Average Error: 0.4 → 0.4
Time: 18.8s
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 r423215 = 3.0;
        double r423216 = x;
        double r423217 = sqrt(r423216);
        double r423218 = r423215 * r423217;
        double r423219 = y;
        double r423220 = 1.0;
        double r423221 = 9.0;
        double r423222 = r423216 * r423221;
        double r423223 = r423220 / r423222;
        double r423224 = r423219 + r423223;
        double r423225 = r423224 - r423220;
        double r423226 = r423218 * r423225;
        return r423226;
}
↓
double f(double x, double y) {
        double r423227 = 3.0;
        double r423228 = x;
        double r423229 = sqrt(r423228);
        double r423230 = r423227 * r423229;
        double r423231 = y;
        double r423232 = 1.0;
        double r423233 = r423232 / r423228;
        double r423234 = 9.0;
        double r423235 = r423233 / r423234;
        double r423236 = r423231 + r423235;
        double r423237 = r423236 - r423232;
        double r423238 = r423230 * r423237;
        return r423238;
}

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)))