Details

sample166.0ms

Algorithm

intervals

Results

90.0ms	106×	body	1280	valid
43.0ms	90×	body	640	valid
9.0ms	26×	body	320	valid
7.0ms	16×	body	160	valid
2.0ms	18×	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

prune4.0ms

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: 1.0b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.9b	(sin (- lambda1 lambda2))
4.0b	(cos (- 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	(sin (- lambda1 lambda2))
4.0ms	(cos (- lambda1 lambda2))

series145.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
95.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
23.0ms	(sin (- lambda1 lambda2))
16.0ms	(cos (- lambda1 lambda2))

simplify115.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	205	421
1	508	375
2	1327	374
3	3684	374
4	5001	374

prune238.0ms

Filtered

52 candidates to 42 candidates (80.8%)

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: 0.8b

Counts

53 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (cos (- lambda1 lambda2)))
0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0b	(cos (- 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`
5×	`cos-diff`
3×	`associate-r` `associate-l`
2×	`distribute-rgt-in` `cos-sum` `associate-+r+` `distribute-lft-in`
1×	`+-commutative` `sub-neg` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `cos-mult` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

5.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))

series183.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos phi2) (cos (- lambda1 lambda2)))
13.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
95.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
19.0ms	(cos (- lambda1 lambda2))

simplify66.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	242	574
1	728	514
2	2584	513
3	5002	513

prune453.0ms

Filtered

63 candidates to 46 candidates (73.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	64	9	73

Merged error: 0.1b

Counts

73 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (* (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))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

7.0ms	(* (cos phi2) (* (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))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

series344.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (cos phi2) (* (sin lambda1) (sin lambda2)))
20.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2))))))
43.0ms	(* (sin lambda1) (sin lambda2))
217.0ms	(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (* (sin lambda1) (sin lambda2)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	295	862
1	1111	732
2	5001	725

prune384.0ms

Filtered

71 candidates to 53 candidates (74.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	5	71
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	71	9	80

Merged error: 0.1b

Counts

80 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2))))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2)))))))
4.6b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
9×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`add-exp-log` `add-cbrt-cube`
3×	`log-prod` `associate-r` `associate-l` `sum-log` `log-pow`
1×	`+-commutative` `associate-+r+` `exp-prod` `exp-to-pow` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `distribute-lft-out` `unswap-sqr`

Counts

4 → 54

Calls

4 calls:

1.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2))))))))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2)))))))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(atan2 (* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2))))))))
47.0ms	(* (sin lambda1) (sin lambda2))
213.0ms	(+ (cos phi1) (+ (* (cos phi2) (* (cos lambda1) (cos lambda2))) (* (cos phi2) (log (exp (* (sin lambda1) (sin lambda2)))))))
47.0ms	(log (exp (* (sin lambda1) (sin lambda2))))

simplify124.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	263	845
1	816	718
2	3939	706
3	5001	706

prune325.0ms

Filtered

66 candidates to 48 candidates (72.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	66	9	75

Merged error: 0.1b

Counts

75 → 9

regimes388.0ms

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	40	35
1	40	35

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.1s	3488×	body	1280	valid
1.2s	2411×	body	640	valid
312.0ms	933×	body	320	valid
90.0ms	404×	body	160	valid
87.0ms	764×	body	80	valid