Average Error: 0.4 → 0.4
Time: 40.4s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)\]
\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(\frac{1}{x \cdot 9} - 1\right) + y\right)\right)
double f(double x, double y) {
        double r280333 = 3.0;
        double r280334 = x;
        double r280335 = sqrt(r280334);
        double r280336 = r280333 * r280335;
        double r280337 = y;
        double r280338 = 1.0;
        double r280339 = 9.0;
        double r280340 = r280334 * r280339;
        double r280341 = r280338 / r280340;
        double r280342 = r280337 + r280341;
        double r280343 = r280342 - r280338;
        double r280344 = r280336 * r280343;
        return r280344;
}
↓
double f(double x, double y) {
        double r280345 = 3.0;
        double r280346 = x;
        double r280347 = sqrt(r280346);
        double r280348 = 1.0;
        double r280349 = 9.0;
        double r280350 = r280346 * r280349;
        double r280351 = r280348 / r280350;
        double r280352 = r280351 - r280348;
        double r280353 = y;
        double r280354 = r280352 + r280353;
        double r280355 = r280347 * r280354;
        double r280356 = r280345 * r280355;
        return r280356;
}

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. Simplified0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019323 +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)))