Details

analyze610.0ms (8%)

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)

sample206.0ms (2.7%)

Algorithm

1×

intervals

Results

31.0ms	76×	body	1024	invalid
28.0ms	51×	body	1024	valid
14.0ms	36×	body	512	invalid
12.0ms	149×	body	128	valid
11.0ms	41×	body	512	valid
8.0ms	103×	body	128	invalid
2.0ms	13×	body	256	valid
2.0ms	11×	body	256	invalid
1.0ms	2×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify71.0ms (0.9%)

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

prune4.0ms (0%)

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

16.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.5b	(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)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	6.6b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series48.0ms (0.6%)

Counts

3 → 80

Calls

3 calls:

37.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
9.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite21.0ms (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:

11.0ms	(*.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)

simplify188.0ms (2.5%)

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

prune137.0ms (1.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	3	170

Error

0.3b

Counts

170 → 3

Alt Table

Status	Error	Program
	16.5b	(fma.f64 (+.f64 (*.f64 (exp.f64 l) J) (neg.f64 (/.f64 J (exp.f64 l)))) (cos.f64 (/.f64 K 2)) U)
▶	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 4525 to 1685 computations (62.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sinh.f64 l)
✓	0.1b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(.f64 J (.f64 2 (sinh.f64 l)))

series109.0ms (1.4%)

Counts

3 → 84

Calls

3 calls:

67.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
31.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
10.0ms	(sinh.f64 l)

rewrite6.0ms (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	(sinh.f64 l)
0.0ms	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)

simplify107.0ms (1.4%)

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 → 88

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

prune75.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Error

0.3b

Counts

91 → 5

Alt Table

Status	Error	Program
	16.5b	(fma.f64 (+.f64 (*.f64 (exp.f64 l) J) (neg.f64 (/.f64 J (exp.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	0.7b	(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)
✓	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
	42.0b	(cbrt.f64 (.f64 (.f64 (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U) (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)) (fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)))
▶	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 2040 to 1218 computations (40.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
✓	0.1b	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
✓	0.1b	(.f64 J (cos.f64 (.f64 1/2 K)))

series55.0ms (0.7%)

Counts

3 → 76

Calls

3 calls:

26.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
20.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
8.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
10×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

3 → 50

Calls

3 calls:

4.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
3.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))
0.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

824×	`fma-neg_binary64`
409×	`fma-def_binary64`
381×	`*-commutative_binary64`
328×	`cancel-sign-sub-inv_binary64`
307×	`distribute-lft-out--_binary64`

Counts

126 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1977
1	294	1809
2	1038	1772
3	2450	1761
4	4893	1761
5	4986	1761

prune109.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Error

0.2b

Counts

114 → 7

Alt Table

Status	Error	Program
	35.2b	(fma.f64 2 (.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (.f64 J (cos.f64 (.f64 1/2 K))))) U)
	22.8b	(fma.f64 2 (.f64 l (fma.f64 (.f64 J (*.f64 K K)) -1/8 J)) U)
	16.5b	(fma.f64 (+.f64 (*.f64 (exp.f64 l) J) (neg.f64 (/.f64 J (exp.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	9.9b	(fma.f64 2 (cbrt.f64 (.f64 (.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))) (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))) U)
▶	0.7b	(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)
✓	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 2098 to 1361 computations (35.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))))
✓	0.2b	(.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))
✓	0.5b	(*.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l)))
✓	0.9b	(cbrt.f64 (sinh.f64 l))

series811.0ms (10.6%)

Counts

4 → 60

Calls

4 calls:

465.0ms	(*.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l)))
308.0ms	(cbrt.f64 (sinh.f64 l))
29.0ms	(.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))))
8.0ms	(.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`pow1_binary64`
29×	`cbrt-div_binary64`
29×	`sinh-def_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`add-exp-log_binary64`

Counts

4 → 137

Calls

4 calls:

14.0ms	(.f64 J (.f64 2 (.f64 (.f64 (cbrt.f64 (sinh.f64 l)) (cbrt.f64 (sinh.f64 l))) (cbrt.f64 (sinh.f64 l)))))
7.0ms	(.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))

simplify103.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

848×	`fma-def_binary64`
517×	`*-commutative_binary64`
334×	`unswap-sqr_binary64`
248×	`associate-r_binary64`
240×	`associate-*r/_binary64`

Counts

197 → 212

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	2893
1	471	2686
2	1441	2568
3	3392	2226
4	4909	2226

prune300.0ms (3.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	266	0	266
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	266	7	273

Error

0.2b

Counts

273 → 7

Alt Table

Status	Error	Program
	35.2b	(fma.f64 2 (.f64 (sqrt.f64 l) (.f64 (sqrt.f64 l) (.f64 J (cos.f64 (.f64 1/2 K))))) U)
	22.8b	(fma.f64 2 (.f64 l (fma.f64 (.f64 J (*.f64 K K)) -1/8 J)) U)
	16.5b	(fma.f64 (+.f64 (*.f64 (exp.f64 l) J) (neg.f64 (/.f64 J (exp.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	9.9b	(fma.f64 2 (cbrt.f64 (.f64 (.f64 (.f64 l (.f64 J (cos.f64 (.f64 1/2 K)))) (.f64 l (.f64 J (cos.f64 (.f64 1/2 K))))) (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))))) U)
✓	0.7b	(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)
✓	0.3b	(fma.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)) U)
✓	0.6b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)

Compiler

Compiled 7109 to 3319 computations (53.3% saved)

regimes568.0ms (7.4%)

Accuracy

Total 0.0b remaining (49.1%)

Threshold costs 0.0b (49.1%)

Counts

58 → 1

Compiler

Compiled 12216 to 8634 computations (29.3% 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

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample3.9s (51.3%)

Algorithm

1×

intervals

Results

927.0ms	1737×	body	1024	valid
780.0ms	1914×	body	1024	invalid
368.0ms	1251×	body	512	valid
366.0ms	4285×	body	128	valid
293.0ms	3410×	body	128	invalid
267.0ms	1036×	body	512	invalid
115.0ms	672×	body	256	valid
84.0ms	487×	body	256	invalid
48.0ms	55×	body	2048	valid

Compiler

Compiled 186 to 130 computations (30.1% saved)

Details

analyze610.0ms (8%)

sample206.0ms (2.7%)

simplify71.0ms (0.9%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series48.0ms (0.6%)

rewrite21.0ms (0.3%)

simplify188.0ms (2.5%)

prune137.0ms (1.8%)

localize9.0ms (0.1%)

series109.0ms (1.4%)

rewrite6.0ms (0.1%)

simplify107.0ms (1.4%)

prune75.0ms (1%)

localize8.0ms (0.1%)

series55.0ms (0.7%)

rewrite9.0ms (0.1%)

simplify91.0ms (1.2%)

prune109.0ms (1.4%)

localize18.0ms (0.2%)

series811.0ms (10.6%)

rewrite37.0ms (0.5%)

simplify103.0ms (1.4%)

prune300.0ms (3.9%)

regimes568.0ms (7.4%)

simplify2.0ms (0%)

end1.0ms (0%)

sample3.9s (51.3%)

Profiling