Average Error: 0.4 → 0.4
Time: 14.7s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111049432054187491303309798}{x}\right) - 1\right)\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111049432054187491303309798}{x}\right) - 1\right)\right) \cdot 3
double f(double x, double y) {
        double r19323157 = 3.0;
        double r19323158 = x;
        double r19323159 = sqrt(r19323158);
        double r19323160 = r19323157 * r19323159;
        double r19323161 = y;
        double r19323162 = 1.0;
        double r19323163 = 9.0;
        double r19323164 = r19323158 * r19323163;
        double r19323165 = r19323162 / r19323164;
        double r19323166 = r19323161 + r19323165;
        double r19323167 = r19323166 - r19323162;
        double r19323168 = r19323160 * r19323167;
        return r19323168;
}
↓
double f(double x, double y) {
        double r19323169 = x;
        double r19323170 = sqrt(r19323169);
        double r19323171 = y;
        double r19323172 = 0.1111111111111111;
        double r19323173 = r19323172 / r19323169;
        double r19323174 = r19323171 + r19323173;
        double r19323175 = 1.0;
        double r19323176 = r19323174 - r19323175;
        double r19323177 = r19323170 * r19323176;
        double r19323178 = 3.0;
        double r19323179 = r19323177 * r19323178;
        return r19323179;
}

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. Taylor expanded around 0 0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\left(y + \color{blue}{\frac{0.1111111111111111049432054187491303309798}{x}}\right) - 1\right)\right)\]

  5. Final simplification0.4

    \[\leadsto \left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111049432054187491303309798}{x}\right) - 1\right)\right) \cdot 3\]

Reproduce

herbie shell --seed 2019192 
(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)))