Average Error: 0.4 → 0.4
Time: 18.0s
Precision: 64
\[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
↓
\[\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0\]
\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)
↓
\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0
double f(double x, double y) {
        double r19689673 = 3.0;
        double r19689674 = x;
        double r19689675 = sqrt(r19689674);
        double r19689676 = r19689673 * r19689675;
        double r19689677 = y;
        double r19689678 = 1.0;
        double r19689679 = 9.0;
        double r19689680 = r19689674 * r19689679;
        double r19689681 = r19689678 / r19689680;
        double r19689682 = r19689677 + r19689681;
        double r19689683 = r19689682 - r19689678;
        double r19689684 = r19689676 * r19689683;
        return r19689684;
}
↓
double f(double x, double y) {
        double r19689685 = x;
        double r19689686 = sqrt(r19689685);
        double r19689687 = y;
        double r19689688 = 0.1111111111111111;
        double r19689689 = r19689688 / r19689685;
        double r19689690 = r19689687 + r19689689;
        double r19689691 = 1.0;
        double r19689692 = r19689690 - r19689691;
        double r19689693 = r19689686 * r19689692;
        double r19689694 = 3.0;
        double r19689695 = r19689693 * r19689694;
        return r19689695;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.4
Target0.4
Herbie0.4
\[3.0 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1.0}{x \cdot 9.0} - 1.0\right) \cdot \sqrt{x}\right)\]

Derivation

  1. Initial program 0.4

    \[\left(3.0 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.4

    \[\leadsto \color{blue}{3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \frac{1.0}{x \cdot 9.0}\right) - 1.0\right)\right)}\]

  4. Taylor expanded around 0 0.4

    \[\leadsto 3.0 \cdot \left(\sqrt{x} \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111}{x}}\right) - 1.0\right)\right)\]

  5. Final simplification0.4

    \[\leadsto \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) - 1.0\right)\right) \cdot 3.0\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))