Average Error: 0.4 → 0.4
Time: 21.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\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{1}{x \cdot 9}\right) - 1\right)\right)
double f(double x, double y) {
        double r260966 = 3.0;
        double r260967 = x;
        double r260968 = sqrt(r260967);
        double r260969 = r260966 * r260968;
        double r260970 = y;
        double r260971 = 1.0;
        double r260972 = 9.0;
        double r260973 = r260967 * r260972;
        double r260974 = r260971 / r260973;
        double r260975 = r260970 + r260974;
        double r260976 = r260975 - r260971;
        double r260977 = r260969 * r260976;
        return r260977;
}
↓
double f(double x, double y) {
        double r260978 = 3.0;
        double r260979 = x;
        double r260980 = sqrt(r260979);
        double r260981 = y;
        double r260982 = 1.0;
        double r260983 = 9.0;
        double r260984 = r260979 * r260983;
        double r260985 = r260982 / r260984;
        double r260986 = r260981 + r260985;
        double r260987 = r260986 - r260982;
        double r260988 = r260980 * r260987;
        double r260989 = r260978 * r260988;
        return r260989;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019323 
(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)))