Details

analyze2.0s

Algorithm: search

sample203.0ms

Algorithm

intervals

Results

127.0ms	127×	body	1280	valid
46.0ms	71×	body	640	valid
8.0ms	22×	body	320	valid
3.0ms	15×	body	160	valid
2.0ms	21×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	21	12
2	21	12

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: 0.8b

Counts

2 → 1

localize27.0ms

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))))
4.8b	(sin (- lambda1 lambda2))
4.9b	(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` `cos-sum` `associate-+r+` `sin-sum`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `flip3-+` `sum-log` `sin-diff` `flip-+`

Counts

4 → 40

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))

series44.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
24.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
5.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- lambda1 lambda2))

simplify122.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	205	421
1	508	374
2	1327	374
3	3684	374
4	5001	374

prune166.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	39	13	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	13	53

Merged error: 0.6b

Counts

53 → 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 phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.9b	(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×	`cos-sum` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 48

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))

series50.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
10.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
27.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify62.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	255	532
1	758	466
2	2312	466
3	5002	466

prune139.0ms

Filtered

45 candidates to 60 candidates (-33.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	62	11	73

Merged error: 0.0b

Counts

73 → 11

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

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:

5.0ms	(* (sin lambda1) (sin lambda2))
5.0ms	(* (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))))))
6.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (cos lambda1) (sin lambda2))
14.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
52.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify125.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	309	746
1	1069	641
2	4897	641
3	5001	641

prune137.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 0.0b

Counts

80 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

4.8b	(sin (- lambda1 lambda2))
4.9b	(cos (- lambda1 lambda2))
4.9b	(cos (- lambda1 lambda2))
4.9b	(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff`
2×	`sin-sum`
1×	`sin-diff`

Counts

4 → 40

Calls

4 calls:

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

series17.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (50.0ms)

Iter	Nodes	Cost
0	83	235
1	149	215
2	390	215
3	1140	215
4	5001	212

prune90.0ms

Filtered

40 candidates to 52 candidates (-30.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	51	11	62

Merged error: 0.0b

Counts

62 → 11

regimes664.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

end0.0ms

analyze2.0s

Algorithm: search

sample6.1s

Algorithm

intervals

Results

3.6s	3545×	body	1280	valid
1.4s	2359×	body	640	valid
605.0ms	940×	body	320	valid
113.0ms	432×	body	160	valid
95.0ms	723×	body	80	valid
2.0ms	1×	body	2560	valid

Details

analyze2.0s

sample203.0ms

simplify5.0ms

prune5.0ms

localize27.0ms

rewrite13.0ms

series44.0ms

simplify122.0ms

prune166.0ms

localize31.0ms

rewrite14.0ms

series50.0ms

simplify62.0ms

prune139.0ms

localize30.0ms

rewrite17.0ms

series87.0ms

simplify125.0ms

prune137.0ms

localize32.0ms

rewrite17.0ms

series17.0ms

simplify56.0ms

prune90.0ms

regimes664.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.0s

sample6.1s

Profiling