Average Error: 0.4 → 0.4
Time: 16.2s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x} \cdot \frac{\sqrt[3]{1}}{9}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{x} \cdot \frac{\sqrt[3]{1}}{9}\right) - 1\right)
double f(double x, double y) {
        double r414582 = 3.0;
        double r414583 = x;
        double r414584 = sqrt(r414583);
        double r414585 = r414582 * r414584;
        double r414586 = y;
        double r414587 = 1.0;
        double r414588 = 9.0;
        double r414589 = r414583 * r414588;
        double r414590 = r414587 / r414589;
        double r414591 = r414586 + r414590;
        double r414592 = r414591 - r414587;
        double r414593 = r414585 * r414592;
        return r414593;
}
↓
double f(double x, double y) {
        double r414594 = 3.0;
        double r414595 = x;
        double r414596 = sqrt(r414595);
        double r414597 = r414594 * r414596;
        double r414598 = y;
        double r414599 = 1.0;
        double r414600 = cbrt(r414599);
        double r414601 = r414600 * r414600;
        double r414602 = r414601 / r414595;
        double r414603 = 9.0;
        double r414604 = r414600 / r414603;
        double r414605 = r414602 * r414604;
        double r414606 = r414598 + r414605;
        double r414607 = r414606 - r414599;
        double r414608 = r414597 * r414607;
        return r414608;
}

Error

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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 add-cube-cbrt0.4

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

  4. Applied times-frac0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020045 
(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)))