Average Error: 0.4 → 0.4
Time: 23.3s
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 r365073 = 3.0;
        double r365074 = x;
        double r365075 = sqrt(r365074);
        double r365076 = r365073 * r365075;
        double r365077 = y;
        double r365078 = 1.0;
        double r365079 = 9.0;
        double r365080 = r365074 * r365079;
        double r365081 = r365078 / r365080;
        double r365082 = r365077 + r365081;
        double r365083 = r365082 - r365078;
        double r365084 = r365076 * r365083;
        return r365084;
}
↓
double f(double x, double y) {
        double r365085 = 3.0;
        double r365086 = x;
        double r365087 = sqrt(r365086);
        double r365088 = y;
        double r365089 = 1.0;
        double r365090 = 9.0;
        double r365091 = r365086 * r365090;
        double r365092 = r365089 / r365091;
        double r365093 = r365088 + r365092;
        double r365094 = r365093 - r365089;
        double r365095 = r365087 * r365094;
        double r365096 = r365085 * r365095;
        return r365096;
}

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 2019323 
(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)))