Details

analyze1.5s (15.2%)

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)

sample5.2s (53.5%)

Results

1.3s	1713×	body	1024	valid
1.2s	2020×	body	1024	invalid
757.0ms	4517×	body	128	valid
589.0ms	1275×	body	512	valid
480.0ms	2710×	body	128	invalid
403.0ms	983×	body	512	invalid
207.0ms	693×	body	256	valid
157.0ms	562×	body	256	invalid
62.0ms	58×	body	2048	valid

Compiler

Compiled 40 to 30 computations (25% saved)

preprocess43.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

672×	`fma-def_binary64`
472×	`associate-l_binary64`
454×	`associate-r_binary64`
251×	`unsub-neg_binary64`
219×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	154
1	113	154
2	244	154
3	610	154
4	1668	154
5	4483	154
0	4	4

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify26.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
464×	`fma-neg_binary64`
394×	`times-frac_binary64`
314×	`associate-l_binary64`
236×	`associate-r_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	55	22
3	121	22
4	306	22
5	771	22
6	2013	22
7	3835	22

Stop Event

1×	node limit

Counts

1 → 2

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

14.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.8b	(+.f64 (.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 71 to 47 computations (33.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 l)
✓	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)))
✓	6.0b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series36.0ms (0.4%)

Counts

4 → 72

Calls

21 calls:

4.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))	J	-inf
3.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))	K	inf
3.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))	J	inf
3.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))	J	0
3.0ms	(.f64 (.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)))	l	inf

rewrite167.0ms (1.7%)

Algorithm

7×	egg-rewrite
1×	batch-egg-rewrite

Rules

252×	`log1p-expm1-u_binary64`
252×	`expm1-log1p-u_binary64`
251×	`add-sqr-sqrt_binary64`
232×	`add-cbrt-cube_binary64`
231×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	21
1	277	21
2	4216	21
0	6	6
1	130	6
2	2131	6
0	6	6
0	13	17
1	277	17
2	4220	17
0	13	17
0	8	9
1	169	9
2	2701	9
0	8	9
0	3	3
1	55	3
2	633	3

Stop Event

1×	node limit
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

4 → 68

simplify74.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

568×	`associate-l_binary64`
423×	`associate-r_binary64`
330×	`sub-neg_binary64`
240×	`*-commutative_binary64`
233×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	132	1717
1	394	1426
2	1225	1363
3	4460	1363

Stop Event

1×	node limit

Counts

140 → 114

prune152.0ms (1.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	108	6	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Error

0.0b

Counts

115 → 6

Alt Table

Status	Error	Program
	14.8b	(+.f64 (.f64 (.f64 J (-.f64 (-.f64 (+.f64 1 (exp.f64 l)) 1) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2))) U)
	0.6b	(+.f64 (+.f64 (.f64 1/60 (.f64 (pow.f64 l 5) (.f64 J (cos.f64 (.f64 1/2 K))))) (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 J (cos.f64 (.f64 1/2 K))))) (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))))) U)
	10.4b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))) (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))))) U)
▶	0.1b	(+.f64 (pow.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) 1) U)
	0.4b	(+.f64 (.f64 (.f64 J (.f64 (.f64 (cbrt.f64 (.f64 2 (sinh.f64 l))) (cbrt.f64 (.f64 2 (sinh.f64 l)))) (cbrt.f64 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
	0.8b	(+.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))) U)

Compiler

Compiled 2878 to 1731 computations (39.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) 1) U)
✓	0.0b	(sinh.f64 l)
✓	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)))

series159.0ms (1.6%)

Counts

4 → 120

Calls

30 calls:

16.0ms	(.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))	K	inf
10.0ms	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))	l	inf
9.0ms	(.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))	J	inf
7.0ms	(+.f64 (pow.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) 1) U)	K	inf
7.0ms	(+.f64 (pow.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) 1) U)	l	-inf

rewrite66.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

351×	`fma-def_binary64`
262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
191×	`fma-neg_binary64`
146×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	305	52
2	3811	52

Stop Event

1×	node limit

Counts

4 → 109

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

501×	`associate--l+_binary64`
459×	`associate--r+_binary64`
458×	`associate-l_binary64`
362×	`cancel-sign-sub-inv_binary64`
359×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	3430
1	594	3345
2	1823	2870

Stop Event

1×	node limit

Counts

229 → 181

prune259.0ms (2.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	177	4	181
Fresh	4	1	5
Picked	0	1	1
Done	0	0	0
Total	181	6	187

Error

0.0b

Counts

187 → 6

Alt Table

Status	Error	Program
	0.8b	(+.f64 (.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))) U)
	10.4b	(+.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (.f64 (sinh.f64 l) (cos.f64 (.f64 K 1/2))) J)) 3)) 1) U)
	32.3b	(+.f64 (pow.f64 (.f64 J (pow.f64 (sqrt.f64 (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (.f64 K 1/2))))) 2)) 1) U)
▶	0.0b	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (*.f64 K 1/2)) J) U)
✓	0.1b	(+.f64 (pow.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) 1) U)
	15.2b	(+.f64 (pow.f64 (*.f64 J (-.f64 (exp.f64 l) (/.f64 1 (exp.f64 l)))) 1) U)

