Average Error: 0.4 → 0.4
Time: 17.0s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right) \cdot \sqrt{x}\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right) \cdot \sqrt{x}
double f(double x, double y) {
        double r476453 = 3.0;
        double r476454 = x;
        double r476455 = sqrt(r476454);
        double r476456 = r476453 * r476455;
        double r476457 = y;
        double r476458 = 1.0;
        double r476459 = 9.0;
        double r476460 = r476454 * r476459;
        double r476461 = r476458 / r476460;
        double r476462 = r476457 + r476461;
        double r476463 = r476462 - r476458;
        double r476464 = r476456 * r476463;
        return r476464;
}
↓
double f(double x, double y) {
        double r476465 = 3.0;
        double r476466 = y;
        double r476467 = 1.0;
        double r476468 = x;
        double r476469 = r476467 / r476468;
        double r476470 = 9.0;
        double r476471 = r476469 / r476470;
        double r476472 = r476466 + r476471;
        double r476473 = r476472 - r476467;
        double r476474 = r476465 * r476473;
        double r476475 = sqrt(r476468);
        double r476476 = r476474 * r476475;
        return r476476;
}

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-sqr-sqrt0.4

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

  4. Applied times-frac0.5

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

  6. Applied pow10.5

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

  7. Applied pow10.5

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

  8. Applied pow10.5

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

  9. Applied pow-prod-down0.5

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

  10. Applied pow-prod-down0.5

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 +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)))