Details

sample1.1s

Algorithm

intervals

Results

889.0ms	140×	body	1280	valid
101.0ms	60×	body	640	valid
30.0ms	25×	body	320	valid
8.0ms	24×	body	80	valid
6.0ms	7×	body	160	valid

simplify55.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize111.0ms

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))

rewrite118.0ms

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:

12.0ms	(* (sin phi1) (cos phi2))
60.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
22.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin phi1) (cos phi2))
140.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
32.0ms	(cos (- lambda1 lambda2))
37.0ms	(sin (- lambda1 lambda2))

simplify2.6s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	3125
2	969
1	433
0	212

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 5.6b

localize78.0ms

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))

rewrite104.0ms

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:

25.0ms	(* (cos phi1) (sin phi2))
24.0ms	(* (sin phi1) (cos phi2))
43.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
10.0ms	(cos (- lambda1 lambda2))

series312.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos phi1) (sin phi2))
81.0ms	(* (sin phi1) (cos phi2))
121.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify2.5s

Counts

101 → 101

Iterations

Iter	Nodes
done	5001
3	3500
2	1103
1	450
0	214

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

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)))

rewrite184.0ms

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

Counts

4 → 100

Calls

4 calls:

12.0ms	(* (sin phi1) (cos phi2))
22.0ms	(* (sin phi1) (cos phi2))
55.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
92.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin phi1) (cos phi2))
76.0ms	(* (sin phi1) (cos phi2))
170.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
133.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.5s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1426
1	391
0	144

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize136.0ms

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)))))

rewrite235.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
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 → 95

Calls

4 calls:

24.0ms	(* (sin phi1) (cos phi2))
91.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
98.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
19.0ms	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))

series498.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (sin phi1) (cos phi2))
154.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
127.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
162.0ms	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))

simplify1.6s

Counts

107 → 107

Iterations

Iter	Nodes
done	5000
2	1496
1	419
0	164

prune998.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes625.0ms

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

sample22.1s

Algorithm

intervals

Results

15.4s	4574×	body	1280	valid
5.0s	1943×	body	640	valid
931.0ms	571×	body	320	valid
225.0ms	679×	body	80	valid
163.0ms	233×	body	160	valid