Details

analyze1.4s (15.7%)

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)

sample5.1s (57.6%)

Results

1.3s	1735×	body	1024	valid
1.2s	1967×	body	1024	invalid
761.0ms	4608×	body	128	valid
542.0ms	1187×	body	512	valid
435.0ms	2686×	body	128	invalid
424.0ms	1035×	body	512	invalid
196.0ms	673×	body	256	valid
145.0ms	507×	body	256	invalid
51.0ms	53×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify25.0ms (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

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

19.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.5b	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)

Compiler

Compiled 69 to 45 computations (34.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)
✓	0.0b	(*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2)))
✓	5.1b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series59.0ms (0.7%)

Counts

3 → 80

Calls

3 calls:

43.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)
13.0ms	(*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2)))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite109.0ms (1.2%)

Algorithm

6×	egg-rewrite
1×	batch-egg-rewrite

Rules

151×	`add-sqr-sqrt_binary64`
141×	`log1p-expm1-u_binary64`
141×	`expm1-log1p-u_binary64`
140×	`add-cbrt-cube_binary64`
140×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	30
1	295	30
2	4411	30
0	6	6
1	130	6
2	2131	6
0	6	6
0	11	14
1	236	14
2	3608	14
0	11	14
0	14	18
1	295	18
2	4408	18
0	14	18

Stop Event

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

Counts

3 → 29

Calls

3 calls:

108.0ms	(fma.f64 J (*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2))) U)
108.0ms	(*.f64 (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))) (cos.f64 (/.f64 K 2)))
108.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

585×	`associate-l_binary64`
443×	`associate-r_binary64`
378×	`cancel-sign-sub-inv_binary64`
357×	`associate--l+_binary64`
302×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	2305
1	537	1898
2	1648	1845

Stop Event

1×	node limit

Counts

109 → 81

prune85.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	5	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Alt Table

Status	Error	Program
	10.6b	(fma.f64 J (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))) U)
	0.5b	(fma.f64 J (.f64 (.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)
▶	0.0b	(fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
	33.7b	(cbrt.f64 (.f64 (.f64 (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (.f64 K 1/2))) U) (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (.f64 K 1/2))) U)) (fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (*.f64 K 1/2))) U)))
	0.1b	(+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (.f64 (cos.f64 (.f64 1/2 K)) J))) (+.f64 (.f64 2 (.f64 l (.f64 (cos.f64 (.f64 1/2 K)) J))) U))

Compiler

Compiled 2206 to 1331 computations (39.7% 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 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
✓	0.1b	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))

series96.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

62.0ms	(fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
27.0ms	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))
7.0ms	(sinh.f64 l)

rewrite50.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

608×	`log-prod_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
207×	`prod-diff_binary64`
202×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	35
1	250	35
2	3045	35

Stop Event

1×	node limit

Counts

3 → 74

Calls

3 calls:

49.0ms	(sinh.f64 l)
49.0ms	(fma.f64 J (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) U)
49.0ms	(.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))

simplify43.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-def_binary64`
408×	`associate-l_binary64`
369×	`associate--l+_binary64`
333×	`associate-r_binary64`
329×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	2263
1	497	2216
2	1504	1883

Stop Event

1×	node limit

Counts

158 → 127

prune127.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	123	4	127
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Status	Error	Program
	10.6b	(fma.f64 J (cbrt.f64 (.f64 (.f64 (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2)))) (.f64 (.f64 2 (sinh.f64 l)) (cos.f64 (/.f64 K 2))))) U)
▶	0.1b	(fma.f64 J (.f64 (.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
	33.7b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J 2) (.f64 (sinh.f64 l) (cos.f64 (*.f64 K 1/2))) U) 3))
	0.4b	(fma.f64 J (pow.f64 (cbrt.f64 (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (*.f64 K 1/2))))) 3) U)
	0.1b	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)

Compiler

Compiled 2921 to 1842 computations (36.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(sinh.f64 l)
✓	0.0b	(fma.f64 J (.f64 (.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
✓	0.1b	(.f64 (.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)))
✓	0.2b	(/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))

series130.0ms (1.5%)

Counts

3 → 84

Calls

3 calls:

