Details

analyze2.3s

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

sample90.0ms

Algorithm

intervals

Results

17.0ms	188×	body	80	valid
14.0ms	14×	body	1280	valid
11.0ms	26×	body	640	valid
7.0ms	15×	body	640	invalid
7.0ms	21×	body	320	valid
7.0ms	73×	body	80	invalid
5.0ms	8×	body	1280	invalid
2.0ms	7×	body	160	valid
1.0ms	3×	body	320	invalid
1.0ms	3×	body	160	invalid

simplify264.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (249.0ms)

Iter	Nodes	Cost
0	5060	49

prune2.0ms

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: 42.1b

Counts

2 → 1

localize17.0ms

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))))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.8b	(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))))

rewrite73.0ms

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` `insert-posit16`
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 → 139

Calls

4 calls:

17.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
28.0ms	(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))))

series1.5s

Counts

4 → 12

Calls

4 calls:

59.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
648.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
676.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
67.0ms	(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))))

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	183	9
1	183	9
0	183	9
1	183	9
0	1	3
1	1	3
0	25085	9
0	25085	9
0	1	3
1	1	3
0	25085	9
0	25085	9
0	1	3
1	1	3
0	131	9
1	131	9
0	131	9
1	131	9
0	1	3
1	1	3

simplify155.0ms

Counts

151 → 151

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	6325	10169

prune171.0ms

Filtered

75 candidates to 151 candidates (-101.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	144	7	151
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	7	152

Merged error: 40.8b

Counts

152 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.8b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--_binary64` `flip--_binary64`
196×	`frac-times_binary64`
138×	`sqrt-div_binary64`
136×	`frac-add_binary64`
98×	`associate-r/_binary64` `associate-l/_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` `insert-posit16`
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 → 196

Calls

4 calls:

6.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
31.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))

series2.1s

Counts

4 → 12

Calls

4 calls:

751.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
669.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
662.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
61.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.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))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	186	9
1	186	9
0	186	9
1	186	9
0	1	3
1	1	3
0	25085	9
0	25085	9
0	1	3
1	1	3
0	25085	9
0	25085	9
0	1	3
1	1	3
0	28229	9
0	28229	9
0	1	3
1	1	3

simplify247.0ms

Counts

208 → 208

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	5159	17492

prune293.0ms

Filtered

136 candidates to 208 candidates (-52.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	208	7	215

Merged error: 40.8b

Counts

215 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))
0.6b	(+.f64 1 (cos.f64 (+.f64 phi1 phi2)))
2.4b	(cos.f64 (+.f64 phi1 phi2))
38.8b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

200×	`flip3--_binary64` `flip--_binary64`
198×	`frac-times_binary64`
138×	`sqrt-div_binary64`
136×	`frac-add_binary64`
100×	`associate-*l/_binary64`
99×	`associate-*r/_binary64`
24×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
14×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`associate-l_binary64`
4×	`distribute-lft-out_binary64` `insert-posit16`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 217

Calls

4 calls:

15.0ms	(*.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))
7.0ms	(+.f64 1 (cos.f64 (+.f64 phi1 phi2)))
6.0ms	(cos.f64 (+.f64 phi1 phi2))
33.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series2.0s

Counts

4 → 12

Calls

4 calls:

59.0ms	(*.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))
901.0ms	(+.f64 1 (cos.f64 (+.f64 phi1 phi2)))
1.0s	(cos.f64 (+.f64 phi1 phi2))
64.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (cos.f64 (+.f64 phi1 phi2))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	170	9
1	170	9
0	170	9
1	170	9
0	1	3
1	1	3
0	41328	9
0	41328	9
0	1	3
1	1	3
0	41343	9
0	41343	9
0	1	3
1	1	3
0	115	9
1	115	9
0	115	9
1	115	9
0	1	3
1	1	3

simplify226.0ms

Counts

229 → 229

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4957	17953
1	4957	17953

prune273.0ms

Filtered

137 candidates to 229 candidates (-67.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	230	6	236

Merged error: 40.2b

Counts

236 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.5b	(+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))
38.8b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

200×	`flip3--_binary64` `flip--_binary64`
198×	`frac-times_binary64`
138×	`sqrt-div_binary64`
136×	`frac-add_binary64`
100×	`associate-*l/_binary64`
99×	`associate-*r/_binary64`
26×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
16×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
8×	`associate-l_binary64`
4×	`distribute-lft-out_binary64` `insert-posit16`
3×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `associate-+r-_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `sin-mult_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64`

Counts

4 → 230

Calls

4 calls:

18.0ms	(.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))
7.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
7.0ms	(+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))
34.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series234.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))
53.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
57.0ms	(+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))))
65.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (/.f64 (+.f64 1 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2)))) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	170	9
1	170	9
0	170	9
1	170	9
0	1	3
1	1	3
0	173	9
1	173	9
0	173	9
1	173	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3
0	108	9
1	108	9
0	108	9
1	108	9
0	1	3
1	1	3

simplify251.0ms

Counts

242 → 242

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4946	20685
1	4946	20685

prune296.0ms

Filtered

144 candidates to 242 candidates (-68.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	242	6	248

Merged error: 40.2b

Counts

248 → 6

regimes215.0ms

Accuracy

-3.4% (1.5b remaining)

Error of 39.5b against oracle of 38.0b and baseline of 39.5b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	90	106
1	90	106

end0.0ms

sample2.6s

Algorithm

intervals

Results

571.0ms	5922×	body	80	valid
370.0ms	835×	body	640	valid
333.0ms	504×	body	1280	valid
230.0ms	2385×	body	80	invalid
202.0ms	300×	body	1280	invalid
179.0ms	411×	body	640	invalid
157.0ms	504×	body	320	valid
71.0ms	234×	body	320	invalid
64.0ms	235×	body	160	valid
20.0ms	99×	body	160	invalid

Iter	Nodes	Cost
0	170	9
1	170	9
0	170	9
1	170	9
0	1	3
1	1	3
0	173	9
1	173	9
0	173	9
1	173	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3
0	108	9
1	108	9
0	108	9
1	108	9
0	1	3
1	1	3

Iter	Nodes	Cost
0	170	9
1	170	9
0	170	9
1	170	9
0	1	3
1	1	3
0	173	9
1	173	9
0	173	9
1	173	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3
0	108	9
1	108	9
0	108	9
1	108	9
0	1	3
1	1	3

Details

analyze2.3s

sample90.0ms

simplify264.0ms

prune2.0ms

localize17.0ms

rewrite73.0ms

series1.5s

simplify155.0ms

prune171.0ms

localize17.0ms

rewrite80.0ms

series2.1s

simplify247.0ms

prune293.0ms

localize18.0ms

rewrite89.0ms

series2.0s

simplify226.0ms

prune273.0ms

localize25.0ms

rewrite98.0ms

series234.0ms

simplify251.0ms

prune296.0ms

regimes215.0ms

bsearch2.0ms

simplify8.0ms

end0.0ms

sample2.6s

Profiling

Iter	Nodes	Cost
0	170	9
1	170	9
0	170	9
1	170	9
0	1	3
1	1	3
0	173	9
1	173	9
0	173	9
1	173	9
0	1	3
1	1	3
0	88	9
1	88	9
0	88	9
1	88	9
0	1	3
1	1	3
0	108	9
1	108	9
0	108	9
1	108	9
0	1	3
1	1	3