Details

sample276.0ms

Algorithm

intervals

Results

209.0ms	172×	body	1280	valid
40.0ms	58×	body	640	valid
6.0ms	13×	body	320	valid
2.0ms	9×	body	160	valid
1.0ms	4×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	19
1	26	19
2	33	19
done	33	19

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.6b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.7b	(cos (- lambda1 lambda2))

rewrite19.0ms

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×	`cos-sum` `*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

10.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

series176.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
47.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms	(cos (- lambda1 lambda2))

simplify5.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (762.0ms)

Iter	Nodes	Cost
0	121	1225
1	263	1213
2	842	1035
3	2539	1033
4	4503	1033
done	5000	1033

prune313.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
0.3b	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

series238.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin lambda1) (sin lambda2))
71.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))) R)
106.0ms	(* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))

simplify2.7s

Counts

82 → 82

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	140	1903
1	310	1683
2	975	1365
3	3902	1365
done	5001	1365

prune436.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))) R)
0.3b	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
1.0b	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
1.5b	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`exp-prod`
8×	`pow1` `log-pow`
7×	`associate-l`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`acos-asin` `log-prod` `associate-r`
2×	`exp-diff`
1×	`log-div` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

7.0ms	(* (log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))) R)
1.0ms	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
2.0ms	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
1.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

series149.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))) R)
44.0ms	(exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2)))))
19.0ms	(log (exp (acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))))
16.0ms	(acos (+ (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) (* (sin phi1) (sin phi2))))

simplify3.5s

Counts

70 → 70

Iterations

Useful iterations: 5 (551.0ms)

Iter	Nodes	Cost
0	107	2374
1	184	2277
2	369	2025
3	564	1929
4	753	1929
5	1443	1927
6	4553	1927
done	5000	1927

prune414.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
7.1b	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
7.1b	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
7.1b	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-div`
6×	`cos-mult` `sin-mult`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`
1×	`acos-asin`

Counts

4 → 44

Calls

4 calls:

1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
10.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
10.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

series603.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (* (cos phi1) (cos phi2)) (* (cos lambda1) (cos lambda2))) (* (* (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))) (cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))))))
193.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
191.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))
201.0ms	(cbrt (* (* (cos phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))))

simplify1.4s

Counts

56 → 56

Iterations

Useful iterations: 4 (341.0ms)

Iter	Nodes	Cost
0	92	1528
1	183	1510
2	379	1081
3	721	967
4	1710	949
done	5000	949

prune347.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 3.0b

regimes997.0ms

Accuracy

0% (0.4b remaining)

Error of 3.9b against oracle of 3.5b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	32
1	32	32
done	32	32

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.2s	4802×	body	1280	valid
1.5s	2068×	body	640	valid
320.0ms	686×	body	320	valid
83.0ms	281×	body	160	valid
32.0ms	10×	body	2560	valid
24.0ms	156×	body	80	valid