Details

sample389.0ms

Algorithm

intervals

Results

227.0ms	108×	body	1280	valid
95.0ms	80×	body	640	valid
27.0ms	30×	body	320	valid
5.0ms	14×	body	160	valid
5.0ms	24×	body	80	valid

simplify18.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize48.0ms

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))))
2.6b	(sin (- lambda1 lambda2))
2.8b	(cos (- lambda1 lambda2))

rewrite72.0ms

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)))))
30.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

series638.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
564.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
39.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify4.9s

Counts

52 → 52

Iterations

Useful iterations: 3 (311.0ms)

Iter	Nodes	Cost
0	97	702
1	204	687
2	458	615
3	967	613
4	2013	613
5	4634	613
done	5000	613

prune357.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (sin (- lambda1 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))))
2.6b	(sin (- lambda1 lambda2))

rewrite77.0ms

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

Counts

4 → 47

Calls

4 calls:

26.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
22.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
23.0ms	(sin (- lambda1 lambda2))

series354.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (sin lambda1) (sin lambda2))
17.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (* (sin lambda1) (sin lambda2)) (cos phi2))))
213.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))
44.0ms	(sin (- lambda1 lambda2))

simplify2.6s

Counts

59 → 59

Iterations

Useful iterations: 2 (163.0ms)

Iter	Nodes	Cost
0	119	889
1	260	872
2	684	733
3	1946	733
done	5000	733

prune476.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

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×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 56

Calls

4 calls:

37.0ms	(* (sin lambda1) (cos lambda2))
25.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(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))))
15.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series368.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin lambda1) (cos lambda2))
92.0ms	(* (sin lambda1) (sin lambda2))
21.0ms	(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))))
195.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify2.3s

Counts

68 → 68

Iterations

Useful iterations: 2 (191.0ms)

Iter	Nodes	Cost
0	132	1053
1	306	1035
2	837	870
3	2309	870
done	5000	870

prune494.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos phi1) 3)
0.3b	(* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
0.6b	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
1.4b	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`pow-unpow` `associate-*r/` `add-log-exp`
4×	`unpow-prod-down` `pow-pow` `cube-prod` `pow-exp` `cos-mult` `rem-cube-cbrt`
3×	`sub-neg` `flip3--` `associate-r` `flip--`
2×	`distribute-rgt-in` `cube-mult` `frac-times` `pow-to-exp` `distribute-lft-in` `unpow3` `sqr-pow`
1×	`cube-div` `diff-log` `associate-l` `associate-l/` `-commutative`

Counts

4 → 91

Calls

4 calls:

3.0ms	(pow (cos phi1) 3)
202.0ms	(* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
27.0ms	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
30.0ms	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

series712.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (cos phi1) 3)
335.0ms	(* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))
154.0ms	(pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)
179.0ms	(- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1))

simplify1.6s

Counts

103 → 103

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	167	1762
1	442	1616
2	2186	1366
done	5000	1364

prune712.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes668.0ms

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	35	108
1	50	108
done	50	108

end0.0ms

sample12.1s

Algorithm

intervals

Results

7.4s	3641×	body	1280	valid
2.8s	2245×	body	640	valid
685.0ms	955×	body	320	valid
490.0ms	426×	body	160	valid
186.0ms	733×	body	80	valid