Average Error: 0.4 → 0.2
Time: 8.6s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{\frac{x}{x + y}}{\frac{1}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{\frac{x}{x + y}}{\frac{1}{100}}
double f(double x, double y) {
        double r51154399 = x;
        double r51154400 = 100.0;
        double r51154401 = r51154399 * r51154400;
        double r51154402 = y;
        double r51154403 = r51154399 + r51154402;
        double r51154404 = r51154401 / r51154403;
        return r51154404;
}
↓
double f(double x, double y) {
        double r51154405 = x;
        double r51154406 = y;
        double r51154407 = r51154405 + r51154406;
        double r51154408 = r51154405 / r51154407;
        double r51154409 = 1.0;
        double r51154410 = 100.0;
        double r51154411 = r51154409 / r51154410;
        double r51154412 = r51154408 / r51154411;
        return r51154412;
}

Error

Bits error versus x

Bits error versus y

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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. Using strategy rm

  5. Applied div-inv0.2

    \[\leadsto \frac{x}{\color{blue}{\left(x + y\right) \cdot \frac{1}{100}}}\]

  6. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{x}{x + y}}{\frac{1}{100}}}\]

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(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)))