Details

sample252.0ms

Algorithm

intervals

Results

171.0ms	140×	body	1280	valid
51.0ms	68×	body	640	valid
10.0ms	17×	body	320	valid
4.0ms	29×	body	80	valid
1.0ms	2×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))
3.5b	(sin (- lambda1 lambda2))

rewrite20.0ms

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

Counts

4 → 59

Calls

4 calls:

5.0ms	(* (cos phi1) (sin phi2))
7.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series178.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
92.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify107.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	286	430
1	1077	367
2	4907	367
3	5001	367

prune324.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite21.0ms

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/`

Counts

4 → 68

Calls

4 calls:

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

series198.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin lambda1) (cos lambda2))
47.0ms	(* (cos phi1) (sin phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify41.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	340	481
1	1343	409
2	5002	409

prune446.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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` `frac-sub` `flip--` `sub-div`
1×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 88

Calls

4 calls:

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

series331.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin lambda1) (cos lambda2))
58.0ms	(* (sin lambda1) (sin (- lambda2)))
44.0ms	(* (cos phi1) (sin phi2))
186.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	505	926
1	2183	804
2	5001	802

prune612.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (sin lambda1) (sin (* -1 lambda2)))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (* (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos lambda2))
5.0ms	(* (sin lambda1) (sin (* -1 lambda2)))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (sin phi1) (* (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)))

series333.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin lambda1) (cos lambda2))
51.0ms	(* (sin lambda1) (sin (* -1 lambda2)))
49.0ms	(* (cos phi1) (sin phi2))
184.0ms	(* (sin phi1) (* (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)))

simplify46.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	417	737
1	1530	624
2	5002	616

prune480.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes418.0ms

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	46	55
1	46	55

end0.0ms

sample8.3s

Algorithm

intervals

Results

6.2s	4624×	body	1280	valid
1.4s	1978×	body	640	valid
255.0ms	540×	body	320	valid
96.0ms	644×	body	80	valid
69.0ms	214×	body	160	valid