Details

sample296.0ms

Algorithm

intervals

Results

211.0ms	151×	body	1280	valid
44.0ms	58×	body	640	valid
11.0ms	23×	body	320	valid
3.0ms	8×	body	160	valid
2.0ms	16×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	65	24
1	65	24

prune12.0ms

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

localize28.0ms

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))

rewrite17.0ms

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)))
3.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series31.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4903	539
1	4903	539

prune168.0ms

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

localize33.0ms

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))

rewrite20.0ms

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))

series48.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
10.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5051	766

prune151.0ms

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

localize35.0ms

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))))

rewrite29.0ms

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))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
8.0ms	(* (cos phi1) (sin phi2))
47.0ms	(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
27.0ms	(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5305	1210

prune156.0ms

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

localize35.0ms

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:

4.0ms	(* (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)))))
7.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))

series85.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda2) (sin phi1))
8.0ms	(* (cos phi1) (sin phi2))
51.0ms	(* (cos phi2) (+ (* (cos lambda1) (* (cos lambda2) (sin phi1))) (* (sin lambda1) (* (sin lambda2) (sin phi1)))))
17.0ms	(* (sin lambda1) (* (sin lambda2) (sin phi1)))

simplify45.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5880	948

prune92.0ms

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

regimes576.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	41
1	35	41

end0.0ms

sample9.1s

Algorithm

intervals

Results

6.6s	4649×	body	1280	valid
1.5s	1928×	body	640	valid
276.0ms	529×	body	320	valid
106.0ms	678×	body	80	valid
76.0ms	216×	body	160	valid

Details

sample296.0ms

simplify3.0ms

prune12.0ms

localize28.0ms

rewrite17.0ms

series31.0ms

simplify59.0ms

prune168.0ms

localize33.0ms

rewrite20.0ms

series48.0ms

simplify56.0ms

prune151.0ms

localize35.0ms

rewrite29.0ms

series91.0ms

simplify44.0ms

prune156.0ms

localize35.0ms

rewrite26.0ms

series85.0ms

simplify45.0ms

prune92.0ms

regimes576.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.1s

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