Average Error: 0.4 → 0.2
Time: 1.8s
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 r744837 = x;
        double r744838 = 100.0;
        double r744839 = r744837 * r744838;
        double r744840 = y;
        double r744841 = r744837 + r744840;
        double r744842 = r744839 / r744841;
        return r744842;
}
↓
double f(double x, double y) {
        double r744843 = x;
        double r744844 = y;
        double r744845 = r744843 + r744844;
        double r744846 = 100.0;
        double r744847 = r744845 / r744846;
        double r744848 = r744843 / r744847;
        return r744848;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020021 +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)))