Details

sample263.0ms

Algorithm

intervals

Results

192.0ms	147×	body	1280	valid
40.0ms	57×	body	640	valid
8.0ms	18×	body	320	valid
4.0ms	27×	body	80	valid
2.0ms	7×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0b	(sin (- lambda1 lambda2))
4.4b	(cos (- lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

series179.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos phi1) (sin phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify113.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	286	430
1	1077	367
2	4907	367
3	5001	367

prune329.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.5b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.4b	(cos (- lambda1 lambda2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

13.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series493.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (+ (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin (- lambda2)))) (cos phi2))
49.0ms	(* (cos phi1) (sin phi2))
297.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify50.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	387	676
1	1684	576
2	5002	575

prune477.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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*`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
4.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos phi1) (sin phi2))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
49.0ms	(* (sin lambda1) (sin lambda2))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	420	779
1	1833	601
2	5001	599

prune498.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
25.3b	(cbrt (pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1` `add-exp-log` `add-cbrt-cube`
17×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
7×	`sin-mult`
6×	`cube-div` `sin-cos-mult`
5×	`pow-pow` `pow-exp` `rem-cube-cbrt`
4×	`associate-r` `associate-l` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-r/` `associate-l/`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

16.0ms	(pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
4.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
5.0ms	(cbrt (pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

series427.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3)
43.0ms	(* (sin lambda1) (sin lambda2))
96.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
98.0ms	(cbrt (pow (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2))) 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	410	827
1	2071	795
2	5002	794

prune575.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes414.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	32
1	41	32

end0.0ms

sample8.2s

Algorithm

intervals

Results

5.9s	4569×	body	1280	valid
1.5s	2015×	body	640	valid
253.0ms	549×	body	320	valid
100.0ms	669×	body	80	valid
56.0ms	198×	body	160	valid