Details

analyze2.0s

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample250.0ms

Algorithm

intervals

Results

156.0ms	112×	body	1280	valid
58.0ms	80×	body	640	valid
14.0ms	27×	body	320	valid
4.0ms	28×	body	80	valid
3.0ms	9×	body	160	valid

simplify33.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	272	32
1	272	32

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: 0.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
2.8b	(sin.f64 (-.f64 lambda1 lambda2))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `associate-+r+_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 38

Calls

4 calls:

0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
108.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
17.0ms	(sin.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify122.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (106.0ms)

Iter	Nodes	Cost
0	4895	950
1	4895	950

prune82.0ms

Filtered

42 candidates to 50 candidates (-19.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	37	13	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	13	51

Merged error: 0.7b

Counts

51 → 13

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`sub-neg_binary64` `associate-r_binary64` `associate-l_binary64` `cos-diff_binary64`
2×	`associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 51

Calls

4 calls:

8.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series320.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
52.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
110.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify120.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5001	1613

prune280.0ms

Filtered

48 candidates to 63 candidates (-31.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	64	12	76

Merged error: 0.0b

Counts

76 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.6b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 61

Calls

4 calls:

8.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
64.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
41.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
229.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5086	2051

prune86.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	73	12	85

Merged error: 0.0b

Counts

85 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))
0.5b	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
2.8b	(sin.f64 (-.f64 lambda1 lambda2))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
2×	`sub-neg_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `sin-diff_binary64` `pow-pow_binary64` `sin-sum_binary64` `sqr-pow_binary64` `cos-diff_binary64` `rem-cube-cbrt_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 52

Calls

4 calls:

4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))
3.0ms	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series194.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))))
55.0ms	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
17.0ms	(sin.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify85.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4913	854
1	4913	854

prune50.0ms

Filtered

41 candidates to 64 candidates (-56.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	65	11	76

Merged error: 0.0b

Counts

76 → 11

regimes172.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.4s	3474×	body	1280	valid
1.4s	2418×	body	640	valid
412.0ms	1022×	body	320	valid
93.0ms	382×	body	160	valid
82.0ms	704×	body	80	valid

Details

analyze2.0s

sample250.0ms

simplify33.0ms

prune2.0ms

localize24.0ms

rewrite14.0ms

series187.0ms

simplify122.0ms

prune82.0ms

localize29.0ms

rewrite19.0ms

series320.0ms

simplify120.0ms

prune280.0ms

localize31.0ms

rewrite20.0ms

series473.0ms

simplify87.0ms

prune86.0ms

localize24.0ms

rewrite17.0ms

series194.0ms

simplify85.0ms

prune50.0ms

regimes172.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample5.7s

Profiling