Details

sample643.0ms

Algorithm

intervals

Results

420.0ms	145×	body	1280	valid
95.0ms	63×	body	640	valid
83.0ms	18×	body	320	valid
6.0ms	21×	body	80	valid
6.0ms	9×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
4	80
3	77
2	47
1	28
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.1b

localize484.0ms

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))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`pow1` `cos-sum` `add-cbrt-cube` `sin-sum` `add-exp-log`
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:

24.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
44.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

series295.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
143.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
32.0ms	(sin (- lambda1 lambda2))

simplify3.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	5008
3	3747
2	1067
1	434
0	210

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.7b

localize73.0ms

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))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow1` `add-cbrt-cube` `add-exp-log`
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:

17.0ms	(* (cos lambda1) (sin lambda2))
17.0ms	(* (sin lambda1) (cos lambda2))
50.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
31.0ms	(cos (- lambda1 lambda2))

series324.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (cos lambda1) (sin lambda2))
84.0ms	(* (sin lambda1) (cos lambda2))
148.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))

simplify2.9s

Counts

97 → 97

Iterations

Iter	Nodes
done	5012
3	4113
2	1225
1	486
0	224

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize110.0ms

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))

rewrite156.0ms

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×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

17.0ms	(* (sin lambda1) (cos lambda2))
65.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
52.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
16.0ms	(* (sin lambda1) (sin lambda2))

series509.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin lambda1) (cos lambda2))
166.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
179.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
85.0ms	(* (sin lambda1) (sin lambda2))

simplify1.8s

Counts

108 → 108

Iterations

Iter	Nodes
done	5001
2	1542
1	420
0	163

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize141.0ms

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))

rewrite16.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 81

Calls

4 calls:

10.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))
1.0ms	(cbrt (cos lambda2))

series741.0ms

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (cbrt (cos lambda2)) (cbrt (cos lambda2)))
186.0ms	(cbrt (cos lambda2))
166.0ms	(cbrt (cos lambda2))
139.0ms	(cbrt (cos lambda2))

simplify4.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
4	4766
3	1197
2	374
1	149
0	68

prune763.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes787.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	42
1	42
0	30

end0.0ms

sample17.1s

Algorithm

intervals

Results

12.4s	4593×	body	1280	valid
3.1s	1988×	body	640	valid
754.0ms	549×	body	320	valid
178.0ms	647×	body	80	valid
98.0ms	223×	body	160	valid