Details

sample248.0ms

Algorithm

intervals

Results

167.0ms	137×	body	1280	valid
48.0ms	69×	body	640	valid
12.0ms	16×	body	320	valid
3.0ms	24×	body	80	valid
3.0ms	10×	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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.1b	(sin (- lambda1 lambda2))
3.2b	(cos (- lambda1 lambda2))

rewrite22.0ms

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:

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

series193.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
17.0ms	(cos (- lambda1 lambda2))

simplify107.0ms

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

prune331.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.2b	(cos (- lambda1 lambda2))

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×	`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` `flip3--` `distribute-lft-in` `sin-cos-mult` `flip--`

Counts

4 → 69

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series282.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
133.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	339	641
1	1438	552
2	5002	552

prune446.0ms

Filtered

81 candidates to 55 candidates (67.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin lambda2))
0.1b	(* (sin lambda1) (sin (- lambda2)))
0.2b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

rewrite31.0ms

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×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`flip3--` `associate-*l/` `flip--` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `frac-sub` `sub-div`
1×	`sin-neg` `distribute-rgt-neg-out`

Counts

4 → 89

Calls

4 calls:

4.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin (- lambda2)))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cos lambda1) (sin lambda2))
52.0ms	(* (sin lambda1) (sin (- lambda2)))
324.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
183.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	513	1086
1	2383	947
2	5003	946

prune596.0ms

Filtered

101 candidates to 73 candidates (72.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))
0.6b	(cbrt (sin lambda2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
2.0ms	(cbrt (sin lambda2))
1.0ms	(cbrt (sin lambda2))
2.0ms	(cbrt (sin lambda2))

series386.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (cbrt (sin lambda2)) (cbrt (sin lambda2)))
91.0ms	(cbrt (sin lambda2))
91.0ms	(cbrt (sin lambda2))
93.0ms	(cbrt (sin lambda2))

simplify88.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	154	453
1	551	401
2	3082	369
3	5002	363

prune464.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

regimes496.0ms

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	38	33
1	38	33

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.2s	4642×	body	1280	valid
1.4s	1936×	body	640	valid
275.0ms	559×	body	320	valid
91.0ms	669×	body	80	valid
62.0ms	194×	body	160	valid