Average Error: 0.4 → 0.4
Time: 15.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} + y\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} + y\right) - 1\right)\right)
double f(double x, double y) {
        double r18673965 = 3.0;
        double r18673966 = x;
        double r18673967 = sqrt(r18673966);
        double r18673968 = r18673965 * r18673967;
        double r18673969 = y;
        double r18673970 = 1.0;
        double r18673971 = 9.0;
        double r18673972 = r18673966 * r18673971;
        double r18673973 = r18673970 / r18673972;
        double r18673974 = r18673969 + r18673973;
        double r18673975 = r18673974 - r18673970;
        double r18673976 = r18673968 * r18673975;
        return r18673976;
}
↓
double f(double x, double y) {
        double r18673977 = 3.0;
        double r18673978 = x;
        double r18673979 = sqrt(r18673978);
        double r18673980 = 1.0;
        double r18673981 = 9.0;
        double r18673982 = r18673978 * r18673981;
        double r18673983 = r18673980 / r18673982;
        double r18673984 = y;
        double r18673985 = r18673983 + r18673984;
        double r18673986 = r18673985 - r18673980;
        double r18673987 = r18673979 * r18673986;
        double r18673988 = r18673977 * r18673987;
        return r18673988;
}

Error

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Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\]
  4. Using strategy rm

  5. Applied +-commutative0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\color{blue}{\left(\frac{1}{x \cdot 9} + y\right)} - 1\right)\right)\]
  6. Using strategy rm

  7. Applied *-commutative0.4

    \[\leadsto 3 \cdot \color{blue}{\left(\left(\left(\frac{1}{x \cdot 9} + y\right) - 1\right) \cdot \sqrt{x}\right)}\]

  8. Final simplification0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} + y\right) - 1\right)\right)\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))