Details

sample249.0ms

Algorithm

intervals

Results

175.0ms	136×	body	1280	valid
44.0ms	68×	body	640	valid
10.0ms	23×	body	320	valid
3.0ms	22×	body	80	valid
2.0ms	7×	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: 12.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.5b	(sin (- lambda1 lambda2))
2.6b	(cos (- lambda1 lambda2))

rewrite36.0ms

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:

4.0ms	(* (sin phi1) (cos phi2))
16.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(sin (- lambda1 lambda2))
7.0ms	(cos (- lambda1 lambda2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	411	1009
1	1289	778
2	5001	776

prune412.0ms

Filtered

98 candidates to 63 candidates (64.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
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` `*-commutative`
2×	`sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 85

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series196.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
46.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	425	787
1	1480	631
2	5001	628

prune531.0ms

Filtered

97 candidates to 65 candidates (67.0%)

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
6×	`sin-cos-mult`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `sin-mult` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (sin phi1) (cos phi2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
16.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (sin phi1) (cos phi2))
46.0ms	(* (sin phi1) (cos phi2))
109.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
97.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))

simplify53.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	368	836
1	1642	658
2	5001	658

prune584.0ms

Filtered

108 candidates to 66 candidates (61.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
0.2b	(* (cbrt (pow (* (sin phi1) (cos phi2)) 3)) (* (sin lambda1) (sin lambda2)))
0.4b	(pow (* (sin phi1) (cos phi2)) 3)
19.8b	(cbrt (pow (* (sin phi1) (cos phi2)) 3))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1` `add-exp-log`
22×	`add-cbrt-cube`
16×	`cbrt-prod`
12×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`sin-cos-mult`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `unpow-prod-down` `pow-unpow` `cbrt-div` `unpow3` `cube-prod` `sqr-pow`
2×	`frac-times` `pow-pow` `associate-r/` `associate-r` `associate-l/` `pow-exp` `cos-mult` `*-commutative` `sin-mult` `rem-cube-cbrt`
1×	`pow-to-exp` `pow1/3` `rem-cbrt-cube`

Counts

4 → 103

Calls

4 calls:

13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
14.0ms	(* (cbrt (pow (* (sin phi1) (cos phi2)) 3)) (* (sin lambda1) (sin lambda2)))
3.0ms	(pow (* (sin phi1) (cos phi2)) 3)
2.0ms	(cbrt (pow (* (sin phi1) (cos phi2)) 3))

series329.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))
101.0ms	(* (cbrt (pow (* (sin phi1) (cos phi2)) 3)) (* (sin lambda1) (sin lambda2)))
68.0ms	(pow (* (sin phi1) (cos phi2)) 3)
47.0ms	(cbrt (pow (* (sin phi1) (cos phi2)) 3))

simplify65.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	440	861
1	2093	757
2	5001	757

prune650.0ms

Filtered

115 candidates to 78 candidates (67.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes416.0ms

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	40	32
1	40	32

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.9s	4485×	body	1280	valid
1.5s	2037×	body	640	valid
267.0ms	559×	body	320	valid
95.0ms	702×	body	80	valid
62.0ms	217×	body	160	valid