Details

sample257.0ms

Algorithm

intervals

Results

191.0ms	154×	body	1280	valid
38.0ms	56×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	22×	body	80	valid
2.0ms	6×	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: 12.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(cos (- lambda1 lambda2))
2.0b	(sin (- 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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

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

series179.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin phi1) (cos phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
23.0ms	(sin (- lambda1 lambda2))

simplify108.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	254	435
1	1026	372
2	4856	372
3	5001	372

prune323.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0b	(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` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 69

Calls

4 calls:

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

series205.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos lambda1) (sin (- lambda2)))
47.0ms	(* (sin phi1) (cos phi2))
91.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify40.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	306	509
1	1298	433
2	5001	433

prune457.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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

Counts

4 → 89

Calls

4 calls:

8.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
25.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos lambda1) (sin (- lambda2)))
48.0ms	(* (sin phi1) (cos phi2))
53.0ms	(* (sin lambda1) (sin (- lambda2)))
188.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	474	954
1	2246	828
2	5002	826

prune604.0ms

Filtered

101 candidates to 76 candidates (75.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 95

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin (- lambda2)))
18.0ms	(* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
32.0ms	(* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series450.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos lambda1) (sin (- lambda2)))
148.0ms	(* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
59.0ms	(* (sin lambda1) (sin (- lambda2)))
188.0ms	(* (sin phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	421	1166
1	1862	985
2	5001	976

prune569.0ms

Filtered

107 candidates to 79 candidates (73.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes612.0ms

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	46	56
1	46	56

end0.0ms

sample8.2s

Algorithm

intervals

Results

6.2s	4684×	body	1280	valid
1.3s	1863×	body	640	valid
267.0ms	575×	body	320	valid
88.0ms	673×	body	80	valid
58.0ms	205×	body	160	valid