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
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

sample187.0ms

Algorithm

intervals

Results

112.0ms	110×	body	1280	valid
46.0ms	82×	body	640	valid
10.0ms	26×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	24×	body	80	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

prune3.0ms

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: 1.2b

Counts

2 → 1

localize20.0ms

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))))
3.3b	(sin.f64 (-.f64 lambda1 lambda2))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite15.0ms

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:

1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series50.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
29.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4947	591
1	4947	591

prune87.0ms

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: 0.9b

Counts

51 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.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))))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite16.0ms

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×	`associate-r_binary64` `associate-l_binary64` `cos-diff_binary64`
2×	`associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 47

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
1.0ms	(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)))))
5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series51.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
11.0ms	(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)))))
25.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify78.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5109	730

prune63.0ms

Filtered

45 candidates to 59 candidates (-31.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 0.0b

Counts

72 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (sin.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))))))
0.4b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite17.0ms

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` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(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 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
14.0ms	(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))))))
54.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4961	985
1	4961	985

prune58.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	69	11	80

Merged error: 0.0b

Counts

80 → 11

localize32.0ms

Local error

Found 4 expressions with local error:

3.3b	(sin.f64 (-.f64 lambda1 lambda2))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `sub-neg_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`cos-diff_binary64` `cos-sum_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64`

Counts

4 → 36

Calls

4 calls:

4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify134.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4733	320
1	4733	320

prune37.0ms

Filtered

40 candidates to 48 candidates (-20.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	48	0	48
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	48	11	59

Merged error: 0.0b

Counts

59 → 11

regimes403.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	34
1	56	34

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.6s	3611×	body	1280	valid
1.3s	2324×	body	640	valid
380.0ms	957×	body	320	valid
101.0ms	409×	body	160	valid
86.0ms	699×	body	80	valid

Details

analyze2.1s

sample187.0ms

simplify19.0ms

prune3.0ms

localize20.0ms

rewrite15.0ms

series50.0ms

simplify49.0ms

prune87.0ms

localize28.0ms

rewrite16.0ms

series51.0ms

simplify78.0ms

prune63.0ms

localize28.0ms

rewrite17.0ms

series86.0ms

simplify50.0ms

prune58.0ms

localize32.0ms

rewrite19.0ms

series17.0ms

simplify134.0ms

prune37.0ms

regimes403.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.8s

Profiling