Average Error: 0.4 → 0.6
Time: 4.0s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right) \cdot \left(\sqrt[3]{3} \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right)
double f(double x, double y) {
        double r442538 = 3.0;
        double r442539 = x;
        double r442540 = sqrt(r442539);
        double r442541 = r442538 * r442540;
        double r442542 = y;
        double r442543 = 1.0;
        double r442544 = 9.0;
        double r442545 = r442539 * r442544;
        double r442546 = r442543 / r442545;
        double r442547 = r442542 + r442546;
        double r442548 = r442547 - r442543;
        double r442549 = r442541 * r442548;
        return r442549;
}
↓
double f(double x, double y) {
        double r442550 = 3.0;
        double r442551 = cbrt(r442550);
        double r442552 = r442551 * r442551;
        double r442553 = x;
        double r442554 = sqrt(r442553);
        double r442555 = y;
        double r442556 = 1.0;
        double r442557 = 9.0;
        double r442558 = r442553 * r442557;
        double r442559 = r442556 / r442558;
        double r442560 = r442555 + r442559;
        double r442561 = r442560 - r442556;
        double r442562 = r442554 * r442561;
        double r442563 = r442551 * r442562;
        double r442564 = r442552 * r442563;
        return r442564;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.4
Target0.4
Herbie0.6
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

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 add-cube-cbrt0.4

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

  6. Applied associate-*l*0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2020018 
(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)))