Details

sample270.0ms

Algorithm

intervals

Results

195.0ms	155×	body	1280	valid
40.0ms	62×	body	640	valid
8.0ms	7×	body	160	valid
6.0ms	14×	body	320	valid
2.0ms	18×	body	80	valid

simplify48.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin phi1) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.1b	(cos (- lambda1 lambda2))
2.1b	(sin (- lambda1 lambda2))

rewrite71.0ms

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:

11.0ms	(* (sin phi1) (cos phi2))
32.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))
13.0ms	(sin (- lambda1 lambda2))

series184.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin phi1) (cos phi2))
96.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify4.9s

Counts

98 → 98

Iterations

Useful iterations: done (4.9s)

Iter	Nodes	Cost
0	208	1720
1	398	1383
2	973	1105
3	2377	1020
4	4163	856
done	5000	747

prune371.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.1b	(* (cos lambda1) (sin (- lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.1b	(cos (- lambda1 lambda2))

rewrite103.0ms

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-neg` `distribute-rgt-neg-out` `sin-cos-mult` `flip-+`

Counts

4 → 87

Calls

4 calls:

40.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
17.0ms	(* (cos lambda1) (sin (- lambda2)))
31.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series306.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
54.0ms	(* (cos lambda1) (sin (- lambda2)))
94.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify3.0s

Counts

99 → 99

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	226	1642
1	480	1424
2	1514	1184
3	4810	1086
done	5000	1086

prune545.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 96

Calls

4 calls:

15.0ms	(* (cos lambda1) (sin (- lambda2)))
12.0ms	(* (sin lambda1) (sin lambda2))
43.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
43.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (cos lambda1) (sin (- lambda2)))
46.0ms	(* (sin lambda1) (sin lambda2))
108.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
124.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify1.0s

Counts

108 → 108

Iterations

Useful iterations: 2 (230.0ms)

Iter	Nodes	Cost
0	175	1334
1	428	1306
2	1721	1042
done	5001	1042

prune608.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))
16.2b	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))
16.2b	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))
16.2b	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-div`
22×	`sin-cos-mult` `sin-mult`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

109.0ms	(* (cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))
31.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))
29.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))
32.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

298.0ms	(* (cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))) (cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))
255.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))
260.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))
255.0ms	(cbrt (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2))))

simplify2.1s

Counts

102 → 102

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	141	2434
1	328	2268
2	1008	1915
3	3703	1831
done	5001	1787

prune797.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes459.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	72
1	42	72
done	42	72

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.1s	4666×	body	1280	valid
1.6s	1928×	body	640	valid
247.0ms	526×	body	320	valid
92.0ms	661×	body	80	valid
61.0ms	219×	body	160	valid