Details

analyze2.6s

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample291.0ms

Algorithm

intervals

Results

206.0ms	148×	body	1280	valid
54.0ms	63×	body	640	valid
10.0ms	19×	body	320	valid
8.0ms	23×	body	80	valid
1.0ms	3×	body	160	valid

simplify44.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	368	39
1	368	39

prune218.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 10.2b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
3.7b	(sin.f64 (-.f64 lambda1 lambda2))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `insert-posit16`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 62

Calls

4 calls:

9.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series1.6s

Counts

4 → 12

Calls

4 calls:

402.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
485.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
346.0ms	(sin.f64 (-.f64 lambda1 lambda2))
324.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	717	111
1	717	111
0	717	111
1	717	111
0	5178	9
0	708	103
1	708	103
0	708	103
1	708	103
0	5038	12
0	837	325
1	837	325
0	837	325
1	837	325
0	4889	9
1	4889	9
0	1719	583
1	1719	583
0	1719	583
1	1719	583
0	1	3
1	1	3

simplify137.0ms

Counts

74 → 74

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	5095	965

prune101.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	63	11	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	11	75

Merged error: 4.0b

Counts

75 → 11

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`cos-diff_binary64` `associate-l/_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `flip--_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
9.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series1.2s

Counts

4 → 12

Calls

4 calls:

161.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
404.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
343.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
323.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	717	111
1	717	111
0	717	111
1	717	111
0	5178	9
0	2811	1013
1	2811	1013
0	2811	1013
1	2811	1013
0	20	9
1	20	9
0	1719	583
1	1719	583
0	1719	583
1	1719	583
0	1	3
1	1	3
0	357	325
1	357	325
0	357	325
1	357	325
0	20	9
1	20	9

simplify67.0ms

Counts

84 → 84

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4987	1349
1	4987	1349

prune118.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 0.1b

Counts

95 → 12

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-l_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `insert-posit16` `*-commutative_binary64`
3×	`associate-r/_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`flip3-+_binary64` `cos-mult_binary64` `frac-add_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`

Counts

4 → 88

Calls

4 calls:

6.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
14.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
9.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series1.1s

Counts

4 → 12

Calls

4 calls:

159.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
402.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
362.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
159.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	397	299
1	397	299
0	397	299
1	397	299
0	1	3
1	1	3
0	2811	1013
1	2811	1013
0	2811	1013
1	2811	1013
0	20	9
1	20	9
0	954	987
1	954	987
0	954	987
1	954	987
0	1	3
1	1	3
0	357	325
1	357	325
0	357	325
1	357	325
0	20	9
1	20	9

simplify109.0ms

Counts

100 → 100

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5113	2033

prune143.0ms

Filtered

78 candidates to 100 candidates (-28.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Merged error: 0.0b

Counts

112 → 12

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
0.5b	(pow.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1_binary64`
36×	`pow-prod-down_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`pow-prod-up_binary64` `pow-sqr_binary64`
6×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`cos-mult_binary64` `sin-mult_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `pow-plus_binary64` `rem-cube-cbrt_binary64` `insert-posit16` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-r/_binary64` `sqr-pow_binary64` `associate-l_binary64` `cube-div_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `frac-times_binary64` `pow2_binary64` `unpow3_binary64` `associate-l/_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 124

Calls

4 calls:

6.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
12.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
11.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
6.0ms	(pow.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3)

series1.1s

Counts

4 → 12

Calls

4 calls:

201.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
215.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
347.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
331.0ms	(pow.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3)

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	505	405
1	505	405
0	505	405
1	505	405
0	5178	9
0	538	399
1	538	399
0	538	399
1	538	399
0	5178	9
0	510	383
1	510	383
0	510	383
1	510	383
0	1	3
1	1	3
0	481	389
1	481	389
0	481	389
1	481	389
0	1	3
1	1	3

simplify87.0ms

Counts

136 → 136

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5213	1316

prune151.0ms

Filtered

68 candidates to 136 candidates (-100.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	136	12	148

Merged error: 0.0b

Counts

148 → 12

regimes227.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	178	129
1	178	129

end0.0ms

sample9.0s

Algorithm

intervals

Results

6.5s	4563×	body	1280	valid
1.6s	2030×	body	640	valid
311.0ms	554×	body	320	valid
119.0ms	658×	body	80	valid
67.0ms	195×	body	160	valid

Details

analyze2.6s

sample291.0ms

simplify44.0ms

prune218.0ms

localize26.0ms

rewrite29.0ms

series1.6s

simplify137.0ms

prune101.0ms

localize33.0ms

rewrite31.0ms

series1.2s

simplify67.0ms

prune118.0ms

localize37.0ms

rewrite38.0ms

series1.1s

simplify109.0ms

prune143.0ms

localize50.0ms

rewrite41.0ms

series1.1s

simplify87.0ms

prune151.0ms

regimes227.0ms

bsearch0.0ms

simplify9.0ms

end0.0ms

sample9.0s

Profiling