Details

sample265.0ms

Algorithm

intervals

Results

186.0ms	147×	body	1280	valid
50.0ms	66×	body	640	valid
9.0ms	21×	body	320	valid
2.0ms	9×	body	160	valid
2.0ms	13×	body	80	valid

simplify43.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	78	24
4	86	24
done	86	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.0b	(sin (- lambda1 lambda2))

rewrite43.0ms

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:

14.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series191.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify4.6s

Counts

98 → 98

Iterations

Useful iterations: 4 (3.9s)

Iter	Nodes	Cost
0	210	1766
1	413	1430
2	1043	1144
3	2782	1059
4	4872	878
done	5000	878

prune427.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize37.0ms

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))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite43.0ms

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` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 87

Calls

4 calls:

16.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin lambda1) (cos lambda2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
47.0ms	(* (sin lambda1) (cos lambda2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify2.2s

Counts

99 → 99

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	224	1587
1	468	1401
2	1379	1179
3	4458	1132
done	5000	1132

prune576.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite39.0ms

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))
4.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
15.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (cos lambda2))
45.0ms	(* (sin lambda1) (sin lambda2))
121.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
102.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify913.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (154.0ms)

Iter	Nodes	Cost
0	169	1310
1	429	1283
2	1525	1023
done	5001	1023

prune642.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

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) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (sin lambda1) (sin (- lambda2)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
5×	`sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `cos-mult` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `flip--` `unswap-sqr`
2×	`sub-neg` `prod-diff` `frac-sub` `sub-div`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 100

Calls

4 calls:

18.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin lambda1) (cos lambda2))
25.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
6.0ms	(* (sin lambda1) (sin (- lambda2)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
47.0ms	(* (sin lambda1) (cos lambda2))
183.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
53.0ms	(* (sin lambda1) (sin (- lambda2)))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	219	1870
1	544	1807
2	2033	1545
done	5001	1543

prune659.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes522.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	41
1	36	41
done	36	41

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.2s	4627×	body	1280	valid
1.4s	1948×	body	640	valid
270.0ms	557×	body	320	valid
107.0ms	652×	body	80	valid
69.0ms	216×	body	160	valid