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

sample192.0ms

Algorithm

intervals

Results

119.0ms	118×	body	1280	valid
42.0ms	75×	body	640	valid
11.0ms	31×	body	320	valid
3.0ms	11×	body	160	valid
2.0ms	21×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	20
1	18	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: 1.2b

Counts

2 → 1

localize25.0ms

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))))
3.2b	(sin (- lambda1 lambda2))
3.2b	(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))

series44.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(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))

simplify73.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4865	591
1	4865	591

prune134.0ms

Filtered

42 candidates to 50 candidates (-19.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	40	10	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	10	51

Merged error: 1.0b

Counts

51 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.2b	(cos (- lambda1 lambda2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

8×	`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` `flip3--` `distribute-lft-in` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 40

Calls

4 calls:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
20.0ms	(- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))
25.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify39.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5385	813

prune112.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	53	9	62

Merged error: 0.1b

Counts

62 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
0.2b	(+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
4×	`sum-log`
3×	`flip3-+` `associate-r` `associate-l` `flip-+` `sin-mult`
2×	`+-commutative` `associate-*r/` `frac-add`
1×	`associate-+l+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
8.0ms	(+ (+ (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))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))
52.0ms	(+ (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))
12.0ms	(* (sin lambda1) (sin lambda2))
29.0ms	(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5053	1219

prune118.0ms

Filtered

47 candidates to 64 candidates (-36.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	64	9	73

Merged error: 0.1b

Counts

73 → 9

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))
0.5b	(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))
0.5b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.7b	(pow (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) 3)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`+-commutative` `unpow-prod-down` `pow-unpow` `cube-prod` `sum-log`
2×	`cube-div` `sub-neg` `associate-+r+`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `pow-pow` `distribute-lft-in` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 60

Calls

4 calls:

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

series171.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))
30.0ms	(+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2))))
54.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
58.0ms	(pow (+ (cos phi1) (* (cos lambda1) (* (cos lambda2) (cos phi2)))) 3)

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5125	1220

prune112.0ms

Filtered

50 candidates to 72 candidates (-44.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	72	9	81

Merged error: 0.0b

Counts

81 → 9

regimes594.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	89
1	56	89

end0.0ms

analyze1.8s

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

sample5.9s

Algorithm

intervals

Results

3.7s	3453×	body	1280	valid
1.4s	2428×	body	640	valid
370.0ms	986×	body	320	valid
102.0ms	417×	body	160	valid
82.0ms	716×	body	80	valid

Details

analyze1.9s

sample192.0ms

simplify3.0ms

prune5.0ms

localize25.0ms

rewrite13.0ms

series44.0ms

simplify73.0ms

prune134.0ms

localize30.0ms

rewrite13.0ms

series59.0ms

simplify39.0ms

prune112.0ms

localize31.0ms

rewrite18.0ms

series108.0ms

simplify49.0ms

prune118.0ms

localize52.0ms

rewrite17.0ms

series171.0ms

simplify42.0ms

prune112.0ms

regimes594.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.8s

sample5.9s

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