Details

sample769.0ms

Algorithm

intervals

Results

487.0ms	145×	body	1280	valid
219.0ms	70×	body	640	valid
25.0ms	19×	body	320	valid
6.0ms	17×	body	80	valid
3.0ms	5×	body	160	valid

simplify47.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.9b

localize61.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.2b	(cos (- lambda1 lambda2))
2.4b	(sin (- lambda1 lambda2))

rewrite68.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

11.0ms	(* (sin phi1) (cos phi2))
36.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))
10.0ms	(sin (- lambda1 lambda2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (sin phi1) (cos phi2))
147.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))
44.0ms	(sin (- lambda1 lambda2))

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	2016
3	2016
2	969
1	433
0	212

prune994.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize76.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.2b	(cos (- lambda1 lambda2))

rewrite108.0ms

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` `insert-posit16` `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 → 89

Calls

4 calls:

11.0ms	(* (cos phi1) (sin phi2))
12.0ms	(* (sin phi1) (cos phi2))
65.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

series291.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cos phi1) (sin phi2))
75.0ms	(* (sin phi1) (cos phi2))
128.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))

simplify1.1s

Counts

101 → 101

Iterations

Iter	Nodes
done	2010
3	2010
2	1103
1	450
0	214

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize132.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `unswap-sqr`

Counts

4 → 100

Calls

4 calls:

10.0ms	(* (sin phi1) (cos phi2))
16.0ms	(* (sin lambda1) (sin lambda2))
50.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
54.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series884.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin phi1) (cos phi2))
52.0ms	(* (sin lambda1) (sin lambda2))
614.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
146.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.4s

Counts

112 → 112

Iterations

Iter	Nodes
done	2006
3	2006
2	1540
1	427
0	163

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize96.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sin-cos-mult` `sin-mult`
2×	`associate-*l/` `unswap-sqr`
1×	`frac-times` `associate-*r/` `cos-mult`

Counts

4 → 94

Calls

4 calls:

18.0ms	(* (sin phi1) (cos phi2))
11.0ms	(* (sin lambda1) (sin lambda2))
73.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
44.0ms	(* (* (cos lambda1) (cos lambda2)) (sin phi1))

series397.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin phi1) (cos phi2))
54.0ms	(* (sin lambda1) (sin lambda2))
166.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
104.0ms	(* (* (cos lambda1) (cos lambda2)) (sin phi1))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	2000
3	2000
2	1319
1	398
0	159

prune1.0s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes622.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	41
1	41
0	29

end0.0ms

sample23.2s

Algorithm

intervals

Results

16.8s	4596×	body	1280	valid
4.6s	1983×	body	640	valid
744.0ms	548×	body	320	valid
586.0ms	660×	body	80	valid
188.0ms	213×	body	160	valid