Details

sample121.0ms

Algorithm

intervals

Results

41.0ms	526×	body	80	nan
39.0ms	262×	body	160	nan
20.0ms	256×	body	80	valid

simplify148.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

148.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.9b

localize22.0ms

Local error

Found 3 expressions with local error:

28.8b	(sqrt (- (* x x) 1))
0.0b	(+ x (sqrt (- (* x x) 1)))
0.0b	(- (* x x) 1)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

Slowest

19.0ms	(+ x (sqrt (- (* x x) 1)))
17.0ms	(sqrt (- (* x x) 1))
11.0ms	(- (* x x) 1)

series195.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

78.0ms	(+ x (sqrt (- (* x x) 1)))
59.0ms	(- (* x x) 1)
57.0ms	(sqrt (- (* x x) 1))

simplify2.4s

Counts

27 → 57

Calls

27 calls:

Slowest

439.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
227.0ms	(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
216.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
215.0ms	(sqrt (- (* (* x x) (* x x)) (* 1 1)))
194.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune402.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

Slowest

23.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
9.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
6.0ms	(sqrt (+ x 1))

series209.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

102.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))
83.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
24.0ms	(sqrt (+ x 1))

simplify3.8s

Counts

61 → 82

Calls

61 calls:

Slowest

338.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
297.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
262.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
251.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
217.0ms	(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune726.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.9s	7868×	body	160	nan
1.2s	16209×	body	80	nan
751.0ms	8000×	body	80	valid