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

sample188.0ms

Algorithm

intervals

Results

113.0ms	111×	body	1280	valid
42.0ms	75×	body	640	valid
12.0ms	33×	body	320	valid
3.0ms	27×	body	80	valid
2.0ms	10×	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: 0.6b

Counts

2 → 1

localize21.0ms

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))))
3.8b	(sin (- lambda1 lambda2))
3.8b	(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))

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))))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- 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

prune134.0ms

Filtered

42 candidates to 50 candidates (-19.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	41	9	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	9	51

Merged error: 0.4b

Counts

51 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin 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))))
3.8b	(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`
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` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 47

Calls

4 calls:

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
9.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (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))

simplify72.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5109	730

prune119.0ms

Filtered

45 candidates to 59 candidates (-31.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	60	8	68

Merged error: 0.1b

Counts

68 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

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` `flip-+` `sin-mult`

Counts

4 → 57

Calls

4 calls:

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

series84.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
15.0ms	(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))
50.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4961	985
1	4961	985

prune113.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	69	8	77

Merged error: 0.1b

Counts

77 → 8

localize25.0ms

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)))))
3.8b	(sin (- lambda1 lambda2))
3.8b	(cos (- lambda1 lambda2))

rewrite16.0ms

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	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series58.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))
24.0ms	(log (exp (+ (cos phi1) (* (cos (- lambda1 lambda2)) (cos phi2)))))
4.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify54.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4892	602
1	4892	602

prune75.0ms

Filtered

42 candidates to 57 candidates (-35.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	57	8	65

Merged error: 0.1b

Counts

65 → 8

regimes530.0ms

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

sample5.9s

Algorithm

intervals

Results

3.6s	3591×	body	1280	valid
1.4s	2355×	body	640	valid
375.0ms	947×	body	320	valid
105.0ms	421×	body	160	valid
87.0ms	685×	body	80	valid
2.0ms	1×	body	2560	valid

Details

analyze2.0s

sample188.0ms

simplify15.0ms

prune5.0ms

localize21.0ms

rewrite13.0ms

series46.0ms

simplify42.0ms

prune134.0ms

localize33.0ms

rewrite14.0ms

series46.0ms

simplify72.0ms

prune119.0ms

localize33.0ms

rewrite15.0ms

series84.0ms

simplify44.0ms

prune113.0ms

localize25.0ms

rewrite16.0ms

series58.0ms

simplify54.0ms

prune75.0ms

regimes530.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.9s

Profiling