Average Error: 0.4 → 0.2
Time: 7.8s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{x}{\frac{y + x}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{x}{\frac{y + x}{100}}
double f(double x, double y) {
        double r37626558 = x;
        double r37626559 = 100.0;
        double r37626560 = r37626558 * r37626559;
        double r37626561 = y;
        double r37626562 = r37626558 + r37626561;
        double r37626563 = r37626560 / r37626562;
        return r37626563;
}
↓
double f(double x, double y) {
        double r37626564 = x;
        double r37626565 = y;
        double r37626566 = r37626565 + r37626564;
        double r37626567 = 100.0;
        double r37626568 = r37626566 / r37626567;
        double r37626569 = r37626564 / r37626568;
        return r37626569;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 
(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)))