Details

sample342.0ms

Algorithm

intervals

Results

183.0ms	113×	body	1280	valid
103.0ms	71×	body	640	valid
22.0ms	35×	body	320	valid
5.0ms	16×	body	160	valid
4.0ms	21×	body	80	valid

simplify15.0ms

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: 1.5b

localize25.0ms

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))))
3.4b	(cos (- lambda1 lambda2))
3.5b	(sin (- lambda1 lambda2))

rewrite81.0ms

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)))))
41.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
22.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series270.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
186.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))
40.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

52 → 52

Iterations

Useful iterations: 3 (350.0ms)

Iter	Nodes	Cost
0	97	702
1	207	687
2	538	615
3	1521	613
done	5000	613

prune429.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
3.5b	(sin (- lambda1 lambda2))

rewrite82.0ms

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
35.0ms	(* (sin lambda1) (sin (- lambda2)))
21.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
22.0ms	(sin (- lambda1 lambda2))

series539.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
79.0ms	(* (sin lambda1) (sin (- lambda2)))
387.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))
38.0ms	(sin (- lambda1 lambda2))

simplify746.0ms

Counts

64 → 64

Iterations

Useful iterations: done (743.0ms)

Iter	Nodes	Cost
0	129	1099
1	286	1070
2	972	949
done	5000	906

prune503.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

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

Counts

4 → 64

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
65.0ms	(* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2)))))
44.0ms	(* (sin lambda1) (sin (- lambda2)))
20.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series825.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(atan2 (* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2))))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
271.0ms	(* (cos phi2) (+ (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin (- lambda2)))))
100.0ms	(* (sin lambda1) (sin (- lambda2)))
432.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify1.5s

Counts

76 → 76

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	157	1588
1	438	1556
2	2050	1367
done	5002	1322

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize102.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos phi1) 3)
0.4b	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
0.7b	(pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3)
1.1b	(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

rewrite172.0ms

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-*r/` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `associate--l+` `flip-+` `sqr-pow`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `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 → 75

Calls

4 calls:

4.0ms	(pow (cos phi1) 3)
34.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
46.0ms	(pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3)
85.0ms	(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

series2.6s

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (cos phi1) 3)
2.0s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3))
282.0ms	(pow (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) 3)
311.0ms	(- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))

simplify2.1s

Counts

87 → 87

Iterations

Useful iterations: 2 (655.0ms)

Iter	Nodes	Cost
0	211	1843
1	727	1658
2	3807	1500
done	5001	1500

prune827.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes632.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	81
1	45	81
done	45	81

end0.0ms

sample10.6s

Algorithm

intervals

Results

5.9s	3498×	body	1280	valid
2.7s	2340×	body	640	valid
869.0ms	974×	body	320	valid
446.0ms	734×	body	80	valid
195.0ms	454×	body	160	valid