Details

sample311.0ms

Algorithm

intervals

Results

230.0ms	163×	body	1280	valid
48.0ms	60×	body	640	valid
11.0ms	19×	body	320	valid
4.0ms	10×	body	160	valid
1.0ms	4×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	12

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.9b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.9b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.7b	(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

3×	`cos-diff` `*-commutative`
2×	`cos-sum` `associate-l`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult`

Counts

4 → 11

Calls

4 calls:

5.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0ms	(cos (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
46.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms	(cos (- lambda1 lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (17.0ms)

Iter	Nodes	Cost
0	128	172
1	281	171
2	632	169
3	1715	168
4	5001	168

prune72.0ms

Filtered

23 candidates to 12 candidates (52.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	19	4	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	4	24

Merged error: 3.0b

Counts

24 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-commutative`
6×	`cos-mult`
4×	`associate-r` `associate-l`
2×	`frac-times` `associate-r/` `associate-l/` `sin-mult`
1×	`acos-asin`

Counts

4 → 18

Calls

4 calls:

7.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
7.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
105.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	186	276
1	459	275
2	1020	274
3	2076	274
4	5002	274

prune145.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Merged error: 2.9b

Counts

34 → 3

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
3×	`sin-mult`
2×	`associate-r` `associate-l` `cos-mult`
1×	`acos-asin` `frac-times` `associate-r/` `associate-l/`

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (sin phi1) (sin phi2))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
7.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (sin phi2))
65.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
110.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify174.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	219
1	284	219
2	567	219
3	793	219
4	986	219
5	1110	219
6	1272	219
7	1503	219
8	2123	219
9	3220	219
10	3637	219
11	3900	219
12	4656	219
13	5001	219

prune102.0ms

Filtered

24 candidates to 14 candidates (58.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	24	3	27

Merged error: 2.9b

Counts

27 → 3

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
0.3b	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
1.0b	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-r`
5×	`*-commutative`
1×	`acos-asin` `sin-mult`

Counts

4 → 9

Calls

4 calls:

3.0ms	(* (sin phi1) (sin phi2))
2.0ms	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
7.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
4.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (sin phi2))
70.0ms	(* (acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2))))) R)
100.0ms	(* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2))))
16.0ms	(acos (+ (* (sin lambda1) (* (cos phi1) (* (cos phi2) (sin lambda2)))) (+ (* (cos lambda1) (* (cos phi1) (* (cos phi2) (cos lambda2)))) (* (sin phi1) (sin phi2)))))

simplify21.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	93	188
1	158	188
2	264	188
3	374	188
4	389	188
5	389	188

prune71.0ms

Filtered

21 candidates to 12 candidates (57.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	21	3	24

Merged error: 2.9b

Counts

24 → 3

regimes146.0ms

Accuracy

0% (0.1b remaining)

Error of 3.9b against oracle of 3.8b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	21
1	34	21

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.6s	4788×	body	1280	valid
1.4s	2121×	body	640	valid
296.0ms	673×	body	320	valid
82.0ms	279×	body	160	valid
46.0ms	12×	body	2560	valid
19.0ms	127×	body	80	valid