Average Error: 0.4 → 0.4
Time: 3.7s
Precision: binary64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot \left(-1 + \left(\frac{\frac{0.1111111111111111}{\sqrt{x}}}{\sqrt{x}} + y\right)\right)\right)\]
\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(-1 + \left(\frac{\frac{0.1111111111111111}{\sqrt{x}}}{\sqrt{x}} + y\right)\right)\right)
(FPCore (x y)
 :precision binary64
 (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))
↓
(FPCore (x y)
 :precision binary64
 (*
  3.0
  (* (sqrt x) (+ -1.0 (+ (/ (/ 0.1111111111111111 (sqrt x)) (sqrt x)) y)))))
double code(double x, double y) {
	return (3.0 * sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
}
↓
double code(double x, double y) {
	return 3.0 * (sqrt(x) * (-1.0 + (((0.1111111111111111 / sqrt(x)) / sqrt(x)) + y)));
}

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*_binary64_116130.4

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

  4. Simplified0.4

    \[\leadsto 3 \cdot \color{blue}{\left(\sqrt{x} \cdot \left(-1 + \left(\frac{0.1111111111111111}{x} + y\right)\right)\right)}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt_binary64_116940.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(-1 + \left(\frac{0.1111111111111111}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}} + y\right)\right)\right)\]

  7. Applied associate-/r*_binary64_116160.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(-1 + \left(\color{blue}{\frac{\frac{0.1111111111111111}{\sqrt{x}}}{\sqrt{x}}} + y\right)\right)\right)\]

  8. Final simplification0.4

    \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(-1 + \left(\frac{\frac{0.1111111111111111}{\sqrt{x}}}{\sqrt{x}} + y\right)\right)\right)\]

Reproduce

herbie shell --seed 2020355 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))