Average Error: 0.4 → 0.4
Time: 20.3s
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 r277987 = 3.0;
        double r277988 = x;
        double r277989 = sqrt(r277988);
        double r277990 = r277987 * r277989;
        double r277991 = y;
        double r277992 = 1.0;
        double r277993 = 9.0;
        double r277994 = r277988 * r277993;
        double r277995 = r277992 / r277994;
        double r277996 = r277991 + r277995;
        double r277997 = r277996 - r277992;
        double r277998 = r277990 * r277997;
        return r277998;
}
↓
double f(double x, double y) {
        double r277999 = 3.0;
        double r278000 = x;
        double r278001 = sqrt(r278000);
        double r278002 = y;
        double r278003 = 1.0;
        double r278004 = 9.0;
        double r278005 = r278000 * r278004;
        double r278006 = r278003 / r278005;
        double r278007 = r278002 + r278006;
        double r278008 = r278007 - r278003;
        double r278009 = r278001 * r278008;
        double r278010 = r277999 * r278009;
        return r278010;
}

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 2019235 +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)))