Details

analyze691.0ms (9.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
49.9%	49.9%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
53%	46.8%	0.2%	8
57.7%	42.1%	0.2%	9
61.6%	38.2%	0.2%	10
63.5%	30%	6.4%	11
63.5%	30%	6.4%	12
67.6%	25.9%	6.4%	13
68.9%	24.7%	6.4%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample148.0ms (2.1%)

Algorithm

1×

intervals

Results

40.0ms	59×	body	1024	valid
35.0ms	74×	body	1024	invalid
11.0ms	46×	body	512	invalid
11.0ms	37×	body	512	valid
10.0ms	126×	body	128	valid
9.0ms	112×	body	128	invalid
6.0ms	32×	body	256	valid
2.0ms	15×	body	256	invalid
2.0ms	2×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

720×	`div-sub_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`
370×	`cancel-sign-sub-inv_binary64`
355×	`distribute-neg-frac_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	28	24
2	50	24
3	96	24
4	205	24
5	441	24
6	997	24
7	1569	24
8	2735	24
9	3755	24
10	4991	24
11	4999	24
12	4815	24

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

21.1b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	21.1b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 38 to 28 computations (26.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 (/.f64 K 2))
0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
0.0b	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
5.9b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite67.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

16×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
11×	`pow1_binary64`

Counts

4 → 75

Calls

4 calls:

7.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
6.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
2.0ms	(cos.f64 (/.f64 K 2))

Compiler

Compiled 1654 to 627 computations (62.1% saved)

series91.0ms (1.3%)

Error

0.0b

Counts

4 → 27

Calls

4 calls:

38.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
18.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
7.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
4.0ms	(cos.f64 (/.f64 K 2))

Compiler

Compiled 1427 to 1010 computations (29.2% saved)

simplify104.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

395×	`*-commutative_binary64`
268×	`distribute-rgt-neg-out_binary64`
266×	`distribute-lft-neg-out_binary64`
230×	`distribute-rgt-in_binary64`
223×	`exp-prod_binary64`

Counts

102 → 69

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	157	1993
1	355	1652
2	1115	1624
3	2345	1624
4	4671	1621
5	4944	1621

prune45.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Error

0.0b

Counts

70 → 3

Alt Table

Status	Error	Program
	21.1b	(+.f64 (.f64 (.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (*.f64 1/2 K))) J) U)
▶	0.1b	(+.f64 (.f64 (.f64 (*.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
	0.8b	(+.f64 (.f64 (+.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J)) U)

Compiler

Compiled 1034 to 522 computations (49.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 (/.f64 K 2))
0.0b	(sinh.f64 l)
0.0b	(.f64 (.f64 2 J) (sinh.f64 l))
0.1b	(.f64 (.f64 (*.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2)))

rewrite74.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

4 → 56

Calls

4 calls:

6.0ms	(.f64 (.f64 (*.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2)))
4.0ms	(.f64 (.f64 2 J) (sinh.f64 l))
2.0ms	(cos.f64 (/.f64 K 2))
1.0ms	(sinh.f64 l)

Compiler

Compiled 1038 to 657 computations (36.7% saved)

series105.0ms (1.5%)

Error

0.0b

Counts

4 → 28

Calls

4 calls:

51.0ms	(.f64 (.f64 (*.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2)))
24.0ms	(.f64 (.f64 2 J) (sinh.f64 l))
9.0ms	(sinh.f64 l)
5.0ms	(cos.f64 (/.f64 K 2))

Compiler

Compiled 1477 to 1068 computations (27.7% saved)

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

532×	`*-commutative_binary64`
437×	`distribute-rgt-in_binary64`
436×	`distribute-lft-in_binary64`
351×	`associate-/l*_binary64`
249×	`associate-l_binary64`

Counts

84 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	135	1475
1	311	1195
2	1093	1181
3	2227	1109
4	5161	1109

prune42.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	54	6	60

Error

Counts

60 → 6

Alt Table

Status	Error	Program
	17.6b	(+.f64 (.f64 (.f64 J (.f64 2 (.f64 (sinh.f64 l) (sqrt.f64 (cos.f64 (/.f64 K 2)))))) (sqrt.f64 (cos.f64 (/.f64 K 2)))) U)
✓	0.1b	(+.f64 (.f64 (.f64 (*.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
	30.7b	(+.f64 (.f64 (.f64 (*.f64 (+.f64 J J) (sqrt.f64 (sinh.f64 l))) (sqrt.f64 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
	0.3b	(+.f64 (.f64 (.f64 J (.f64 2 (.f64 (sinh.f64 l) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) U)
▶	0.1b	(+.f64 (pow.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) 1) U)
	0.8b	(+.f64 (.f64 (+.f64 (+.f64 l l) (.f64 1/3 (pow.f64 l 3))) (.f64 (cos.f64 (.f64 1/2 K)) J)) U)

Compiler

Compiled 868 to 597 computations (31.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 (/.f64 K 2))
0.0b	(sinh.f64 l)
0.1b	(.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))))
0.1b	(*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))

rewrite81.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

15×	`add-cbrt-cube_binary64`
15×	`add-exp-log_binary64`
15×	`pow1_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`

Counts

4 → 56

Calls

4 calls:

6.0ms	(.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))))
3.0ms	(*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))
2.0ms	(cos.f64 (/.f64 K 2))
1.0ms	(sinh.f64 l)

Compiler

Compiled 1134 to 756 computations (33.3% saved)

series129.0ms (1.8%)

Error

Counts

4 → 28

Calls

4 calls:

55.0ms	(.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))))
27.0ms	(*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))
11.0ms	(sinh.f64 l)
5.0ms	(cos.f64 (/.f64 K 2))

Compiler

Compiled 1719 to 1300 computations (24.4% saved)

