Details

sample372.0ms

Algorithm

intervals

Results

211.0ms	120×	body	1280	valid
101.0ms	75×	body	640	valid
19.0ms	29×	body	320	valid
6.0ms	13×	body	160	valid
4.0ms	19×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune56.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize53.0ms

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))))
2.0b	(cos (- lambda1 lambda2))
2.1b	(sin (- lambda1 lambda2))

rewrite34.0ms

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`
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 → 40

Calls

4 calls:

0.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))
9.0ms	(sin (- lambda1 lambda2))

series227.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
147.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
30.0ms	(cos (- lambda1 lambda2))
38.0ms	(sin (- lambda1 lambda2))

simplify2.5s

Counts

52 → 52

Iterations

Iter	Nodes
done	5001
4	2583
3	1180
2	482
1	207
0	97

prune520.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize69.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.0b	(cos (- lambda1 lambda2))

rewrite26.0ms

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

Counts

4 → 49

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))

series260.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin lambda1) (cos lambda2))
17.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
161.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))

simplify2.8s

Counts

61 → 61

Iterations

Iter	Nodes
done	5004
4	4646
3	1854
2	692
1	281
0	123

prune737.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize78.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.3b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `sin-cos-mult` `sin-mult`

Counts

4 → 56

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
9.0ms	(* (sin lambda1) (sin lambda2))
20.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

series317.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin lambda1) (cos lambda2))
38.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
60.0ms	(* (sin lambda1) (sin lambda2))
142.0ms	(+ (cos phi1) (* (cos phi2) (* (cos lambda1) (cos lambda2))))

simplify3.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
3	3241
2	830
1	316
0	132

prune848.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize165.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
0.4b	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
0.4b	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
1.2b	(- (cos phi1) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))

rewrite809.0ms

Algorithm

rewrite-expression-head

Rules

232×	`pow1`
132×	`pow-prod-down`
76×	`add-cbrt-cube` `add-exp-log`
54×	`prod-exp` `cbrt-unprod`
27×	`cos-mult`
25×	`associate-*l/`
18×	`pow-sqr` `pow-prod-up`
14×	`associate-*r/`
8×	`add-log-exp`
7×	`frac-times` `frac-add`
6×	`pow-plus`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
2×	`pow2` `sqr-cos` `associate-+r+` `cube-unmult` `swap-sqr` `associate-r` `associate-l` `*-commutative`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `sub-neg` `distribute-lft-in` `flip3-+` `flip3--` `diff-log` `sum-cubes` `flip-+` `flip--`

Counts

4 → 159

Calls

4 calls:

522.0ms	(+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
115.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
148.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
6.0ms	(- (cos phi1) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))

series811.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(+ (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))) (* (cos phi1) (* (cos phi1) (cos phi1))))
153.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
167.0ms	(* (* (* (cos lambda1) (cos phi2)) (cos lambda2)) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))
223.0ms	(- (cos phi1) (* (* (cos lambda1) (cos phi2)) (cos lambda2)))

simplify2.3s

Counts

171 → 171

Iterations

Iter	Nodes
done	5006
2	2681
1	563
0	188

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify25.0ms

Iterations

Iter	Nodes
done	47
1	47
0	32

end0.0ms

sample11.1s

Algorithm

intervals

Results

6.8s	3592×	body	1280	valid
2.4s	2352×	body	640	valid
1.0s	922×	body	320	valid
204.0ms	433×	body	160	valid
146.0ms	700×	body	80	valid
2.0ms	1×	body	2560	valid