Average Error: 0.4 → 0.4
Time: 4.4s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\]
\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{1}{x \cdot 9}\right) - 1\right)\right)
double f(double x, double y) {
        double r414988 = 3.0;
        double r414989 = x;
        double r414990 = sqrt(r414989);
        double r414991 = r414988 * r414990;
        double r414992 = y;
        double r414993 = 1.0;
        double r414994 = 9.0;
        double r414995 = r414989 * r414994;
        double r414996 = r414993 / r414995;
        double r414997 = r414992 + r414996;
        double r414998 = r414997 - r414993;
        double r414999 = r414991 * r414998;
        return r414999;
}
↓
double f(double x, double y) {
        double r415000 = 3.0;
        double r415001 = x;
        double r415002 = sqrt(r415001);
        double r415003 = y;
        double r415004 = 1.0;
        double r415005 = 9.0;
        double r415006 = r415001 * r415005;
        double r415007 = r415004 / r415006;
        double r415008 = r415003 + r415007;
        double r415009 = r415008 - r415004;
        double r415010 = r415002 * r415009;
        double r415011 = r415000 * r415010;
        return r415011;
}

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

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 +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)))