Average Error: 0.4 → 0.4
Time: 20.3s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{9}}{x}\right) - 1\right)\right)\]
\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}{9}}{x}\right) - 1\right)\right)
double f(double x, double y) {
        double r364023 = 3.0;
        double r364024 = x;
        double r364025 = sqrt(r364024);
        double r364026 = r364023 * r364025;
        double r364027 = y;
        double r364028 = 1.0;
        double r364029 = 9.0;
        double r364030 = r364024 * r364029;
        double r364031 = r364028 / r364030;
        double r364032 = r364027 + r364031;
        double r364033 = r364032 - r364028;
        double r364034 = r364026 * r364033;
        return r364034;
}
↓
double f(double x, double y) {
        double r364035 = 3.0;
        double r364036 = x;
        double r364037 = sqrt(r364036);
        double r364038 = y;
        double r364039 = 1.0;
        double r364040 = 9.0;
        double r364041 = r364039 / r364040;
        double r364042 = r364041 / r364036;
        double r364043 = r364038 + r364042;
        double r364044 = r364043 - r364039;
        double r364045 = r364037 * r364044;
        double r364046 = r364035 * r364045;
        return r364046;
}

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 *-un-lft-identity0.4

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

  4. Applied times-frac0.4

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

  6. Applied associate-*l*0.4

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

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(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)))