Details

sample380.0ms

Algorithm

intervals

Results

236.0ms	109×	body	1280	valid
74.0ms	71×	body	640	valid
30.0ms	39×	body	320	valid
8.0ms	15×	body	160	valid
4.0ms	22×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 1.0b

localize99.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b	(cos (- lambda1 lambda2))
4.0b	(sin (- lambda1 lambda2))

rewrite68.0ms

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)))))
20.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

series264.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
182.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
33.0ms	(cos (- lambda1 lambda2))
29.0ms	(sin (- lambda1 lambda2))

simplify4.9s

Counts

52 → 52

Iterations

Useful iterations: 3 (346.0ms)

Iter	Nodes	Cost
0	97	702
1	204	687
2	458	615
3	970	613
4	2017	613
5	4604	613
done	5000	613

prune430.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.8b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b	(cos (- lambda1 lambda2))

rewrite141.0ms

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`
3×	`distribute-rgt-in` `cos-diff` `sub-neg` `distribute-lft-in` `associate-r` `associate-l`
2×	`cos-sum` `associate-+r+` `associate-*r/`
1×	`+-commutative` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

104.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
15.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms	(cos (- lambda1 lambda2))

series424.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
24.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
142.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))

simplify2.5s

Counts

66 → 66

Iterations

Useful iterations: 3 (926.0ms)

Iter	Nodes	Cost
0	121	1182
1	289	1166
2	868	1032
3	2751	1030
done	5001	1030

prune525.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.5b	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite171.0ms

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-l` `add-log-exp`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`associate-*r/`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `*-commutative`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `cos-mult` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

42.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
113.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
14.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series625.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cos phi2) (* (cos lambda1) (cos lambda2)))
273.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
23.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
189.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify3.8s

Counts

73 → 73

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	141	1458
1	365	1422
2	1242	1242
3	4601	1209
done	5000	1209

prune504.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
0.3b	(exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
0.6b	(log (exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1`
4×	`add-exp-log` `log-prod` `log-pow` `add-cbrt-cube`
2×	`exp-sum` `sum-log` `rem-exp-log`
1×	`+-commutative` `flip3-+` `rem-log-exp` `flip-+`

Counts

4 → 47

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
28.0ms	(exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))
17.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
29.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (log (exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
279.0ms	(exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))))
190.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
200.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))))

simplify2.1s

Counts

59 → 59

Iterations

Useful iterations: 3 (502.0ms)

Iter	Nodes	Cost
0	103	1295
1	224	1220
2	603	1068
3	1948	1035
done	5000	1035

prune441.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes586.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	68
1	46	68
done	46	68

end0.0ms

sample11.5s

Algorithm

intervals

Results

6.4s	3545×	body	1280	valid
3.2s	2386×	body	640	valid
765.0ms	1003×	body	320	valid
540.0ms	704×	body	80	valid
127.0ms	362×	body	160	valid