Details

sample174.0ms

Algorithm

intervals

Results

106.0ms	113×	body	1280	valid
41.0ms	84×	body	640	valid
8.0ms	23×	body	320	valid
3.0ms	25×	body	80	valid
2.0ms	11×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 0.4b

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))))
2.8b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 40

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))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series153.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
100.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify117.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	205	421
1	508	375
2	1327	374
3	3685	374
4	5002	374

prune230.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	39	13	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	13	53

Merged error: 0.3b

Counts

53 → 13

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos 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))))
2.8b	(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 49

Calls

4 calls:

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

series270.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin lambda1) (cos lambda2))
22.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
154.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms	(cos (- lambda1 lambda2))

simplify76.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	264	537
1	790	472
2	2426	471
3	5001	471

prune295.0ms

Filtered

61 candidates to 46 candidates (75.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	62	12	74

Merged error: 0.1b

Counts

74 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.4b	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 56

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
4.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin lambda1) (cos lambda2))
44.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
129.0ms	(+ (cos phi1) (* (* (cos lambda1) (cos lambda2)) (cos phi2)))

simplify112.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	305	677
1	1090	587
2	4149	586
3	5002	586

prune309.0ms

Filtered

68 candidates to 50 candidates (73.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	68	12	80

Merged error: 0.1b

Counts

80 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff`
2×	`sin-sum`
1×	`sin-diff`

Counts

4 → 40

Calls

4 calls:

4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series74.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cos (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	83	235
1	149	215
2	390	215
3	1141	215
4	5002	215

prune227.0ms

Filtered

52 candidates to 40 candidates (76.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	52	12	64

Merged error: 0.1b

Counts

64 → 12

regimes386.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	24
1	32	24

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.3s	3543×	body	1280	valid
1.3s	2388×	body	640	valid
338.0ms	933×	body	320	valid
99.0ms	427×	body	160	valid
87.0ms	709×	body	80	valid

Details

sample174.0ms

simplify6.0ms

prune4.0ms

localize21.0ms

rewrite14.0ms

series153.0ms

simplify117.0ms

prune230.0ms

localize42.0ms

rewrite24.0ms

series270.0ms

simplify76.0ms

prune295.0ms

localize30.0ms

rewrite15.0ms

series238.0ms

simplify112.0ms

prune309.0ms

localize29.0ms

rewrite17.0ms

series74.0ms

simplify53.0ms

prune227.0ms

regimes386.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.5s

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