Details

analyze1.5s (16.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
12.5%	87.3%	0.2%	9
18.7%	81.1%	0.2%	10
21.8%	67.1%	11.1%	11
21.8%	67.1%	11.1%	12
32.7%	56.1%	11.1%	13
35.1%	53%	11.9%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample5.3s (59.1%)

Results

1.4s	1779×	body	1024	valid
1.3s	1974×	body	1024	invalid
756.0ms	4468×	body	128	valid
560.0ms	1247×	body	512	valid
453.0ms	2642×	body	128	invalid
392.0ms	993×	body	512	invalid
206.0ms	696×	body	256	valid
157.0ms	526×	body	256	invalid
66.0ms	66×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify68.0ms (0.8%)

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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

17.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.2b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(exp.f64 (neg.f64 l))
✓	0.0b	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
✓	5.8b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series39.0ms (0.4%)

Counts

4 → 76

Calls

4 calls:

27.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
1.0ms	(exp.f64 (neg.f64 l))

rewrite28.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 127

Calls

4 calls:

8.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))
7.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
2.0ms	(exp.f64 (neg.f64 l))

simplify127.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

512×	`fma-neg_binary64`
359×	`associate-l_binary64`
346×	`times-frac_binary64`
332×	`associate-r_binary64`
327×	`cancel-sign-sub-inv_binary64`

Counts

203 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	297	4155
1	640	3445
2	2312	3186
3	4510	3184
4	4897	3184

prune151.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	204	2	206
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	2	207

Error

0.0b

Counts

207 → 2

Alt Table

Status	Error	Program
	0.4b	(+.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))) U)
▶	0.0b	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 5492 to 2237 computations (59.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series153.0ms (1.7%)

Counts

4 → 120

Calls

4 calls:

64.0ms	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
55.0ms	(.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))
26.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
8.0ms	(sinh.f64 l)

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

7.0ms	(+.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) U)
6.0ms	(.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))
4.0ms	(.f64 J (.f64 2 (sinh.f64 l)))
1.0ms	(sinh.f64 l)

simplify126.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-neg_binary64`
373×	`associate--l+_binary64`
372×	`cancel-sign-sub-inv_binary64`
278×	`associate-l_binary64`
252×	`associate-r_binary64`

Counts

189 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	260	4367
1	663	4209
2	2256	3738
3	4692	3737
4	5092	3737

prune121.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	136	6	142

Error

0.0b

Counts

142 → 6

Alt Table

Status	Error	Program
	22.8b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) U)
	10.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) 3)) U)
	0.4b	(+.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))) U)
	32.1b	(+.f64 (.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
▶	0.0b	(+.f64 U (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))
	17.8b	(expm1.f64 (log1p.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)))

Compiler

Compiled 3560 to 2188 computations (38.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series67.0ms (0.7%)

Counts

1 → 48

Calls

1 calls:

66.0ms

(+.f64 U (*.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 16

Calls

1 calls:

3.0ms

(+.f64 U (*.f64 (*.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

735×	`fma-neg_binary64`
693×	`fma-def_binary64`
361×	`*-commutative_binary64`
262×	`associate-+l+_binary64`
248×	`cancel-sign-sub-inv_binary64`

Counts

64 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	1917
1	373	1831
2	1291	1567
3	4252	1567
4	4976	1567

prune140.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	144	5	149

Error

Counts

149 → 5

Alt Table

Status	Error	Program
	22.8b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) U)
	10.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) 3)) U)
▶	0.1b	(+.f64 U (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))))
	32.1b	(+.f64 (.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	0.4b	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)

Compiler

Compiled 3561 to 2177 computations (38.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series145.0ms (1.6%)

Counts

3 → 108

Calls

3 calls:

62.0ms	(+.f64 U (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))))
54.0ms	(.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))
29.0ms	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 61

Calls

3 calls:

5.0ms	(.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))
4.0ms	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))
3.0ms	(+.f64 U (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))))

simplify123.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

440×	`cancel-sign-sub-inv_binary64`
287×	`fma-neg_binary64`
285×	`associate-r_binary64`
257×	`associate-l_binary64`
215×	`fma-def_binary64`

Counts

169 → 133

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4552
1	715	4328
2	2485	3854
3	4483	3853
4	4987	3853

prune134.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	153	5	158

Error

Counts

158 → 5

Alt Table

Status	Error	Program
	22.8b	(+.f64 (.f64 (sqrt.f64 (.f64 (.f64 J (.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2)))) (sqrt.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))))) U)
	10.1b	(+.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 J (*.f64 2 (sinh.f64 l))) (cos.f64 (/.f64 K 2))) 3)) U)
✓	0.1b	(+.f64 U (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))))
	32.1b	(+.f64 (.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (.f64 2 (sinh.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	0.4b	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 l 2 (*.f64 1/3 (pow.f64 l 3))) U)

Compiler

Compiled 3829 to 2335 computations (39% saved)

regimes537.0ms (6%)

Accuracy

Total 0.0b remaining (56.9%)

Threshold costs 0.0b (56.9%)

Counts

61 → 1

Compiler

Compiled 11546 to 8646 computations (25.1% saved)

simplify2.0ms (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

end89.0ms (1%)

Compiler: Compiled 143 to 108 computations (24.5% saved)

Details

analyze1.5s (16.3%)

sample5.3s (59.1%)

simplify68.0ms (0.8%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series39.0ms (0.4%)

rewrite28.0ms (0.3%)

simplify127.0ms (1.4%)

prune151.0ms (1.7%)

localize9.0ms (0.1%)

series153.0ms (1.7%)

rewrite21.0ms (0.2%)

simplify126.0ms (1.4%)

prune121.0ms (1.3%)

localize11.0ms (0.1%)

series67.0ms (0.7%)

rewrite3.0ms (0%)

simplify69.0ms (0.8%)

prune140.0ms (1.6%)

localize9.0ms (0.1%)

series145.0ms (1.6%)

rewrite17.0ms (0.2%)

simplify123.0ms (1.4%)

prune134.0ms (1.5%)

regimes537.0ms (6%)

simplify2.0ms (0%)

end89.0ms (1%)

Profiling