Details

sample112.0ms

Algorithm

intervals

Results

30.0ms	569×	body	80	nan
28.0ms	249×	body	160	nan
17.0ms	256×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	10	9
2	11	9
done	11	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
27.6b	(sqrt (- (* x x) 1.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

39.0ms	(+ x (sqrt (- (* x x) 1.0)))
32.0ms	(sqrt (- (* x x) 1.0))

series194.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(+ x (sqrt (- (* x x) 1.0)))
83.0ms	(sqrt (- (* x x) 1.0))

simplify1.3s

Counts

34 → 34

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	91	451
1	216	402
2	541	366
3	1508	358
done	5001	351

prune135.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.4b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
10×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 53

Calls

2 calls:

6.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
74.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series381.0ms

Counts

2 → 6

Calls

2 calls:

160.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
220.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify2.3s

Counts

59 → 59

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	152	1150
1	358	964
2	996	924
3	3410	904
done	5001	902

prune195.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))
0.1b	(sqrt (- (sqrt x) (sqrt (sqrt 1.0))))
0.3b	(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))
0.4b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0)))))

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

70×	`sqrt-div`
66×	`sqrt-prod`
46×	`add-sqr-sqrt`
32×	`frac-times`
30×	`*-un-lft-identity`
25×	`flip3-+` `flip-+`
22×	`associate-r`
18×	`pow1`
16×	`associate-*l/`
12×	`add-cube-cbrt` `difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `associate-*r/` `pow-prod-down` `flip--`
8×	`associate-l`
7×	`sqrt-pow1` `pow1/2`
5×	`distribute-lft-out`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `unswap-sqr`
3×	`sqrt-unprod`
2×	`rem-sqrt-square` `*-commutative`

Counts

4 → 139

Calls

4 calls:

37.0ms	(sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))
20.0ms	(sqrt (- (sqrt x) (sqrt (sqrt 1.0))))
185.0ms	(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))
94.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

233.0ms	(sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))
260.0ms	(sqrt (- (sqrt x) (sqrt (sqrt 1.0))))
998.0ms	(* (* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0))))) (sqrt (- (sqrt x) (sqrt (sqrt 1.0)))))
375.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (+ (sqrt x) (sqrt (sqrt 1.0)))))

simplify2.1s

Counts

151 → 151

Iterations

Useful iterations: 2 (796.0ms)

Iter	Nodes	Cost
0	387	4606
1	1034	3776
2	3251	3595
done	5001	3595

prune844.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	24
1	20	24
done	20	24

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.3s	7537×	body	160	nan
987.0ms	16063×	body	80	nan
533.0ms	8000×	body	80	valid