Details

sample795.0ms

Algorithm

intervals

Results

657.0ms	107×	body	1280	valid
78.0ms	77×	body	640	valid
17.0ms	29×	body	320	valid
6.0ms	14×	body	160	valid
5.0ms	29×	body	80	valid

simplify14.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1)))
0.6b	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
2.9b	(cos (- lambda1 lambda2))
3.1b	(sin (- lambda1 lambda2))

rewrite46.0ms

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×	`associate-+l+` `cos-sum` `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 phi2) (cos (- lambda1 lambda2))) (cos phi1)))
10.0ms	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
26.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

series238.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1)))
165.0ms	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
26.0ms	(cos (- lambda1 lambda2))
32.0ms	(sin (- lambda1 lambda2))

simplify1.0s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	2243
2	591
1	201
0	95

prune423.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1))))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1)))
0.6b	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
2.9b	(cos (- lambda1 lambda2))

rewrite89.0ms

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

Counts

4 → 56

Calls

4 calls:

66.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1)))
12.0ms	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
9.0ms	(cos (- lambda1 lambda2))

series410.0ms

Counts

4 → 12

Calls

4 calls:

215.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1))))
27.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1)))
146.0ms	(+ (* (cos phi2) (cos (- lambda1 lambda2))) (cos phi1))
21.0ms	(cos (- lambda1 lambda2))

simplify677.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
2	1232
1	334
0	134

prune657.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

90.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1))))
0.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (+ (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1)))))
41.0ms	(* (* (cos phi2) (sin lambda2)) (sin lambda1))
46.0ms	(+ (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (+ (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))

series730.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1))))
37.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (sin lambda2) (cos lambda1)))) (+ (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (+ (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1)))))
120.0ms	(* (* (cos phi2) (sin lambda2)) (sin lambda1))
337.0ms	(+ (* (* (cos lambda1) (cos lambda2)) (cos phi2)) (+ (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))))

simplify1.7s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	2859
1	513
0	177

prune876.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda2) (sin lambda1))
0.2b	(exp (+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
0.6b	(+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
0.7b	(log (exp (+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1))))

rewrite158.0ms

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`
3×	`associate-r` `associate-l`
2×	`associate-+l+` `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 → 61

Calls

4 calls:

12.0ms	(* (sin lambda2) (sin lambda1))
69.0ms	(exp (+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
29.0ms	(+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
46.0ms	(log (exp (+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1))))

series1.2s

Counts

4 → 12

Calls

4 calls:

84.0ms	(* (sin lambda2) (sin lambda1))
494.0ms	(exp (+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1)))
344.0ms	(+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1))
272.0ms	(log (exp (+ (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda2) (sin lambda1)))) (cos phi1))))

simplify969.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5002
2	1454
1	303
0	124

prune674.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

regimes1.1s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	23

end0.0ms

sample14.2s

Algorithm

intervals

Results

9.4s	3615×	body	1280	valid
2.8s	2298×	body	640	valid
908.0ms	975×	body	320	valid
255.0ms	397×	body	160	valid
249.0ms	715×	body	80	valid