Details

analyze2.8s

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

sample281.0ms

Algorithm

intervals

Results

188.0ms	133×	body	1280	valid
55.0ms	69×	body	640	valid
11.0ms	22×	body	320	valid
8.0ms	25×	body	80	valid
2.0ms	7×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune17.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 12.8b

Counts

2 → 2

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (- lambda1 lambda2)) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b	(cos (- lambda1 lambda2))
3.0b	(sin (- lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `*-commutative` `sin-cos-mult`
1×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `sin-sum` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

7.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sin (- lambda1 lambda2)) (cos phi2))
23.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify46.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4879	620
1	4879	620

prune179.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	56	14	70
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	58	14	72

Merged error: 6.0b

Counts

72 → 14

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
0.1b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.0b	(cos (- lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`cos-diff` `associate-*l/`
2×	`sub-neg` `flip3--` `*-commutative` `flip--`
1×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `diff-log` `sin-cos-mult` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

5.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
6.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

series74.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))
28.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
22.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(cos (- lambda1 lambda2))

simplify27.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5074	943

prune147.0ms

Filtered

54 candidates to 73 candidates (-35.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Merged error: 0.1b

Counts

87 → 9

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
0.2b	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
0.2b	(* (sin lambda1) (* (sin lambda2) (* (sin phi1) (cos phi2))))
0.3b	(* (sin lambda2) (* (sin phi1) (cos phi2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`associate-l`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
5×	`associate-*r/`
4×	`*-commutative` `add-log-exp`
3×	`sin-cos-mult`
2×	`associate-*l/`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 83

Calls

4 calls:

8.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
8.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
9.0ms	(* (sin lambda1) (* (sin lambda2) (* (sin phi1) (cos phi2))))
6.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))

series101.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))) (cos phi2))
30.0ms	(* (cos lambda1) (* (cos lambda2) (* (sin phi1) (cos phi2))))
25.0ms	(* (sin lambda1) (* (sin lambda2) (* (sin phi1) (cos phi2))))
17.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))

simplify39.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5400	1121

prune169.0ms

Filtered

65 candidates to 95 candidates (-46.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	96	8	104

Merged error: 0.0b

Counts

104 → 8

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin lambda2) (* (sin phi1) (cos phi2)))
0.3b	(cbrt (cos lambda1))
0.3b	(cbrt (cos lambda1))
0.3b	(cbrt (cos lambda1))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`pow1/3` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-r/` `associate-r` `-commutative` `sin-cos-mult`

Counts

4 → 52

Calls

4 calls:

6.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))
1.0ms	(cbrt (cos lambda1))
1.0ms	(cbrt (cos lambda1))
1.0ms	(cbrt (cos lambda1))

series68.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (sin lambda2) (* (sin phi1) (cos phi2)))
17.0ms	(cbrt (cos lambda1))
17.0ms	(cbrt (cos lambda1))
17.0ms	(cbrt (cos lambda1))

simplify43.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5481	403

prune72.0ms

Filtered

43 candidates to 64 candidates (-48.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	63	9	72

Merged error: 0.0b

Counts

72 → 9

regimes587.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	175	53
1	175	53

end0.0ms

sample9.0s

Algorithm

intervals

Results

6.6s	4623×	body	1280	valid
1.6s	1965×	body	640	valid
293.0ms	559×	body	320	valid
115.0ms	668×	body	80	valid
62.0ms	185×	body	160	valid

Details

analyze2.8s

sample281.0ms

simplify13.0ms

prune17.0ms

localize26.0ms

rewrite25.0ms

series45.0ms

simplify46.0ms

prune179.0ms

localize37.0ms

rewrite24.0ms

series74.0ms

simplify27.0ms

prune147.0ms

localize39.0ms

rewrite33.0ms

series101.0ms

simplify39.0ms

prune169.0ms

localize42.0ms

rewrite11.0ms

series68.0ms

simplify43.0ms

prune72.0ms

regimes587.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.0s

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