Average Error: 0.4 → 0.2
Time: 8.4s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[\frac{\frac{x}{y + x}}{\frac{1}{100}}\]
\frac{x \cdot 100}{x + y}
↓
\frac{\frac{x}{y + x}}{\frac{1}{100}}
double f(double x, double y) {
        double r35525636 = x;
        double r35525637 = 100.0;
        double r35525638 = r35525636 * r35525637;
        double r35525639 = y;
        double r35525640 = r35525636 + r35525639;
        double r35525641 = r35525638 / r35525640;
        return r35525641;
}
↓
double f(double x, double y) {
        double r35525642 = x;
        double r35525643 = y;
        double r35525644 = r35525643 + r35525642;
        double r35525645 = r35525642 / r35525644;
        double r35525646 = 1.0;
        double r35525647 = 100.0;
        double r35525648 = r35525646 / r35525647;
        double r35525649 = r35525645 / r35525648;
        return r35525649;
}

Error

Bits error versus x

Bits error versus y

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Results

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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

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

Reproduce

herbie shell --seed 2019192 +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)))