Compiler

Compiled 4489 to 2883 computations (35.8% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series66.0ms (0.7%)

Counts

2 → 72

Calls

18 calls:

8.0ms	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (*.f64 K 1/2)) J) U)	l	-inf
7.0ms	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (*.f64 K 1/2)) J) U)	l	inf
5.0ms	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (*.f64 K 1/2)) J) U)	K	inf
5.0ms	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (*.f64 K 1/2)) J) U)	K	-inf
5.0ms	(fma.f64 (.f64 2 (sinh.f64 l)) (.f64 (cos.f64 (*.f64 K 1/2)) J) U)	J	inf

rewrite50.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

605×	`log-prod_binary64`
235×	`expm1-udef_binary64`
235×	`log1p-udef_binary64`
224×	`prod-diff_binary64`
207×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
1	261	27
2	3024	27

Stop Event

1×	node limit

Counts

2 → 47

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

891×	`fma-neg_binary64`
549×	`fma-def_binary64`
336×	`associate-l_binary64`
277×	`associate-r_binary64`
240×	`associate-+l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	118	1739
1	371	1719
2	1086	1461
3	4457	1460

Stop Event

1×	node limit

Counts

119 → 83

prune118.0ms (1.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	116	5	121

Error

0.0b

Counts

121 → 5

Alt Table

Status	Error	Program
▶	0.8b	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
	32.3b	(+.f64 (pow.f64 (.f64 J (pow.f64 (sqrt.f64 (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (.f64 K 1/2))))) 2)) 1) U)
✓	0.1b	(+.f64 (pow.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) 1) U)
	15.2b	(+.f64 (pow.f64 (*.f64 J (-.f64 (exp.f64 l) (/.f64 1 (exp.f64 l)))) 1) U)
	10.4b	(+.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (.f64 (sinh.f64 l) (cos.f64 (.f64 K 1/2))) J)) 3)) 1) U)

Compiler

Compiled 2459 to 1548 computations (37% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l))
✓	0.0b	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
✓	0.1b	(.f64 J (cos.f64 (.f64 K 1/2)))

series60.0ms (0.6%)

Counts

3 → 84

Calls

21 calls:

7.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)	K	-inf
5.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)	J	inf
5.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)	U	-inf
5.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)	K	inf
4.0ms	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)	J	-inf

rewrite55.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

309×	`prod-diff_binary64`
274×	`expm1-udef_binary64`
274×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
147×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	324	43
2	3584	43

Stop Event

1×	node limit

Counts

3 → 61

simplify49.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

683×	`fma-def_binary64`
601×	`associate-l_binary64`
514×	`associate-r_binary64`
352×	`cancel-sign-sub-inv_binary64`
295×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	99	1915
1	301	1580
2	1035	1481

Stop Event

1×	node limit

Counts

145 → 96

prune98.0ms (1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	96	5	101

Error

0.0b

Counts

101 → 5

Alt Table

Status	Error	Program
✓	0.8b	(fma.f64 (.f64 J (cos.f64 (.f64 K 1/2))) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
	32.3b	(+.f64 (pow.f64 (.f64 J (pow.f64 (sqrt.f64 (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (.f64 K 1/2))))) 2)) 1) U)
✓	0.1b	(+.f64 (pow.f64 (.f64 J (.f64 (*.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) 1) U)
	15.2b	(+.f64 (pow.f64 (*.f64 J (-.f64 (exp.f64 l) (/.f64 1 (exp.f64 l)))) 1) U)
	10.4b	(+.f64 (pow.f64 (cbrt.f64 (pow.f64 (.f64 2 (.f64 (.f64 (sinh.f64 l) (cos.f64 (.f64 K 1/2))) J)) 3)) 1) U)

Compiler

Compiled 2311 to 1657 computations (28.3% saved)

regimes1.3s (13.1%)

Accuracy

Total 0.0b remaining (59.9%)

Threshold costs 0.0b (59.9%)

Counts

121 → 1

Compiler

Compiled 25305 to 19245 computations (23.9% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
1×	`*-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	22	18

Stop Event

1×

saturated

end105.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 132 to 102 computations (22.7% saved)

Details

analyze1.5s (15.2%)

sample5.2s (53.5%)

preprocess43.0ms (0.4%)

simplify26.0ms (0.3%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series36.0ms (0.4%)

rewrite167.0ms (1.7%)

simplify74.0ms (0.8%)

prune152.0ms (1.6%)

localize10.0ms (0.1%)

series159.0ms (1.6%)

rewrite66.0ms (0.7%)

simplify73.0ms (0.8%)

prune259.0ms (2.7%)

localize9.0ms (0.1%)

series66.0ms (0.7%)

rewrite50.0ms (0.5%)

simplify58.0ms (0.6%)

prune118.0ms (1.2%)

localize12.0ms (0.1%)

series60.0ms (0.6%)

rewrite55.0ms (0.6%)

simplify49.0ms (0.5%)

prune98.0ms (1%)

regimes1.3s (13.1%)

simplify2.0ms (0%)

end105.0ms (1.1%)

Profiling