Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	249×	body	160	nan
19.0ms	533×	body	80	nan
12.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
30.6b	(sqrt (- (* x x) 1.0))

rewrite28.0ms

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:

14.0ms	(+ x (sqrt (- (* x x) 1.0)))
13.0ms	(sqrt (- (* x x) 1.0))

series154.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(+ x (sqrt (- (* x x) 1.0)))
68.0ms	(sqrt (- (* x x) 1.0))

simplify1.6s

Counts

41 → 41

Iterations

Iter	Nodes
done	5000
3	2088
2	660
1	231
0	94

prune205.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

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))))

rewrite64.0ms

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:

7.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
56.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series435.0ms

Counts

2 → 6

Calls

2 calls:

184.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
251.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify3.0s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
3	3839
2	1125
1	386
0	156

prune326.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
done	13
1	13
0	10

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	7707×	body	160	nan
894.0ms	16160×	body	80	nan
625.0ms	8000×	body	80	valid