Details

analyze2.9s

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

sample293.0ms

Algorithm

intervals

Results

208.0ms	155×	body	1280	valid
55.0ms	75×	body	640	valid
9.0ms	18×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	4×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	19
1	30	19

prune24.0ms

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: 19.8b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.2b	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.5b	(cos (- lambda1 lambda2))

rewrite16.0ms

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×	`*-commutative`
1×	`distribute-rgt-in` `acos-asin` `sub-neg` `cos-sum` `distribute-lft-in` `associate-*l/` `cos-mult` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

3.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
6.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

series66.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
26.0ms	(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))

simplify49.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5031	1022

prune162.0ms

Filtered

48 candidates to 68 candidates (-41.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	55	13	68
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Merged error: 3.3b

Counts

70 → 13

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2))))
0.2b	(* (sin lambda2) (* (cos phi1) (cos phi2)))
0.2b	(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1` `add-exp-log` `add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-l`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`associate-*r/`
4×	`add-log-exp`
3×	`associate-r` `cos-mult` `*-commutative`
1×	`acos-asin`

Counts

4 → 71

Calls

4 calls:

9.0ms	(* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2))))
6.0ms	(* (sin lambda2) (* (cos phi1) (cos phi2)))
9.0ms	(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2))))
16.0ms	(* (sin lambda2) (* (cos phi1) (cos phi2)))
29.0ms	(* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2))))
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (sin lambda1) (* (sin lambda2) (* (cos phi1) (cos phi2)))))))

simplify52.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5376	1067

prune206.0ms

Filtered

54 candidates to 83 candidates (-53.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	73	10	83
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	79	17	96

Merged error: 3.3b

Counts

96 → 17

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi2) (sin lambda2)) (sin lambda1))
0.3b	(pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3)
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (cbrt (pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3)))))
26.8b	(cbrt (pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow-pow` `pow-exp` `add-log-exp` `rem-cube-cbrt`
3×	`pow-unpow` `associate-r`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `sqr-pow`
1×	`acos-asin` `pow-to-exp` `pow1/3` `associate-l` `*-commutative` `rem-cbrt-cube`

Counts

4 → 71

Calls

4 calls:

7.0ms	(* (* (cos phi2) (sin lambda2)) (sin lambda1))
10.0ms	(pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3)
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (cbrt (pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3)))))
4.0ms	(cbrt (pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3))

series118.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* (cos phi2) (sin lambda2)) (sin lambda1))
56.0ms	(pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3)
13.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (cbrt (pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3)))))
30.0ms	(cbrt (pow (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (sin lambda1))) 3))

simplify34.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5153	1106

prune198.0ms

Filtered

54 candidates to 83 candidates (-53.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	83	17	100

Merged error: 3.3b

Counts

100 → 17

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
0.6b	(cbrt (sin lambda1))
1.5b	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (cbrt (sin lambda1))))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
1×	`acos-asin`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt (sin lambda1))
1.0ms	(cbrt (sin lambda1))
2.0ms	(cbrt (sin lambda1))
1.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (cbrt (sin lambda1))))))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin lambda1))
18.0ms	(cbrt (sin lambda1))
20.0ms	(cbrt (sin lambda1))
16.0ms	(acos (+ (* (sin phi1) (sin phi2)) (+ (* (cos lambda1) (* (cos lambda2) (* (cos phi1) (cos phi2)))) (* (* (cbrt (sin lambda1)) (cbrt (sin lambda1))) (* (cos phi1) (* (* (cos phi2) (sin lambda2)) (cbrt (sin lambda1))))))))

simplify31.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4997	517
1	4997	517

prune60.0ms

Filtered

39 candidates to 53 candidates (-35.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	53	17	70

Merged error: 3.3b

Counts

70 → 17

regimes1.3s

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	35
1	37	35

end0.0ms

analyze2.7s

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

sample8.8s

Algorithm

intervals

Results

6.3s	4797×	body	1280	valid
1.6s	2120×	body	640	valid
346.0ms	667×	body	320	valid
95.0ms	281×	body	160	valid
34.0ms	10×	body	2560	valid
21.0ms	125×	body	80	valid
3.0ms	3×	body	1280	invalid
2.0ms	3×	body	640	invalid
0.0ms	1×	body	320	invalid

Details

analyze2.9s

sample293.0ms

simplify3.0ms

prune24.0ms

localize24.0ms

rewrite16.0ms

series66.0ms

simplify49.0ms

prune162.0ms

localize34.0ms

rewrite27.0ms

series87.0ms

simplify52.0ms

prune206.0ms

localize38.0ms

rewrite24.0ms

series118.0ms

simplify34.0ms

prune198.0ms

localize39.0ms

rewrite7.0ms

series72.0ms

simplify31.0ms

prune60.0ms

regimes1.3s

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze2.7s

sample8.8s

Profiling