Average Error: 0.5 → 0.2
Time: 2.1s
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 r815195 = x;
        double r815196 = 100.0;
        double r815197 = r815195 * r815196;
        double r815198 = y;
        double r815199 = r815195 + r815198;
        double r815200 = r815197 / r815199;
        return r815200;
}
↓
double f(double x, double y) {
        double r815201 = x;
        double r815202 = y;
        double r815203 = r815201 + r815202;
        double r815204 = 100.0;
        double r815205 = r815203 / r815204;
        double r815206 = r815201 / r815205;
        return r815206;
}

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)))