Average Error: 0.4 → 0.4
Time: 23.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\left(y + \frac{1}{x \cdot 9}\right) \cdot \sqrt{x}\right) \cdot 3 + \left(\left(-1\right) \cdot \sqrt{x}\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\left(y + \frac{1}{x \cdot 9}\right) \cdot \sqrt{x}\right) \cdot 3 + \left(\left(-1\right) \cdot \sqrt{x}\right) \cdot 3
double f(double x, double y) {
        double r307467 = 3.0;
        double r307468 = x;
        double r307469 = sqrt(r307468);
        double r307470 = r307467 * r307469;
        double r307471 = y;
        double r307472 = 1.0;
        double r307473 = 9.0;
        double r307474 = r307468 * r307473;
        double r307475 = r307472 / r307474;
        double r307476 = r307471 + r307475;
        double r307477 = r307476 - r307472;
        double r307478 = r307470 * r307477;
        return r307478;
}
↓
double f(double x, double y) {
        double r307479 = y;
        double r307480 = 1.0;
        double r307481 = x;
        double r307482 = 9.0;
        double r307483 = r307481 * r307482;
        double r307484 = r307480 / r307483;
        double r307485 = r307479 + r307484;
        double r307486 = sqrt(r307481);
        double r307487 = r307485 * r307486;
        double r307488 = 3.0;
        double r307489 = r307487 * r307488;
        double r307490 = -r307480;
        double r307491 = r307490 * r307486;
        double r307492 = r307491 * r307488;
        double r307493 = r307489 + r307492;
        return r307493;
}

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 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. Using strategy rm

  8. Applied sub-neg0.6

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

  9. Applied distribute-lft-in0.6

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

  10. Applied distribute-lft-in0.6

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

  11. Applied distribute-lft-in0.6

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

  12. Simplified0.5

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

  13. Simplified0.4

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

  14. Final simplification0.4

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

Reproduce

herbie shell --seed 2019303 
(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)))