Details

sample333.0ms

Algorithm

intervals

Results

178.0ms	116×	body	1280	valid
68.0ms	71×	body	640	valid
42.0ms	15×	body	160	valid
23.0ms	37×	body	320	valid
3.0ms	17×	body	80	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	20
0	14

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize79.0ms

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))))
1.8b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite26.0ms

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)))))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
8.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
140.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
28.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	1522
2	538
1	207
0	97

prune580.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize99.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
0.6b	(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
1.8b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

14.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
8.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

series394.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
164.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))))
26.0ms	(cos (- lambda1 lambda2))
27.0ms	(sin (- lambda1 lambda2))

simplify2.0s

Counts

61 → 61

Iterations

Iter	Nodes
done	5000
3	3578
2	741
1	234
0	109

prune677.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize92.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (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)))))))
1.9b	(sin (- lambda1 lambda2))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

17.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
20.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
16.0ms	(sin (- lambda1 lambda2))

series784.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin lambda1) (sin lambda2))
326.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
342.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
38.0ms	(sin (- lambda1 lambda2))

simplify1.6s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1048
1	298
0	131

prune950.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize93.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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-+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 → 61

Calls

4 calls:

18.0ms	(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))
7.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
18.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

459.0ms	(exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
63.0ms	(* (sin lambda1) (sin lambda2))
346.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
323.0ms	(log (exp (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	5001
2	1222
1	299
0	123

prune736.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.1b

regimes867.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	23

end0.0ms

sample10.9s

Algorithm

intervals

Results

5.5s	3491×	body	1280	valid
3.8s	2417×	body	640	valid
934.0ms	954×	body	320	valid
200.0ms	436×	body	160	valid
108.0ms	702×	body	80	valid