Average Error: 0.5 → 0.2
Time: 2.4s
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 r889607 = x;
        double r889608 = 100.0;
        double r889609 = r889607 * r889608;
        double r889610 = y;
        double r889611 = r889607 + r889610;
        double r889612 = r889609 / r889611;
        return r889612;
}
↓
double f(double x, double y) {
        double r889613 = x;
        double r889614 = y;
        double r889615 = r889613 + r889614;
        double r889616 = 100.0;
        double r889617 = r889615 / r889616;
        double r889618 = r889613 / r889617;
        return r889618;
}

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 +o rules:numerics
(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)))