Average Error: 0.4 → 0.4
Time: 15.7s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot y + \sqrt{x} \cdot \left(\left(\frac{\frac{1}{x} \cdot 1}{9} - 1\right) \cdot 3\right)\]
\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 y + \sqrt{x} \cdot \left(\left(\frac{\frac{1}{x} \cdot 1}{9} - 1\right) \cdot 3\right)
double f(double x, double y) {
        double r342219 = 3.0;
        double r342220 = x;
        double r342221 = sqrt(r342220);
        double r342222 = r342219 * r342221;
        double r342223 = y;
        double r342224 = 1.0;
        double r342225 = 9.0;
        double r342226 = r342220 * r342225;
        double r342227 = r342224 / r342226;
        double r342228 = r342223 + r342227;
        double r342229 = r342228 - r342224;
        double r342230 = r342222 * r342229;
        return r342230;
}
↓
double f(double x, double y) {
        double r342231 = 3.0;
        double r342232 = x;
        double r342233 = sqrt(r342232);
        double r342234 = r342231 * r342233;
        double r342235 = y;
        double r342236 = r342234 * r342235;
        double r342237 = 1.0;
        double r342238 = r342237 / r342232;
        double r342239 = 1.0;
        double r342240 = r342238 * r342239;
        double r342241 = 9.0;
        double r342242 = r342240 / r342241;
        double r342243 = r342242 - r342239;
        double r342244 = r342243 * r342231;
        double r342245 = r342233 * r342244;
        double r342246 = r342236 + r342245;
        return r342246;
}

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 div-inv0.4

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

  4. Simplified0.4

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

  6. Applied associate--l+0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  9. Simplified0.4

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

  11. Applied associate-*r*0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))