Details

sample719.0ms

Algorithm

intervals

Results

389.0ms	144×	body	1280	valid
103.0ms	76×	body	640	valid
90.0ms	19×	body	320	valid
8.0ms	12×	body	160	valid
5.0ms	1×	body	2560	valid
1.0ms	4×	body	80	valid

simplify43.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
3	34
2	33
1	26
0	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.9b	(cos (- lambda1 lambda2))
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

rewrite118.0ms

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` `insert-posit16` `add-log-exp`
3×	`cos-diff`
2×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

74.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
15.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
20.0ms	(cos (- lambda1 lambda2))
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
82.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
37.0ms	(cos (- lambda1 lambda2))
31.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))

simplify2.8s

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
3	3268
2	826
1	281
0	125

prune838.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.1b

localize117.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `cos-mult` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-l/` `associate-r/` `sin-mult`
1×	`acos-asin` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

59.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
76.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
14.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
4.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

series518.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
157.0ms	(* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))
118.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2)))))) R)
24.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (* (sin lambda1) (sin lambda2)) (* (cos phi1) (cos phi2))))))

simplify2.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5005
2	1576
1	449
0	172

prune942.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 5.9b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))))) R)
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))))))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`cos-mult` `insert-posit16` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`acos-asin` `frac-times` `associate-l/` `associate-r/` `sin-mult`

Counts

4 → 74

Calls

4 calls:

14.0ms	(* (sin lambda2) (sin lambda1))
67.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
7.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (sin lambda2) (sin lambda1))
185.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2)))
79.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))))) R)
23.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1)))))))

simplify3.1s

Counts

86 → 86

Iterations

Iter	Nodes
done	5002
3	4492
2	1149
1	386
0	166

prune978.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 5.9b

localize104.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))) R)
0.3b	(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
2.0b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))))
28.9b	(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
18×	`add-cbrt-cube` `pow-prod-down` `add-exp-log`
16×	`sin-mult`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`cbrt-div`
6×	`frac-times` `-un-lft-identity` `associate-l/` `add-cube-cbrt`
4×	`associate-r` `associate-l` `associate-*r/` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
2×	`pow-plus` `*-commutative`
1×	`cbrt-prod` `pow2` `acos-asin` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

12.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))) R)
69.0ms	(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
5.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))))
226.0ms	(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))

series288.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))))))) R)
102.0ms	(* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1)))
30.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos lambda1) (cos lambda2)) (* (cos phi1) (cos phi2))) (* (cos phi1) (* (cos phi2) (cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1)))))))))
63.0ms	(cbrt (* (* (* (sin lambda2) (sin lambda1)) (* (sin lambda2) (sin lambda1))) (* (sin lambda2) (sin lambda1))))

simplify2.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5003
3	3085
2	1054
1	353
0	160

prune925.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.9b

regimes2.6s

Accuracy

0% (0.4b remaining)

Error of 3.7b against oracle of 3.3b and baseline of 3.7b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample18.0s

Algorithm

intervals

Results

12.5s	4823×	body	1280	valid
4.1s	2129×	body	640	valid
667.0ms	633×	body	320	valid
169.0ms	257×	body	160	valid
54.0ms	12×	body	2560	valid
42.0ms	147×	body	80	valid