Average Error: 0.4 → 0.4
Time: 4.5s
Precision: binary64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[\sqrt{x} \cdot \left(3 \cdot \left(-1 + \left(\frac{0.1111111111111111}{x} + y\right)\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
\sqrt{x} \cdot \left(3 \cdot \left(-1 + \left(\frac{0.1111111111111111}{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
 (* (sqrt x) (* 3.0 (+ -1.0 (+ (/ 0.1111111111111111 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 sqrt(x) * (3.0 * (-1.0 + ((0.1111111111111111 / x) + y)));
}

Error

Bits error versus x

Bits error versus y

Try it out

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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_119540.4

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

  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_120350.4

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

  7. Applied associate-/r*_binary64_119570.4

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

  9. Applied associate-*r*_binary64_119530.4

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

  10. Simplified0.4

    \[\leadsto \color{blue}{\frac{\sqrt{x}}{0.3333333333333333}} \cdot \left(-1 + \left(\frac{\frac{0.1111111111111111}{\sqrt{x}}}{\sqrt{x}} + y\right)\right)\]
  11. Using strategy rm

  12. Applied div-inv_binary64_120100.4

    \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \frac{1}{0.3333333333333333}\right)} \cdot \left(-1 + \left(\frac{\frac{0.1111111111111111}{\sqrt{x}}}{\sqrt{x}} + y\right)\right)\]

  13. Applied associate-*l*_binary64_119540.4

    \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{1}{0.3333333333333333} \cdot \left(-1 + \left(\frac{\frac{0.1111111111111111}{\sqrt{x}}}{\sqrt{x}} + y\right)\right)\right)}\]

  14. Simplified0.4

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

  15. Final simplification0.4

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

Reproduce

herbie shell --seed 2020356 
(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)))