Average Error: 0.4 → 0.4
Time: 14.7s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt{x} \cdot \left(\frac{\frac{1}{9}}{x} - 1\right) + \sqrt{x} \cdot y\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt{x} \cdot \left(\frac{\frac{1}{9}}{x} - 1\right) + \sqrt{x} \cdot y\right) \cdot 3
double f(double x, double y) {
        double r341049 = 3.0;
        double r341050 = x;
        double r341051 = sqrt(r341050);
        double r341052 = r341049 * r341051;
        double r341053 = y;
        double r341054 = 1.0;
        double r341055 = 9.0;
        double r341056 = r341050 * r341055;
        double r341057 = r341054 / r341056;
        double r341058 = r341053 + r341057;
        double r341059 = r341058 - r341054;
        double r341060 = r341052 * r341059;
        return r341060;
}
↓
double f(double x, double y) {
        double r341061 = x;
        double r341062 = sqrt(r341061);
        double r341063 = 1.0;
        double r341064 = 9.0;
        double r341065 = r341063 / r341064;
        double r341066 = r341065 / r341061;
        double r341067 = r341066 - r341063;
        double r341068 = r341062 * r341067;
        double r341069 = y;
        double r341070 = r341062 * r341069;
        double r341071 = r341068 + r341070;
        double r341072 = 3.0;
        double r341073 = r341071 * r341072;
        return r341073;
}

Error

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Bits error versus y

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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. Simplified0.4

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

  6. Applied associate--l+0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019194 
(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)))