69.0ms

(fma.f64 J (*.f64 (*.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)

33.0ms

(/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))

27.0ms

(*.f64 (*.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)))

rewrite53.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

260×	`log1p-udef_binary64`
225×	`prod-diff_binary64`
164×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	339	35
2	4170	35

Stop Event

1×	node limit

Counts

3 → 72

Calls

3 calls:

52.0ms

(fma.f64 J (*.f64 (*.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)

52.0ms

(*.f64 (*.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2)))

52.0ms

(/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-def_binary64`
405×	`associate-l_binary64`
369×	`associate--l+_binary64`
331×	`associate-r_binary64`
329×	`associate--r+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	163	2263
1	497	2216
2	1503	1883

Stop Event

1×	node limit

Counts

156 → 125

prune160.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	160	1	161
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	161	5	166

Error

Counts

166 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 J (.f64 (.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
	33.7b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J 2) (.f64 (sinh.f64 l) (cos.f64 (*.f64 K 1/2))) U) 3))
	0.4b	(fma.f64 J (pow.f64 (cbrt.f64 (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (*.f64 K 1/2))))) 3) U)
▶	0.1b	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
	0.1b	(fma.f64 J (/.f64 (.f64 2 (cos.f64 (.f64 K 1/2))) (/.f64 1 (sinh.f64 l))) U)

Compiler

Compiled 3603 to 2344 computations (34.9% saved)

localize11.0ms (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))
✓	0.1b	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) J)

series59.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

44.0ms	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
11.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)
3.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l))

rewrite48.0ms (0.5%)

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

Calls

3 calls:

47.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l))
47.0ms	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
47.0ms	(.f64 (cos.f64 (.f64 1/2 K)) J)

simplify34.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	98	1807
1	291	1472
2	1025	1373

Stop Event

1×	node limit

Counts

133 → 95

prune99.0ms (1.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	95	5	100

Error

Counts

100 → 5

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 J (.f64 (.f64 2 (/.f64 1 (/.f64 2 (*.f64 2 (sinh.f64 l))))) (cos.f64 (/.f64 K 2))) U)
	33.7b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J 2) (.f64 (sinh.f64 l) (cos.f64 (*.f64 K 1/2))) U) 3))
	0.4b	(fma.f64 J (pow.f64 (cbrt.f64 (.f64 2 (.f64 (sinh.f64 l) (cos.f64 (*.f64 K 1/2))))) 3) U)
✓	0.1b	(fma.f64 (.f64 (cos.f64 (.f64 1/2 K)) J) (fma.f64 1/3 (pow.f64 l 3) (*.f64 2 l)) U)
	0.1b	(fma.f64 J (/.f64 (.f64 2 (cos.f64 (.f64 K 1/2))) (/.f64 1 (sinh.f64 l))) U)

Compiler

Compiled 2284 to 1637 computations (28.3% saved)

regimes942.0ms (10.7%)

Accuracy

Total 0.0b remaining (66.2%)

Threshold costs 0.0b (66.2%)

Counts

92 → 1

Compiler

Compiled 19724 to 14960 computations (24.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	20	18

Stop Event

1×

saturated

end98.0ms (1.1%)

Compiler: Compiled 130 to 101 computations (22.3% saved)

Details

analyze1.4s (15.7%)

sample5.1s (57.6%)

simplify25.0ms (0.3%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series59.0ms (0.7%)

rewrite109.0ms (1.2%)

simplify49.0ms (0.6%)

prune85.0ms (1%)

localize9.0ms (0.1%)

series96.0ms (1.1%)

rewrite50.0ms (0.6%)

simplify43.0ms (0.5%)

prune127.0ms (1.4%)

localize12.0ms (0.1%)

series130.0ms (1.5%)

rewrite53.0ms (0.6%)

simplify47.0ms (0.5%)

prune160.0ms (1.8%)

localize11.0ms (0.1%)

series59.0ms (0.7%)

rewrite48.0ms (0.5%)

simplify34.0ms (0.4%)

prune99.0ms (1.1%)

regimes942.0ms (10.7%)

simplify2.0ms (0%)

end98.0ms (1.1%)

Profiling