Details

sample256.0ms

Algorithm

intervals

Results

175.0ms	156×	body	1280	valid
52.0ms	73×	body	640	valid
5.0ms	2×	body	2560	valid
5.0ms	13×	body	320	valid
2.0ms	8×	body	160	valid
1.0ms	4×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	12
1	39	12
2	44	12
3	45	12
4	45	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: 15.1b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.3b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.4b	(cos (- lambda1 lambda2))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`cos-sum` `*-commutative`
1×	`acos-asin` `cos-diff` `sub-neg` `sin-mult`

Counts

4 → 7

Calls

4 calls:

3.0ms	(* (sin phi1) (sin phi2))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0ms	(cos (- lambda1 lambda2))

series120.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin phi1) (sin phi2))
42.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
16.0ms	(cos (- lambda1 lambda2))

simplify271.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	86	122
1	133	122
2	260	121
3	684	120
4	4497	120
5	5001	120

prune51.0ms

Filtered

19 candidates to 9 candidates (47.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	17	2	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	2	20

Merged error: 3.1b

Counts

20 → 2

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin phi2))
0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.1b	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-commutative`
2×	`sin-mult`
1×	`acos-asin`

Counts

4 → 6

Calls

4 calls:

3.0ms	(* (sin phi1) (sin phi2))
3.0ms	(* (sin lambda1) (sin lambda2))
2.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (sin phi2))
46.0ms	(* (sin lambda1) (sin lambda2))
70.0ms	(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms	(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify22.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	103	164
1	215	164
2	443	164
3	500	164
4	506	164
5	506	164

prune56.0ms

Filtered

18 candidates to 9 candidates (50.0%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	18	2	20

Merged error: 3.0b

Counts

20 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.2b	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.9b	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

2×	`asin-acos` `flip3--` `associate-l/` `-commutative` `flip--`
1×	`sub-neg` `fma-neg` `div-inv` `sin-mult` `associate--r-`

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
2.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
4.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series277.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin lambda1) (sin lambda2))
163.0ms	(* (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))) R)
16.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
52.0ms	(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 5 (103.0ms)

Iter	Nodes	Cost
0	152	448
1	344	435
2	807	429
3	1443	426
4	3657	424
5	5001	412

prune133.0ms

Filtered

24 candidates to 14 candidates (58.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	18	6	24
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	19	7	26

Merged error: 2.8b

Counts

26 → 7

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin lambda1) (sin lambda2))
0.3b	(* R (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.4b	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.8b	(fma PI (* 1/2 R) (- (* R (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`*-commutative`
1×	`asin-acos` `fma-udef` `sin-mult`

Counts

4 → 5

Calls

4 calls:

3.0ms	(* (sin lambda1) (sin lambda2))
3.0ms	(* R (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
2.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
1.0ms	(fma PI (* 1/2 R) (- (* R (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))

series188.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin lambda1) (sin lambda2))
41.0ms	(* R (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
16.0ms	(asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
85.0ms	(fma PI (* 1/2 R) (- (* R (asin (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	116	224
1	272	224
2	619	224
3	858	223
4	1280	223
5	2203	223
6	2431	223
7	2657	223
8	3002	223
9	5002	223

prune53.0ms

Filtered

17 candidates to 8 candidates (47.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	15	9	24

Merged error: 2.8b

Counts

24 → 9

regimes366.0ms

Accuracy

0% (0.4b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.7s	4826×	body	1280	valid
1.4s	2044×	body	640	valid
284.0ms	682×	body	320	valid
81.0ms	288×	body	160	valid
34.0ms	9×	body	2560	valid
23.0ms	153×	body	80	valid