Details

sample260.0ms

Algorithm

intervals

Results

190.0ms	145×	body	1280	valid
40.0ms	59×	body	640	valid
10.0ms	22×	body	320	valid
3.0ms	25×	body	80	valid
1.0ms	5×	body	160	valid

simplify42.0ms

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	86	24
done	86	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.1b	(sin (- lambda1 lambda2))

rewrite36.0ms

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:

4.0ms	(* (sin phi1) (cos phi2))
15.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series174.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify4.4s

Counts

98 → 98

Iterations

Useful iterations: 4 (3.6s)

Iter	Nodes	Cost
0	208	1720
1	408	1383
2	1029	1105
3	2665	1020
4	4815	856
done	5000	856

prune383.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite30.0ms

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` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series195.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi1) (sin phi2))
45.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify3.1s

Counts

97 → 97

Iterations

Useful iterations: 3 (806.0ms)

Iter	Nodes	Cost
0	210	1312
1	422	1135
2	1167	936
3	3076	893
done	5001	893

prune506.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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` `sin-cos-mult` `cbrt-unprod`
5×	`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` `unswap-sqr`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div`
1×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 98

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
27.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series319.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi1) (sin phi2))
41.0ms	(* (sin phi1) (cos phi2))
54.0ms	(* (sin lambda1) (sin (- lambda2)))
179.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify1.0s

Counts

110 → 110

Iterations

Useful iterations: done (999.0ms)

Iter	Nodes	Cost
0	212	1595
1	513	1541
2	1900	1302
done	5000	1300

prune632.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
0.3b	(pow (* (sin lambda1) (sin (- lambda2))) 3)
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.5b	(pow (* (cos lambda1) (cos lambda2)) 3)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

88×	`pow1`
36×	`pow-prod-down`
34×	`add-exp-log` `add-cbrt-cube`
18×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr` `pow-prod-up`
6×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity` `distribute-rgt-neg-out`
5×	`sin-neg` `cos-mult` `sin-mult`
4×	`expm1-log1p-u` `pow-pow` `pow-plus` `pow-exp` `log1p-expm1-u` `add-log-exp` `rem-cube-cbrt`
2×	`cube-div` `pow2` `cube-mult` `frac-times` `pow-to-exp` `unpow-prod-down` `unpow3` `cube-prod` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `*-commutative` `sqr-pow`
1×	`distribute-lft-neg-out` `cube-neg` `sqr-neg`

Counts

4 → 132

Calls

4 calls:

19.0ms	(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
4.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
17.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
3.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

series255.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* (sin lambda1) (sin (- lambda2))) (* (sin lambda1) (sin (- lambda2))))
76.0ms	(pow (* (sin lambda1) (sin (- lambda2))) 3)
53.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
63.0ms	(pow (* (cos lambda1) (cos lambda2)) 3)

simplify896.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (209.0ms)

Iter	Nodes	Cost
0	188	1722
1	487	1134
2	1963	1040
done	5000	1040

prune689.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes370.0ms

Accuracy

0% (0.1b 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	36	86
1	48	86
done	48	86

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4646×	body	1280	valid
1.4s	1891×	body	640	valid
277.0ms	572×	body	320	valid
104.0ms	695×	body	80	valid
57.0ms	196×	body	160	valid