Average Error: 0.4 → 0.4
Time: 26.0s
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 r284218 = 3.0;
        double r284219 = x;
        double r284220 = sqrt(r284219);
        double r284221 = r284218 * r284220;
        double r284222 = y;
        double r284223 = 1.0;
        double r284224 = 9.0;
        double r284225 = r284219 * r284224;
        double r284226 = r284223 / r284225;
        double r284227 = r284222 + r284226;
        double r284228 = r284227 - r284223;
        double r284229 = r284221 * r284228;
        return r284229;
}
↓
double f(double x, double y) {
        double r284230 = 3.0;
        double r284231 = x;
        double r284232 = sqrt(r284231);
        double r284233 = y;
        double r284234 = 1.0;
        double r284235 = r284234 / r284231;
        double r284236 = 9.0;
        double r284237 = r284235 / r284236;
        double r284238 = r284233 + r284237;
        double r284239 = r284238 - r284234;
        double r284240 = r284232 * r284239;
        double r284241 = r284230 * r284240;
        return r284241;
}

Error

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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-/r*0.4

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

  5. Applied associate-*l*0.4

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

  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 2019322 
(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)))