Average Error: 0.4 → 0.4
Time: 4.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\right)
double f(double x, double y) {
        double r503336 = 3.0;
        double r503337 = x;
        double r503338 = sqrt(r503337);
        double r503339 = r503336 * r503338;
        double r503340 = y;
        double r503341 = 1.0;
        double r503342 = 9.0;
        double r503343 = r503337 * r503342;
        double r503344 = r503341 / r503343;
        double r503345 = r503340 + r503344;
        double r503346 = r503345 - r503341;
        double r503347 = r503339 * r503346;
        return r503347;
}
↓
double f(double x, double y) {
        double r503348 = 3.0;
        double r503349 = x;
        double r503350 = sqrt(r503349);
        double r503351 = y;
        double r503352 = 1.0;
        double r503353 = r503352 / r503349;
        double r503354 = 9.0;
        double r503355 = r503353 / r503354;
        double r503356 = r503351 + r503355;
        double r503357 = r503356 - r503352;
        double r503358 = r503350 * r503357;
        double r503359 = r503348 * r503358;
        return r503359;
}

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 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 associate-/r*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020060 +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)))