Details

analyze2.1s (10.8%)

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
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

sample96.0ms (0.5%)

Algorithm

1×

intervals

Results

16.0ms	171×	body	80	valid
15.0ms	34×	body	640	valid
11.0ms	20×	body	320	valid
10.0ms	15×	body	1280	valid
7.0ms	73×	body	80	invalid
5.0ms	8×	body	1280	invalid
5.0ms	11×	body	640	invalid
4.0ms	16×	body	160	valid
2.0ms	6×	body	320	invalid
0.0ms	1×	body	160	invalid

simplify125.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	5091	32

prune8.0ms (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

Merged error: 43.4b

Counts

2 → 1

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite59.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64`
102×	`flip3--_binary64` `flip--_binary64`
68×	`frac-times_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64`
44×	`pow1_binary64`
34×	`associate-*r/_binary64`
17×	`pow-prod-down_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-plus_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

21.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))

series246.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
42.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5172	6821

prune289.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 30.8b

Counts

148 → 8

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite68.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip3--_binary64` `flip--_binary64`
196×	`frac-times_binary64`
138×	`sqrt-div_binary64`
136×	`frac-add_binary64`
130×	`associate-*l/_binary64`
74×	`associate-*r/_binary64`
73×	`cos-mult_binary64`
12×	`pow1_binary64` `add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-prod_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `sqr-cos-a_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 192

Calls

4 calls:

30.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))

series216.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
12.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))

simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4962	11780
1	4962	11780

prune400.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	199	5	204
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Merged error: 29.5b

Counts

212 → 8

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
0.5b	(+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))
3.5b	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite164.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

656×	`frac-times_binary64`
600×	`flip3--_binary64` `flip--_binary64`
442×	`associate-*r/_binary64`
420×	`sqrt-div_binary64`
416×	`frac-add_binary64`
328×	`associate-*l/_binary64`
147×	`flip3-+_binary64` `flip-+_binary64`
13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-rgt-out_binary64` `distribute-rgt1-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 475

Calls

4 calls:

51.0ms	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
31.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
4.0ms	(+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))
3.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))

series1.4s (7.2%)

Counts

4 → 12

Calls

4 calls:

771.0ms	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
621.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
9.0ms	(+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))
6.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))

simplify234.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

487 → 487

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5065	41906

prune3.7s (18.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	477	10	487
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	480	15	495

Merged error: 29.1b

Counts

495 → 15

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.5b	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
3.5b	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 1/2 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite146.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

656×	`frac-times_binary64`
600×	`flip3--_binary64` `flip--_binary64`
420×	`sqrt-div_binary64`
416×	`frac-add_binary64`
328×	`associate-*l/_binary64`
232×	`associate-*r/_binary64`
146×	`flip3-+_binary64` `flip-+_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 460

Calls

4 calls:

34.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 1/2 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
31.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
3.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
3.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))

series1.5s (7.4%)

Counts

4 → 12

Calls

4 calls:

827.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
614.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 1/2 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
6.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))

simplify238.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

472 → 472

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5158	48456

prune4.6s (23.5%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	472	0	472
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	472	15	487

Merged error: 29.1b

Counts

487 → 15

regimes1.0s (5.1%)

Accuracy

Total 9.7b remaining (28.2%)

Threshold costs 0b (0%)

bsearch68.0ms (0.3%)

Steps

Iters	Range		Point
8	1.3494950881789206e+33	8.829228194545741e+36	8.698164444328864e+36

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	72
1	64	72

end0.0ms (0%)

sample2.7s (13.9%)

Algorithm

1×

intervals

Results

578.0ms	5873×	body	80	valid
399.0ms	868×	body	640	valid
337.0ms	483×	body	1280	valid
216.0ms	2293×	body	80	invalid
205.0ms	300×	body	1280	invalid
200.0ms	438×	body	640	invalid
173.0ms	524×	body	320	valid
80.0ms	248×	body	320	invalid
58.0ms	252×	body	160	valid
23.0ms	106×	body	160	invalid

Details

analyze2.1s (10.8%)

sample96.0ms (0.5%)

simplify125.0ms (0.6%)

prune8.0ms (0%)

localize20.0ms (0.1%)

rewrite59.0ms (0.3%)

series246.0ms (1.3%)

simplify50.0ms (0.3%)

prune289.0ms (1.5%)

localize18.0ms (0.1%)

rewrite68.0ms (0.3%)

series216.0ms (1.1%)

simplify118.0ms (0.6%)

prune400.0ms (2%)

localize19.0ms (0.1%)

rewrite164.0ms (0.8%)

series1.4s (7.2%)

simplify234.0ms (1.2%)

prune3.7s (18.8%)

localize30.0ms (0.2%)

rewrite146.0ms (0.7%)

series1.5s (7.4%)

simplify238.0ms (1.2%)

prune4.6s (23.5%)

regimes1.0s (5.1%)

bsearch68.0ms (0.3%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (13.9%)

Profiling