Details

analyze2.1s

Algorithm

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

sample100.0ms

Algorithm

intervals

Results

22.0ms	171×	body	80	valid
16.0ms	34×	body	640	valid
10.0ms	15×	body	1280	valid
7.0ms	73×	body	80	invalid
6.0ms	20×	body	320	valid
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

simplify129.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5091	32

prune4.0ms

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

localize21.0ms

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))))

rewrite56.0ms

Algorithm

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:

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))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
20.0ms	(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))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(.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))
8.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
194.0ms	(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))))

simplify50.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5172	6821

prune171.0ms

Filtered

76 candidates to 147 candidates (-93.4%)

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

localize17.0ms

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))))

rewrite66.0ms

Algorithm

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:

5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
29.0ms	(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))))

series219.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.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))
196.0ms	(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))))

simplify121.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4962	11780
1	4962	11780

prune215.0ms

Filtered

107 candidates to 204 candidates (-90.7%)

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

localize22.0ms

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

Algorithm

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:

50.0ms	(.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)))))
3.0ms	(+.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))
30.0ms	(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))))

series1.4s

Counts

4 → 12

Calls

4 calls:

794.0ms	(.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)))))
10.0ms	(+.f64 1/2 (.f64 (cos.f64 (.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2)) 1/2))
9.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
634.0ms	(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))))

simplify235.0ms

Algorithm

egg-herbie

Counts

487 → 487

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5065	41906

prune1.5s

Filtered

264 candidates to 487 candidates (-84.5%)

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

localize31.0ms

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))))

rewrite136.0ms

Algorithm

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:

3.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
3.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
30.0ms	(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))))
29.0ms	(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))))

series1.3s

Counts

4 → 12

Calls

4 calls:

6.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
6.0ms	(cos.f64 (*.f64 (/.f64 (+.f64 phi1 phi2) 2.0) 2))
635.0ms	(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))))
636.0ms	(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))))

simplify237.0ms

Algorithm

egg-herbie

Counts

472 → 472

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5158	48456

prune5.7s

Filtered

464 candidates to 472 candidates (-1.7%)

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

regimes992.0ms

Accuracy

34.9% (9.7b remaining)

Error of 34.2b against oracle of 24.6b and baseline of 39.4b

bsearch64.0ms

Steps

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	72
1	64	72

end0.0ms

sample2.7s

Algorithm

intervals

Results

572.0ms	5873×	body	80	valid
396.0ms	868×	body	640	valid
337.0ms	483×	body	1280	valid
226.0ms	2293×	body	80	invalid
217.0ms	300×	body	1280	invalid
191.0ms	438×	body	640	invalid
178.0ms	524×	body	320	valid
81.0ms	248×	body	320	invalid
58.0ms	252×	body	160	valid
22.0ms	106×	body	160	invalid

Details

analyze2.1s

sample100.0ms

simplify129.0ms

prune4.0ms

localize21.0ms

rewrite56.0ms

series250.0ms

simplify50.0ms

prune171.0ms

localize17.0ms

rewrite66.0ms

series219.0ms

simplify121.0ms

prune215.0ms

localize22.0ms

rewrite164.0ms

series1.4s

simplify235.0ms

prune1.5s

localize31.0ms

rewrite136.0ms

series1.3s

simplify237.0ms

prune5.7s

regimes992.0ms

bsearch64.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling