Details

sample173.0ms

Algorithm

intervals

Results

98.0ms	112×	body	1280	valid
39.0ms	77×	body	640	valid
17.0ms	37×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	16×	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

prune3.0ms

Filtered

1 candidates to 0 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: 1.3b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (sin (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b	(cos (- lambda1 lambda2))
2.7b	(sin (- lambda1 lambda2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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

series191.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
98.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify76.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	249	435
1	795	393
2	2920	393
3	5001	393

prune262.0ms

Filtered

67 candidates to 49 candidates (73.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	54	13	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	13	68

Merged error: 1.1b

Counts

68 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.6b	(cos (- lambda1 lambda2))

rewrite22.0ms

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`
5×	`cos-diff`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`sub-neg`
2×	`cos-sum` `associate-+r+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `cos-mult` `flip--` `flip-+`

Counts

4 → 68

Calls

4 calls:

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

series307.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
133.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
97.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
20.0ms	(cos (- lambda1 lambda2))

simplify126.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	332	676
1	1175	609
2	4956	609
3	5002	609

prune327.0ms

Filtered

80 candidates to 56 candidates (70.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	82	11	93

Merged error: 0.1b

Counts

93 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `associate-+r+` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `sin-mult`

Counts

4 → 63

Calls

4 calls:

10.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (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)))))

series408.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
21.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
43.0ms	(* (sin lambda1) (sin lambda2))
211.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	345	962
1	1380	833
2	5001	833

prune311.0ms

Filtered

75 candidates to 52 candidates (69.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	72	14	86

Merged error: 0.1b

Counts

86 → 14

localize32.0ms

Local error

Found 4 expressions with local error:

2.6b	(cos (- lambda1 lambda2))
2.6b	(cos (- lambda1 lambda2))
2.6b	(cos (- lambda1 lambda2))
2.7b	(sin (- 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	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series71.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(cos (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify54.0ms

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	1141	215
4	5001	212

prune218.0ms

Filtered

52 candidates to 40 candidates (76.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	52	14	66

Merged error: 0.1b

Counts

66 → 14

regimes466.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	30	22
1	30	22

end0.0ms

sample5.3s

Algorithm

intervals

Results

3.4s	3657×	body	1280	valid
1.2s	2330×	body	640	valid
302.0ms	882×	body	320	valid
91.0ms	406×	body	160	valid
76.0ms	725×	body	80	valid

Details

sample173.0ms

simplify5.0ms

prune3.0ms

localize20.0ms

rewrite20.0ms

series191.0ms

simplify76.0ms

prune262.0ms

localize28.0ms

rewrite22.0ms

series307.0ms

simplify126.0ms

prune327.0ms

localize29.0ms

rewrite22.0ms

series408.0ms

simplify44.0ms

prune311.0ms

localize32.0ms

rewrite17.0ms

series71.0ms

simplify54.0ms

prune218.0ms

regimes466.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.3s

Profiling