Average Error: 0.5 → 0.2
Time: 2.0s
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 r947412 = x;
        double r947413 = 100.0;
        double r947414 = r947412 * r947413;
        double r947415 = y;
        double r947416 = r947412 + r947415;
        double r947417 = r947414 / r947416;
        return r947417;
}
↓
double f(double x, double y) {
        double r947418 = x;
        double r947419 = y;
        double r947420 = r947418 + r947419;
        double r947421 = 100.0;
        double r947422 = r947420 / r947421;
        double r947423 = r947418 / r947422;
        return r947423;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.5
Target0.2
Herbie0.2
\[\frac{x}{1} \cdot \frac{100}{x + y}\]

Derivation

  1. Initial program 0.5

    \[\frac{x \cdot 100}{x + y}\]
  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 2020060 
(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)))