Details

sample277.0ms

Algorithm

intervals

Results

204.0ms	152×	body	1280	valid
44.0ms	61×	body	640	valid
6.0ms	27×	body	80	valid
5.0ms	11×	body	320	valid
2.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(sin (- lambda1 lambda2))
2.7b	(cos (- lambda1 lambda2))

rewrite31.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

11.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series192.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))

simplify105.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	260	456
1	1016	389
2	4756	389
3	5001	389

prune319.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.7b	(cos (- lambda1 lambda2))

rewrite38.0ms

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` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip--`

Counts

4 → 70

Calls

4 calls:

16.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (sin phi1) (cos phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series272.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
40.0ms	(* (sin phi1) (cos phi2))
86.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	322	653
1	1423	557
2	5001	557

prune431.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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

Counts

4 → 88

Calls

4 calls:

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

series291.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin phi1) (cos phi2))
47.0ms	(* (sin phi1) (cos phi2))
96.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
108.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	361	788
1	1627	610
2	5001	610

prune680.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

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 phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
2.3b	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
2.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

series342.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin phi1) (cos phi2))
93.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
106.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
97.0ms	(log (exp (* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	380	846
1	1725	657
2	5001	655

prune422.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes394.0ms

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	37	31
1	37	31

end0.0ms

sample8.5s

Algorithm

intervals

Results

6.3s	4616×	body	1280	valid
1.5s	1919×	body	640	valid
259.0ms	550×	body	320	valid
97.0ms	699×	body	80	valid
68.0ms	216×	body	160	valid