Details

analyze2.5s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample310.0ms

Algorithm

intervals

Results

231.0ms	155×	body	1280	valid
49.0ms	55×	body	640	valid
9.0ms	17×	body	320	valid
4.0ms	25×	body	80	valid
2.0ms	4×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	24
1	29	24

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.2b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(sin (- lambda1 lambda2))
3.4b	(cos (- lambda1 lambda2))

rewrite19.0ms

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

Counts

4 → 57

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series44.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos phi1) (sin phi2))
25.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5214	577

prune183.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	53	16	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	55	16	71

Merged error: 7.2b

Counts

71 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.4b	(cos (- lambda1 lambda2))

rewrite21.0ms

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` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`cos-diff`
2×	`sub-neg` `*-commutative`
1×	`distribute-rgt-in` `cos-sum` `flip3--` `distribute-lft-in` `diff-log` `associate-*l/` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

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

series51.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos phi1) (sin phi2))
17.0ms	(- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))
22.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5028	722

prune157.0ms

Filtered

50 candidates to 71 candidates (-42.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Merged error: 0.1b

Counts

87 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

6.0ms	(* (cos lambda2) (* (sin phi1) (cos phi2)))
10.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
6.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))
9.0ms	(* (sin lambda1) (* (sin lambda2) (* (sin phi1) (cos phi2))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (cos lambda2) (* (sin phi1) (cos phi2)))
27.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
16.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))
25.0ms	(* (sin lambda1) (* (sin lambda2) (* (sin phi1) (cos phi2))))

simplify65.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5275	946

prune158.0ms

Filtered

58 candidates to 94 candidates (-62.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	95	11	106

Merged error: 0.1b

Counts

106 → 11

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))
0.2b	(* (cos lambda2) (* (sin phi1) (cos phi2)))
0.2b	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
2.7b	(log (pow (pow (exp (sin lambda2)) (* (sin phi1) (cos phi2))) (sin lambda1)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
18×	`pow1` `add-cbrt-cube`
11×	`log-prod`
10×	`unpow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
5×	`rem-log-exp`
4×	`pow-exp`
3×	`associate-*r/`
2×	`pow-to-exp` `associate-r` `*-commutative` `sin-cos-mult` `sqr-pow`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--`

Counts

4 → 76

Calls

4 calls:

4.0ms	(- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))
6.0ms	(* (cos lambda2) (* (sin phi1) (cos phi2)))
8.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
5.0ms	(log (pow (pow (exp (sin lambda2)) (* (sin phi1) (cos phi2))) (sin lambda1)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))
16.0ms	(* (cos lambda2) (* (sin phi1) (cos phi2)))
27.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
51.0ms	(log (pow (pow (exp (sin lambda2)) (* (sin phi1) (cos phi2))) (sin lambda1)))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5015	1087

prune95.0ms

Filtered

63 candidates to 88 candidates (-39.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	86	13	99

Merged error: 0.1b

Counts

99 → 13

regimes689.0ms

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	35	46
1	35	46

end0.0ms

analyze2.8s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample8.9s

Algorithm

intervals

Results

6.5s	4621×	body	1280	valid
1.6s	1959×	body	640	valid
275.0ms	515×	body	320	valid
108.0ms	693×	body	80	valid
82.0ms	212×	body	160	valid

Details

analyze2.5s

sample310.0ms

simplify3.0ms

prune15.0ms

localize26.0ms

rewrite19.0ms

series44.0ms

simplify46.0ms

prune183.0ms

localize36.0ms

rewrite21.0ms

series51.0ms

simplify44.0ms

prune157.0ms

localize35.0ms

rewrite34.0ms

series87.0ms

simplify65.0ms

prune158.0ms

localize40.0ms

rewrite25.0ms

series110.0ms

simplify47.0ms

prune95.0ms

regimes689.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.8s

sample8.9s

Profiling