Details

sample756.0ms

Algorithm

intervals

Results

375.0ms	56×	body	640	valid
333.0ms	155×	body	1280	valid
16.0ms	22×	body	320	valid
4.0ms	18×	body	80	valid
3.0ms	5×	body	160	valid

simplify70.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize68.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.8b	(cos (- lambda1 lambda2))
1.9b	(sin (- lambda1 lambda2))

rewrite96.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 85

Calls

4 calls:

13.0ms	(* (cos phi1) (sin phi2))
38.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
28.0ms	(cos (- lambda1 lambda2))
15.0ms	(sin (- lambda1 lambda2))

series251.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (cos phi1) (sin phi2))
127.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
29.0ms	(cos (- lambda1 lambda2))
28.0ms	(sin (- lambda1 lambda2))

simplify2.8s

Counts

97 → 97

Iterations

Iter	Nodes
done	5004
3	3623
2	1051
1	459
0	222

prune997.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.8b	(cos (- lambda1 lambda2))

rewrite89.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-cos-mult`

Counts

4 → 84

Calls

4 calls:

15.0ms	(* (cos lambda1) (sin lambda2))
16.0ms	(* (cos phi1) (sin phi2))
30.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(cos (- lambda1 lambda2))

series259.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (cos lambda1) (sin lambda2))
69.0ms	(* (cos phi1) (sin phi2))
100.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))

simplify2.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
3	4108
2	1164
1	477
0	222

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize85.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (sin lambda1) (sin lambda2))
58.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series419.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin lambda2))
54.0ms	(* (cos phi1) (sin phi2))
72.0ms	(* (sin lambda1) (sin lambda2))
243.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify1.8s

Counts

102 → 102

Iterations

Iter	Nodes
done	5003
2	2099
1	563
0	197

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize76.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(log1p (* (cos lambda1) (sin lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite95.0ms

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×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`log1p-expm1-u` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative` `sin-mult`
2×	`flip3-+` `frac-add` `cos-mult` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `log1p-udef` `distribute-lft-in` `associate-*l/` `log1p-expm1`

Counts

4 → 81

Calls

4 calls:

14.0ms	(* (cos phi1) (sin phi2))
15.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(log1p (* (cos lambda1) (sin lambda2)))
62.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series562.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos phi1) (sin phi2))
88.0ms	(* (sin lambda1) (sin lambda2))
129.0ms	(log1p (* (cos lambda1) (sin lambda2)))
284.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify2.0s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1968
1	529
0	190

prune953.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes860.0ms

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	34
1	34
0	27

end0.0ms

sample19.7s

Algorithm

intervals

Results

15.1s	4598×	body	1280	valid
3.3s	1974×	body	640	valid
554.0ms	550×	body	320	valid
169.0ms	686×	body	80	valid
100.0ms	192×	body	160	valid