Details

sample275.0ms

Algorithm

intervals

Results

199.0ms	146×	body	1280	valid
48.0ms	67×	body	640	valid
7.0ms	16×	body	320	valid
3.0ms	20×	body	80	valid
3.0ms	7×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 11.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(sin (- lambda1 lambda2))
3.3b	(cos (- lambda1 lambda2))

rewrite24.0ms

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

series177.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
25.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify111.0ms

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

prune333.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(cos (- lambda1 lambda2))

rewrite25.0ms

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

Counts

4 → 68

Calls

4 calls:

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

series207.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos lambda1) (sin (- lambda2)))
47.0ms	(* (cos phi1) (sin phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
18.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	338	504
1	1347	428
2	5001	428

prune478.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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

series307.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
50.0ms	(* (sin lambda1) (sin lambda2))
100.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
113.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	420	777
1	1833	599
2	5001	599

prune711.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt` `associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l`
4×	`associate-l/` `-commutative` `sin-cos-mult` `add-log-exp`
2×	`cos-mult`
1×	`frac-times` `associate-*r/` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
26.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
69.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
97.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify65.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	422	787
1	2117	605
2	5001	605

prune416.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes445.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	32
1	41	32

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.2s	4640×	body	1280	valid
1.5s	1986×	body	640	valid
258.0ms	564×	body	320	valid
95.0ms	623×	body	80	valid
55.0ms	187×	body	160	valid