Details

sample176.0ms

Algorithm

intervals

Results

105.0ms	111×	body	1280	valid
43.0ms	86×	body	640	valid
9.0ms	27×	body	320	valid
2.0ms	23×	body	80	valid
2.0ms	9×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	20
1	20	20
2	21	20
done	21	20

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b	(sin (- lambda1 lambda2))
3.3b	(cos (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
3.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series156.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
102.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
26.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

52 → 52

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	97	702
1	204	687
2	446	635
3	1009	633
4	2281	633
done	5000	633

prune249.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.4b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.3b	(cos (- lambda1 lambda2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

5.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
101.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
17.0ms	(cos (- lambda1 lambda2))

simplify2.1s

Counts

63 → 63

Iterations

Useful iterations: 3 (247.0ms)

Iter	Nodes	Cost
0	109	950
1	241	918
2	592	876
3	1465	874
4	2985	874
done	5000	874

prune515.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
0.4b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `flip-+` `sin-mult`

Counts

4 → 57

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
4.0ms	(* (sin lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
3.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))

series326.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos lambda1) (sin lambda2))
48.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
214.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))

simplify1.5s

Counts

69 → 69

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	131	1162
1	305	1138
2	841	985
3	2912	985
done	5000	985

prune344.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
0.4b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
0.5b	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
4×	`log-prod` `log-pow`
3×	`associate-r` `associate-l`
2×	`associate-+r+` `exp-sum` `sum-log` `rem-exp-log`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
3.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
7.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))

series751.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (sin lambda2))
275.0ms	(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))
214.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))
216.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))))))

simplify1.3s

Counts

73 → 73

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	123	1366
1	273	1302
2	750	1140
3	2918	1140
done	5001	1140

prune359.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes428.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	77
1	40	77
done	40	77

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.3s	3551×	body	1280	valid
1.3s	2449×	body	640	valid
331.0ms	943×	body	320	valid
82.0ms	372×	body	160	valid
78.0ms	685×	body	80	valid