Details

sample80.0ms

Algorithm

intervals

Results

25.0ms	234×	body	160	nan
24.0ms	505×	body	80	nan
15.0ms	256×	body	80	valid

simplify124.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

124.0ms

(log (+ x (sqrt (- (* x x) 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize29.0ms

Local error

Found 2 expressions with local error:

29.5b	(sqrt (- (* x x) 1))
0.0b	(+ x (sqrt (- (* x x) 1)))

rewrite39.0ms

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

24.0ms	(+ x (sqrt (- (* x x) 1)))
15.0ms	(sqrt (- (* x x) 1))

series139.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

77.0ms	(+ x (sqrt (- (* x x) 1)))
62.0ms	(sqrt (- (* x x) 1))

simplify2.4s

Counts

18 → 38

Calls

18 calls:

Slowest

443.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
273.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
235.0ms	(sqrt (- (* (* x x) (* x x)) (* 1 1)))
219.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
218.0ms	(sqrt (- (pow (* x x) 3) (pow 1 3)))

prune321.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

Slowest

34.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
5.0ms	(sqrt (- x 1))
5.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
5.0ms	(sqrt (+ x 1))

series273.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

110.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
88.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
38.0ms	(sqrt (- x 1))
37.0ms	(sqrt (+ x 1))

simplify3.8s

Counts

75 → 105

Calls

75 calls:

Slowest

372.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
336.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
222.0ms	(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))))
221.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
213.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- x 1)))

prune836.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.8s	16256×	body	80	nan
1.3s	7567×	body	160	nan
740.0ms	8000×	body	80	valid