Details

analyze2.1s

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

sample177.0ms

Algorithm

intervals

Results

97.0ms	103×	body	1280	valid
43.0ms	78×	body	640	valid
13.0ms	25×	body	320	valid
5.0ms	19×	body	160	valid
4.0ms	31×	body	80	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

prune10.0ms

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: 1.2b

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)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(cos (- lambda1 lambda2))
4.0b	(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))

series43.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
26.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4947	591
1	4947	591

prune162.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	37	13	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	13	51

Merged error: 1.0b

Counts

51 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin lambda2))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.7b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(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) (- (* (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:

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

simplify70.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5109	730

prune167.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	58	14	72

Merged error: 0.1b

Counts

72 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos 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))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.7b	(+ (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) (- (* (sin lambda1) (cos lambda2)) (* (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)))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos 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))))))
9.0ms	(* (sin lambda1) (sin lambda2))
50.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4961	985
1	4961	985

prune170.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	70	13	83

Merged error: 0.1b

Counts

83 → 13

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

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×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+` `sin-mult`

Counts

4 → 55

Calls

4 calls:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos lambda1) (sin lambda2))
12.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
9.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5077	861

prune90.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	67	13	80

Merged error: 0.1b

Counts

80 → 13

regimes693.0ms

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	58	37
1	58	37

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.4s	3477×	body	1280	valid
1.3s	2441×	body	640	valid
351.0ms	970×	body	320	valid
107.0ms	413×	body	160	valid
80.0ms	699×	body	80	valid

Details

analyze2.1s

sample177.0ms

simplify15.0ms

prune10.0ms

localize21.0ms

rewrite13.0ms

series43.0ms

simplify44.0ms

prune162.0ms

localize30.0ms

rewrite14.0ms

series45.0ms

simplify70.0ms

prune167.0ms

localize29.0ms

rewrite15.0ms

series79.0ms

simplify45.0ms

prune170.0ms

localize31.0ms

rewrite14.0ms

series58.0ms

simplify47.0ms

prune90.0ms

regimes693.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.6s

Profiling