Details

sample266.0ms

Algorithm

intervals

Results

197.0ms	155×	body	1280	valid
35.0ms	52×	body	640	valid
9.0ms	20×	body	320	valid
3.0ms	24×	body	80	valid
1.0ms	5×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	46	24
3	71	24
4	72	24
done	72	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `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:

29.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
35.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
14.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series217.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
103.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
26.0ms	(sin (- lambda1 lambda2))

simplify6.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (994.0ms)

Iter	Nodes	Cost
0	116	760
1	258	748
2	816	644
3	2194	642
4	3730	642
done	5000	642

prune486.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

48.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
21.0ms	(* (cos lambda1) (sin (- lambda2)))
45.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series408.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
73.0ms	(* (cos lambda1) (sin (- lambda2)))
111.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

simplify3.8s

Counts

82 → 82

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	150	1090
1	362	1063
2	1317	927
3	4315	898
done	5000	897

prune712.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

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×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 88

Calls

4 calls:

22.0ms	(* (cos lambda1) (sin (- lambda2)))
90.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
13.0ms	(* (sin lambda1) (sin lambda2))
79.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (cos lambda1) (sin (- lambda2)))
156.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
70.0ms	(* (sin lambda1) (sin lambda2))
184.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.5s

Counts

100 → 100

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	171	1260
1	430	1233
2	1708	979
done	5000	969

prune722.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(pow (* (sin lambda2) (sin lambda1)) 3)
26.6b	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`pow-unpow` `sin-mult`
2×	`cube-div` `cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-exp` `cos-mult` `*-commutative` `sin-cos-mult` `rem-cube-cbrt` `sqr-pow`
1×	`frac-times` `pow-to-exp` `cbrt-div` `pow1/3` `associate-r/` `associate-l/` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

13.0ms	(* (sin lambda2) (sin lambda1))
63.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
19.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
6.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

series417.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin lambda2) (sin lambda1))
218.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
81.0ms	(pow (* (sin lambda2) (sin lambda1)) 3)
56.0ms	(cbrt (pow (* (sin lambda2) (sin lambda1)) 3))

simplify1.3s

Counts

97 → 97

Iterations

Useful iterations: 2 (286.0ms)

Iter	Nodes	Cost
0	160	1115
1	368	971
2	1353	829
done	5001	829

prune786.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes654.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	48
1	41	48
done	41	48

end0.0ms

sample11.3s

Algorithm

intervals

Results

8.3s	4567×	body	1280	valid
2.0s	2012×	body	640	valid
349.0ms	555×	body	320	valid
115.0ms	662×	body	80	valid
77.0ms	204×	body	160	valid