Details

sample173.0ms

Algorithm

intervals

Results

110.0ms	122×	body	1280	valid
35.0ms	75×	body	640	valid
9.0ms	28×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	17×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	23	12
2	23	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: 1.2b

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))))
3.7b	(cos (- lambda1 lambda2))
3.8b	(sin (- lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`sin-sum`
4×	`sub-neg`
3×	`distribute-rgt-in` `cos-diff` `distribute-lft-in`
2×	`cos-sum` `associate-+r+`
1×	`+-commutative` `flip3-+` `sin-diff` `*-commutative` `flip-+`

Counts

4 → 16

Calls

4 calls:

4.0ms	(* (cos phi2) (sin (- lambda1 lambda2)))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))
3.0ms	(sin (- lambda1 lambda2))

series193.0ms

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))
22.0ms	(sin (- lambda1 lambda2))

simplify92.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (30.0ms)

Iter	Nodes	Cost
0	162	184
1	403	177
2	1121	174
3	2947	173
4	5001	173

prune93.0ms

Filtered

28 candidates to 16 candidates (57.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	23	5	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	5	29

Merged error: 1.0b

Counts

29 → 5

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (cos lambda2))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.6b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.7b	(cos (- lambda1 lambda2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
7×	`distribute-rgt-in` `distribute-lft-in`
3×	`cos-diff` `sub-neg`
2×	`cos-sum` `associate-+r+` `associate-*r/`
1×	`+-commutative` `flip3--` `flip3-+` `sin-cos-mult` `flip--` `flip-+`

Counts

4 → 25

Calls

4 calls:

5.0ms	(* (sin lambda1) (cos lambda2))
8.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0ms	(cos (- lambda1 lambda2))

series303.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (cos lambda2))
133.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
109.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
16.0ms	(cos (- lambda1 lambda2))

simplify55.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 3 (51.0ms)

Iter	Nodes	Cost
0	245	356
1	671	348
2	2027	337
3	5001	336

prune126.0ms

Filtered

37 candidates to 19 candidates (51.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	33	4	37
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.2b

Counts

42 → 4

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.2b	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
0.2b	(* (sin lambda1) (sin (- lambda2)))
0.7b	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-commutative`
24×	`prod-diff`
18×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-+r+`
6×	`sub-neg` `associate-*r/`
3×	`sin-mult`
2×	`flip3--` `cos-mult` `flip--`
1×	`+-commutative` `flip3-+` `sin-neg` `distribute-rgt-neg-out` `frac-sub` `flip-+` `sub-div`

Counts

4 → 50

Calls

4 calls:

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

series572.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
145.0ms	(* (cos phi2) (- (* (sin lambda1) (cos lambda2)) (* (cos lambda1) (sin lambda2))))
55.0ms	(* (sin lambda1) (sin (- lambda2)))
226.0ms	(+ (cos phi1) (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify92.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	380	792
1	1047	763
2	3901	712
3	5001	705

prune216.0ms

Filtered

62 candidates to 31 candidates (50.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	59	3	62
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	62	4	66

Merged error: 0.2b

Counts

66 → 4

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin (- lambda2)))
0.3b	(* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
0.4b	(/ (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
0.7b	(+ (cos phi1) (/ (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-commutative`
4×	`associate-l` `associate-/l*`
3×	`associate-/r/`
2×	`flip3-+` `flip-+` `fma-udef` `sin-mult`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `frac-add` `sin-neg` `clear-num` `cos-mult` `distribute-rgt-neg-out` `div-inv`

Counts

4 → 21

Calls

4 calls:

4.0ms	(* (sin lambda1) (sin (- lambda2)))
4.0ms	(* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
10.0ms	(/ (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
10.0ms	(+ (cos phi1) (/ (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin lambda1) (sin (- lambda2)))
227.0ms	(* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2))))
310.0ms	(/ (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))
655.0ms	(+ (cos phi1) (/ (* (* (fma (cos lambda2) (cos lambda1) (* (sin lambda1) (sin (* -1 lambda2)))) (cos phi2)) (fma (sin lambda2) (sin lambda1) (* (cos lambda1) (cos lambda2)))) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))

simplify41.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	363	647
1	1269	623
2	5001	550

prune210.0ms

Filtered

33 candidates to 28 candidates (84.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Merged error: 0.2b

Counts

37 → 5

regimes277.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms

sample5.1s

Algorithm

intervals

Results

3.2s	3592×	body	1280	valid
1.2s	2338×	body	640	valid
305.0ms	949×	body	320	valid
84.0ms	401×	body	160	valid
70.0ms	720×	body	80	valid