Details

analyze1.9s

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

sample185.0ms

Algorithm

intervals

Results

101.0ms	106×	body	1280	valid
49.0ms	84×	body	640	valid
11.0ms	30×	body	320	valid
3.0ms	12×	body	160	valid
3.0ms	24×	body	80	valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

prune15.0ms

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: 0.9b

Counts

2 → 1

localize36.0ms

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))))
2.7b	(cos (- lambda1 lambda2))
2.9b	(sin (- lambda1 lambda2))

rewrite22.0ms

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)))))
7.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
7.0ms	(cos (- lambda1 lambda2))
6.0ms	(sin (- lambda1 lambda2))

series53.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
30.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
6.0ms	(cos (- lambda1 lambda2))
8.0ms	(sin (- lambda1 lambda2))

simplify42.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4947	591
1	4947	591

prune136.0ms

Filtered

42 candidates to 50 candidates (-19.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	39	11	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	11	51

Merged error: 0.7b

Counts

51 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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))

rewrite13.0ms

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

Counts

4 → 48

Calls

4 calls:

4.0ms	(* (sin lambda1) (cos 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))

series45.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(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))

simplify55.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4928	739
1	4928	739

prune120.0ms

Filtered

49 candidates to 60 candidates (-22.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 0.1b

Counts

71 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin lambda1) (cos 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))))))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite16.0ms

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`
2×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-cos-mult` `flip-+` `sin-mult`

Counts

4 → 58

Calls

4 calls:

6.0ms	(* (sin lambda1) (cos 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)))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (sin lambda1) (cos lambda2))
9.0ms	(* (sin lambda1) (sin lambda2))
12.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
47.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4943	994
1	4943	994

prune116.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	70	10	80

Merged error: 0.1b

Counts

80 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
0.7b	(log (exp (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))))
2.7b	(cos (- lambda1 lambda2))
2.9b	(sin (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

4 calls:

4.0ms	(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
4.0ms	(log (exp (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series57.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
24.0ms	(log (exp (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify57.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4892	602
1	4892	602

prune73.0ms

Filtered

43 candidates to 57 candidates (-32.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	57	10	67

Merged error: 0.1b

Counts

67 → 10

regimes544.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	56	34
1	56	34

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.5s	3589×	body	1280	valid
1.3s	2324×	body	640	valid
346.0ms	941×	body	320	valid
105.0ms	409×	body	160	valid
90.0ms	737×	body	80	valid

Details

analyze1.9s

sample185.0ms

simplify25.0ms

prune15.0ms

localize36.0ms

rewrite22.0ms

series53.0ms

simplify42.0ms

prune136.0ms

localize28.0ms

rewrite13.0ms

series45.0ms

simplify55.0ms

prune120.0ms

localize28.0ms

rewrite16.0ms

series76.0ms

simplify52.0ms

prune116.0ms

localize24.0ms

rewrite17.0ms

series57.0ms

simplify57.0ms

prune73.0ms

regimes544.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.6s

Profiling