Details

sample569.0ms

Algorithm

intervals

Results

434.0ms	153×	body	1280	valid
83.0ms	59×	body	640	valid
15.0ms	19×	body	320	valid
4.0ms	19×	body	80	valid
3.0ms	6×	body	160	valid

simplify91.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize42.0ms

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))

rewrite74.0ms

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

Counts

4 → 59

Calls

4 calls:

12.0ms	(* (cos phi1) (sin phi2))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(sin (- lambda1 lambda2))
11.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (cos phi1) (sin phi2))
135.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms	(sin (- lambda1 lambda2))
31.0ms	(cos (- lambda1 lambda2))

simplify6.1s

Counts

71 → 71

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	128	709
1	284	697
2	873	607
3	2313	599
4	4027	599
done	5000	599

prune507.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.4b

localize54.0ms

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))

rewrite159.0ms

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-cos-mult` `flip-+`

Counts

4 → 69

Calls

4 calls:

63.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
25.0ms	(* (cos phi1) (sin phi2))
47.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

series428.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
58.0ms	(* (cos phi1) (sin phi2))
161.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))

simplify3.2s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	154	1059
1	379	1045
2	1358	901
3	4351	872
done	5000	872

prune690.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

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

rewrite126.0ms

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`

Counts

4 → 87

Calls

4 calls:

13.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (sin lambda1) (sin lambda2))
46.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
52.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

series794.0ms

Counts

4 → 12

Calls

4 calls:

385.0ms	(* (cos phi1) (sin phi2))
58.0ms	(* (sin lambda1) (sin lambda2))
159.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
192.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts

99 → 99

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	169	1229
1	428	1203
2	1704	947
done	5001	943

prune664.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.3b	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
0.5b	(pow (* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3)
19.1b	(cbrt (pow (* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

61.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
101.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
55.0ms	(pow (* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3)
26.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3))

series774.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
195.0ms	(* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
279.0ms	(pow (* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3)
135.0ms	(cbrt (pow (* (sin phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) 3))

simplify1.4s

Counts

106 → 106

Iterations

Useful iterations: 2 (369.0ms)

Iter	Nodes	Cost
0	180	1704
1	449	1472
2	1887	1274
done	5000	1274

prune841.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes457.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	51
1	45	51
done	45	51

end0.0ms

sample19.7s

Algorithm

intervals

Results

14.4s	4588×	body	1280	valid
3.5s	2027×	body	640	valid
696.0ms	569×	body	320	valid
309.0ms	647×	body	80	valid
99.0ms	169×	body	160	valid