Details

sample272.0ms

Algorithm

intervals

Results

198.0ms	148×	body	1280	valid
41.0ms	58×	body	640	valid
11.0ms	21×	body	320	valid
3.0ms	22×	body	80	valid
2.0ms	7×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

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: 15.5b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.3b	(sin (- lambda1 lambda2))
5.3b	(cos (- lambda1 lambda2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

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

series177.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
23.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	411	1009
1	1289	778
2	5001	776

prune419.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	84	14	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	14	99

Merged error: 8.1b

Counts

99 → 14

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.3b	(cos (- lambda1 lambda2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

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

series197.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
47.0ms	(* (sin lambda1) (cos lambda2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	455	787
1	1637	630
2	5002	628

prune487.0ms

Filtered

97 candidates to 65 candidates (67.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Merged error: 0.1b

Counts

111 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

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

series317.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (cos lambda2))
121.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
48.0ms	(* (sin lambda1) (sin lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	418	830
1	1802	652
2	5001	652

prune520.0ms

Filtered

108 candidates to 66 candidates (61.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	105	15	120

Merged error: 0.1b

Counts

120 → 15

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
13×	`add-sqr-sqrt`
10×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/` `sin-mult`
2×	`unswap-sqr`
1×	`frac-times` `associate-*r/`

Counts

4 → 93

Calls

4 calls:

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

series306.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin lambda1) (cos lambda2))
113.0ms	(* (* (* (sin phi1) (cos phi2)) (cos lambda1)) (cos lambda2))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
51.0ms	(* (sin lambda1) (sin lambda2))

simplify59.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	410	789
1	1891	626
2	5001	626

prune413.0ms

Filtered

105 candidates to 67 candidates (63.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	105	15	120

Merged error: 0.1b

Counts

120 → 15

regimes566.0ms

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	29
1	35	29

end0.0ms

sample8.7s

Algorithm

intervals

Results

6.4s	4619×	body	1280	valid
1.5s	1945×	body	640	valid
274.0ms	562×	body	320	valid
96.0ms	664×	body	80	valid
72.0ms	210×	body	160	valid