Details

sample183.0ms

Algorithm

intervals

Results

113.0ms	124×	body	1280	valid
43.0ms	71×	body	640	valid
9.0ms	26×	body	320	valid
3.0ms	11×	body	160	valid
3.0ms	24×	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: 1.3b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.6b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 11

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))
3.0ms	(sin (- lambda1 lambda2))

series286.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
237.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify87.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	148	164
1	346	164
2	925	163
3	2424	163
4	5003	163

prune92.0ms

Filtered

23 candidates to 14 candidates (60.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	17	6	23
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	6	24

Merged error: 1.1b

Counts

24 → 6

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
1.6b	(cos (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 15

Calls

4 calls:

8.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))

series266.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
12.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
98.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify129.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	183	242
1	492	242
2	1411	241
3	3907	241
4	5002	241

prune107.0ms

Filtered

27 candidates to 15 candidates (55.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	29	4	33

Merged error: 0.2b

Counts

33 → 4

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

4×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in`
2×	`associate-r/` `-commutative`
1×	`+-commutative` `flip3--` `flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip--` `flip-+` `sin-mult`

Counts

4 → 17

Calls

4 calls:

8.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms	(* (sin lambda1) (sin (- lambda2)))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
7.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
52.0ms	(* (sin lambda1) (sin (- lambda2)))
17.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
225.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	213	323
1	547	323
2	1945	318
3	5002	318

prune116.0ms

Filtered

29 candidates to 17 candidates (58.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0.2b

Counts

33 → 4

localize47.0ms

Local error

Found 4 expressions with local error:

0.4b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
1.1b	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate--l+`
3×	`sub-neg`
2×	`distribute-rgt-in` `pow-to-exp` `unpow-prod-down` `distribute-lft-in` `unpow3` `sqr-pow`
1×	`+-commutative` `flip3--` `flip3-+` `sum-cubes` `*-commutative` `flip--` `flip-+`

Counts

4 → 20

Calls

4 calls:

8.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
1.0ms	(pow (cos phi1) 3)
5.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
11.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.1s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3))
33.0ms	(pow (cos phi1) 3)
198.0ms	(pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)
205.0ms	(- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))

simplify44.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	416	514
1	1558	500
2	5001	477

prune190.0ms

Filtered

32 candidates to 23 candidates (71.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	28	4	32
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	29	7	36

Merged error: 0.2b

Counts

36 → 7

regimes392.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	23
1	31	23

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.4s	3653×	body	1280	valid
1.3s	2318×	body	640	valid
347.0ms	903×	body	320	valid
99.0ms	406×	body	160	valid
77.0ms	720×	body	80	valid