Average Error: 0.3 → 0.2
Time: 15.2s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{y + x} \cdot 100\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{y + x} \cdot 100
double f(double x, double y) {
        double r32667481 = x;
        double r32667482 = 100.0;
        double r32667483 = r32667481 * r32667482;
        double r32667484 = y;
        double r32667485 = r32667481 + r32667484;
        double r32667486 = r32667483 / r32667485;
        return r32667486;
}
↓
double f(double x, double y) {
        double r32667487 = x;
        double r32667488 = y;
        double r32667489 = r32667488 + r32667487;
        double r32667490 = r32667487 / r32667489;
        double r32667491 = 100.0;
        double r32667492 = r32667490 * r32667491;
        return r32667492;
}

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
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.3

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

  3. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{x + y}{100}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y)
  :name "Development.Shake.Progress:message from shake-0.15.5"

  :herbie-target
  (* (/ x 1.0) (/ 100.0 (+ x y)))

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