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

487×	`*-commutative_binary64`
385×	`distribute-rgt-in_binary64`
381×	`distribute-lft-in_binary64`
311×	`associate-/l*_binary64`
197×	`associate-r_binary64`

Counts

84 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	141	1574
1	306	1286
2	1000	1267
3	2178	1140
4	4701	1140
5	5121	1140

prune40.0ms (0.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	42	6	48

Error

Counts

48 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (pow.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) 1) U)
	0.4b	(+.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))) (cbrt.f64 J))) 1) U)
	30.7b	(+.f64 (.f64 (.f64 (*.f64 (+.f64 J J) (sqrt.f64 (sinh.f64 l))) (sqrt.f64 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
▶	0.1b	(+.f64 (pow.f64 (.f64 (.f64 (sinh.f64 l) 2) (.f64 (cos.f64 (.f64 1/2 K)) J)) 1) U)
✓	0.1b	(+.f64 (.f64 (.f64 (*.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
	0.3b	(+.f64 (.f64 (.f64 J (.f64 2 (.f64 (sinh.f64 l) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) U)

Compiler

Compiled 695 to 495 computations (28.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(cos.f64 (*.f64 1/2 K))
0.0b	(sinh.f64 l)
0.1b	(.f64 (cos.f64 (.f64 1/2 K)) J)
0.1b	(.f64 (.f64 (sinh.f64 l) 2) (.f64 (cos.f64 (.f64 1/2 K)) J))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
18×	`pow1_binary64`
9×	`cbrt-unprod_binary64`
9×	`prod-exp_binary64`

Counts

4 → 56

Calls

4 calls:

6.0ms	(.f64 (.f64 (sinh.f64 l) 2) (.f64 (cos.f64 (.f64 1/2 K)) J))
3.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)
1.0ms	(cos.f64 (*.f64 1/2 K))
1.0ms	(sinh.f64 l)

Compiler

Compiled 1135 to 773 computations (31.9% saved)

series105.0ms (1.5%)

Error

Counts

4 → 27

Calls

4 calls:

51.0ms	(.f64 (.f64 (sinh.f64 l) 2) (.f64 (cos.f64 (.f64 1/2 K)) J))
15.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)
12.0ms	(sinh.f64 l)
5.0ms	(cos.f64 (*.f64 1/2 K))

Compiler

Compiled 1483 to 1118 computations (24.6% saved)

simplify83.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

490×	`*-commutative_binary64`
357×	`distribute-rgt-in_binary64`
353×	`distribute-lft-in_binary64`
304×	`associate-/l*_binary64`
204×	`associate-r_binary64`

Counts

83 → 54

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1399
1	291	1159
2	1002	1148
3	2070	1081
4	4812	1081
5	4946	1081

prune50.0ms (0.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	54	6	60

Error

Counts

60 → 6

Alt Table

Status	Error	Program
	0.1b	(+.f64 (pow.f64 (.f64 J (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2))))) 1) U)
	0.4b	(+.f64 (pow.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (.f64 2 (*.f64 (sinh.f64 l) (cos.f64 (/.f64 K 2)))) (cbrt.f64 J))) 1) U)
	30.7b	(+.f64 (.f64 (.f64 (*.f64 (+.f64 J J) (sqrt.f64 (sinh.f64 l))) (sqrt.f64 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
	0.1b	(+.f64 (pow.f64 (.f64 (.f64 (sinh.f64 l) 2) (.f64 (cos.f64 (.f64 1/2 K)) J)) 1) U)
	0.1b	(+.f64 (.f64 (.f64 (*.f64 2 J) (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
	0.3b	(+.f64 (.f64 (.f64 J (.f64 2 (.f64 (sinh.f64 l) (*.f64 (cbrt.f64 (cos.f64 (/.f64 K 2))) (cbrt.f64 (cos.f64 (/.f64 K 2))))))) (cbrt.f64 (cos.f64 (/.f64 K 2)))) U)

Compiler

Compiled 773 to 554 computations (28.3% saved)

regimes806.0ms (11.3%)

Accuracy

Total 0.0b remaining (45.6%)

Threshold costs 0.0b (45.6%)

Compiler

Compiled 17713 to 13196 computations (25.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	21	20
2	20	20

end1.0ms (0%)

Compiler: Compiled 17 to 13 computations (23.5% saved)

sample4.1s (57.7%)

Algorithm

1×

intervals

Results

901.0ms	1666×	body	1024	valid
888.0ms	2059×	body	1024	invalid
432.0ms	4439×	body	128	valid
339.0ms	1156×	body	512	valid
304.0ms	3496×	body	128	invalid
239.0ms	976×	body	512	invalid
121.0ms	686×	body	256	valid
76.0ms	471×	body	256	invalid
39.0ms	53×	body	2048	valid

Compiler

Compiled 174 to 131 computations (24.7% saved)

Details

analyze691.0ms (9.7%)

sample148.0ms (2.1%)

simplify95.0ms (1.3%)

prune2.0ms (0%)

localize11.0ms (0.2%)

rewrite67.0ms (0.9%)

series91.0ms (1.3%)

simplify104.0ms (1.5%)

prune45.0ms (0.6%)

localize11.0ms (0.1%)

rewrite74.0ms (1%)

series105.0ms (1.5%)

simplify64.0ms (0.9%)

prune42.0ms (0.6%)

localize11.0ms (0.2%)

rewrite81.0ms (1.1%)

series129.0ms (1.8%)

simplify82.0ms (1.1%)

prune40.0ms (0.6%)

localize12.0ms (0.2%)

rewrite71.0ms (1%)

series105.0ms (1.5%)

simplify83.0ms (1.2%)

prune50.0ms (0.7%)

regimes806.0ms (11.3%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.1s (57.7%)

Profiling