Details

sample267.0ms

Algorithm

intervals

Results

194.0ms	148×	body	1280	valid
46.0ms	66×	body	640	valid
5.0ms	12×	body	320	valid
3.0ms	22×	body	80	valid
2.0ms	8×	body	160	valid

simplify9.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))
2.6b	(sin (- lambda1 lambda2))

rewrite29.0ms

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 (- lambda1 lambda2)) (cos phi2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
106.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
25.0ms	(sin (- lambda1 lambda2))

simplify236.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	416	1032
1	1286	797
2	5002	771

prune410.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(cos (- lambda1 lambda2))

rewrite29.0ms

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` `associate-l/` `-commutative`
2×	`unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 86

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (cos lambda1) (sin lambda2))
8.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series280.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
46.0ms	(* (cos lambda1) (sin lambda2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	462	959
1	1689	784
2	5002	783

prune489.0ms

Filtered

98 candidates to 65 candidates (66.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`sin-cos-mult` `sin-mult`
4×	`expm1-log1p-u` `frac-times` `associate-r/` `cos-mult` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `associate-*l/` `flip--` `unswap-sqr`
2×	`sub-neg` `prod-diff` `frac-sub` `sub-div`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 99

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
5.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
45.0ms	(* (cos lambda1) (sin lambda2))
56.0ms	(* (sin lambda1) (sin (- lambda2)))
184.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	550	1197
1	2477	1052
2	5001	1051

prune669.0ms

Filtered

111 candidates to 81 candidates (73.0%)

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	(* (cos lambda1) (sin lambda2))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.4b	(log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))

rewrite24.0ms

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×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod` `sin-mult`
4×	`frac-times` `associate-*r/` `cos-mult` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
2×	`sub-neg` `flip3--` `prod-diff` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`log1p-udef` `log1p-expm1` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 88

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
11.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
1.0ms	(log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos lambda1) (sin lambda2))
56.0ms	(* (sin lambda1) (sin (- lambda2)))
182.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
182.0ms	(log1p (* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2)))

simplify63.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	512	1078
1	2241	943
2	5003	936

prune601.0ms

Filtered

100 candidates to 73 candidates (73.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes289.0ms

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	36	28
1	36	28

end0.0ms

sample8.1s

Algorithm

intervals

Results

6.0s	4601×	body	1280	valid
1.4s	2010×	body	640	valid
253.0ms	557×	body	320	valid
89.0ms	633×	body	80	valid
57.0ms	199×	body	160	valid