Details

sample577.0ms

Algorithm

intervals

Results

347.0ms	114×	body	1280	valid
141.0ms	74×	body	640	valid
49.0ms	38×	body	320	valid
8.0ms	22×	body	80	valid
6.0ms	8×	body	160	valid

simplify18.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.3b	(cos (- lambda1 lambda2))
4.4b	(sin (- lambda1 lambda2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
3×	`cos-diff`
2×	`cos-sum` `associate-+r+` `sub-neg` `sin-sum`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `flip3-+` `sin-diff` `flip-+`

Counts

4 → 44

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
16.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

series283.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
183.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
29.0ms	(cos (- lambda1 lambda2))
53.0ms	(sin (- lambda1 lambda2))

simplify1.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	2001
4	2001
3	1179
2	486
1	211
0	101

prune565.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize95.0ms

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)))))
4.4b	(sin (- lambda1 lambda2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`insert-posit16`
3×	`associate-r` `associate-l`
2×	`associate-+r+` `sin-sum`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sin-diff` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
19.0ms	(* (sin lambda1) (sin lambda2))
16.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
14.0ms	(sin (- lambda1 lambda2))

series452.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
64.0ms	(* (sin lambda1) (sin lambda2))
333.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
39.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
3	2000
2	796
1	280
0	124

prune762.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

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

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
4×	`insert-posit16`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`associate-+r+` `sub-neg` `associate-*r/`
1×	`+-commutative` `sum-log` `flip3-+` `flip3--` `flip-+` `sin-cos-mult` `flip--` `sin-mult`

Counts

4 → 79

Calls

4 calls:

100.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
30.0ms	(* (sin lambda1) (cos lambda2))
23.0ms	(* (sin lambda1) (sin lambda2))
18.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series740.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
79.0ms	(* (sin lambda1) (cos lambda2))
87.0ms	(* (sin lambda1) (sin lambda2))
357.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify1.5s

Counts

91 → 91

Iterations

Iter	Nodes
done	2009
3	2009
2	1476
1	436
0	168

prune938.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
7×	`pow1`
6×	`exp-prod` `add-cbrt-cube` `add-exp-log`
4×	`log-prod` `log-pow` `insert-posit16`
3×	`associate-r` `associate-l`
2×	`associate-+r+` `sum-log` `exp-sum` `rem-exp-log`
1×	`distribute-rgt-in` `+-commutative` `distribute-lft-in` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

23.0ms	(* (sin lambda1) (sin lambda2))
24.0ms	(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
15.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
33.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin lambda1) (sin lambda2))
417.0ms	(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
356.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
380.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify1.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	2000
3	2000
2	842
1	302
0	127

prune855.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes781.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	36
1	36
0	26

end0.0ms

sample16.9s

Algorithm

intervals

Results

10.8s	3625×	body	1280	valid
3.8s	2310×	body	640	valid
1.5s	976×	body	320	valid
253.0ms	410×	body	160	valid
221.0ms	679×	body	80	valid