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

sample88.0ms

Algorithm

intervals

Results

18.0ms	185×	body	80	valid
15.0ms	32×	body	640	valid
9.0ms	13×	body	1280	valid
7.0ms	16×	body	640	invalid
5.0ms	16×	body	320	valid
5.0ms	56×	body	80	invalid
5.0ms	7×	body	1280	invalid
2.0ms	10×	body	160	valid
2.0ms	6×	body	320	invalid
1.0ms	4×	body	160	invalid

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	5091	32

prune10.0ms

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: 37.6b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
34.8b	(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))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

130×	`associate-*l/_binary64`
97×	`flip3--_binary64` `flip--_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64` `frac-times_binary64`
32×	`associate-*r/_binary64`
12×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64` `sqrt-prod_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

7.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)))
6.0ms	(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))))

series224.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(*.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))
188.0ms	(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))))

simplify45.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	5062	6382

prune151.0ms

Filtered

76 candidates to 127 candidates (-67.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	121	6	127
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	6	128

Merged error: 23.4b

Counts

128 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
34.8b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/_binary64`
96×	`flip3--_binary64` `flip--_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64` `frac-times_binary64`
32×	`associate-*r/_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
22.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series211.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
183.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify45.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5110	5951

prune136.0ms

Filtered

70 candidates to 128 candidates (-82.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	128	6	134

Merged error: 23.4b

Counts

134 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
34.8b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

128×	`associate-*l/_binary64`
96×	`flip3--_binary64` `flip--_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64` `frac-times_binary64`
32×	`associate-*r/_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `sqrt-prod_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 116

Calls

4 calls:

3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
25.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
180.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3))) (.f64 (-.f64 lambda1 lambda2) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0)) 3)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify46.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5239	5951

prune137.0ms

Filtered

70 candidates to 128 candidates (-82.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	128	6	134

Merged error: 23.4b

Counts

134 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
35.8b	(cbrt.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))))
35.8b	(cbrt.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))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

256×	`associate-*l/_binary64`
192×	`flip3--_binary64` `flip--_binary64`
132×	`cbrt-div_binary64`
128×	`frac-add_binary64` `frac-times_binary64`
64×	`associate-*r/_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`

Counts

4 → 168

Calls

4 calls:

5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
21.0ms	(cbrt.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))))
23.0ms	(cbrt.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))))

series510.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2.0))
248.0ms	(cbrt.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))))
251.0ms	(cbrt.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))))

simplify93.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4980	12142
1	4980	12142

prune265.0ms

Filtered

100 candidates to 180 candidates (-80.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	180	6	186

Merged error: 23.4b

Counts

186 → 6

regimes676.0ms

Accuracy

70.6% (4.1b remaining)

Error of 29.7b against oracle of 25.6b and baseline of 39.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	72
1	62	72

end0.0ms

sample3.0s

Algorithm

intervals

Results

826.0ms	5891×	body	80	valid
420.0ms	898×	body	640	valid
345.0ms	503×	body	1280	valid
215.0ms	2277×	body	80	invalid
204.0ms	445×	body	640	invalid
201.0ms	303×	body	1280	invalid
151.0ms	436×	body	320	valid
68.0ms	215×	body	320	invalid
67.0ms	272×	body	160	valid
25.0ms	116×	body	160	invalid

Details

analyze2.1s

sample88.0ms

simplify127.0ms

prune10.0ms

localize16.0ms

rewrite50.0ms

series224.0ms

simplify45.0ms

prune151.0ms

localize23.0ms

rewrite47.0ms

series211.0ms

simplify45.0ms

prune136.0ms

localize20.0ms

rewrite52.0ms

series207.0ms

simplify46.0ms

prune137.0ms

localize21.0ms

rewrite76.0ms

series510.0ms

simplify93.0ms

prune265.0ms

regimes676.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling