Details

sample467.0ms

Algorithm

intervals

Results

328.0ms	158×	body	1280	valid
99.0ms	57×	body	640	valid
7.0ms	11×	body	320	valid
5.0ms	9×	body	160	valid
4.0ms	21×	body	80	valid

simplify462.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite154.0ms

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:

41.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
38.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
37.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

series298.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
155.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
41.0ms	(sin (- lambda1 lambda2))

simplify7.1s

Counts

98 → 98

Iterations

Useful iterations: done (7.1s)

Iter	Nodes	Cost
0	210	1766
1	403	1430
2	995	1144
3	2481	1059
4	4281	878
done	5000	787

prune614.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.1b

localize65.0ms

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 phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))

rewrite160.0ms

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:

26.0ms	(* (cos phi1) (sin phi2))
54.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
58.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

series444.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (cos phi1) (sin phi2))
187.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
139.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
32.0ms	(cos (- lambda1 lambda2))

simplify4.8s

Counts

98 → 98

Iterations

Useful iterations: 3 (3.0s)

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

prune762.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

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

rewrite196.0ms

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`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `flip3-+` `associate-r/` `associate-l/` `flip-+` `sin-mult` `unswap-sqr`
2×	`frac-add` `cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 92

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
72.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
19.0ms	(* (sin lambda1) (sin lambda2))
86.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (cos phi1) (sin phi2))
201.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
58.0ms	(* (sin lambda1) (sin lambda2))
211.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify1.5s

Counts

104 → 104

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	209	1624
1	570	1526
2	2425	1341
done	5000	1340

prune898.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

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

rewrite154.0ms

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`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/` `unswap-sqr`
2×	`fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 86

Calls

4 calls:

18.0ms	(* (cos phi1) (sin phi2))
66.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
19.0ms	(* (sin lambda1) (sin lambda2))
48.0ms	(* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))

series561.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos phi1) (sin phi2))
183.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
57.0ms	(* (sin lambda1) (sin lambda2))
267.0ms	(* (* (sin phi1) (cos phi2)) (fma (cos lambda1) (cos lambda2) (* (sin lambda1) (sin lambda2))))

simplify1.3s

Counts

98 → 98

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	188	1372
1	439	1326
2	1621	1133
done	5001	1132

prune812.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes336.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	42
1	37	42
done	37	42

end0.0ms

sample18.5s

Algorithm

intervals

Results

12.6s	4602×	body	1280	valid
4.3s	1994×	body	640	valid
525.0ms	511×	body	320	valid
355.0ms	668×	body	80	valid
192.0ms	225×	body	160	valid