Details

sample53.0ms

Algorithm

intervals

Results

13.0ms	494×	body	80	nan
12.0ms	193×	body	160	nan
9.0ms	256×	body	80	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) 1.0)
0.0b	(+ x (sqrt (- (* x x) 1.0)))
29.3b	(sqrt (- (* x x) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

9.0ms	(- (* x x) 1.0)
38.0ms	(+ x (sqrt (- (* x x) 1.0)))
12.0ms	(sqrt (- (* x x) 1.0))

series175.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(- (* x x) 1.0)
68.0ms	(+ x (sqrt (- (* x x) 1.0)))
61.0ms	(sqrt (- (* x x) 1.0))

simplify79.0ms

Counts: 50 → 50

prune125.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

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))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 53

Calls

2 calls:

6.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
63.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series364.0ms

Counts

2 → 6

Calls

2 calls:

154.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
211.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify38.0ms

Counts: 59 → 59

prune176.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.3b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
0.4b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

rewrite203.0ms

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×	`add-cube-cbrt` `associate-*r/`
13×	`sqrt-pow1`
12×	`flip3--` `flip--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-r` `pow-prod-down` `associate-*l/`
9×	`pow1/2`
6×	`unswap-sqr`
4×	`rem-sqrt-square` `prod-exp` `cbrt-unprod` `distribute-lft-out` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 145

Calls

4 calls:

11.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
12.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
108.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
64.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

series962.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
134.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
216.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0)))))
371.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (- x (sqrt 1.0))))

simplify73.0ms

Counts: 157 → 157

prune527.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

end0.0ms

sample2.5s

Algorithm

intervals

Results

846.0ms	7501×	body	160	nan
756.0ms	16059×	body	80	nan
326.0ms	8000×	body	80	valid