Details

sample473.0ms

Algorithm

intervals

Results

314.0ms	140×	body	1280	valid
74.0ms	60×	body	640	valid
18.0ms	25×	body	320	valid
5.0ms	24×	body	80	valid
3.0ms	7×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.0b

localize55.0ms

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))

rewrite65.0ms

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:

16.0ms	(* (sin phi1) (cos phi2))
29.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
9.0ms	(cos (- lambda1 lambda2))
9.0ms	(sin (- lambda1 lambda2))

series222.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin phi1) (cos phi2))
103.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
27.0ms	(cos (- lambda1 lambda2))
34.0ms	(sin (- lambda1 lambda2))

simplify2.1s

Counts

102 → 102

Iterations

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

prune961.0ms

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))

rewrite80.0ms

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:

14.0ms	(* (cos phi1) (sin phi2))
14.0ms	(* (sin phi1) (cos phi2))
38.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
13.0ms	(cos (- lambda1 lambda2))

series273.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (cos phi1) (sin phi2))
63.0ms	(* (sin phi1) (cos phi2))
126.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
24.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

101 → 101

Iterations

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

prune888.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

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)))

rewrite435.0ms

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:

19.0ms	(* (sin phi1) (cos phi2))
17.0ms	(* (sin phi1) (cos phi2))
335.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
61.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

series389.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin phi1) (cos phi2))
53.0ms	(* (sin phi1) (cos phi2))
139.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
135.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))

simplify1.3s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1426
1	391
0	144

prune997.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize94.0ms

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)))))

rewrite156.0ms

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:

17.0ms	(* (sin phi1) (cos phi2))
63.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
65.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
8.0ms	(log (exp (* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin phi1) (cos phi2))
171.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin phi1) (cos phi2)))
141.0ms	(* (* (sin lambda1) (sin lambda2)) (* (sin phi1) (cos phi2)))
143.0ms	(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

prune922.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

regimes673.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample18.8s

Algorithm

intervals

Results

14.0s	4574×	body	1280	valid
3.2s	1943×	body	640	valid
942.0ms	571×	body	320	valid
219.0ms	679×	body	80	valid
121.0ms	233×	body	160	valid