Details

sample559.0ms

Algorithm

intervals

Results

380.0ms	153×	body	1280	valid
114.0ms	58×	body	640	valid
25.0ms	22×	body	320	valid
4.0ms	18×	body	80	valid
2.0ms	5×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	28	24
2	47	24
3	78	24
4	88	24
done	88	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b	(sin (- lambda1 lambda2))
3.1b	(cos (- lambda1 lambda2))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

49.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
73.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
131.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms	(sin (- lambda1 lambda2))
22.0ms	(cos (- lambda1 lambda2))

simplify7.4s

Counts

98 → 98

Iterations

Useful iterations: done (7.4s)

Iter	Nodes	Cost
0	210	1766
1	403	1430
2	995	1144
3	2466	1059
4	4346	878
done	5001	787

prune542.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))

rewrite216.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `sin-cos-mult` `flip-+`

Counts

4 → 86

Calls

4 calls:

23.0ms	(* (cos phi1) (sin phi2))
86.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
78.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))

series420.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cos phi1) (sin phi2))
199.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
126.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
30.0ms	(cos (- lambda1 lambda2))

simplify4.6s

Counts

98 → 98

Iterations

Useful iterations: 3 (2.7s)

Iter	Nodes	Cost
0	230	1609
1	497	1404
2	1548	1150
3	4830	1058
done	5000	1058

prune926.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize80.0ms

Local error

Found 4 expressions with local error:

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

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult` `sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `cos-mult` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div`
1×	`flip3-+` `sin-neg` `distribute-rgt-neg-out` `flip-+`

Counts

4 → 99

Calls

4 calls:

15.0ms	(* (cos phi1) (sin phi2))
51.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
22.0ms	(* (sin lambda1) (sin (- lambda2)))
165.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series614.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos phi1) (sin phi2))
188.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
79.0ms	(* (sin lambda1) (sin (- lambda2)))
294.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.5s

Counts

111 → 111

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	229	1892
1	576	1810
2	2256	1534
done	5000	1500

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (- (sin lambda2)) (cos lambda1))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult` `sin-mult`
4×	`distribute-rgt-in` `expm1-log1p-u` `frac-times` `distribute-lft-in` `associate-r/` `cos-mult` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `fma-udef` `sub-div`
1×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 99

Calls

4 calls:

14.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (- (sin lambda2)) (cos lambda1))))
30.0ms	(* (sin lambda1) (sin (- lambda2)))
117.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series550.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos phi1) (sin phi2))
188.0ms	(* (cos phi2) (fma (sin lambda1) (cos lambda2) (* (- (sin lambda2)) (cos lambda1))))
60.0ms	(* (sin lambda1) (sin (- lambda2)))
252.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.4s

Counts

111 → 111

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	225	1851
1	536	1798
2	2003	1523
done	5001	1490

prune788.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes652.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify13.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	41
1	37	41
2	41	41
3	42	41
done	42	41

end0.0ms

sample19.9s

Algorithm

intervals

Results

14.5s	4656×	body	1280	valid
3.7s	1930×	body	640	valid
623.0ms	568×	body	320	valid
259.0ms	236×	body	160	valid
161.0ms	610×	body	80	valid