Average Error: 0.4 → 0.4
Time: 4.5s
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 r517050 = 3.0;
        double r517051 = x;
        double r517052 = sqrt(r517051);
        double r517053 = r517050 * r517052;
        double r517054 = y;
        double r517055 = 1.0;
        double r517056 = 9.0;
        double r517057 = r517051 * r517056;
        double r517058 = r517055 / r517057;
        double r517059 = r517054 + r517058;
        double r517060 = r517059 - r517055;
        double r517061 = r517053 * r517060;
        return r517061;
}
↓
double f(double x, double y) {
        double r517062 = 3.0;
        double r517063 = x;
        double r517064 = sqrt(r517063);
        double r517065 = y;
        double r517066 = 1.0;
        double r517067 = 9.0;
        double r517068 = r517063 * r517067;
        double r517069 = r517066 / r517068;
        double r517070 = r517065 + r517069;
        double r517071 = r517070 - r517066;
        double r517072 = r517064 * r517071;
        double r517073 = r517062 * r517072;
        return r517073;
}

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 2020027 
(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)))