Details

sample179.0ms

Algorithm

intervals

Results

111.0ms	117×	body	1280	valid
37.0ms	71×	body	640	valid
12.0ms	33×	body	320	valid
3.0ms	24×	body	80	valid
2.0ms	11×	body	160	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: 0.6b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (cos (- lambda1 lambda2)))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.5b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite18.0ms

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

Counts

4 → 54

Calls

4 calls:

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

series196.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
98.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
21.0ms	(cos (- lambda1 lambda2))
21.0ms	(sin (- lambda1 lambda2))

simplify67.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	254	414
1	744	380
2	2615	380
3	5002	380

prune256.0ms

Filtered

66 candidates to 49 candidates (74.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	54	12	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	12	67

Merged error: 0.5b

Counts

67 → 12

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 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)))))
3.6b	(sin (- lambda1 lambda2))

rewrite15.0ms

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

Counts

4 → 49

Calls

4 calls:

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

series301.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
49.0ms	(* (sin lambda1) (sin lambda2))
213.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
24.0ms	(sin (- lambda1 lambda2))

simplify99.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	266	635
1	830	549
2	3809	549
3	5002	549

prune415.0ms

Filtered

61 candidates to 45 candidates (73.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Merged error: 0.1b

Counts

73 → 13

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin 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)))))

rewrite21.0ms

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

Counts

4 → 62

Calls

4 calls:

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

series447.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
18.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
49.0ms	(* (sin lambda1) (sin lambda2))
248.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	376	922
1	1530	827
2	5001	827

prune310.0ms

Filtered

74 candidates to 53 candidates (71.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	75	12	87

Merged error: 0.1b

Counts

87 → 12

localize32.0ms

Local error

Found 4 expressions with local error:

3.5b	(cos (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))
3.5b	(cos (- lambda1 lambda2))
3.6b	(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))

series73.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cos (- lambda1 lambda2))
21.0ms	(cos (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify53.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (49.0ms)

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

prune278.0ms

Filtered

52 candidates to 40 candidates (76.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	52	12	64

Merged error: 0.1b

Counts

64 → 12

regimes423.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	30
1	28	30

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.3s	3567×	body	1280	valid
1.2s	2320×	body	640	valid
348.0ms	966×	body	320	valid
94.0ms	411×	body	160	valid
78.0ms	736×	body	80	valid

Details

sample179.0ms

simplify5.0ms

prune3.0ms

localize20.0ms

rewrite18.0ms

series196.0ms

simplify67.0ms

prune256.0ms

localize28.0ms

rewrite15.0ms

series301.0ms

simplify99.0ms

prune415.0ms

localize55.0ms

rewrite21.0ms

series447.0ms

simplify54.0ms

prune310.0ms

localize32.0ms

rewrite17.0ms

series73.0ms

simplify53.0ms

prune278.0ms

regimes423.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.4s

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