Details

sample156.0ms

Algorithm

intervals

Results

98.0ms	717×	body	80	nan
35.0ms	256×	body	80	valid

simplify28.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

28.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 3 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
37×	`times-frac`
34×	`add-sqr-sqrt`
28×	`sqrt-prod`
25×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`distribute-lft-out` `associate-/l*`
7×	`div-inv`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1` `sqrt-div`
3×	`associate-/r*` `distribute-rgt-out` `insert-posit16`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `frac-add` `distribute-rgt1-in` `flip-+`

Counts

3 → 93

Calls

3 calls:

Slowest

29.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
10.0ms	(/ (sqrt (- 1 (* x x))) x)
8.0ms	(sqrt (- 1 (* x x)))

series284.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

123.0ms	(/ (sqrt (- 1 (* x x))) x)
102.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))
59.0ms	(sqrt (- 1 (* x x)))

simplify5.2s

Counts

103 → 102

Calls

103 calls:

Slowest

342.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
336.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))
330.0ms	(- (/ 1 x) (+ (* 1/2 x) (* 1/8 (pow x 3))))
328.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))
309.0ms	(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))

prune940.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 75

Calls

3 calls:

Slowest

80.0ms	(* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x))
26.0ms	(+ (sqrt (- 1 (* x x))) 1)
4.0ms	(sqrt (- 1 (* x x)))

series224.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

114.0ms	(* (+ (sqrt (- 1 (* x x))) 1) (/ 1 x))
66.0ms	(sqrt (- 1 (* x x)))
44.0ms	(+ (sqrt (- 1 (* x x))) 1)

simplify6.1s

Counts

57 → 84

Calls

57 calls:

Slowest

883.0ms	(* (* (* (+ (sqrt (- 1 (* x x))) 1) (+ (sqrt (- 1 (* x x))) 1)) (+ (sqrt (- 1 (* x x))) 1)) (/ (* (* 1 1) 1) (* (* x x) x)))
497.0ms	(* (* (* (+ (sqrt (- 1 (* x x))) 1) (+ (sqrt (- 1 (* x x))) 1)) (+ (sqrt (- 1 (* x x))) 1)) (* (* (/ 1 x) (/ 1 x)) (/ 1 x)))
374.0ms	(+ (* 1/2 (/ 1 (* x (sqrt -1)))) (+ (* 1/8 (/ 1 (* (pow x 3) (sqrt -1)))) (* x (sqrt -1))))
327.0ms	(- (* 2 (/ 1 x)) (+ (* 1/2 x) (* 1/8 (pow x 3))))
296.0ms	(sqrt (- (pow 1 3) (pow (* x x) 3)))

prune848.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.8s	23852×	body	80	nan
1.9s	8000×	body	80	valid