Average Error: 0.4 → 0.4
Time: 4.8s
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 r389860 = 3.0;
        double r389861 = x;
        double r389862 = sqrt(r389861);
        double r389863 = r389860 * r389862;
        double r389864 = y;
        double r389865 = 1.0;
        double r389866 = 9.0;
        double r389867 = r389861 * r389866;
        double r389868 = r389865 / r389867;
        double r389869 = r389864 + r389868;
        double r389870 = r389869 - r389865;
        double r389871 = r389863 * r389870;
        return r389871;
}
↓
double f(double x, double y) {
        double r389872 = 3.0;
        double r389873 = x;
        double r389874 = sqrt(r389873);
        double r389875 = y;
        double r389876 = 1.0;
        double r389877 = r389876 / r389873;
        double r389878 = 9.0;
        double r389879 = r389877 / r389878;
        double r389880 = r389875 + r389879;
        double r389881 = r389880 - r389876;
        double r389882 = r389874 * r389881;
        double r389883 = r389872 * r389882;
        return r389883;
}

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 2020057 +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)))