Details

analyze2.6s

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample313.0ms

Algorithm

intervals

Results

224.0ms	151×	body	1280	valid
57.0ms	69×	body	640	valid
6.0ms	11×	body	320	valid
3.0ms	19×	body	80	valid
2.0ms	6×	body	160	valid

simplify156.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune22.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.8b

Counts

2 → 1

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.6b	(sin.f64 (-.f64 lambda1 lambda2))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1_binary64_3088` `add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106`
9×	`add-sqr-sqrt_binary64_3127`
7×	`*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113`
6×	`associate-r_binary64_3201`
4×	`associate-l_binary64_3202` `cbrt-unprod_binary64_3111` `pow-prod-down_binary64_3069` `add-log-exp_binary64_3107` `prod-exp_binary64_3093`
3×	`cos-diff_binary64_2995`
2×	`*-commutative_binary64_3210` `sub-neg_binary64_3146`
1×	`sin-sum_binary64_2991` `unswap-sqr_binary64_3170` `associate-*l/_binary64_3204` `sin-cos-mult_binary64_3014` `cos-sum_binary64_2992` `distribute-rgt-in_binary64_3185` `distribute-lft-in_binary64_3184` `sin-diff_binary64_2994`

Counts

4 → 57

Calls

4 calls:

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

series191.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
112.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify70.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5220	929

prune391.0ms

Filtered

51 candidates to 69 candidates (-35.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 7.7b

Counts

70 → 12

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1_binary64_3088` `add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106` `add-sqr-sqrt_binary64_3127`
9×	`associate-r_binary64_3201` `*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113`
7×	`associate-l_binary64_3202`
5×	`cbrt-unprod_binary64_3111` `pow-prod-down_binary64_3069` `prod-exp_binary64_3093`
4×	`add-log-exp_binary64_3107`
3×	`associate-l/_binary64_3204` `-commutative_binary64_3210` `cos-diff_binary64_2995`
2×	`unswap-sqr_binary64_3170`
1×	`sin-cos-mult_binary64_3014` `cos-sum_binary64_2992` `distribute-rgt-in_binary64_3185` `sub-neg_binary64_3146` `distribute-lft-in_binary64_3184` `flip--_binary64_3168` `flip3--_binary64_3141`

Counts

4 → 68

Calls

4 calls:

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

series295.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
41.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
107.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4989	1404
1	4989	1404

prune445.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 0.1b

Counts

92 → 12

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_3127`
15×	`pow1_binary64_3088` `add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106`
12×	`associate-r_binary64_3201`
11×	`*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113`
10×	`associate-l_binary64_3202`
6×	`cbrt-unprod_binary64_3111` `pow-prod-down_binary64_3069` `prod-exp_binary64_3093`
4×	`sin-cos-mult_binary64_3014` `*-commutative_binary64_3210` `add-log-exp_binary64_3107`
3×	`frac-times_binary64_3134` `unswap-sqr_binary64_3170` `associate-l/_binary64_3204` `associate-r/_binary64_3203` `sin-mult_binary64_3013`
2×	`frac-add_binary64_3132` `flip-+_binary64_3167` `flip3-+_binary64_3140` `cos-mult_binary64_3012`
1×	`distribute-rgt-in_binary64_3185` `distribute-lft-in_binary64_3184` `flip--_binary64_3168` `flip3--_binary64_3141`

Counts

4 → 84

Calls

4 calls:

8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series648.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
39.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
41.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
431.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify81.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4984	2099
1	4984	2099

prune529.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 0.0b

Counts

108 → 14

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.3b	(/.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.4b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

87×	`pow1_binary64_3088`
78×	`sin-mult_binary64_3013` `cos-mult_binary64_3012`
74×	`associate-*r/_binary64_3203`
66×	`frac-times_binary64_3134`
44×	`associate-*l/_binary64_3204`
42×	`add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106`
37×	`pow-prod-down_binary64_3069` `frac-sub_binary64_3133`
34×	`sin-cos-mult_binary64_3014`
33×	`associate-/l/_binary64_3208`
22×	`cbrt-unprod_binary64_3111` `prod-exp_binary64_3093`
21×	`sub-div_binary64_3131`
8×	`pow-prod-up_binary64_3068` `pow-sqr_binary64_3175`
7×	`*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113` `add-sqr-sqrt_binary64_3127`
6×	`associate-r_binary64_3201`
5×	`flip--_binary64_3168` `flip3--_binary64_3141`
4×	`associate-/r/_binary64_3207` `add-log-exp_binary64_3107` `pow-plus_binary64_3083`
3×	`associate-l_binary64_3202` `cbrt-undiv_binary64_3112` `associate-/r_binary64_3205` `div-exp_binary64_3095` `-commutative_binary64_3210` `times-frac_binary64_3137`
2×	`pow2_binary64_3079` `sub-neg_binary64_3146` `swap-sqr_binary64_3169`
1×	`associate-/l*_binary64_3206` `clear-num_binary64_3145` `difference-of-squares_binary64_3171` `frac-2neg_binary64_3135` `distribute-rgt-in_binary64_3185` `distribute-lft-in_binary64_3184` `div-inv_binary64_3143`

Counts

4 → 188

Calls

4 calls:

29.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
28.0ms	(/.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

367.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
840.0ms	(/.f64 (.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (-.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) (-.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
66.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
63.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))

simplify110.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5158	6797

prune759.0ms

Filtered

118 candidates to 200 candidates (-69.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	201	13	214

Merged error: 0.0b

Counts

214 → 13

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify17.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	474	103
1	474	103

end0.0ms

sample9.3s

Algorithm

intervals

Results

6.9s	4723×	body	1280	valid
1.6s	1885×	body	640	valid
313.0ms	540×	body	320	valid
105.0ms	658×	body	80	valid
66.0ms	194×	body	160	valid

Details

analyze2.6s

sample313.0ms

simplify156.0ms

prune22.0ms

localize36.0ms

rewrite22.0ms

series191.0ms

simplify70.0ms

prune391.0ms

localize58.0ms

rewrite24.0ms

series295.0ms

simplify56.0ms

prune445.0ms

localize51.0ms

rewrite36.0ms

series648.0ms

simplify81.0ms

prune529.0ms

localize70.0ms

rewrite88.0ms

series1.3s

simplify110.0ms

prune759.0ms

regimes1.0s

bsearch0.0ms

simplify17.0ms

end0.0ms

sample9.3s

Profiling