Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	251×	body	160	nan
11.0ms	513×	body	80	nan
7.0ms	256×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
32.6b	(sqrt (- (* x x) 1.0))

rewrite16.0ms

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×	`add-exp-log` `expm1-log1p-u` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 35

Calls

2 calls:

9.0ms	(+ x (sqrt (- (* x x) 1.0)))
6.0ms	(sqrt (- (* x x) 1.0))

series126.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ x (sqrt (- (* x x) 1.0)))
57.0ms	(sqrt (- (* x x) 1.0))

simplify1.0s

Counts

41 → 41

Iterations

Useful iterations: 3 (290.0ms)

Iter	Nodes	Cost
0	95	483
1	236	428
2	693	392
3	2600	355
done	5001	355

prune112.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(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))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 80

Calls

3 calls:

6.0ms	(sqrt (+ x (sqrt 1.0)))
3.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
32.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series409.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(sqrt (+ x (sqrt 1.0)))
149.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
195.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify472.0ms

Counts

89 → 89

Iterations

Useful iterations: done (470.0ms)

Iter	Nodes	Cost
0	181	1459
1	442	1236
2	1503	1161
done	5001	1155

prune260.0ms

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	10	14
1	13	14
done	13	14

end0.0ms

sample1.4s

Algorithm

intervals

Results

375.0ms	7559×	body	160	nan
359.0ms	16369×	body	80	nan
244.0ms	8000×	body	80	valid