Average Error: 0.4 → 0.5
Time: 4.6s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(3 \cdot \left(y + \frac{\frac{1}{x}}{9}\right)\right) \cdot \sqrt{x} + 3 \cdot \left(\left(-1\right) \cdot \sqrt{x}\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(3 \cdot \left(y + \frac{\frac{1}{x}}{9}\right)\right) \cdot \sqrt{x} + 3 \cdot \left(\left(-1\right) \cdot \sqrt{x}\right)
double f(double x, double y) {
        double r504204 = 3.0;
        double r504205 = x;
        double r504206 = sqrt(r504205);
        double r504207 = r504204 * r504206;
        double r504208 = y;
        double r504209 = 1.0;
        double r504210 = 9.0;
        double r504211 = r504205 * r504210;
        double r504212 = r504209 / r504211;
        double r504213 = r504208 + r504212;
        double r504214 = r504213 - r504209;
        double r504215 = r504207 * r504214;
        return r504215;
}
↓
double f(double x, double y) {
        double r504216 = 3.0;
        double r504217 = y;
        double r504218 = 1.0;
        double r504219 = x;
        double r504220 = r504218 / r504219;
        double r504221 = 9.0;
        double r504222 = r504220 / r504221;
        double r504223 = r504217 + r504222;
        double r504224 = r504216 * r504223;
        double r504225 = sqrt(r504219);
        double r504226 = r504224 * r504225;
        double r504227 = -r504218;
        double r504228 = r504227 * r504225;
        double r504229 = r504216 * r504228;
        double r504230 = r504226 + r504229;
        return r504230;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.4
Target0.4
Herbie0.5
\[3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right)\]

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. Using strategy rm

  5. Applied sub-neg0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  9. Simplified0.4

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

  11. Applied associate-*r*0.5

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

  13. Applied associate-/r*0.5

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

  14. Final simplification0.5

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(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)))