Details

sample390.0ms

Algorithm

intervals

Results

300.0ms	150×	body	1280	valid
50.0ms	59×	body	640	valid
8.0ms	15×	body	320	valid
5.0ms	12×	body	160	valid
3.0ms	20×	body	80	valid

simplify396.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 lambda2))
4.0b	(sin (- lambda1 lambda2))

rewrite142.0ms

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:

45.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
56.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
23.0ms	(cos (- lambda1 lambda2))
15.0ms	(sin (- lambda1 lambda2))

series275.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
136.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
35.0ms	(sin (- lambda1 lambda2))

simplify6.8s

Counts

98 → 98

Iterations

Useful iterations: done (6.8s)

Iter	Nodes	Cost
0	210	1766
1	403	1430
2	995	1144
3	2481	1059
4	4281	878
done	5000	787

prune559.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.9b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.9b	(cos (- lambda1 lambda2))

rewrite117.0ms

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:

12.0ms	(* (sin phi1) (cos phi2))
46.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
42.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series401.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin phi1) (cos phi2))
198.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
129.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify4.1s

Counts

99 → 99

Iterations

Useful iterations: done (4.1s)

Iter	Nodes	Cost
0	213	1618
1	462	1413
2	1466	1159
3	4648	1067
done	5000	1066

prune787.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite220.0ms

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` `distribute-lft-in` `associate-*l/` `unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 100

Calls

4 calls:

25.0ms	(* (sin lambda1) (sin (- lambda2)))
14.0ms	(* (sin phi1) (cos phi2))
73.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
103.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series601.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin lambda1) (sin (- lambda2)))
48.0ms	(* (sin phi1) (cos phi2))
180.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
305.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.5s

Counts

112 → 112

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	212	1901
1	541	1819
2	2177	1543
done	5000	1509

prune884.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

113.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
1.0ms	(cbrt (cos phi2))
1.0ms	(cbrt (cos phi2))
1.0ms	(cbrt (cos phi2))

series646.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
109.0ms	(cbrt (cos phi2))
125.0ms	(cbrt (cos phi2))
136.0ms	(cbrt (cos phi2))

simplify1.2s

Counts

86 → 86

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	142	1303
1	363	1263
2	1414	1056
done	5000	1008

prune600.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes511.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	48
1	35	48
done	35	48

end0.0ms

sample19.7s

Algorithm

intervals

Results

13.8s	4584×	body	1280	valid
3.3s	1973×	body	640	valid
1.5s	593×	body	320	valid
277.0ms	654×	body	80	valid
205.0ms	196×	body	160	valid