Details

sample269.0ms

Algorithm

intervals

Results

195.0ms	150×	body	1280	valid
49.0ms	70×	body	640	valid
6.0ms	12×	body	320	valid
3.0ms	20×	body	80	valid
1.0ms	4×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	15
1	48	15
2	79	15
3	94	15
4	94	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(sin (- lambda1 lambda2))
2.9b	(cos (- lambda1 lambda2))

rewrite37.0ms

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:

8.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	411	1009
1	1289	778
2	5001	776

prune405.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.9b	(cos (- lambda1 lambda2))

rewrite31.0ms

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series202.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos lambda1) (sin (- lambda2)))
47.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify47.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	429	817
1	1608	656
2	5001	655

prune517.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
5×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
17.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin phi1) (cos phi2))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
44.0ms	(* (sin lambda1) (sin lambda2))
112.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	397	830
1	1810	652
2	5001	652

prune555.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (* (sin phi1) (cos phi2))))
0.2b	(* (log1p (expm1 (* (sin phi1) (cos phi2)))) (* (sin lambda1) (sin lambda2)))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-*r/` `cos-mult` `sin-cos-mult` `sin-mult`
1×	`frac-times` `log1p-udef` `log1p-expm1` `associate-*l/` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

0.0ms	(log1p (expm1 (* (sin phi1) (cos phi2))))
8.0ms	(* (log1p (expm1 (* (sin phi1) (cos phi2)))) (* (sin lambda1) (sin lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(log1p (expm1 (* (sin phi1) (cos phi2))))
132.0ms	(* (log1p (expm1 (* (sin phi1) (cos phi2)))) (* (sin lambda1) (sin lambda2)))
49.0ms	(* (sin lambda1) (sin lambda2))
112.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify49.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	358	749
1	1558	593
2	5001	590

prune501.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

regimes348.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	32
1	40	32

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.3s	4635×	body	1280	valid
1.4s	1990×	body	640	valid
252.0ms	544×	body	320	valid
80.0ms	613×	body	80	valid
62.0ms	218×	body	160	valid