Details

sample52.0ms

Algorithm

intervals

Results

22.0ms	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

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	19	5

prune2.0ms

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

localize14.0ms

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))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

2×	`*-commutative`
1×	`sub-neg` `flip3--` `flip--`

Counts

3 → 6

Calls

3 calls:

4.0ms	(- (* x (cos y)) (* z (sin y)))
2.0ms	(* x (cos y))
3.0ms	(* z (sin y))

series137.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(- (* x (cos y)) (* z (sin y)))
34.0ms	(* x (cos y))
35.0ms	(* z (sin y))

simplify103.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	62
1	195	62
2	531	62
3	974	62
4	2017	62
5	5002	62

prune27.0ms

Filtered

15 candidates to 8 candidates (53.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	2	16

Merged error: 0.1b

Counts

16 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
2.1b	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
2.9b	(- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
38.5b	(/ (- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

5×	`+-commutative`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `sqr-pow`
3×	`flip3-+` `flip-+`
2×	`difference-cubes` `flip3--` `associate-r/` `associate-l` `associate-/r/` `-commutative` `flip--` `associate-/l/` `associate-/l*` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

4 → 32

Calls

4 calls:

15.0ms	(+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
8.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
6.0ms	(- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
19.0ms	(/ (- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

series606.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
105.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
183.0ms	(- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3))
195.0ms	(/ (- (pow (* x (cos y)) 3) (pow (* z (sin y)) 3)) (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

simplify56.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	306	608
1	1310	595
2	5001	594

prune294.0ms

Filtered

44 candidates to 35 candidates (79.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	41	5	46

Merged error: 0.1b

Counts

46 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
2.1b	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
2.1b	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
38.5b	(/ (* (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (- (* x (cos y)) (* (sin y) z))) (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`+-commutative` `flip3-+` `flip-+`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
5×	`*-commutative`
4×	`frac-times` `associate-+l+` `associate-l`
3×	`flip3--` `flip--`
2×	`associate-l/` `associate-/r/` `associate-/l`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 40

Calls

4 calls:

17.0ms	(+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
7.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
7.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
32.0ms	(/ (* (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (- (* x (cos y)) (* (sin y) z))) (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y))))
101.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
101.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
108.0ms	(/ (* (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (pow x 2) (pow (cos y) 2))) (- (* x (cos y)) (* (sin y) z))) (+ (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))) (* (* x (cos y)) (* x (cos y)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	341	881
1	1669	821
2	5002	795

prune216.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	2	2
Picked	0	1	1
Done	1	1	2
Total	52	5	57

Merged error: 0.1b

Counts

57 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))))
2.1b	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
2.1b	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
28.9b	(/ (+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))) (+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

7×	`+-commutative`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`flip3-+` `flip-+`
4×	`associate-+r+` `associate-r/` `associate-l` `-commutative`
2×	`associate-/r/` `associate-/l/`
1×	`frac-2neg` `*-inverses` `clear-num` `div-inv`

Counts

4 → 33

Calls

4 calls:

13.0ms	(+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))))
8.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
8.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
26.0ms	(/ (+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))) (+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))))

series306.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y)))))
99.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
101.0ms	(* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))
7.0ms	(/ (+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))) (+ (* (pow x 2) (pow (cos y) 2)) (* (* z (sin y)) (+ (* z (sin y)) (* x (cos y))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	199	517
1	903	474
2	5001	474

prune153.0ms

Filtered

45 candidates to 31 candidates (68.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	42	8	50

Merged error: 0.1b

Counts

50 → 8

regimes172.0ms

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	10	5
1	10	5

end0.0ms

sample1.6s

Algorithm

intervals

Results

625.0ms	1497×	body	1280	valid
331.0ms	1267×	body	640	valid
234.0ms	4256×	body	80	valid
114.0ms	657×	body	320	valid
45.0ms	323×	body	160	valid