Average Error: 0.4 → 0.2
Time: 2.2s
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 r779211 = x;
        double r779212 = 100.0;
        double r779213 = r779211 * r779212;
        double r779214 = y;
        double r779215 = r779211 + r779214;
        double r779216 = r779213 / r779215;
        return r779216;
}
↓
double f(double x, double y) {
        double r779217 = x;
        double r779218 = y;
        double r779219 = r779217 + r779218;
        double r779220 = 100.0;
        double r779221 = r779219 / r779220;
        double r779222 = r779217 / r779221;
        return r779222;
}

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 2020036 
(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)))