Average Error: 0.4 → 0.4
Time: 13.1s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)
double f(double x, double y) {
        double r565082 = 3.0;
        double r565083 = x;
        double r565084 = sqrt(r565083);
        double r565085 = r565082 * r565084;
        double r565086 = y;
        double r565087 = 1.0;
        double r565088 = 9.0;
        double r565089 = r565083 * r565088;
        double r565090 = r565087 / r565089;
        double r565091 = r565086 + r565090;
        double r565092 = r565091 - r565087;
        double r565093 = r565085 * r565092;
        return r565093;
}
↓
double f(double x, double y) {
        double r565094 = 3.0;
        double r565095 = x;
        double r565096 = sqrt(r565095);
        double r565097 = r565094 * r565096;
        double r565098 = y;
        double r565099 = 1.0;
        double r565100 = r565099 / r565095;
        double r565101 = 9.0;
        double r565102 = r565100 / r565101;
        double r565103 = r565098 + r565102;
        double r565104 = r565103 - r565099;
        double r565105 = r565097 * r565104;
        return r565105;
}

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
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

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-/r*0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \color{blue}{\frac{\frac{1}{x}}{9}}\right) - 1\right)\]

  4. Final simplification0.4

    \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{\frac{1}{x}}{9}\right) - 1\right)\]

Reproduce

herbie shell --seed 2020047 
(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)))