Details

sample222.0ms

Algorithm

intervals

Results

141.0ms	122×	body	1280	valid
47.0ms	75×	body	640	valid
12.0ms	28×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	17×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	21	12
2	21	12

prune3.0ms

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: 1.2b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.7b	(cos (- lambda1 lambda2))
3.8b	(sin (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`sin-sum`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `flip3-+` `sin-diff` `*-commutative` `flip-+`

Counts

4 → 16

Calls

4 calls:

4.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))
3.0ms	(sin (- lambda1 lambda2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
117.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify87.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	158	184
1	371	184
2	966	183
3	2475	183
4	5001	183

prune96.0ms

Filtered

28 candidates to 16 candidates (57.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	24	4	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	4	29

Merged error: 1.0b

Counts

29 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
0.2b	(* (cos phi2) (sin lambda1))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.7b	(cos (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

3×	`cos-diff` `*-commutative`
2×	`cos-sum` `associate-+r+` `associate-r` `distribute-rgt-neg-out`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-neg` `flip-+`

Counts

4 → 13

Calls

4 calls:

4.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
3.0ms	(* (cos phi2) (sin lambda1))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))

series247.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (cos phi2) (* (cos lambda1) (sin (- lambda2))))
42.0ms	(* (cos phi2) (sin lambda1))
101.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify115.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	164	141
1	388	141
2	1069	140
3	3157	140
4	5001	140

prune135.0ms

Filtered

25 candidates to 18 candidates (72.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	26	3	29

Merged error: 0.2b

Counts

29 → 3

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (cos phi2) (sin lambda1))
0.2b	(* (sin lambda1) (sin lambda2))
0.7b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

5×	`+-commutative`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
3×	`associate-r/` `-commutative`
2×	`flip3-+` `flip-+` `sin-mult`
1×	`frac-add` `cos-mult`

Counts

4 → 18

Calls

4 calls:

9.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
3.0ms	(* (cos phi2) (sin lambda1))
3.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
43.0ms	(* (cos phi2) (sin lambda1))
50.0ms	(* (sin lambda1) (sin lambda2))
226.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	234	264
1	623	260
2	2731	258
3	5001	258

prune153.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0.2b

Counts

33 → 3

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(/ (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.7b	(+ (cos phi1) (/ (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

28×	`associate-*r/`
24×	`cos-mult` `sin-mult`
16×	`associate-/l/`
15×	`*-commutative`
12×	`associate-*l/`
10×	`frac-times` `frac-sub`
8×	`associate-r`
6×	`associate-/l*` `sub-div`
4×	`swap-sqr` `associate-l` `associate-/r/` `difference-of-squares`
2×	`pow2` `flip3--` `flip--`
1×	`+-commutative` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`

Counts

4 → 54

Calls

4 calls:

7.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
29.0ms	(/ (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
7.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
20.0ms	(+ (cos phi1) (/ (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2)))
326.0ms	(/ (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
59.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
781.0ms	(+ (cos phi1) (/ (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda1) (sin lambda2)) (* (sin lambda1) (sin lambda2))))) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	386	803
1	1668	736
2	5002	735

prune421.0ms

Filtered

66 candidates to 53 candidates (80.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	65	4	69

Merged error: 0.2b

Counts

69 → 4

regimes292.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	101
1	48	101

end0.0ms

sample5.2s

Algorithm

intervals

Results

3.3s	3592×	body	1280	valid
1.2s	2338×	body	640	valid
312.0ms	949×	body	320	valid
86.0ms	401×	body	160	valid
72.0ms	720×	body	80	valid