Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
99.8%	0%	0.2%	1

Compiler

Compiled 20 to 15 computations (25% saved)

sample3.6s (48.9%)

Results

1.7s	1862×	body	1024	valid
960.0ms	4699×	body	128	valid
563.0ms	1091×	body	512	valid
213.0ms	576×	body	256	valid
39.0ms	28×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
657×	`div-sub_binary64`
464×	`fma-neg_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	53	22
3	105	22
4	233	22
5	540	22
6	1242	22
7	2242	22
8	3501	22
9	4490	22
10	4976	22

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

7.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize19.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	2.9b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series56.0ms (0.8%)

Counts

3 → 80

Calls

3 calls:

41.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
12.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
3.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
27×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

7.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify229.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

374×	`times-frac_binary64`
336×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
281×	`associate-r_binary64`
279×	`associate-l_binary64`

Counts

172 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	3960
1	572	3266
2	2075	3044
3	4373	3044
4	4843	3044
5	4992	3044
6	4994	3044
7	4848	3044

prune134.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	2	170

Error

0.0b

Counts

170 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	21.9b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 4485 to 1659 computations (63% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 J (.f64 2 (sinh.f64 l)))
✓	0.0b	(sinh.f64 l)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

series133.0ms (1.8%)

Counts

3 → 84

Calls

3 calls:

78.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
36.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
17.0ms	(sinh.f64 l)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`

Counts

3 → 41

Calls

3 calls:

4.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
1.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
1.0ms	(sinh.f64 l)

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-def_binary64`
581×	`fma-neg_binary64`
432×	`*-commutative_binary64`
278×	`associate-+l+_binary64`
224×	`associate--l+_binary64`

Counts

125 → 89

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	201	2596
1	465	2480
2	1467	2171
3	4147	2171
4	4936	2171
5	4957	2171

prune143.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Error

0.0b

Counts

91 → 4

Alt Table

Status	Error	Program
	6.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	4.8b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (cos.f64 (/.f64 K 2)) U)
▶	0.1b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 1973 to 1179 computations (40.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))
✓	0.3b	(*.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l)))
✓	0.3b	(cbrt.f64 (sinh.f64 l))

series1.2s (16.3%)

Counts

4 → 84

Calls

4 calls:

700.0ms	(*.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l)))
409.0ms	(cbrt.f64 (sinh.f64 l))
78.0ms	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
13.0ms	(.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64`
25×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
17×	`cbrt-div_binary64`
17×	`sinh-def_binary64`

Counts

4 → 114

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))
5.0ms	(*.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l)))
1.0ms	(cbrt.f64 (sinh.f64 l))
0.0ms	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)

simplify134.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
550×	`fma-neg_binary64`
406×	`*-commutative_binary64`
294×	`associate-+l+_binary64`
235×	`associate--l+_binary64`

Counts

198 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	269	3668
1	592	3496
2	1706	3148
3	4554	3148
4	4992	3148

prune383.0ms (5.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	253	1	254
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	253	5	258

Error

0.0b

Counts

258 → 5

Alt Table

Status	Error	Program
	6.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	34.6b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (pow.f64 (sqrt.f64 (cbrt.f64 (sinh.f64 l))) 3)) (sqrt.f64 (cbrt.f64 (sinh.f64 l)))))) (cos.f64 (/.f64 K 2)) U)
▶	4.8b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 6865 to 3243 computations (52.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sinh.f64 l)
✓	0.0b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)
✓	15.0b	(cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3))

series181.0ms (2.4%)

Counts

3 → 96

Calls

3 calls:

83.0ms	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (cos.f64 (/.f64 K 2)) U)
57.0ms	(pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)
40.0ms	(cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`cbrt-prod_binary64`
5×	`*-un-lft-identity_binary64`

Counts

3 → 58

Calls

3 calls:

4.0ms	(pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)
2.0ms	(cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3))
0.0ms	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (cos.f64 (/.f64 K 2)) U)

simplify112.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

277×	`associate-r_binary64`
261×	`cancel-sign-sub-inv_binary64`
232×	`fma-neg_binary64`
206×	`associate-/l*_binary64`
200×	`associate-l_binary64`

Counts

154 → 128

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	3440
1	601	3238
2	2215	2956
3	4612	2954
4	5023	2954

prune266.0ms (3.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	148	5	153

Error

0.0b

Counts

153 → 5

Alt Table

Status	Error	Program
	6.2b	(fma.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)
	34.6b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (pow.f64 (sqrt.f64 (cbrt.f64 (sinh.f64 l))) 3)) (sqrt.f64 (cbrt.f64 (sinh.f64 l)))))) (cos.f64 (/.f64 K 2)) U)
✓	4.8b	(fma.f64 (cbrt.f64 (pow.f64 (.f64 J (.f64 2 (sinh.f64 l))) 3)) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 3516 to 2311 computations (34.3% saved)

regimes360.0ms (4.9%)

Accuracy

Total 0.0b remaining (59.1%)

Threshold costs 0.0b (59.1%)

Counts

30 → 1

Compiler

Compiled 6359 to 4559 computations (28.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	14	18
2	14	18

end107.0ms (1.5%)

Compiler: Compiled 141 to 99 computations (29.8% saved)

Details

analyze5.0ms (0.1%)

sample3.6s (48.9%)

simplify84.0ms (1.1%)

prune6.0ms (0.1%)

localize19.0ms (0.3%)

series56.0ms (0.8%)

rewrite20.0ms (0.3%)

simplify229.0ms (3.1%)

prune134.0ms (1.8%)

localize10.0ms (0.1%)

series133.0ms (1.8%)

rewrite8.0ms (0.1%)

simplify124.0ms (1.7%)

prune143.0ms (1.9%)

localize17.0ms (0.2%)

series1.2s (16.3%)

rewrite23.0ms (0.3%)

simplify134.0ms (1.8%)

prune383.0ms (5.2%)

localize11.0ms (0.2%)

series181.0ms (2.4%)

rewrite10.0ms (0.1%)

simplify112.0ms (1.5%)

prune266.0ms (3.6%)

regimes360.0ms (4.9%)

simplify2.0ms (0%)

end107.0ms (1.5%)

Profiling