Details

sample259.0ms

Algorithm

intervals

Results

181.0ms	156×	body	1280	valid
46.0ms	73×	body	640	valid
5.0ms	13×	body	320	valid
5.0ms	2×	body	2560	valid
2.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	12
1	34	12
2	36	12
3	36	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: 15.1b

Counts

2 → 1

localize30.0ms

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 lambda2))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.4b	(cos (- lambda1 lambda2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`cos-sum` `*-commutative`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 7

Calls

4 calls:

3.0ms	(* (sin phi1) (sin phi2))
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))

series117.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin phi1) (sin phi2))
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)))))
18.0ms	(cos (- lambda1 lambda2))

simplify263.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	122
1	121	122
2	230	122
3	603	122
4	4246	122
5	5001	122

prune54.0ms

Filtered

19 candidates to 9 candidates (47.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	2	20

Merged error: 3.1b

Counts

20 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 6

Calls

4 calls:

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

series206.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (sin phi2))
72.0ms	(* (sin lambda1) (sin lambda2))
68.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
19.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify16.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	164
1	188	164
2	300	164
3	306	164
4	306	164

prune57.0ms

Filtered

18 candidates to 9 candidates (50.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	18	2	20

Merged error: 3.0b

Counts

20 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.9b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

2×	`asin-acos` `flip3--` `associate-l/` `-commutative` `flip--`
1×	`sub-neg` `sin-mult` `associate--r-`

Counts

4 → 11

Calls

4 calls:

3.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
2.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series280.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (sin lambda2))
165.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
16.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
56.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify97.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 3 (17.0ms)

Iter	Nodes	Cost
0	141	431
1	305	419
2	621	413
3	1147	410
4	3159	410
5	5003	410

prune124.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	17	6	23
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	18	7	25

Merged error: 2.8b

Counts

25 → 7

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.9b	(- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.1b	(- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`frac-sub`
9×	`flip3--` `flip--`
8×	`associate-*l/`
4×	`frac-2neg` `clear-num`
3×	`acos-asin` `sub-neg` `associate--r+` `associate--r-`
1×	`*-commutative`

Counts

4 → 29

Calls

4 calls:

7.0ms	(* (- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
7.0ms	(- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series160.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
18.0ms	(- (/ PI 2) (- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
56.0ms	(- (/ PI 2) (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	311	1666
1	1196	1533
2	5001	1461

prune220.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	34	7	41
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	38	10	48

Merged error: 2.7b

Counts

48 → 10

regimes493.0ms

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.6s	4826×	body	1280	valid
1.4s	2044×	body	640	valid
314.0ms	682×	body	320	valid
89.0ms	288×	body	160	valid
29.0ms	153×	body	80	valid
27.0ms	9×	body	2560	valid