Details

sample798.0ms

Algorithm

intervals

Results

612.0ms	148×	body	1280	valid
127.0ms	64×	body	640	valid
21.0ms	17×	body	320	valid
9.0ms	23×	body	80	valid
3.0ms	4×	body	160	valid

simplify73.0ms

Counts

1 → 1

Iterations

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

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.1b	(cos (- lambda1 lambda2))
5.2b	(sin (- lambda1 lambda2))

rewrite116.0ms

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:

21.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
61.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
16.0ms	(sin (- lambda1 lambda2))

series288.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
139.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
35.0ms	(cos (- lambda1 lambda2))
36.0ms	(sin (- lambda1 lambda2))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	2066
3	2066
2	805
1	276
0	120

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.9b

localize124.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.1b	(cos (- lambda1 lambda2))

rewrite180.0ms

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` `associate-l/` `-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3--` `sin-cos-mult` `flip--`

Counts

4 → 73

Calls

4 calls:

79.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
21.0ms	(* (cos lambda1) (sin lambda2))
62.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

series449.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
75.0ms	(* (cos lambda1) (sin lambda2))
158.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
34.0ms	(cos (- lambda1 lambda2))

simplify1.2s

Counts

85 → 85

Iterations

Iter	Nodes
done	2007
3	2007
2	1183
1	369
0	149

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize142.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

rewrite117.0ms

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

Counts

4 → 91

Calls

4 calls:

38.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
10.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (cos lambda1) (sin lambda2))
57.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series432.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
75.0ms	(* (sin lambda1) (sin lambda2))
46.0ms	(* (cos lambda1) (sin lambda2))
129.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify1.5s

Counts

103 → 103

Iterations

Iter	Nodes
done	2003
3	2003
2	1513
1	415
0	157

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize130.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (cos lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
2.9b	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

11.0ms	(* (sin lambda1) (sin lambda2))
11.0ms	(* (cos lambda1) (sin lambda2))
70.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (sin lambda1) (sin lambda2))
79.0ms	(* (cos lambda1) (sin lambda2))
167.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
154.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify1.2s

Counts

92 → 92

Iterations

Iter	Nodes
done	2001
3	2001
2	960
1	323
0	141

prune2.5s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes723.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	27

end0.0ms

sample23.1s

Algorithm

intervals

Results

16.2s	4509×	body	1280	valid
5.1s	2043×	body	640	valid
657.0ms	555×	body	320	valid
624.0ms	664×	body	80	valid
171.0ms	229×	body	160	valid