Details

sample91.0ms

Algorithm

intervals

Results

31.0ms	268×	body	160	nan
27.0ms	527×	body	80	nan
17.0ms	256×	body	80	valid

simplify163.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

162.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.8b

localize26.0ms

Local error

Found 1 expressions with local error:

30.7b

(sqrt (- (* x x) 1))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 19

Calls

1 calls:

Slowest

15.0ms

(sqrt (- (* x x) 1))

series57.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

57.0ms

(sqrt (- (* x x) 1))

simplify1.8s

Counts

13 → 22

Calls

13 calls:

Slowest

429.0ms	(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
292.0ms	(sqrt (- (pow (* x x) 3) (pow 1 3)))
266.0ms	(sqrt (- (* (* x x) (* x x)) (* 1 1)))
228.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
202.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune151.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 1 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 44

Calls

1 calls:

Slowest

33.0ms

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

series123.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

123.0ms

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

simplify2.4s

Counts

46 → 47

Calls

46 calls:

Slowest

355.0ms	(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
277.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
203.0ms	(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (* x x) (* 1 1))))
177.0ms	(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
173.0ms	(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune537.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	7498×	body	160	nan
1.1s	16015×	body	80	nan
760.0ms	8000×	body	80	valid