Details

sample298.0ms

Algorithm

intervals

Results

212.0ms	151×	body	1280	valid
48.0ms	58×	body	640	valid
12.0ms	23×	body	320	valid
3.0ms	8×	body	160	valid
2.0ms	16×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	24
1	65	24

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 11.7b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
4.1b	(sin (- lambda1 lambda2))
4.1b	(cos (- lambda1 lambda2))

rewrite18.0ms

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`
4×	`add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `sin-diff` `sin-cos-mult`

Counts

4 → 59

Calls

4 calls:

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

series33.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify61.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4903	539
1	4903	539

prune183.0ms

Filtered

52 candidates to 71 candidates (-36.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 6.0b

Counts

72 → 13

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
4.1b	(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`cos-diff` `associate-r`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`*-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`sub-neg` `associate-*r/`

Counts

4 → 72

Calls

4 calls:

6.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
4.0ms	(* (cos phi1) (sin phi2))
5.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series54.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
12.0ms	(* (cos phi1) (sin phi2))
13.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify58.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5051	766

prune162.0ms

Filtered

59 candidates to 84 candidates (-42.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.0b

Counts

97 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
9×	`associate-*r/`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
8.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (cos phi1) (sin phi2))
50.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
28.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5305	1210

prune169.0ms

Filtered

66 candidates to 97 candidates (-47.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 0.0b

Counts

107 → 9

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-r`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
3×	`associate-*r/` `unswap-sqr`
2×	`sin-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 78

Calls

4 calls:

5.0ms	(* (sin lambda2) (sin phi1))
4.0ms	(* (cos phi1) (sin phi2))
8.0ms	(* (cos phi2) (+ (* (cos lambda1) (* (cos lambda2) (sin phi1))) (* (sin lambda1) (* (sin lambda2) (sin phi1)))))
6.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin lambda2) (sin phi1))
9.0ms	(* (cos phi1) (sin phi2))
54.0ms	(* (cos phi2) (+ (* (cos lambda1) (* (cos lambda2) (sin phi1))) (* (sin lambda1) (* (sin lambda2) (sin phi1)))))
18.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))

simplify47.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5880	948

prune99.0ms

Filtered

62 candidates to 90 candidates (-45.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 0.0b

Counts

99 → 9

regimes591.0ms

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	35	41
1	35	41

end0.0ms

sample9.1s

Algorithm

intervals

Results

6.6s	4649×	body	1280	valid
1.6s	1928×	body	640	valid
271.0ms	529×	body	320	valid
111.0ms	678×	body	80	valid
72.0ms	216×	body	160	valid

Details

sample298.0ms

simplify4.0ms

prune13.0ms

localize26.0ms

rewrite18.0ms

series33.0ms

simplify61.0ms

prune183.0ms

localize35.0ms

rewrite21.0ms

series54.0ms

simplify58.0ms

prune162.0ms

localize37.0ms

rewrite30.0ms

series96.0ms

simplify47.0ms

prune169.0ms

localize36.0ms

rewrite26.0ms

series91.0ms

simplify47.0ms

prune99.0ms

regimes591.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.1s

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