Details

sample533.0ms

Algorithm

intervals

Results

399.0ms	138×	body	1280	valid
79.0ms	65×	body	640	valid
14.0ms	22×	body	320	valid
5.0ms	23×	body	80	valid
4.0ms	8×	body	160	valid

simplify95.0ms

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	88	24
done	88	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite179.0ms

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:

63.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
82.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(sin (- lambda1 lambda2))
15.0ms	(cos (- lambda1 lambda2))

series310.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
175.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

simplify8.3s

Counts

98 → 98

Iterations

Useful iterations: done (8.3s)

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

prune615.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.7b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite168.0ms

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:

13.0ms	(* (sin lambda1) (cos lambda2))
92.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series456.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin lambda1) (cos lambda2))
190.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
183.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify3.4s

Counts

99 → 99

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	224	1587
1	465	1401
2	1338	1175
3	4133	1132
done	5000	1130

prune700.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

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*`
4×	`expm1-log1p-u` `associate-l/` `-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 97

Calls

4 calls:

75.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
13.0ms	(* (sin lambda1) (sin lambda2))
52.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
63.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
68.0ms	(* (sin lambda1) (sin lambda2))
141.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
153.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.4s

Counts

109 → 109

Iterations

Useful iterations: 2 (329.0ms)

Iter	Nodes	Cost
0	171	1576
1	440	1550
2	1840	1253
done	5000	1253

prune896.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
0.6b	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
0.6b	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
0.6b	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

rewrite287.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
22×	`cos-mult` `sin-cos-mult`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

154.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
43.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
36.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
45.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

368.0ms	(* (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))) (cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))))
357.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
331.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))
306.0ms	(cbrt (* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))))

simplify2.2s

Counts

102 → 102

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	131	2314
1	283	2150
2	834	1850
3	2996	1784
done	5000	1764

prune922.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes485.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	73
1	41	73
done	41	73

end0.0ms

sample19.7s

Algorithm

intervals

Results

13.9s	4526×	body	1280	valid
3.3s	1971×	body	640	valid
1.6s	599×	body	320	valid
170.0ms	701×	body	80	valid
107.0ms	203×	body	160	valid