Details

sample581.0ms

Algorithm

intervals

Results

410.0ms	136×	body	1280	valid
107.0ms	75×	body	640	valid
25.0ms	23×	body	320	valid
5.0ms	18×	body	80	valid
3.0ms	4×	body	160	valid

simplify178.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	31	24
2	71	24
3	110	24
4	112	24
done	112	24

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.5b	(sin (- lambda1 lambda2))
6.0b	(cos (- lambda1 lambda2))

rewrite137.0ms

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))
45.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

series302.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
152.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(sin (- lambda1 lambda2))
20.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

98 → 98

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	210	1766
1	786	1322
done	5001	1144

prune552.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.5b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
6.0b	(cos (- lambda1 lambda2))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

16.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
12.0ms	(* (sin lambda1) (cos lambda2))
41.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

series415.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
74.0ms	(* (sin lambda1) (cos lambda2))
122.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify1.9s

Counts

95 → 95

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	222	1615
1	1072	1348
done	5001	1208

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

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:

12.0ms	(* (sin lambda1) (cos lambda2))
13.0ms	(* (sin lambda1) (sin lambda2))
56.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
50.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin lambda1) (cos lambda2))
74.0ms	(* (sin lambda1) (sin lambda2))
168.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
160.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify6.0s

Counts

108 → 108

Iterations

Useful iterations: done (6.0s)

Iter	Nodes	Cost
0	165	1310
1	735	1283
done	5000	1023

prune877.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(log1p (* (sin lambda1) (cos lambda2)))
0.3b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

14.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(log1p (* (sin lambda1) (cos lambda2)))
61.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
54.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin lambda1) (sin lambda2))
98.0ms	(log1p (* (sin lambda1) (cos lambda2)))
166.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
185.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify7.5s

Counts

98 → 98

Iterations

Useful iterations: done (7.5s)

Iter	Nodes	Cost
0	155	1244
1	663	1216
done	5001	959

prune808.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	47
1	39	47
done	39	47

end0.0ms

sample20.6s

Algorithm

intervals

Results

14.8s	4619×	body	1280	valid
4.1s	1988×	body	640	valid
682.0ms	570×	body	320	valid
164.0ms	189×	body	160	valid
159.0ms	634×	body	80	valid