Average Error: 0.4 → 0.4
Time: 13.9s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right) \cdot \sqrt{x}\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right) \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r299133 = 3.0;
        double r299134 = x;
        double r299135 = sqrt(r299134);
        double r299136 = r299133 * r299135;
        double r299137 = y;
        double r299138 = 1.0;
        double r299139 = 9.0;
        double r299140 = r299134 * r299139;
        double r299141 = r299138 / r299140;
        double r299142 = r299137 + r299141;
        double r299143 = r299142 - r299138;
        double r299144 = r299136 * r299143;
        return r299144;
}
↓
double f(double x, double y) {
        double r299145 = 3.0;
        double r299146 = y;
        double r299147 = 1.0;
        double r299148 = x;
        double r299149 = r299147 / r299148;
        double r299150 = 9.0;
        double r299151 = r299149 / r299150;
        double r299152 = r299146 + r299151;
        double r299153 = r299152 - r299147;
        double r299154 = sqrt(r299148);
        double r299155 = r299153 * r299154;
        double r299156 = r299145 * r299155;
        return r299156;
}

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 *-un-lft-identity0.4

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

  6. Applied *-un-lft-identity0.4

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

  7. Applied distribute-lft-out0.4

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019209 
(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)))