Average Error: 0.4 → 0.4
Time: 19.8s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)\]
\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(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)
double f(double x, double y) {
        double r473003 = 3.0;
        double r473004 = x;
        double r473005 = sqrt(r473004);
        double r473006 = r473003 * r473005;
        double r473007 = y;
        double r473008 = 1.0;
        double r473009 = 9.0;
        double r473010 = r473004 * r473009;
        double r473011 = r473008 / r473010;
        double r473012 = r473007 + r473011;
        double r473013 = r473012 - r473008;
        double r473014 = r473006 * r473013;
        return r473014;
}
↓
double f(double x, double y) {
        double r473015 = 3.0;
        double r473016 = x;
        double r473017 = sqrt(r473016);
        double r473018 = y;
        double r473019 = 1.0;
        double r473020 = r473019 / r473016;
        double r473021 = 9.0;
        double r473022 = r473020 / r473021;
        double r473023 = r473018 + r473022;
        double r473024 = r473023 - r473019;
        double r473025 = r473017 * r473024;
        double r473026 = r473015 * r473025;
        return r473026;
}

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-/r*0.4

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020043 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x))))

  (* (* 3 (sqrt x)) (- (+ y (/ 1 (* x 9))) 1)))