Details

sample107.0ms

Algorithm

intervals

Results

32.0ms	270×	body	160	nan
23.0ms	433×	body	80	nan
17.0ms	256×	body	80	valid

simplify17.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.6b

localize53.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
24.8b	(sqrt (- (* x x) 1.0))

rewrite64.0ms

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:

35.0ms	(+ x (sqrt (- (* x x) 1.0)))
27.0ms	(sqrt (- (* x x) 1.0))

series242.0ms

Counts

2 → 6

Calls

2 calls:

134.0ms	(+ x (sqrt (- (* x x) 1.0)))
102.0ms	(sqrt (- (* x x) 1.0))

simplify3.0s

Counts

41 → 41

Iterations

Iter	Nodes
done	5001
3	2141
2	678
1	235
0	95

prune328.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize37.0ms

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))))

rewrite141.0ms

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:

20.0ms	(sqrt (+ x (sqrt 1.0)))
12.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
104.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series722.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(sqrt (+ x (sqrt 1.0)))
252.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
357.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify5.1s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	4244
2	1255
1	443
0	181

prune738.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify5.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	16520×	body	80	nan
1.1s	7734×	body	160	nan
640.0ms	8000×	body	80	valid