Average Error: 0.4 → 0.4
Time: 21.1s
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 r17757901 = 3.0;
        double r17757902 = x;
        double r17757903 = sqrt(r17757902);
        double r17757904 = r17757901 * r17757903;
        double r17757905 = y;
        double r17757906 = 1.0;
        double r17757907 = 9.0;
        double r17757908 = r17757902 * r17757907;
        double r17757909 = r17757906 / r17757908;
        double r17757910 = r17757905 + r17757909;
        double r17757911 = r17757910 - r17757906;
        double r17757912 = r17757904 * r17757911;
        return r17757912;
}
↓
double f(double x, double y) {
        double r17757913 = 3.0;
        double r17757914 = x;
        double r17757915 = sqrt(r17757914);
        double r17757916 = y;
        double r17757917 = 1.0;
        double r17757918 = r17757917 / r17757914;
        double r17757919 = 9.0;
        double r17757920 = r17757918 / r17757919;
        double r17757921 = r17757916 + r17757920;
        double r17757922 = r17757921 - r17757917;
        double r17757923 = r17757915 * r17757922;
        double r17757924 = r17757913 * r17757923;
        return r17757924;
}

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. Using strategy rm

  5. Applied associate-/r*0.4

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

  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 2019174 +o rules:numerics
(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)))