Details

sample1.1s

Algorithm

intervals

Results

919.0ms	140×	body	1280	valid
137.0ms	60×	body	640	valid
36.0ms	25×	body	320	valid
11.0ms	24×	body	80	valid
7.0ms	7×	body	160	valid

simplify81.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	73
4	73
3	69
2	45
1	27
0	17

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(cos (- lambda1 lambda2))
3.2b	(sin (- lambda1 lambda2))

rewrite79.0ms

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` `insert-posit16` `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 → 64

Calls

4 calls:

18.0ms	(* (sin phi1) (cos phi2))
26.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))
24.0ms	(sin (- lambda1 lambda2))

series268.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin phi1) (cos phi2))
144.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))
29.0ms	(sin (- lambda1 lambda2))

simplify2.7s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	3120
2	783
1	272
0	118

prune653.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize74.0ms

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)))
3.1b	(cos (- lambda1 lambda2))

rewrite78.0ms

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×	`insert-posit16` `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 → 72

Calls

4 calls:

10.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (sin phi1) (cos phi2))
49.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
8.0ms	(cos (- lambda1 lambda2))

series300.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos phi1) (sin phi2))
70.0ms	(* (sin phi1) (cos phi2))
151.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(cos (- lambda1 lambda2))

simplify2.6s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
3	3475
2	918
1	325
0	138

prune912.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize108.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

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`
6×	`sin-cos-mult`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `sin-mult` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

10.0ms	(* (sin phi1) (cos phi2))
10.0ms	(* (sin phi1) (cos phi2))
63.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
80.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series390.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin phi1) (cos phi2))
46.0ms	(* (sin phi1) (cos phi2))
168.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
115.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5003
2	1442
1	382
0	138

prune997.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
0.2b	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
4.6b	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1`
30×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r` `associate-l` `sin-cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`log-prod` `log-pow` `*-commutative`
2×	`frac-times` `associate-l/` `associate-r/` `cos-mult` `sin-mult`
1×	`exp-prod` `exp-to-pow` `rem-log-exp` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

10.0ms	(* (sin phi1) (cos phi2))
55.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
76.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
15.0ms	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))

series490.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin phi1) (cos phi2))
150.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
149.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
136.0ms	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))

simplify1.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5001
2	1500
1	418
0	156

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes558.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample23.3s

Algorithm

intervals

Results

16.6s	4574×	body	1280	valid
4.8s	1943×	body	640	valid
729.0ms	571×	body	320	valid
665.0ms	679×	body	80	valid
231.0ms	233×	body	160	valid