4s
Precision: 64
\[\frac{x \cdot 100.0}{x + y}\]
↓
\[\frac{x}{y + x} \cdot 100.0\]
\frac{x \cdot 100.0}{x + y}
↓
\frac{x}{y + x} \cdot 100.0
double f(double x, double y) {
        double r40228773 = x;
        double r40228774 = 100.0;
        double r40228775 = r40228773 * r40228774;
        double r40228776 = y;
        double r40228777 = r40228773 + r40228776;
        double r40228778 = r40228775 / r40228777;
        return r40228778;
}
↓
double f(double x, double y) {
        double r40228779 = x;
        double r40228780 = y;
        double r40228781 = r40228780 + r40228779;
        double r40228782 = r40228779 / r40228781;
        double r40228783 = 100.0;
        double r40228784 = r40228782 * r40228783;
        return r40228784;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100.0}{x + y}\]

Derivation

  1. Initial program 0.3

    \[\frac{x \cdot 100.0}{x + y}\]
  2. Using strategy rm

  3. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100.0}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.2

    \[\leadsto \color{blue}{\frac{x}{x + y} \cdot 100.0}\]

  6. Final simplification0.2

    \[\leadsto \frac{x}{y + x} \cdot 100.0\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1) (/ 100.0 (+ x y)))

  (/ (* x 100.0) (+ x y)))