Details

sample44.0ms

Algorithm

intervals

Results

20.0ms	736×	body	80	nan
9.0ms	256×	body	80	valid

simplify5.0ms

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 3 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)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

3.0ms	(sqrt (- 1.0 (* x x)))
24.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
6.0ms	(/ (sqrt (- 1.0 (* x x))) x)

series477.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(sqrt (- 1.0 (* x x)))
290.0ms	(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))
124.0ms	(/ (sqrt (- 1.0 (* x x))) x)

simplify566.0ms

Counts

90 → 90

Iterations

Useful iterations: done (563.0ms)

Iter	Nodes	Cost
0	215	1548
1	471	1432
2	1380	1343
done	5000	1333

prune236.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ (/ 1.0 x) (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))))
0.3b	(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
0.3b	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
0.4b	(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

285×	`sqrt-prod`
269×	`add-sqr-sqrt`
232×	`times-frac`
179×	`*-un-lft-identity`
127×	`add-cube-cbrt`
58×	`associate-r`
46×	`associate-l`
26×	`difference-of-squares`
25×	`unswap-sqr`
21×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/l*`
13×	`distribute-lft-out` `distribute-lft-out--`
12×	`associate-/r*`
7×	`pow1`
6×	`cbrt-undiv` `div-exp`
5×	`log-div`
4×	`sqrt-undiv` `sqrt-div` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
3×	`log-prod` `frac-add`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `associate-l/` `clear-num` `flip-+`
1×	`flip3--` `sqrt-unprod` `rem-log-exp` `pow-prod-down` `log-pow` `*-commutative` `flip--`

Counts

4 → 321

Calls

4 calls:

6.0ms	(log (+ (/ 1.0 x) (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))))
15.0ms	(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
13.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
82.0ms	(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

series787.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(log (+ (/ 1.0 x) (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))))
123.0ms	(/ (sqrt (- (sqrt 1.0) x)) (sqrt x))
120.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
195.0ms	(* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (/ (sqrt (- (sqrt 1.0) x)) (sqrt x)))

simplify1.3s

Counts

333 → 333

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	431	7181
1	1119	6578
2	3572	6188
done	5000	6155

prune770.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt (sqrt 1.0)) (sqrt x)))
0.3b	(/ (sqrt (- (sqrt (sqrt 1.0)) (sqrt x))) (sqrt x))
0.3b	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
0.4b	(* (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (sqrt (+ (sqrt (sqrt 1.0)) (sqrt x)))) (/ (sqrt (- (sqrt (sqrt 1.0)) (sqrt x))) (sqrt x)))

rewrite182.0ms

Algorithm

rewrite-expression-head

Rules

432×	`sqrt-prod`
277×	`add-sqr-sqrt`
210×	`times-frac`
190×	`*-un-lft-identity`
120×	`add-cube-cbrt`
88×	`associate-r`
78×	`difference-of-squares`
29×	`add-exp-log` `add-cbrt-cube`
26×	`distribute-lft-out--`
21×	`associate-/l*`
14×	`sqrt-div`
12×	`associate-/r*`
10×	`pow1` `prod-exp` `cbrt-unprod`
9×	`frac-times` `distribute-lft-out`
7×	`cbrt-undiv` `div-exp` `associate-*l/`
6×	`flip3-+` `flip-+`
5×	`associate-*r/`
4×	`sqrt-undiv` `associate-/l/` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`frac-2neg` `sqrt-unprod` `clear-num`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `flip--`

Counts

4 → 329

Calls

4 calls:

13.0ms	(sqrt (+ (sqrt (sqrt 1.0)) (sqrt x)))
24.0ms	(/ (sqrt (- (sqrt (sqrt 1.0)) (sqrt x))) (sqrt x))
13.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
109.0ms	(* (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (sqrt (+ (sqrt (sqrt 1.0)) (sqrt x)))) (/ (sqrt (- (sqrt (sqrt 1.0)) (sqrt x))) (sqrt x)))

series1.9s

Counts

4 → 12

Calls

4 calls:

161.0ms	(sqrt (+ (sqrt (sqrt 1.0)) (sqrt x)))
278.0ms	(/ (sqrt (- (sqrt (sqrt 1.0)) (sqrt x))) (sqrt x))
113.0ms	(/ (sqrt (+ (sqrt 1.0) x)) (sqrt x))
1.3s	(* (* (/ (sqrt (+ (sqrt 1.0) x)) (sqrt x)) (sqrt (+ (sqrt (sqrt 1.0)) (sqrt x)))) (/ (sqrt (- (sqrt (sqrt 1.0)) (sqrt x))) (sqrt x)))

simplify1.7s

Counts

341 → 341

Iterations

Useful iterations: 2 (927.0ms)

Iter	Nodes	Cost
0	539	8731
1	1428	7834
2	4982	7448
done	5000	7448

prune805.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	32
1	23	32
done	23	32

end0.0ms

sample1.3s

Algorithm

intervals

Results

677.0ms	23884×	body	80	nan
284.0ms	8000×	body	80	valid