Details

sample529.0ms

Algorithm

intervals

Results

387.0ms	148×	body	1280	valid
76.0ms	61×	body	640	valid
24.0ms	19×	body	320	valid
7.0ms	21×	body	80	valid
5.0ms	7×	body	160	valid

simplify80.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
4	95
3	78
2	47
1	28
0	17

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (cos phi1))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
4.6b	(cos (- lambda1 lambda2))
4.6b	(sin (- lambda1 lambda2))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`prod-diff`
11×	`cos-sum` `sin-sum`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `sin-diff`

Counts

4 → 86

Calls

4 calls:

9.0ms	(* (sin phi2) (cos phi1))
24.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
33.0ms	(sin (- lambda1 lambda2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sin phi2) (cos phi1))
74.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
36.0ms	(cos (- lambda1 lambda2))
33.0ms	(sin (- lambda1 lambda2))

simplify723.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1265
1	424
0	217

prune889.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin phi2) (cos phi1))
0.2b	(* (sin phi1) (cos (- lambda1 lambda2)))
4.6b	(cos (- lambda1 lambda2))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cube-cbrt`
11×	`cos-sum`
10×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`associate-r` `associate-l` `prod-diff`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`

Counts

4 → 86

Calls

4 calls:

9.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin phi2) (cos phi1))
13.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
19.0ms	(cos (- lambda1 lambda2))

series255.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (sin lambda1) (cos lambda2))
58.0ms	(* (sin phi2) (cos phi1))
98.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
26.0ms	(cos (- lambda1 lambda2))

simplify814.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1531
1	454
0	221

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`associate-r`
14×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`distribute-lft-neg-in` `distribute-rgt-in` `distribute-rgt-neg-in` `distribute-lft-in`
2×	`sub-neg` `prod-diff` `associate-*r/` `sin-cos-mult`
1×	`neg-mul-1` `flip3--` `distribute-rgt-neg-out` `flip--`

Counts

4 → 98

Calls

4 calls:

21.0ms	(* (sin lambda1) (cos lambda2))
19.0ms	(* (sin phi2) (cos phi1))
80.0ms	(* (sin phi1) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (- (sin lambda2)))))
28.0ms	(* (sin lambda1) (- (sin lambda2)))

series430.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (sin lambda1) (cos lambda2))
72.0ms	(* (sin phi2) (cos phi1))
213.0ms	(* (sin phi1) (- (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (- (sin lambda2)))))
81.0ms	(* (sin lambda1) (- (sin lambda2)))

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	2325
1	490
0	199

prune1.3s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize121.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi2) (cos phi1))
0.2b	(* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))))
0.5b	(pow (* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) 3)
19.8b	(cbrt (pow (* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`cbrt-prod`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-exp` `*-commutative` `fma-udef` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/3` `rem-cbrt-cube` `sin-cos-mult`

Counts

4 → 86

Calls

4 calls:

17.0ms	(* (sin phi2) (cos phi1))
15.0ms	(* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))))
11.0ms	(pow (* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) 3)
5.0ms	(cbrt (pow (* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) 3))

series762.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin phi2) (cos phi1))
205.0ms	(* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1))))
300.0ms	(pow (* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) 3)
190.0ms	(cbrt (pow (* (sin phi1) (fma (sin lambda1) (sin lambda2) (* (cos lambda2) (cos lambda1)))) 3))

simplify1.5s

Counts

98 → 98

Iterations

Iter	Nodes
done	5002
2	1911
1	370
0	152

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes940.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	44
2	44
1	42
0	29

end0.0ms

sample20.2s

Algorithm

intervals

Results

14.9s	4551×	body	1280	valid
3.8s	2024×	body	640	valid
644.0ms	555×	body	320	valid
168.0ms	664×	body	80	valid
109.0ms	206×	body	160	valid