Average Error: 0.4 → 0.4
Time: 3.2s
Precision: binary64
\[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\]
↓
\[3 \cdot \left(\sqrt{x} \cdot y + \sqrt{x} \cdot \left(\frac{1}{x \cdot 9} - 1\right)\right)\]
\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)
↓
3 \cdot \left(\sqrt{x} \cdot y + \sqrt{x} \cdot \left(\frac{1}{x \cdot 9} - 1\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) y) (* (sqrt x) (- (/ 1.0 (* x 9.0)) 1.0)))))
double code(double x, double y) {
	return ((double) (((double) (3.0 * ((double) sqrt(x)))) * ((double) (((double) (y + (1.0 / ((double) (x * 9.0))))) - 1.0))));
}
↓
double code(double x, double y) {
	return ((double) (3.0 * ((double) (((double) (((double) sqrt(x)) * y)) + ((double) (((double) sqrt(x)) * ((double) ((1.0 / ((double) (x * 9.0))) - 1.0))))))));
}

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 Error: 0.4 bits

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

  2. SimplifiedError: 0.4 bits

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

  4. Applied distribute-lft-inError: 0.4 bits

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

  5. Final simplificationError: 0.4 bits

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

Reproduce

herbie shell --seed 2020204 
(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)))