Average Error: 0.4 → 0.4
Time: 3.5s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot y + \left(3 \cdot \sqrt{x}\right) \cdot \left(\sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}} - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot y + \left(3 \cdot \sqrt{x}\right) \cdot \left(\sqrt{\frac{1}{x \cdot 9}} \cdot \sqrt{\frac{1}{x \cdot 9}} - 1\right)
double f(double x, double y) {
        double r487988 = 3.0;
        double r487989 = x;
        double r487990 = sqrt(r487989);
        double r487991 = r487988 * r487990;
        double r487992 = y;
        double r487993 = 1.0;
        double r487994 = 9.0;
        double r487995 = r487989 * r487994;
        double r487996 = r487993 / r487995;
        double r487997 = r487992 + r487996;
        double r487998 = r487997 - r487993;
        double r487999 = r487991 * r487998;
        return r487999;
}
↓
double f(double x, double y) {
        double r488000 = 3.0;
        double r488001 = x;
        double r488002 = sqrt(r488001);
        double r488003 = r488000 * r488002;
        double r488004 = y;
        double r488005 = r488003 * r488004;
        double r488006 = 1.0;
        double r488007 = 9.0;
        double r488008 = r488001 * r488007;
        double r488009 = r488006 / r488008;
        double r488010 = sqrt(r488009);
        double r488011 = r488010 * r488010;
        double r488012 = r488011 - r488006;
        double r488013 = r488003 * r488012;
        double r488014 = r488005 + r488013;
        return r488014;
}

Error

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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

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

  4. Applied distribute-lft-in0.4

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

  6. Applied add-sqr-sqrt0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020065 
(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)))