Details

sample477.0ms

Algorithm

intervals

Results

293.0ms	130×	body	1280	valid
134.0ms	75×	body	640	valid
12.0ms	16×	body	320	valid
7.0ms	28×	body	80	valid
3.0ms	7×	body	160	valid

simplify88.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	78	24
4	88	24
done	88	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(sin (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))

rewrite478.0ms

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:

40.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
358.0ms	(sin (- lambda1 lambda2))
29.0ms	(cos (- lambda1 lambda2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
141.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
39.0ms	(sin (- lambda1 lambda2))
25.0ms	(cos (- lambda1 lambda2))

simplify6.5s

Counts

98 → 98

Iterations

Useful iterations: done (6.5s)

Iter	Nodes	Cost
0	210	1766
1	403	1430
2	995	1144
3	2466	1059
4	4346	878
done	5001	787

prune564.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.5b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.8b	(cos (- lambda1 lambda2))

rewrite128.0ms

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` `associate-l/` `-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`

Counts

4 → 87

Calls

4 calls:

53.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
12.0ms	(* (sin lambda1) (cos lambda2))
46.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series420.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
55.0ms	(* (sin lambda1) (cos lambda2))
150.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))

simplify3.7s

Counts

99 → 99

Iterations

Useful iterations: 3 (2.4s)

Iter	Nodes	Cost
0	230	1618
1	488	1403
2	1516	1159
3	4750	1067
done	5000	1067

prune721.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

Local error

Found 4 expressions with local error:

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

rewrite180.0ms

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:

22.0ms	(* (sin lambda1) (cos lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
56.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
84.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda1) (cos lambda2))
56.0ms	(* (sin lambda1) (sin lambda2))
123.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
166.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.4s

Counts

108 → 108

Iterations

Useful iterations: 2 (278.0ms)

Iter	Nodes	Cost
0	165	1310
1	415	1283
2	1644	1023
done	5000	1023

prune868.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

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-l`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/` `sin-cos-mult` `sin-mult`
2×	`unswap-sqr`
1×	`frac-times` `associate-*l/` `cos-mult`

Counts

4 → 93

Calls

4 calls:

13.0ms	(* (sin lambda1) (cos lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
47.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
91.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series378.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin lambda1) (cos lambda2))
64.0ms	(* (sin lambda1) (sin lambda2))
116.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
131.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.2s

Counts

105 → 105

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	174	1237
1	430	1214
2	1675	984
done	5000	976

prune814.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes710.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	54
1	44	54
done	44	54

end0.0ms

sample21.2s

Algorithm

intervals

Results

15.6s	4655×	body	1280	valid
3.8s	1872×	body	640	valid
667.0ms	552×	body	320	valid
324.0ms	716×	body	80	valid
113.0ms	205×	body	160	valid