Details

sample496.0ms

Algorithm

intervals

Results

332.0ms	153×	body	1280	valid
124.0ms	59×	body	640	valid
12.0ms	19×	body	320	valid
4.0ms	19×	body	80	valid
3.0ms	6×	body	160	valid

simplify107.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.7b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite98.0ms

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`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
40.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms	(sin (- lambda1 lambda2))
14.0ms	(cos (- lambda1 lambda2))

series289.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos phi1) (sin phi2))
162.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
40.0ms	(sin (- lambda1 lambda2))
27.0ms	(cos (- lambda1 lambda2))

simplify7.7s

Counts

97 → 97

Iterations

Useful iterations: done (7.7s)

Iter	Nodes	Cost
0	222	1711
1	430	1374
2	1058	1096
3	2633	1011
4	4589	847
done	5001	738

prune683.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.8b	(cos (- lambda1 lambda2))

rewrite490.0ms

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×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-cos-mult` `flip-+`

Counts

4 → 86

Calls

4 calls:

63.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
20.0ms	(* (cos phi1) (sin phi2))
42.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
363.0ms	(cos (- lambda1 lambda2))

series507.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
90.0ms	(* (cos phi1) (sin phi2))
179.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))

simplify4.4s

Counts

98 → 98

Iterations

Useful iterations: 3 (2.7s)

Iter	Nodes	Cost
0	230	1609
1	497	1404
2	1548	1154
3	4782	1058
done	5000	1058

prune972.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin 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)))

rewrite170.0ms

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

Counts

4 → 95

Calls

4 calls:

21.0ms	(* (cos phi1) (sin phi2))
21.0ms	(* (sin lambda1) (sin lambda2))
48.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
76.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (cos phi1) (sin phi2))
71.0ms	(* (sin lambda1) (sin lambda2))
181.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
183.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.4s

Counts

107 → 107

Iterations

Useful iterations: 2 (310.0ms)

Iter	Nodes	Cost
0	173	1301
1	426	1274
2	1661	1014
done	5000	1014

prune850.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin 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))))

rewrite189.0ms

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-mult`
2×	`sin-cos-mult` `unswap-sqr`
1×	`frac-times` `associate-*l/` `cos-mult`

Counts

4 → 92

Calls

4 calls:

13.0ms	(* (cos phi1) (sin phi2))
21.0ms	(* (sin lambda1) (sin lambda2))
69.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
83.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (cos phi1) (sin phi2))
53.0ms	(* (sin lambda1) (sin lambda2))
164.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
174.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify1.6s

Counts

104 → 104

Iterations

Useful iterations: 2 (278.0ms)

Iter	Nodes	Cost
0	182	1228
1	441	1205
2	1704	967
done	5001	967

prune878.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes562.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	56
1	48	54
done	48	54

end0.0ms

sample20.0s

Algorithm

intervals

Results

15.3s	4588×	body	1280	valid
3.3s	2027×	body	640	valid
583.0ms	569×	body	320	valid
213.0ms	647×	body	80	valid
150.0ms	169×	body	160	valid