Details

sample273.0ms

Algorithm

intervals

Results

198.0ms	148×	body	1280	valid
48.0ms	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	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize34.0ms

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))

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	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series186.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune336.0ms

Filtered

72 candidates to 51 candidates (70.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

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 phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.6b	(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:

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

series275.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
42.0ms	(* (cos lambda1) (sin lambda2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	339	641
1	1438	552
2	5001	552

prune441.0ms

Filtered

81 candidates to 55 candidates (67.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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))))

rewrite32.0ms

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

Counts

4 → 84

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
4.0ms	(* (cos lambda1) (sin lambda2))
5.0ms	(* (sin lambda1) (sin lambda2))
10.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
42.0ms	(* (cos lambda1) (sin lambda2))
48.0ms	(* (sin lambda1) (sin lambda2))
166.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify72.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	506	945
1	2508	823
2	5001	823

prune567.0ms

Filtered

96 candidates to 65 candidates (67.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(pow (* (sin lambda1) (sin lambda2)) 3)
0.3b	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
27.4b	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`cbrt-prod`
6×	`associate-r`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`
4×	`cube-div` `associate-l` `sin-cos-mult` `add-log-exp`
3×	`frac-times` `pow-unpow` `cbrt-div` `associate-*r/`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `frac-add` `pow-exp` `cos-mult` `*-commutative` `flip-+` `rem-cube-cbrt` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow1/3` `associate-*l/` `rem-cbrt-cube` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
12.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
3.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series331.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin lambda1) (sin lambda2))
66.0ms	(pow (* (sin lambda1) (sin lambda2)) 3)
166.0ms	(* (* (sin phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))
50.0ms	(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify72.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	469	859
1	2493	741
2	5002	740

prune540.0ms

Filtered

99 candidates to 68 candidates (68.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes364.0ms

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	27
1	36	27

end0.0ms

sample8.8s

Algorithm

intervals

Results

6.3s	4601×	body	1280	valid
1.8s	2010×	body	640	valid
273.0ms	557×	body	320	valid
93.0ms	633×	body	80	valid
61.0ms	199×	body	160	valid