Average Error: 0.4 → 0.2
Time: 2.8s
Precision: 64
\[\frac{x \cdot 100}{x + y}\]
↓
\[x \cdot \frac{100}{x + y}\]
\frac{x \cdot 100}{x + y}
↓
x \cdot \frac{100}{x + y}
double f(double x, double y) {
        double r638329 = x;
        double r638330 = 100.0;
        double r638331 = r638329 * r638330;
        double r638332 = y;
        double r638333 = r638329 + r638332;
        double r638334 = r638331 / r638333;
        return r638334;
}
↓
double f(double x, double y) {
        double r638335 = x;
        double r638336 = 100.0;
        double r638337 = y;
        double r638338 = r638335 + r638337;
        double r638339 = r638336 / r638338;
        double r638340 = r638335 * r638339;
        return r638340;
}

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 *-un-lft-identity0.4

    \[\leadsto \frac{x \cdot 100}{\color{blue}{1 \cdot \left(x + y\right)}}\]

  4. Applied times-frac0.2

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

  5. Simplified0.2

    \[\leadsto \color{blue}{x} \cdot \frac{100}{x + y}\]

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 +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)))