Details

sample73.0ms

Algorithm

intervals

Results

25.0ms	243×	body	160	nan
21.0ms	477×	body	80	nan
14.0ms	256×	body	80	valid

simplify6.1s

Counts: 1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize26.0ms

Local error

Found 2 expressions with local error:

27.3b	(sqrt (- (* x x) 1))
0.0b	(+ x (sqrt (- (* x x) 1)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity` `sqrt-prod`
5×	`add-sqr-sqrt`
4×	`add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `flip3--` `pow1/2` `difference-of-sqr-1` `flip-+` `flip--` `distribute-lft-out`

Counts

2 → 32

Calls

2 calls:

Slowest

15.0ms	(sqrt (- (* x x) 1))
14.0ms	(+ x (sqrt (- (* x x) 1)))

series112.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

68.0ms	(+ x (sqrt (- (* x x) 1)))
44.0ms	(sqrt (- (* x x) 1))

simplify1.3s

Counts: 38 → 38

prune328.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
11×	`*-un-lft-identity`
10×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`frac-times` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `insert-posit16` `difference-of-squares`
1×	`+-commutative` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 56

Calls

2 calls:

Slowest

33.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
5.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

series200.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

118.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
81.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

simplify781.0ms

Counts: 62 → 62

prune546.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.7s	7651×	body	160	nan
1.3s	15988×	body	80	nan
805.0ms	8000×	body	80	valid