Details

analyze1.9s

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

sample162.0ms

Algorithm

intervals

Results

108.0ms	140×	body	1024	valid
27.0ms	65×	body	512	valid
6.0ms	3×	body	2048	valid
5.0ms	20×	body	256	valid
4.0ms	28×	body	128	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	271	32
1	271	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: 0.5b

Counts

2 → 1

localize25.0ms

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))))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))
2.4b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite17.0ms

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

series342.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
209.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))
34.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify63.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4909	950
1	4909	950

prune84.0ms

Filtered

42 candidates to 50 candidates (-19.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	39	11	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	11	51

Merged error: 0.3b

Counts

51 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
2.4b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms

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×	`add-log-exp_binary64` `associate-r_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `sub-neg_binary64` `sin-sum_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`

Counts

4 → 58

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series459.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
71.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
225.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))
36.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify65.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4978	1025
1	4978	1025

prune79.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	71	10	81

Merged error: 0.1b

Counts

81 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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×	`add-log-exp_binary64` `associate-r_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
2×	`sin-mult_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
7.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
138.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
74.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
243.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (cos.f64 phi2)))

simplify69.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5091	1501

prune81.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	68	10	78

Merged error: 0.1b

Counts

78 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
0.6b	(pow.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3)
2.2b	(cos.f64 (-.f64 lambda1 lambda2))
2.4b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite26.0ms

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×	`flip3-+_binary64` `sub-neg_binary64` `cube-div_binary64` `flip-+_binary64`
1×	`pow-to-exp_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` `pow-exp_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 54

Calls

4 calls:

4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
5.0ms	(pow.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3)
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series789.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
520.0ms	(pow.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))) 3)
24.0ms	(cos.f64 (-.f64 lambda1 lambda2))
33.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4949	1262
1	4949	1262

prune60.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	66	10	76

Merged error: 0.0b

Counts

76 → 10

regimes173.0ms

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	59	61
1	59	61

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.5s	4376×	body	1024	valid
779.0ms	1810×	body	512	valid
215.0ms	119×	body	2048	valid
200.0ms	740×	body	256	valid
118.0ms	955×	body	128	valid

Details

analyze1.9s

sample162.0ms

simplify26.0ms

prune2.0ms

localize25.0ms

rewrite17.0ms

series342.0ms

simplify63.0ms

prune84.0ms

localize30.0ms

rewrite30.0ms

series459.0ms

simplify65.0ms

prune79.0ms

localize30.0ms

rewrite24.0ms

series572.0ms

simplify69.0ms

prune81.0ms

localize24.0ms

rewrite26.0ms

series789.0ms

simplify44.0ms

prune60.0ms

regimes173.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.1s

Profiling