Details

sample509.0ms

Algorithm

intervals

Results

379.0ms	148×	body	1280	valid
72.0ms	61×	body	640	valid
18.0ms	19×	body	320	valid
6.0ms	21×	body	80	valid
5.0ms	7×	body	160	valid

simplify90.0ms

Counts

1 → 1

Iterations

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.8b

localize394.0ms

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))

rewrite67.0ms

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:

18.0ms	(* (sin phi2) (cos phi1))
20.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
12.0ms	(cos (- lambda1 lambda2))
12.0ms	(sin (- lambda1 lambda2))

series203.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (sin phi2) (cos phi1))
68.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
39.0ms	(sin (- lambda1 lambda2))

simplify733.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1265
1	424
0	217

prune789.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

localize71.0ms

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))

rewrite73.0ms

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:

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

series207.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (sin lambda1) (cos lambda2))
64.0ms	(* (sin phi2) (cos phi1))
68.0ms	(* (sin phi1) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))

simplify850.0ms

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1531
1	454
0	221

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize98.0ms

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))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

15.0ms	(* (sin lambda1) (cos lambda2))
18.0ms	(* (sin phi2) (cos phi1))
60.0ms	(* (sin phi1) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
11.0ms	(* (sin lambda1) (sin lambda2))

series408.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (sin lambda1) (cos lambda2))
83.0ms	(* (sin phi2) (cos phi1))
180.0ms	(* (sin phi1) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))
58.0ms	(* (sin lambda1) (sin lambda2))

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	2340
1	469
0	183

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize115.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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` `rem-cube-cbrt` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube` `sin-cos-mult`

Counts

4 → 84

Calls

4 calls:

10.0ms	(* (sin phi2) (cos phi1))
8.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (sin phi1))
14.0ms	(pow (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (sin phi1)) 3)
3.0ms	(cbrt (pow (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (sin phi1)) 3))

series772.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (sin phi2) (cos phi1))
218.0ms	(* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (sin phi1))
270.0ms	(pow (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (sin phi1)) 3)
201.0ms	(cbrt (pow (* (fma (sin lambda1) (sin lambda2) (* (cos lambda1) (cos lambda2))) (sin phi1)) 3))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1924
1	361
0	147

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes1.0s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	44
2	44
1	42
0	29

end0.0ms

sample21.4s

Algorithm

intervals

Results

14.0s	4551×	body	1280	valid
5.4s	2024×	body	640	valid
947.0ms	555×	body	320	valid
180.0ms	664×	body	80	valid
164.0ms	206×	body	160	valid