Details

analyze1.5s (13.8%)

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)

sample5.8s (54.3%)

Results

1.4s	2038×	body	1024	invalid
1.3s	1650×	body	1024	valid
909.0ms	4618×	body	128	valid
609.0ms	1243×	body	512	valid
520.0ms	2728×	body	128	invalid
518.0ms	1051×	body	512	invalid
219.0ms	696×	body	256	valid
158.0ms	505×	body	256	invalid
54.0ms	49×	body	2048	valid

Compiler

Compiled 59 to 44 computations (25.4% saved)

simplify76.0ms (0.7%)

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

prune5.0ms (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

14.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	14.4b	(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)

localize14.0ms (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)
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	7.3b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series51.0ms (0.5%)

Counts

3 → 80

Calls

3 calls:

38.0ms	(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))))
3.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite23.0ms (0.2%)

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:

10.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
5.0ms	(-.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)

simplify210.0ms (2%)

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

prune182.0ms (1.7%)

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

0.0b

Counts

170 → 3

Alt Table

Status	Error	Program
	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	14.4b	(fma.f64 (*.f64 J (/.f64 (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2)) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))) (cos.f64 (/.f64 K 2)) U)
▶	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4559 to 1711 computations (62.5% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
✓	0.0b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
✓	0.1b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

series189.0ms (1.8%)

Counts

4 → 84

Calls

4 calls:

136.0ms	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)
41.0ms	(.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
6.0ms	(*.f64 1/60 (pow.f64 l 5))
5.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64`
10×	`associate-r_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 69

Calls

4 calls:

5.0ms	(.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))
4.0ms	(*.f64 1/60 (pow.f64 l 5))
1.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
0.0ms	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)

simplify145.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-neg_binary64`
406×	`associate--l+_binary64`
395×	`distribute-rgt-in_binary64`
394×	`distribute-lft-in_binary64`
360×	`cancel-sign-sub-inv_binary64`

Counts

153 → 140

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	4446
1	518	3894
2	1839	3475
3	4786	3475
4	5452	3475

prune202.0ms (1.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	4	140
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Error

0.0b

Counts

143 → 7

Alt Table

Status	Error	Program
▶	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	14.4b	(fma.f64 (*.f64 J (/.f64 (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2)) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	28.6b	(fma.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
	0.6b	(fma.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
	34.7b	(.f64 (sqrt.f64 (fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)) (sqrt.f64 (fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)))
	39.7b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4617 to 3358 computations (27.3% 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)))

series63.0ms (0.6%)

Counts

3 → 76

Calls

3 calls:

27.0ms	(.f64 l (.f64 J (cos.f64 (*.f64 1/2 K))))
26.0ms	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
10.0ms	(.f64 J (cos.f64 (.f64 1/2 K)))

rewrite10.0ms (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:

5.0ms	(.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)

simplify106.0ms (1%)

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

prune149.0ms (1.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	109	7	116

Error

0.0b

Counts

116 → 7

Alt Table

Status	Error	Program
	9.9b	(fma.f64 2 (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) l) 3)) U)
✓	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	17.6b	(fma.f64 2 (.f64 l (cbrt.f64 (.f64 (.f64 (.f64 J J) J) (.f64 (.f64 (cos.f64 (.f64 1/2 K)) (cos.f64 (.f64 1/2 K))) (cos.f64 (*.f64 1/2 K)))))) U)
	14.4b	(fma.f64 (*.f64 J (/.f64 (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2)) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))) (cos.f64 (/.f64 K 2)) U)
▶	0.8b	(fma.f64 2 (.f64 l (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (*.f64 1/2 K))))) U)
	28.6b	(fma.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
✓	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 2131 to 1396 computations (34.5% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K))))
✓	0.5b	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
✓	0.6b	(cbrt.f64 J)

series289.0ms (2.7%)

Counts

4 → 72

Calls

4 calls:

181.0ms	(.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))
47.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
39.0ms	(cbrt.f64 J)
22.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K))))

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

12.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K))))
7.0ms	(.f64 (cbrt.f64 J) (cos.f64 (.f64 1/2 K)))
6.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
1.0ms	(cbrt.f64 J)

simplify161.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
457×	`*-commutative_binary64`
421×	`cancel-sign-sub-inv_binary64`
385×	`unswap-sqr_binary64`
323×	`sub-neg_binary64`

Counts

175 → 151

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	141	1945
1	299	1727
2	1130	1668
3	2242	1652
4	4280	1554
5	4570	1554
6	4885	1554
7	4873	1554

prune249.0ms (2.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	188	6	194

Error

0.0b

Counts

194 → 6

Alt Table

Status	Error	Program
	9.9b	(fma.f64 2 (cbrt.f64 (pow.f64 (.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) l) 3)) U)
✓	0.5b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	14.4b	(fma.f64 (*.f64 J (/.f64 (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2)) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))) (cos.f64 (/.f64 K 2)) U)
	28.6b	(fma.f64 (.f64 (sqrt.f64 J) (.f64 (sqrt.f64 J) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
	0.8b	(fma.f64 2 (.f64 l (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (cbrt.f64 J)))) (.f64 (cbrt.f64 J) (cos.f64 (*.f64 1/2 K))))) U)
✓	0.3b	(fma.f64 (.f64 J (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4379 to 2233 computations (49% saved)

regimes1.0s (9.6%)

Accuracy

Total 0.1b remaining (61.1%)

Threshold costs 0.1b (61.1%)

Counts

90 → 1

Compiler

Compiled 21349 to 15029 computations (29.6% 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

end140.0ms (1.3%)

Compiler: Compiled 176 to 125 computations (29% saved)

Details

analyze1.5s (13.8%)

sample5.8s (54.3%)

simplify76.0ms (0.7%)

prune5.0ms (0%)

localize14.0ms (0.1%)

series51.0ms (0.5%)

rewrite23.0ms (0.2%)

simplify210.0ms (2%)

prune182.0ms (1.7%)

localize17.0ms (0.2%)

series189.0ms (1.8%)

rewrite17.0ms (0.2%)

simplify145.0ms (1.4%)

prune202.0ms (1.9%)

localize8.0ms (0.1%)

series63.0ms (0.6%)

rewrite10.0ms (0.1%)

simplify106.0ms (1%)

prune149.0ms (1.4%)

localize22.0ms (0.2%)

series289.0ms (2.7%)

rewrite34.0ms (0.3%)

simplify161.0ms (1.5%)

prune249.0ms (2.3%)

regimes1.0s (9.6%)

simplify2.0ms (0%)

end140.0ms (1.3%)

Profiling