Details

sample54.0ms

Algorithm

intervals

Results

23.0ms	56×	body	1280	valid
8.0ms	33×	body	640	valid
7.0ms	131×	body	80	valid
4.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	21	5
2	25	5
3	25	5

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: 0.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x (cos y)) (* z (sin y)))
0.1b	(* x (cos y))
0.1b	(* z (sin y))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-commutative`
4×	`prod-diff`
2×	`fma-neg`
1×	`sub-neg` `flip3--` `flip--`

Counts

3 → 12

Calls

3 calls:

5.0ms	(- (* x (cos y)) (* z (sin y)))
2.0ms	(* x (cos y))
2.0ms	(* z (sin y))

series142.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(- (* x (cos y)) (* z (sin y)))
35.0ms	(* x (cos y))
40.0ms	(* z (sin y))

simplify92.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 3 (21.0ms)

Iter	Nodes	Cost
0	86	106
1	263	100
2	721	100
3	1341	84
4	2683	84
5	5003	84

prune38.0ms

Filtered

21 candidates to 11 candidates (52.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	2	22

Merged error: 0.1b

Counts

22 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma x (cos y) (- (* z (sin y))))
0.1b	(* z (sin y))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

1×	`*-commutative` `fma-udef`

Counts

2 → 2

Calls

2 calls:

1.0ms	(fma x (cos y) (- (* z (sin y))))
3.0ms	(* z (sin y))

series107.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(fma x (cos y) (- (* z (sin y))))
36.0ms	(* z (sin y))

simplify7.0ms

Algorithm

egg-herbie

Counts

8 → 8

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	17
1	23	17
2	27	17
3	27	17

prune17.0ms

Filtered

8 candidates to 5 candidates (62.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	8	0	8
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	8	2	10

Merged error: 0.1b

Counts

10 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (cos y)) (* x (cos y)))
0.3b	(pow (* z (sin y)) 3)
2.9b	(- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
38.5b	(/ (- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (fma (* (sin y) z) (fma x (cos y) (* z (sin y))) (* (* x (cos y)) (* x (cos y)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

20×	`unpow-prod-down`
16×	`prod-diff`
15×	`*-commutative`
14×	`sqr-pow`
10×	`unpow3`
4×	`fma-neg`
2×	`difference-cubes` `flip3--` `swap-sqr` `associate-r` `associate-l` `flip--` `associate-/l/` `associate-/l*` `difference-of-squares`
1×	`pow2` `pow-to-exp` `sub-neg` `frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

4 → 47

Calls

4 calls:

5.0ms	(* (* x (cos y)) (* x (cos y)))
3.0ms	(pow (* z (sin y)) 3)
7.0ms	(- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
9.0ms	(/ (- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (fma (* (sin y) z) (fma x (cos y) (* z (sin y))) (* (* x (cos y)) (* x (cos y)))))

series477.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* x (cos y)) (* x (cos y)))
63.0ms	(pow (* z (sin y)) 3)
175.0ms	(- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
186.0ms	(/ (- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (fma (* (sin y) z) (fma x (cos y) (* z (sin y))) (* (* x (cos y)) (* x (cos y)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	275	720
1	1006	613
2	5002	575

prune186.0ms

Filtered

59 candidates to 35 candidates (59.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	57	4	61

Merged error: 0.1b

Counts

61 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin y) z)
0.2b	(* (* x (cos y)) (* x (cos y)))
0.2b	(pow (cos y) 2)
38.5b	(/ (* (fma (* z (sin y)) (fma x (cos y) (* z (sin y))) (* (pow x 2) (pow (cos y) 2))) (- (* x (cos y)) (* (sin y) z))) (fma (* (sin y) z) (fma x (cos y) (* z (sin y))) (* (* x (cos y)) (* x (cos y)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-commutative`
2×	`associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-/l/` `associate-/l`
1×	`pow2` `pow-to-exp` `flip3--` `frac-2neg` `clear-num` `flip--` `div-inv` `unpow2` `sqr-pow`

Counts

4 → 19

Calls

4 calls:

3.0ms	(* (sin y) z)
5.0ms	(* (* x (cos y)) (* x (cos y)))
2.0ms	(pow (cos y) 2)
11.0ms	(/ (* (fma (* z (sin y)) (fma x (cos y) (* z (sin y))) (* (pow x 2) (pow (cos y) 2))) (- (* x (cos y)) (* (sin y) z))) (fma (* (sin y) z) (fma x (cos y) (* z (sin y))) (* (* x (cos y)) (* x (cos y)))))

series185.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sin y) z)
54.0ms	(* (* x (cos y)) (* x (cos y)))
22.0ms	(pow (cos y) 2)
74.0ms	(/ (* (fma (* z (sin y)) (fma x (cos y) (* z (sin y))) (* (pow x 2) (pow (cos y) 2))) (- (* x (cos y)) (* (sin y) z))) (fma (* (sin y) z) (fma x (cos y) (* z (sin y))) (* (* x (cos y)) (* x (cos y)))))

simplify114.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	139	220
1	621	189
2	3083	164
3	5001	164

prune100.0ms

Filtered

31 candidates to 22 candidates (71.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	29	2	31
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	30	5	35

Merged error: 0.1b

Counts

35 → 5

regimes92.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	5
1	15	5
2	15	5

end0.0ms

sample1.5s

Algorithm

intervals

Results

618.0ms	1497×	body	1280	valid
321.0ms	1267×	body	640	valid
246.0ms	4256×	body	80	valid
122.0ms	657×	body	320	valid
44.0ms	323×	body	160	valid