Details

sample813.0ms

Algorithm

intervals

Results

618.0ms	153×	body	1280	valid
126.0ms	69×	body	640	valid
18.0ms	17×	body	320	valid
6.0ms	7×	body	160	valid
3.0ms	10×	body	80	valid

simplify98.0ms

Counts

1 → 1

Iterations

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

prune39.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize104.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
11×	`pow1` `add-exp-log` `cos-sum` `sin-sum` `add-cbrt-cube`
6×	`associate-r`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `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 → 86

Calls

4 calls:

66.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
81.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))
29.0ms	(sin (- lambda1 lambda2))

series391.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
181.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
42.0ms	(cos (- lambda1 lambda2))
55.0ms	(sin (- lambda1 lambda2))

simplify6.5s

Counts

98 → 98

Iterations

Iter	Nodes
done	5004
3	4250
2	1097
1	434
0	210

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

localize110.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`cos-sum`
9×	`associate-r` `prod-diff`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 86

Calls

4 calls:

23.0ms	(* (cos lambda1) (sin lambda2))
115.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
53.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
33.0ms	(cos (- lambda1 lambda2))

series562.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (cos lambda1) (sin lambda2))
266.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
181.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
37.0ms	(cos (- lambda1 lambda2))

simplify4.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1425
1	484
0	219

prune1.9s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize156.0ms

Local error

Found 4 expressions with local error:

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

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `*-commutative` `sin-cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-r/` `associate-l/` `sin-mult` `unswap-sqr`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+`
1×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 92

Calls

4 calls:

27.0ms	(* (cos lambda1) (sin lambda2))
36.0ms	(* (sin lambda1) (sin lambda2))
115.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
113.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (cos lambda1) (sin lambda2))
99.0ms	(* (sin lambda1) (sin lambda2))
254.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
369.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify3.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	2178
1	547
0	191

prune1.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize321.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)))
0.3b	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
0.4b	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
0.4b	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

rewrite573.0ms

Algorithm

rewrite-expression-head

Rules

249×	`pow1`
111×	`pow-prod-down`
81×	`add-exp-log` `add-cbrt-cube`
55×	`prod-exp` `cbrt-unprod`
42×	`pow-prod-up`
22×	`cos-mult`
21×	`pow-plus`
20×	`pow-sqr`
8×	`frac-times` `associate-*l/`
6×	`associate-*r/`
5×	`pow2`
4×	`add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l` `-commutative` `log1p-expm1-u` `add-log-exp`
2×	`swap-sqr` `sin-mult`
1×	`pow3`

Counts

4 → 188

Calls

4 calls:

279.0ms	(* (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)))
92.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
89.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
91.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

series569.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1))) (* (cos lambda2) (cos lambda1)))
209.0ms	(* (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))
116.0ms	(* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2)))
111.0ms	(* (* (cos lambda2) (cos lambda1)) (* (cos lambda2) (cos lambda1)))

simplify4.4s

Counts

200 → 200

Iterations

Iter	Nodes
done	5006
2	2663
1	529
0	178

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes1.2s

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	49
1	49
0	38

end0.0ms

sample27.9s

Algorithm

intervals

Results

19.2s	4600×	body	1280	valid
5.7s	1990×	body	640	valid
1.8s	544×	body	320	valid
221.0ms	659×	body	80	valid
153.0ms	207×	body	160	valid