Details

sample259.0ms

Algorithm

intervals

Results

166.0ms	125×	body	1280	valid
48.0ms	66×	body	640	valid
15.0ms	30×	body	320	valid
3.0ms	25×	body	80	valid
3.0ms	10×	body	160	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize37.0ms

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

rewrite34.0ms

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)))))
9.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
11.0ms	(cos (- lambda1 lambda2))
13.0ms	(sin (- lambda1 lambda2))

series219.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
136.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))
41.0ms	(sin (- lambda1 lambda2))

simplify4.3s

Counts

52 → 52

Iterations

Useful iterations: 3 (313.0ms)

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

prune396.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.8b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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))))
2.6b	(cos (- lambda1 lambda2))

rewrite56.0ms

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

Counts

4 → 48

Calls

4 calls:

20.0ms	(* (cos lambda1) (sin lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
18.0ms	(cos (- lambda1 lambda2))

series294.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (cos lambda1) (sin lambda2))
28.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
174.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

simplify3.3s

Counts

60 → 60

Iterations

Useful iterations: 3 (445.0ms)

Iter	Nodes	Cost
0	115	857
1	255	841
2	640	743
3	1357	741
4	2836	741
done	5000	741

prune501.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

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

rewrite72.0ms

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

Counts

4 → 60

Calls

4 calls:

14.0ms	(* (cos lambda1) (sin lambda2))
37.0ms	(* (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)))))))
20.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series515.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cos lambda1) (sin lambda2))
77.0ms	(* (sin lambda1) (sin (- lambda2)))
20.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))
352.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	146	1254
1	329	1224
2	918	1077
3	2539	1034
done	5002	1034

prune548.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac` `frac-add` `cos-mult`
14×	`associate-*r/`
13×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `flip3-+` `flip-+`
6×	`frac-times`
5×	`flip3--` `sum-cubes` `flip--` `distribute-lft-out` `associate-/l*`
4×	`sin-mult`
3×	`cube-div` `pow-unpow` `associate-l/` `associate-/r`
2×	`pow-pow` `pow-exp` `associate--l+` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `unpow-prod-down` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

232.0ms	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))
24.0ms	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) 3))
23.0ms	(pow (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) 3)
61.0ms	(- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

series8.5s

Counts

4 → 12

Calls

4 calls:

6.1s	(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1)))))
1.8s	(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) 3))
278.0ms	(pow (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) 3)
333.0ms	(- (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))) (cos phi1))

simplify2.5s

Counts

114 → 114

Iterations

Useful iterations: 2 (821.0ms)

Iter	Nodes	Cost
0	332	7034
1	1001	6636
2	4553	6111
done	5000	6111

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes662.0ms

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	42	80
done	42	80

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.5s	3577×	body	1280	valid
1.7s	2352×	body	640	valid
448.0ms	950×	body	320	valid
123.0ms	396×	body	160	valid
98.0ms	724×	body	80	valid
4.0ms	1×	body	2560	valid