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

sample305.0ms

Algorithm

intervals

Results

117.0ms	117×	body	1280	valid
46.0ms	85×	body	640	valid
9.0ms	23×	body	320	valid
2.0ms	22×	body	80	valid
2.0ms	9×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

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: 0.5b

Counts

2 → 1

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.4b	(cos (- lambda1 lambda2))
13.5b	(sin (- 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	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series46.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
27.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))
6.0ms	(sin (- 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

prune144.0ms

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: 0.3b

Counts

51 → 12

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (cos (- lambda1 lambda2)) 3)
0.6b	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
13.4b	(cos (- lambda1 lambda2))
13.5b	(sin (- lambda1 lambda2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`sub-neg`
1×	`+-commutative` `cos-diff` `cube-mult` `pow-to-exp` `cos-sum` `pow-pow` `flip3-+` `sin-sum` `unpow3` `pow-exp` `sum-log` `sin-diff` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 52

Calls

4 calls:

3.0ms	(pow (cos (- lambda1 lambda2)) 3)
4.0ms	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series42.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (cos (- lambda1 lambda2)) 3)
24.0ms	(+ (cos phi1) (* (cos phi2) (cbrt (pow (cos (- lambda1 lambda2)) 3))))
4.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

simplify29.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5166	545

prune144.0ms

Filtered

41 candidates to 64 candidates (-56.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	64	12	76

Merged error: 0.3b

Counts

76 → 12

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
13.4b	(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) (- (* (sin lambda1) (cos lambda2)) (* (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)))
11.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
24.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify86.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4831	813
1	4831	813

prune139.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	9	10
Picked	1	0	1
Done	1	0	1
Total	63	11	74

Merged error: 0.1b

Counts

74 → 11

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.6b	(+ (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:

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
11.0ms	(* (sin lambda1) (sin lambda2))
13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
50.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5013	1270

prune82.0ms

Filtered

54 candidates to 74 candidates (-37.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.1b

Counts

85 → 10

regimes618.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	36
1	57	36

end0.0ms

sample10.4s

Algorithm

intervals

Results

3.7s	3609×	body	1280	valid
1.3s	2305×	body	640	valid
356.0ms	979×	body	320	valid
98.0ms	402×	body	160	valid
79.0ms	705×	body	80	valid

Details

analyze2.0s

sample305.0ms

simplify15.0ms

prune5.0ms

localize38.0ms

rewrite13.0ms

series46.0ms

simplify43.0ms

prune144.0ms

localize44.0ms

rewrite16.0ms

series42.0ms

simplify29.0ms

prune144.0ms

localize54.0ms

rewrite14.0ms

series52.0ms

simplify86.0ms

prune139.0ms

localize54.0ms

rewrite20.0ms

series103.0ms

simplify42.0ms

prune82.0ms

regimes618.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample10.4s

Profiling