Details

sample192.0ms

Algorithm

intervals

Results

122.0ms	121×	body	1280	valid
33.0ms	60×	body	640	valid
12.0ms	33×	body	320	valid
4.0ms	14×	body	160	valid
3.0ms	28×	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: 1.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b	(sin (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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

series197.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
100.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
25.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify76.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	249	435
1	795	394
2	2920	393
3	5001	393

prune271.0ms

Filtered

67 candidates to 49 candidates (73.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	55	12	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	12	68

Merged error: 0.9b

Counts

68 → 12

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.4b	(cos (- lambda1 lambda2))

rewrite18.0ms

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×	`distribute-rgt-in` `cos-diff` `sub-neg` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+` `associate-*r/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

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

series273.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
141.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
100.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms	(cos (- lambda1 lambda2))

simplify124.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	289	748
1	1037	659
2	4438	658
3	5002	658

prune300.0ms

Filtered

66 candidates to 48 candidates (72.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	68	10	78

Merged error: 0.1b

Counts

78 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos lambda1) (sin lambda2))
143.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
45.0ms	(* (sin lambda1) (sin lambda2))
221.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	396	770
1	1621	684
2	5001	683

prune336.0ms

Filtered

86 candidates to 59 candidates (68.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	86	10	96

Merged error: 0.1b

Counts

96 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

4.2b	(sin (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))
4.4b	(cos (- 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	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series77.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify58.0ms

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	1140	215
4	5002	215

prune236.0ms

Filtered

52 candidates to 40 candidates (76.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	52	10	62

Merged error: 0.1b

Counts

62 → 10

regimes353.0ms

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	30	22
1	30	22

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.4s	3565×	body	1280	valid
1.3s	2350×	body	640	valid
326.0ms	909×	body	320	valid
99.0ms	426×	body	160	valid
79.0ms	750×	body	80	valid

Details

sample192.0ms

simplify5.0ms

prune3.0ms

localize21.0ms

rewrite21.0ms

series197.0ms

simplify76.0ms

prune271.0ms

localize31.0ms

rewrite18.0ms

series273.0ms

simplify124.0ms

prune300.0ms

localize32.0ms

rewrite25.0ms

series453.0ms

simplify50.0ms

prune336.0ms

localize36.0ms

rewrite17.0ms

series77.0ms

simplify58.0ms

prune236.0ms

regimes353.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.4s

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