Details

sample919.0ms

Algorithm

intervals

Results

782.0ms	149×	body	1280	valid
80.0ms	59×	body	640	valid
16.0ms	18×	body	320	valid
6.0ms	25×	body	80	valid
2.0ms	5×	body	160	valid

simplify66.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	46	24
3	71	24
4	79	24
done	79	24

prune42.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `sub-neg` `sin-sum` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

20.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
52.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

series283.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
124.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
38.0ms	(sin (- lambda1 lambda2))
33.0ms	(cos (- lambda1 lambda2))

simplify935.0ms

Counts

72 → 72

Iterations

Useful iterations: done (931.0ms)

Iter	Nodes	Cost
0	116	760
1	272	748
2	1349	652
done	5000	642

prune637.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.3b

localize81.0ms

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)))
3.7b	(cos (- lambda1 lambda2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`cos-sum` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `flip--`

Counts

4 → 70

Calls

4 calls:

9.0ms	(* (sin phi1) (cos phi2))
49.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))

series420.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin phi1) (cos phi2))
208.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
133.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	133	1039
1	344	1026
2	1886	892
done	5000	882

prune939.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize70.0ms

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

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-*r/` `cos-mult` `unswap-sqr`
1×	`flip3--` `flip--`

Counts

4 → 89

Calls

4 calls:

42.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
12.0ms	(* (sin lambda1) (sin lambda2))
54.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
54.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series643.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
59.0ms	(* (sin lambda1) (sin lambda2))
198.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
156.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.2s

Counts

101 → 101

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	165	1486
1	455	1460
2	2146	1174
done	5000	1164

prune930.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-l`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r`
4×	`associate-r/` `-commutative` `add-log-exp`
3×	`sin-mult`
2×	`cos-mult` `sin-cos-mult`
1×	`frac-times` `associate-*l/` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
51.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
76.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (sin lambda1) (sin lambda2))
124.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
169.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
182.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify986.0ms

Counts

97 → 97

Iterations

Useful iterations: done (982.0ms)

Iter	Nodes	Cost
0	147	1242
1	391	1218
2	1760	966
done	5001	952

prune889.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes745.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	44
1	37	44
done	37	44

end0.0ms

sample21.4s

Algorithm

intervals

Results

15.8s	4571×	body	1280	valid
3.9s	1969×	body	640	valid
578.0ms	558×	body	320	valid
219.0ms	685×	body	80	valid
124.0ms	217×	body	160	valid