Details

sample48.0ms

Algorithm

intervals

Results

12.0ms	565×	body	80	nan
11.0ms	231×	body	160	nan
8.0ms	256×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
29.8b	(sqrt (- (* x x) 1.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
10.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series382.0ms

Counts

3 → 9

Calls

3 calls:

210.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
97.0ms	(+ x (sqrt (- (* x x) 1.0)))
75.0ms	(sqrt (- (* x x) 1.0))

simplify1.8s

Counts

52 → 52

Iterations

Useful iterations: 3 (438.0ms)

Iter	Nodes	Cost
0	140	780
1	317	714
2	950	637
3	4390	621
done	5000	621

prune172.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
42.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series759.0ms

Counts

3 → 9

Calls

3 calls:

359.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
166.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
233.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify650.0ms

Counts

76 → 76

Iterations

Useful iterations: done (647.0ms)

Iter	Nodes	Cost
0	191	1601
1	450	1365
2	1506	1272
done	5001	1271

prune223.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.5b	(* (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

384×	`sqrt-div`
144×	`frac-times`
77×	`pow1`
64×	`sqrt-pow1`
61×	`flip3-+` `flip-+`
60×	`flip3--` `flip--`
48×	`associate-r/` `associate-l/`
44×	`pow-prod-down`
42×	`add-sqr-sqrt`
34×	`sqrt-prod`
30×	`pow1/2`
24×	`*-un-lft-identity`
22×	`associate-r`
18×	`associate-l`
16×	`add-cube-cbrt`
14×	`pow-prod-up`
10×	`add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`pow-sqr`
6×	`add-log-exp`
4×	`swap-sqr` `difference-of-squares`
3×	`sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`
2×	`distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `pow2` `pow-plus` `sum-log` `rem-square-sqrt`

Counts

4 → 232

Calls

4 calls:

2.0ms	(+ x (* (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
29.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
30.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
81.0ms	(* (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

174.0ms	(+ x (* (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))
242.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
265.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
465.0ms	(* (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))) (sqrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))

simplify1.2s

Counts

244 → 244

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	352	8624
1	607	6242
2	2301	6110
done	5000	6107

prune793.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	15	28
done	15	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

387.0ms	7787×	body	160	nan
368.0ms	16432×	body	80	nan
246.0ms	8000×	body	80	valid