Details

sample90.0ms

Algorithm

intervals

Results

32.0ms	544×	body	80	nan
17.0ms	223×	body	160	nan
12.0ms	256×	body	80	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	11	9
2	12	9
done	12	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.9b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
31.5b	(sqrt (- (* x x) 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`add-cube-cbrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `fma-def`
2×	`expm1-log1p-u` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `flip-+` `flip--` `distribute-lft-out` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

25.0ms	(+ x (sqrt (- (* x x) 1.0)))
20.0ms	(sqrt (- (* x x) 1.0))

series198.0ms

Counts

2 → 6

Calls

2 calls:

109.0ms	(+ x (sqrt (- (* x x) 1.0)))
89.0ms	(sqrt (- (* x x) 1.0))

simplify679.0ms

Counts

41 → 41

Iterations

Useful iterations: done (677.0ms)

Iter	Nodes	Cost
0	94	483
1	240	427
2	970	392
done	5001	356

prune250.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize33.0ms

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))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l` `add-cube-cbrt`
6×	`pow1`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`fma-def` `flip3--` `pow-prod-down` `flip--`
2×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `log1p-expm1-u` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 60

Calls

2 calls:

9.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
71.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series501.0ms

Counts

2 → 6

Calls

2 calls:

209.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
291.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.0s

Counts

66 → 66

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	156	1202
1	389	1026
2	1580	950
done	5000	944

prune373.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.2b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
0.3b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

116×	`sqrt-div`
62×	`sqrt-prod`
36×	`add-sqr-sqrt`
32×	`frac-times`
26×	`*-un-lft-identity`
23×	`flip3-+` `flip-+`
20×	`pow1` `associate-l`
16×	`associate-*r/` `add-cube-cbrt`
13×	`sqrt-pow1`
12×	`flip3--` `flip--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-r` `pow-prod-down` `associate-*l/`
9×	`pow1/2`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `rem-sqrt-square` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 153

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
9.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
113.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
78.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

229.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
174.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
360.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
480.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

simplify1.6s

Counts

165 → 165

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	311	3869
1	838	3337
2	3470	2910
done	5002	2833

prune970.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	16	22
done	16	22

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.3s	7736×	body	160	nan
923.0ms	16578×	body	80	nan
414.0ms	8000×	body	80	valid