Average Error: 0.4 → 0.4
Time: 3.6s
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 r564240 = 3.0;
        double r564241 = x;
        double r564242 = sqrt(r564241);
        double r564243 = r564240 * r564242;
        double r564244 = y;
        double r564245 = 1.0;
        double r564246 = 9.0;
        double r564247 = r564241 * r564246;
        double r564248 = r564245 / r564247;
        double r564249 = r564244 + r564248;
        double r564250 = r564249 - r564245;
        double r564251 = r564243 * r564250;
        return r564251;
}
↓
double f(double x, double y) {
        double r564252 = 3.0;
        double r564253 = x;
        double r564254 = sqrt(r564253);
        double r564255 = y;
        double r564256 = 1.0;
        double r564257 = r564256 / r564253;
        double r564258 = 9.0;
        double r564259 = r564257 / r564258;
        double r564260 = r564255 + r564259;
        double r564261 = r564260 - r564256;
        double r564262 = r564254 * r564261;
        double r564263 = r564252 * r564262;
        return r564263;
}

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 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)))