Details

sample577.0ms

Algorithm

intervals

Results

428.0ms	145×	body	1280	valid
92.0ms	63×	body	640	valid
16.0ms	18×	body	320	valid
6.0ms	21×	body	80	valid
6.0ms	9×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	79
4	79
3	71
2	46
1	27
0	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(cos (- lambda1 lambda2))
2.1b	(sin (- lambda1 lambda2))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

35.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
17.0ms	(sin (- lambda1 lambda2))

series303.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
150.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
33.0ms	(sin (- lambda1 lambda2))

simplify1.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1355
1	272
0	116

prune741.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.7b

localize75.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(cos (- lambda1 lambda2))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

19.0ms	(* (cos lambda1) (sin lambda2))
14.0ms	(* (sin lambda1) (cos lambda2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series315.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (cos lambda1) (sin lambda2))
60.0ms	(* (sin lambda1) (cos lambda2))
141.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify1.3s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1752
1	357
0	148

prune853.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize115.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.3b	(* (sin lambda1) (sin lambda2))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
52.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
66.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
11.0ms	(* (sin lambda1) (sin lambda2))

series468.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin lambda1) (cos lambda2))
140.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
192.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
75.0ms	(* (sin lambda1) (sin lambda2))

simplify1.7s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1913
1	412
0	155

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize133.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))
0.3b	(cbrt (cos lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

11.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))

series675.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
157.0ms	(cbrt (cos lambda2))
137.0ms	(cbrt (cos lambda2))
133.0ms	(cbrt (cos lambda2))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
2	622
1	146
0	64

prune951.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	28

end0.0ms

sample17.3s

Algorithm

intervals

Results

13.3s	4593×	body	1280	valid
2.9s	1988×	body	640	valid
470.0ms	549×	body	320	valid
138.0ms	647×	body	80	valid
110.0ms	223×	body	160	valid