Average Error: 0.4 → 0.4
Time: 6.8s
Precision: 64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\left(\sqrt{x} \cdot \left(y + \left(\frac{1}{x \cdot 9} - 1\right)\right)\right) \cdot 3\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\left(\sqrt{x} \cdot \left(y + \left(\frac{1}{x \cdot 9} - 1\right)\right)\right) \cdot 3
double f(double x, double y) {
        double r282061 = 3.0;
        double r282062 = x;
        double r282063 = sqrt(r282062);
        double r282064 = r282061 * r282063;
        double r282065 = y;
        double r282066 = 1.0;
        double r282067 = 9.0;
        double r282068 = r282062 * r282067;
        double r282069 = r282066 / r282068;
        double r282070 = r282065 + r282069;
        double r282071 = r282070 - r282066;
        double r282072 = r282064 * r282071;
        return r282072;
}
↓
double f(double x, double y) {
        double r282073 = x;
        double r282074 = sqrt(r282073);
        double r282075 = y;
        double r282076 = 1.0;
        double r282077 = 9.0;
        double r282078 = r282073 * r282077;
        double r282079 = r282076 / r282078;
        double r282080 = r282079 - r282076;
        double r282081 = r282075 + r282080;
        double r282082 = r282074 * r282081;
        double r282083 = 3.0;
        double r282084 = r282082 * r282083;
        return r282084;
}

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

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. Using strategy rm

  5. Applied associate--l+0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Applied distribute-lft-in0.4

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

  8. Simplified0.4

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 1978988140 
(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)))