Details

sample47.0ms

Algorithm

intervals

Results

20.0ms	680×	body	80	nan
12.0ms	256×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	13
1	12	13
2	16	13
done	16	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* x x)))
0.0b	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.0b	(/ (sqrt (- 1.0 (* x x))) x)
0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
33×	`times-frac`
32×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
20×	`sqrt-prod`
8×	`log-prod` `distribute-lft-out`
7×	`add-exp-log` `associate-/l*`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`div-inv` `difference-of-squares`
4×	`sqrt-div`
3×	`log-div` `associate-/r*`
2×	`distribute-rgt-out` `flip3--` `flip3-+` `frac-add` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `clear-num` `sum-log` `log-pow`

Counts

4 → 98

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* x x)))
27.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms	(/ (sqrt (- 1.0 (* x x))) x)
27.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

series574.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sqrt (- 1.0 (* x x)))
285.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
126.0ms	(/ (sqrt (- 1.0 (* x x))) x)
102.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))

simplify475.0ms

Counts

110 → 110

Iterations

Useful iterations: done (472.0ms)

Iter	Nodes	Cost
0	226	1924
1	513	1800
2	1521	1665
done	5000	1652

prune277.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.2b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.2b	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
0.5b	(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

90×	`*-un-lft-identity`
58×	`sqrt-prod`
42×	`add-sqr-sqrt` `times-frac`
30×	`sqrt-div` `distribute-lft-out`
28×	`add-cube-cbrt`
21×	`pow1`
15×	`swap-sqr`
14×	`div-inv`
11×	`flip3-+` `associate-r` `associate-l` `frac-add` `flip-+`
10×	`sqrt-pow1` `pow1/2`
9×	`frac-times`
7×	`distribute-rgt-out`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`unswap-sqr`
3×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr`
2×	`rem-sqrt-square`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 140

Calls

4 calls:

26.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
49.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
49.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
203.0ms	(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

series667.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
197.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
201.0ms	(sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
161.0ms	(* (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (sqrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))

simplify157.0ms

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	236	4553
1	508	3433