Average Error: 0.4 → 0.4
Time: 20.4s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\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{1}{x \cdot 9}\right) - 1\right)\right)
double f(double x, double y) {
        double r17014438 = 3.0;
        double r17014439 = x;
        double r17014440 = sqrt(r17014439);
        double r17014441 = r17014438 * r17014440;
        double r17014442 = y;
        double r17014443 = 1.0;
        double r17014444 = 9.0;
        double r17014445 = r17014439 * r17014444;
        double r17014446 = r17014443 / r17014445;
        double r17014447 = r17014442 + r17014446;
        double r17014448 = r17014447 - r17014443;
        double r17014449 = r17014441 * r17014448;
        return r17014449;
}
↓
double f(double x, double y) {
        double r17014450 = 3.0;
        double r17014451 = x;
        double r17014452 = sqrt(r17014451);
        double r17014453 = y;
        double r17014454 = 1.0;
        double r17014455 = 9.0;
        double r17014456 = r17014451 * r17014455;
        double r17014457 = r17014454 / r17014456;
        double r17014458 = r17014453 + r17014457;
        double r17014459 = r17014458 - r17014454;
        double r17014460 = r17014452 * r17014459;
        double r17014461 = r17014450 * r17014460;
        return r17014461;
}

Error

Bits error versus x

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 +-commutative0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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)))