Details

sample321.0ms

Algorithm

intervals

Results

210.0ms	125×	body	1280	valid
64.0ms	68×	body	640	valid
14.0ms	25×	body	320	valid
7.0ms	17×	body	160	valid
3.0ms	21×	body	80	valid

simplify15.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.9b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite38.0ms

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)))))
13.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series515.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
144.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms	(cos (- lambda1 lambda2))
336.0ms	(sin (- lambda1 lambda2))

simplify4.7s

Counts

52 → 52

Iterations

Useful iterations: 3 (350.0ms)

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

prune485.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.9b	(cos (- lambda1 lambda2))

rewrite114.0ms

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:

1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
81.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
10.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

series441.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
235.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
170.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

simplify2.1s

Counts

66 → 66

Iterations

Useful iterations: 3 (788.0ms)

Iter	Nodes	Cost
0	121	1182
1	289	1166
2	870	1032
3	2753	1030
done	5000	1030

prune608.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

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)))))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

rewrite125.0ms

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

Counts

4 → 66

Calls

4 calls:

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)))))))
67.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
36.0ms	(* (sin lambda1) (sin (- lambda2)))
20.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

series685.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2)))))))
186.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
90.0ms	(* (sin lambda1) (sin (- lambda2)))
382.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin (- lambda2))))))

simplify2.9s

Counts

78 → 78

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	152	1579
1	356	1549
2	1128	1366
3	3882	1323
done	5001	1323

prune609.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize136.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (pow (cos phi1) 3) (pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) 3))
0.4b	(pow (cos phi1) 3)
0.6b	(pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) 3)
1.0b	(- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`pow-unpow`
4×	`unpow-prod-down` `cube-prod`
3×	`cube-div` `pow-pow` `associate-*l/` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `flip-+` `sqr-pow`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `cos-mult` `sum-cubes` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out`

Counts

4 → 73

Calls

4 calls:

22.0ms	(+ (pow (cos phi1) 3) (pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) 3))
3.0ms	(pow (cos phi1) 3)
32.0ms	(pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) 3)
62.0ms	(- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))

series2.4s

Counts

4 → 12

Calls

4 calls:

1.8s	(+ (pow (cos phi1) 3) (pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) 3))
43.0ms	(pow (cos phi1) 3)
289.0ms	(pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) 3)
327.0ms	(- (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) (cos phi1))

simplify1.8s

Counts

85 → 85

Iterations

Useful iterations: 2 (530.0ms)

Iter	Nodes	Cost
0	207	1821
1	595	1640
2	2302	1474
done	5001	1474

prune673.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes818.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	80
1	43	80
done	43	80

end0.0ms

sample12.3s

Algorithm

intervals

Results

7.1s	3522×	body	1280	valid
3.5s	2401×	body	640	valid
741.0ms	915×	body	320	valid
191.0ms	734×	body	80	valid
167.0ms	428×	body	160	valid