Details

sample226.0ms

Algorithm

intervals

Results

64.0ms	256×	body	80	valid
25.0ms	257×	body	80	nan

simplify75.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

74.0ms

(* 2 (atan (sqrt (/ (- 1 x) (+ 1 x)))))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize647.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- 1 x) (+ 1 x))
0.0b	(sqrt (/ (- 1 x) (+ 1 x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
49×	`times-frac`
30×	`sqrt-prod`
25×	`add-cube-cbrt`
18×	`difference-of-squares`
13×	`distribute-lft-out`
9×	`distribute-lft-out--`
6×	`associate-/l*`
4×	`associate-/r*` `add-cbrt-cube` `add-exp-log` `associate-/r/`
3×	`pow1`
2×	`expm1-log1p-u` `rem-sqrt-square` `flip3-+` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `sqrt-div` `div-sub` `div-exp` `flip--`

Counts

2 → 99

Calls

2 calls:

Slowest

38.0ms	(/ (- 1 x) (+ 1 x))
21.0ms	(sqrt (/ (- 1 x) (+ 1 x)))

series149.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

79.0ms	(sqrt (/ (- 1 x) (+ 1 x)))
70.0ms	(/ (- 1 x) (+ 1 x))

simplify3.6s

Counts

103 → 105

Calls

103 calls:

Slowest

460.0ms	(/ (* (* (- 1 x) (- 1 x)) (- 1 x)) (* (* (+ 1 x) (+ 1 x)) (+ 1 x)))
250.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
240.0ms	(- (+ (sqrt -1) (/ 1 (* x (sqrt -1)))) (* 1/2 (/ 1 (* (pow x 2) (sqrt -1)))))
157.0ms	(- (+ (* 2 (pow x 2)) 1) (* 2 x))
153.0ms	(- (* 2 (/ 1 x)) (+ (* 2 (/ 1 (pow x 2))) 1))

prune970.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x))
0.0b	(sqrt (* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
30×	`associate-l`
26×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
16×	`difference-of-squares`
11×	`distribute-rgt-in` `distribute-lft-in`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r`
5×	`flip3--` `sqrt-div` `flip--` `distribute-lft-out--`
4×	`frac-times` `associate-*r/`
2×	`expm1-log1p-u` `sub-neg` `sqrt-pow1` `pow-prod-down` `associate-*l/` `prod-exp` `associate-/r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
1×	`cbrt-undiv` `pow1/2` `div-exp` `*-commutative` `sqrt-prod` `div-inv`

Counts

2 → 100

Calls

2 calls:

Slowest

59.0ms	(* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x))
22.0ms	(sqrt (* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x)))

series117.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

64.0ms	(sqrt (* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x)))
53.0ms	(* (/ (- 1 x) (- (* 1 1) (* x x))) (- 1 x))

simplify12.6s

Counts

87 → 106

Calls

87 calls:

Slowest

541.0ms	(sqrt (* (/ (- 1 x) (- (* 1 1) (* x x))) (- (* 1 1) (* x x))))
478.0ms	(* (- x) (/ (- 1 x) (- (* 1 1) (* x x))))
430.0ms	(* (- x) (/ (- 1 x) (- (* 1 1) (* x x))))
398.0ms	(* (fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x))) (/ (- 1 x) (- (* 1 1) (* x x))))
379.0ms	(* (fma (- (sqrt x)) (sqrt x) (* (sqrt x) (sqrt x))) (/ (- 1 x) (- (* 1 1) (* x x))))

prune1.1s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	8000×	body	80	valid
777.0ms	7749×	body	80	nan