Details

sample143.0ms

Algorithm

intervals

Results

81.0ms	713×	body	80	nan
39.0ms	256×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	18
2	18
1	14
0	9

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
50×	`times-frac`
43×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `sqrt-prod`
16×	`distribute-lft-out`
15×	`log-prod`
13×	`div-inv`
10×	`difference-of-squares`
8×	`associate-/l*`
7×	`add-exp-log`
6×	`pow1` `distribute-rgt-out` `add-cbrt-cube` `add-log-exp`
4×	`sqrt-div` `insert-posit16`
3×	`log-div` `associate-/r*`
2×	`flip3-+` `flip3--` `frac-add` `distribute-rgt1-in` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `rem-log-exp` `log-pow`

Counts

4 → 121

Calls

4 calls:

25.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
20.0ms	(/ (sqrt (- 1 (* x x))) x)
8.0ms	(sqrt (- 1 (* x x)))
29.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

series646.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x)))
171.0ms	(/ (sqrt (- 1 (* x x))) x)
75.0ms	(sqrt (- 1 (* x x)))
100.0ms	(+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))

simplify1.8s

Counts

133 → 133

Iterations

Iter	Nodes
3	4259
2	1270
1	490
0	239

prune1.1s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (sqrt x))
0.3b	(/ 1 (sqrt x))
0.3b	(/ (sqrt (- 1 (* x x))) (sqrt x))
0.5b	(* (/ 1 (sqrt x)) (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x))))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac`
129×	`*-un-lft-identity`
123×	`add-sqr-sqrt`
122×	`sqrt-prod`
88×	`add-cube-cbrt`
26×	`associate-r`
23×	`add-exp-log`
22×	`associate-l`
18×	`associate-/r*` `distribute-lft-out`
15×	`add-cbrt-cube`
14×	`associate-/l*` `difference-of-squares`
11×	`div-inv`
10×	`pow1`
7×	`div-exp`
6×	`pow-flip`
5×	`unswap-sqr`
4×	`cbrt-undiv` `distribute-rgt-out` `prod-exp` `insert-posit16` `add-log-exp`
3×	`frac-times` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-*r/`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `frac-add` `cbrt-unprod` `flip-+` `inv-pow` `associate-/l/`
1×	`distribute-rgt-in` `sqrt-undiv` `distribute-lft-in` `flip3--` `pow-prod-down` `associate-l/` `distribute-rgt1-in` `-commutative` `flip--`

Counts

4 → 248

Calls

4 calls:

5.0ms	(/ 1 (sqrt x))
5.0ms	(/ 1 (sqrt x))
10.0ms	(/ (sqrt (- 1 (* x x))) (sqrt x))
120.0ms	(* (/ 1 (sqrt x)) (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x))))

series493.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (sqrt x))
53.0ms	(/ 1 (sqrt x))
105.0ms	(/ (sqrt (- 1 (* x x))) (sqrt x))
281.0ms	(* (/ 1 (sqrt x)) (+ (/ 1 (sqrt x)) (/ (sqrt (- 1 (* x x))) (sqrt x))))

simplify901.0ms

Counts

260 → 260

Iterations

Iter	Nodes
2	2289
1	805
0	292

prune2.7s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Iter	Nodes
2	15
1	15
0	11

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.3s	24407×	body	80	nan
1.5s	8000×	body	80	valid