Details

analyze2.0s

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample213.0ms

Algorithm

intervals

Results

133.0ms	124×	body	1280	valid
48.0ms	77×	body	640	valid
12.0ms	27×	body	320	valid
3.0ms	20×	body	80	valid
2.0ms	8×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

prune5.0ms

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: 0.7b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.5b	(sin (- lambda1 lambda2))
2.7b	(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `cos-sum` `distribute-lft-in` `flip3-+` `sin-sum` `sum-log` `sin-diff` `flip-+`

Counts

4 → 38

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series40.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4947	591
1	4947	591

prune147.0ms

Filtered

42 candidates to 50 candidates (-19.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	38	12	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	12	51

Merged error: 0.4b

Counts

51 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.7b	(cos (- lambda1 lambda2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
5×	`cos-diff`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
1×	`+-commutative` `sub-neg` `cos-sum` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `cos-mult` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 50

Calls

4 calls:

5.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

series52.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
10.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
25.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify85.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4831	813
1	4831	813

prune127.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	64	10	74

Merged error: 0.1b

Counts

74 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.4b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
3×	`associate-*r/`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`
1×	`+-commutative` `frac-add` `sum-log` `cos-mult`

Counts

4 → 62

Calls

4 calls:

8.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
13.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))
49.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5013	1270

prune131.0ms

Filtered

53 candidates to 74 candidates (-39.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	74	10	84

Merged error: 0.1b

Counts

84 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(+ (cos phi1) (log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.8b	(log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`log-prod`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
8×	`associate-+r+`
7×	`add-exp-log`
6×	`pow1` `unpow-prod-down` `add-cbrt-cube`
5×	`add-log-exp`
3×	`rem-log-exp` `associate-r` `associate-l`
2×	`unpow-prod-up` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `distribute-lft-out` `unswap-sqr`

Counts

4 → 65

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
9.0ms	(+ (cos phi1) (log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms	(log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
66.0ms	(+ (cos phi1) (log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
43.0ms	(log (pow (exp (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4938	1342
1	4938	1342

prune94.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	77	10	87

Merged error: 0.1b

Counts

87 → 10

regimes573.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	36
1	57	36

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.6s	3603×	body	1280	valid
1.4s	2357×	body	640	valid
370.0ms	948×	body	320	valid
101.0ms	402×	body	160	valid
82.0ms	690×	body	80	valid

Details

analyze2.0s

sample213.0ms

simplify15.0ms

prune5.0ms

localize26.0ms

rewrite13.0ms

series40.0ms

simplify43.0ms

prune147.0ms

localize29.0ms

rewrite14.0ms

series52.0ms

simplify85.0ms

prune127.0ms

localize29.0ms

rewrite20.0ms

series101.0ms

simplify43.0ms

prune131.0ms

localize37.0ms

rewrite20.0ms

series131.0ms

simplify59.0ms

prune94.0ms

regimes573.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.8s

Profiling