Average Error: 0.4 → 0.4
Time: 4.2s
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 r369017 = 3.0;
        double r369018 = x;
        double r369019 = sqrt(r369018);
        double r369020 = r369017 * r369019;
        double r369021 = y;
        double r369022 = 1.0;
        double r369023 = 9.0;
        double r369024 = r369018 * r369023;
        double r369025 = r369022 / r369024;
        double r369026 = r369021 + r369025;
        double r369027 = r369026 - r369022;
        double r369028 = r369020 * r369027;
        return r369028;
}
↓
double f(double x, double y) {
        double r369029 = 3.0;
        double r369030 = x;
        double r369031 = sqrt(r369030);
        double r369032 = y;
        double r369033 = 1.0;
        double r369034 = 9.0;
        double r369035 = r369030 * r369034;
        double r369036 = r369033 / r369035;
        double r369037 = r369032 + r369036;
        double r369038 = r369037 - r369033;
        double r369039 = r369031 * r369038;
        double r369040 = r369029 * r369039;
        return r369040;
}

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 2020036 +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)))