Average Error: 0.4 → 0.4
Time: 5.0s
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 r335981 = 3.0;
        double r335982 = x;
        double r335983 = sqrt(r335982);
        double r335984 = r335981 * r335983;
        double r335985 = y;
        double r335986 = 1.0;
        double r335987 = 9.0;
        double r335988 = r335982 * r335987;
        double r335989 = r335986 / r335988;
        double r335990 = r335985 + r335989;
        double r335991 = r335990 - r335986;
        double r335992 = r335984 * r335991;
        return r335992;
}
↓
double f(double x, double y) {
        double r335993 = 3.0;
        double r335994 = x;
        double r335995 = sqrt(r335994);
        double r335996 = y;
        double r335997 = 1.0;
        double r335998 = r335997 / r335994;
        double r335999 = 9.0;
        double r336000 = r335998 / r335999;
        double r336001 = r335996 + r336000;
        double r336002 = r336001 - r335997;
        double r336003 = r335995 * r336002;
        double r336004 = r335993 * r336003;
        return r336004;
}

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-*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 2020021 
(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)))