Details

analyze7.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample62.0ms (2.3%)

Algorithm

1×

intervals

Results

35.0ms	114×	body	1280	valid
14.0ms	75×	body	640	valid
5.0ms	42×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	13×	body	80	valid

simplify46.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5032	8

prune8.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 57.1b

Counts

2 → 1

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

3.6b	(- (exp x) (exp (neg x)))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `sinh-undef` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 14

Calls

1 calls:

5.0ms

(- (exp x) (exp (neg x)))

series5.0ms (0.2%)

Counts

1 → 3

Calls

1 calls:

5.0ms

(- (exp x) (exp (neg x)))

simplify67.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4847	155
1	4847	155

prune33.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	13	4	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	4	18

Merged error: 0.0b

Counts

18 → 4

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b

(sinh x)

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `sinh-def` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

1 → 8

Calls

1 calls:

1.0ms

(sinh x)

series9.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

9.0ms

(sinh x)

simplify36.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

11 → 11

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5343	61

prune28.0ms (1.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	8	3	11
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	10	5	15

Merged error: 0b

Counts

15 → 5

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/6 (pow x 3)) (* 1/120 (pow x 5)))
0.0b	(+ x (+ (* 1/6 (pow x 3)) (* 1/120 (pow x 5))))
0.0b	(* 1/120 (pow x 5))
0.1b	(* 1/6 (pow x 3))

rewrite25.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

6.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/120 (pow x 5))))
6.0ms	(* 1/6 (pow x 3))
5.0ms	(+ (* 1/6 (pow x 3)) (* 1/120 (pow x 5)))
5.0ms	(* 1/120 (pow x 5))

series26.0ms (1%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1/6 (pow x 3)) (* 1/120 (pow x 5)))
7.0ms	(+ x (+ (* 1/6 (pow x 3)) (* 1/120 (pow x 5))))
4.0ms	(* 1/120 (pow x 5))
4.0ms	(* 1/6 (pow x 3))

simplify46.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5046	884

prune194.0ms (7.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	93	5	98

Merged error: 0b

Counts

98 → 5

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sinh x)
0.0b	(sinh x)
0.2b	(* (sqrt (sinh x)) (sqrt (sinh x)))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
18×	`pow1` `sqrt-prod`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`sinh-def` `associate-r` `associate-l`
5×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
4×	`sqrt-div` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `add-log-exp`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

3 → 68

Calls

3 calls:

7.0ms	(* (sqrt (sinh x)) (sqrt (sinh x)))
1.0ms	(sinh x)
1.0ms	(sinh x)

series24.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (sqrt (sinh x)) (sqrt (sinh x)))
7.0ms	(sinh x)
7.0ms	(sinh x)

simplify48.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4909	373
1	4909	373

prune87.0ms (3.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	77	5	82

Merged error: 0b

Counts

82 → 5

regimes34.0ms (1.3%)

Accuracy

Total 0.0b remaining (69.8%)

Threshold costs 0.0b (69.8%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	6
1	7	6

end0.0ms (0%)

sample1.8s (68.5%)

Algorithm

1×

intervals

Results

1.0s	3328×	body	1280	valid
481.0ms	2588×	body	640	valid
136.0ms	1187×	body	320	valid
45.0ms	606×	body	160	valid
11.0ms	291×	body	80	valid
0.0ms	2×	body	80	invalid

Details

analyze7.0ms (0.3%)

sample62.0ms (2.3%)

simplify46.0ms (1.8%)

prune8.0ms (0.3%)

localize6.0ms (0.2%)

rewrite5.0ms (0.2%)

series5.0ms (0.2%)

simplify67.0ms (2.5%)

prune33.0ms (1.3%)

localize4.0ms (0.2%)

rewrite1.0ms (0.1%)

series9.0ms (0.3%)

simplify36.0ms (1.4%)

prune28.0ms (1.1%)

localize11.0ms (0.4%)

rewrite25.0ms (0.9%)

series26.0ms (1%)

simplify46.0ms (1.7%)

prune194.0ms (7.4%)

localize6.0ms (0.2%)

rewrite11.0ms (0.4%)

series24.0ms (0.9%)

simplify48.0ms (1.8%)

prune87.0ms (3.3%)

regimes34.0ms (1.3%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample1.8s (68.5%)

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