Details

analyze3.2s (12.6%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample118.0ms (0.5%)

Algorithm

1×

intervals

Results

28.0ms	192×	body	128	valid
18.0ms	24×	body	1024	valid
12.0ms	26×	body	512	valid
11.0ms	83×	body	128	invalid
11.0ms	18×	body	1024	invalid
4.0ms	13×	body	256	valid
4.0ms	8×	body	512	invalid
2.0ms	5×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify397.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (219.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

40.5b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.3b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite137.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_362`
102×	`flip3--_binary64_423` `flip--_binary64_394`
68×	`frac-times_binary64_429`
66×	`sqrt-div_binary64_436`
64×	`frac-add_binary64_427`
44×	`pow1_binary64_480`
34×	`associate-*r/_binary64_361`
17×	`pow-prod-down_binary64_490`
16×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
6×	`add-sqr-sqrt_binary64_441`
5×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
4×	`add-log-exp_binary64_458` `pow-sqr_binary64_392` `pow-prod-up_binary64_489`
3×	`sqrt-prod_binary64_435`
2×	`pow-plus_binary64_482`
1×	`flip3-+_binary64_422` `pow1/2_binary64_499` `associate-r_binary64_359` `-commutative_binary64_350` `swap-sqr_binary64_386` `associate-l*_binary64_360` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `pow2_binary64_500`

Counts

4 → 135

Calls

4 calls:

31.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
26.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.2s (4.6%)

Counts

4 → 12

Calls

4 calls:

925.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
194.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
18.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
17.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify123.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5228	10334

prune438.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Error

24.0b

Counts

148 → 8

Compiler

Compiled 8816 to 2945 computations (66.6% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.3b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite123.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip3--_binary64_423` `flip--_binary64_394`
196×	`frac-times_binary64_429`
138×	`sqrt-div_binary64_436`
136×	`frac-add_binary64_427`
130×	`associate-*l/_binary64_362`
74×	`associate-*r/_binary64_361`
73×	`cos-mult_binary64_573`
12×	`add-sqr-sqrt_binary64_441` `pow1_binary64_480`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
4×	`add-log-exp_binary64_458`
3×	`associate-r_binary64_359` `swap-sqr_binary64_386` `associate-l_binary64_360` `sqrt-prod_binary64_435`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `pow1/2_binary64_499` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-plus_binary64_482` `*-commutative_binary64_350` `flip-+_binary64_393` `sqrt-pow1_binary64_437` `sqr-cos-a_binary64_568` `pow-sqr_binary64_392` `rem-sqrt-square_binary64_432` `pow-prod-up_binary64_489` `pow2_binary64_500`

Counts

4 → 192

Calls

4 calls:

37.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series982.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

914.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
36.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
16.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
15.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify222.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5037	17590

prune587.0ms (2.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	204	8	212

Error

23.6b

Counts

212 → 8

Compiler

Compiled 13752 to 4220 computations (69.3% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.4b	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.4b	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite182.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

256×	`associate-*l/_binary64_362`
192×	`flip3--_binary64_423` `flip--_binary64_394`
132×	`cbrt-div_binary64_451`
128×	`frac-add_binary64_427` `frac-times_binary64_429`
64×	`associate-*r/_binary64_361`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `cbrt-prod_binary64_450` `add-sqr-sqrt_binary64_441`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
2×	`flip3-+_binary64_422` `pow1/3_binary64_501` `flip-+_binary64_393`

Counts

4 → 168

Calls

4 calls:

25.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
21.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
9.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series3.0s (12.1%)

Counts

4 → 12

Calls

4 calls:

1.5s	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
1.5s	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
25.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify257.0ms (1%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4997	18474
1	4997	18474

prune906.0ms (3.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	178	2	180
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	179	9	188

Error

23.6b

Counts

188 → 9

Compiler

Compiled 19555 to 6664 computations (65.9% saved)

localize34.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.5b	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
38.4b	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.4b	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite246.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

384×	`associate-*l/_binary64_362`
288×	`flip3--_binary64_423` `flip--_binary64_394`
198×	`cbrt-div_binary64_451`
192×	`frac-add_binary64_427` `frac-times_binary64_429`
96×	`associate-*r/_binary64_361`
66×	`exp-diff_binary64_467` `log-div_binary64_506`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `cbrt-prod_binary64_450` `add-sqr-sqrt_binary64_441`
6×	`log-prod_binary64_505` `exp-sum_binary64_465`
5×	`exp-prod_binary64_471` `pow1_binary64_480`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`flip3-+_binary64_422` `pow1/3_binary64_501` `flip-+_binary64_393`
2×	`log-pow_binary64_508`
1×	`rem-exp-log_binary64_459`

Counts

4 → 246

Calls

4 calls:

51.0ms	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
36.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
30.0ms	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series4.5s (17.8%)

Counts

4 → 12

Calls

4 calls:

1.8s	(exp.f64 (log.f64 (cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))))
1.3s	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
1.3s	(cbrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
19.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify279.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

258 → 258

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5211	27608

prune1.8s (7.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	257	1	258
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	258	9	267

Error

23.6b

Counts

267 → 9

Compiler

Compiled 28516 to 9739 computations (65.8% saved)

regimes1.7s (6.6%)

Accuracy

Total 4.2b remaining (14.8%)

Threshold costs 0b (0%)

Compiler

Compiled 13869 to 8470 computations (38.9% saved)

bsearch4.0ms (0%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	97
1	61	97

end0.0ms (0%)

sample4.8s (18.9%)

Algorithm

1×

intervals

Results

900.0ms	6144×	body	128	valid
493.0ms	759×	body	1024	valid
351.0ms	2464×	body	128	invalid
341.0ms	716×	body	512	valid
300.0ms	460×	body	1024	invalid
176.0ms	346×	body	512	invalid
120.0ms	375×	body	256	valid
57.0ms	197×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 1522 to 929 computations (39% saved)

Details

analyze3.2s (12.6%)

sample118.0ms (0.5%)

simplify397.0ms (1.6%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite137.0ms (0.5%)

series1.2s (4.6%)

simplify123.0ms (0.5%)

prune438.0ms (1.7%)

localize17.0ms (0.1%)

rewrite123.0ms (0.5%)

series982.0ms (3.9%)

simplify222.0ms (0.9%)

prune587.0ms (2.3%)

localize22.0ms (0.1%)

rewrite182.0ms (0.7%)

series3.0s (12.1%)

simplify257.0ms (1%)

prune906.0ms (3.6%)

localize34.0ms (0.1%)

rewrite246.0ms (1%)

series4.5s (17.8%)

simplify279.0ms (1.1%)

prune1.8s (7.3%)

regimes1.7s (6.6%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.8s (18.9%)

Profiling