Details

sample203.0ms

Algorithm

intervals

Results

98.0ms	106×	body	1280	valid
44.0ms	74×	body	640	valid
13.0ms	35×	body	320	valid
9.0ms	15×	body	160	valid
3.0ms	26×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 1.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b	(cos (- lambda1 lambda2))
4.3b	(sin (- 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	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

series43.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
23.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))

simplify125.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	205	421
1	508	374
2	1327	374
3	3685	374
4	5001	374

prune136.0ms

Filtered

52 candidates to 42 candidates (19.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	42	10	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	10	53

Merged error: 0.9b

Counts

53 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.2b	(* (cos lambda1) (sin lambda2))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.2b	(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:

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
8.0ms	(* (cos lambda1) (sin lambda2))
25.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

simplify63.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 1 (8.0ms)

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

prune127.0ms

Filtered

60 candidates to 45 candidates (25.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Merged error: 0.1b

Counts

70 → 9

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) (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)))))

rewrite15.0ms

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:

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) (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)))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos lambda1) (sin lambda2))
12.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))
50.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify127.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 1 (9.0ms)

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

prune126.0ms

Filtered

69 candidates to 49 candidates (29.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	68	10	78

Merged error: 0.1b

Counts

78 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

4.2b	(cos (- lambda1 lambda2))
4.2b	(cos (- lambda1 lambda2))
4.2b	(cos (- lambda1 lambda2))
4.3b	(sin (- lambda1 lambda2))

rewrite16.0ms

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))

series16.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify59.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	83	235
1	149	215
2	390	215
3	1141	215
4	5001	212

prune88.0ms

Filtered

52 candidates to 40 candidates (23.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	52	10	62

Merged error: 0.1b

Counts

62 → 10

regimes599.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	30	22
1	30	22

end0.0ms

sample5.7s

Algorithm

intervals

Results

3.4s	3476×	body	1280	valid
1.3s	2320×	body	640	valid
374.0ms	974×	body	320	valid
119.0ms	434×	body	160	valid
96.0ms	796×	body	80	valid

Details

sample203.0ms

simplify6.0ms

prune5.0ms

localize21.0ms

rewrite13.0ms

series43.0ms

simplify125.0ms

prune136.0ms

localize31.0ms

rewrite14.0ms

series47.0ms

simplify63.0ms

prune127.0ms

localize31.0ms

rewrite15.0ms

series81.0ms

simplify127.0ms

prune126.0ms

localize32.0ms

rewrite16.0ms

series16.0ms

simplify59.0ms

prune88.0ms

regimes599.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.7s

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