Details

sample17.0ms

Algorithm

intervals

Results

4.0ms	48×	body	640	valid
3.0ms	141×	body	80	valid
3.0ms	47×	body	320	valid
1.0ms	20×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	15	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: 12.8b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
3.2b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-/r/`
11×	`div-inv`
9×	`prod-diff` `frac-sub`
8×	`frac-2neg` `clear-num`
6×	`flip--` `flip-+`
5×	`flip3--` `flip3-+`
3×	`fma-neg`
2×	`distribute-lft-out--`
1×	`sub-neg`

Counts

3 → 37

Calls

3 calls:

3.0ms	(/ 1.0 (- x 1.0))
3.0ms	(/ 1.0 (+ x 1.0))
7.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series228.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ 1.0 (- x 1.0))
31.0ms	(/ 1.0 (+ x 1.0))
169.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	392	513
1	1483	423
2	5001	388

prune99.0ms

Filtered

46 candidates to 35 candidates (76.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	2	47

Merged error: 0.4b

Counts

47 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- 1.0) (- x 1.0))
0.0b	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
0.0b	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
28.3b	(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (/ (- 1.0) (- x 1.0)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate-+r+`
5×	`*-commutative`
4×	`prod-diff` `associate-/r/`
2×	`fma-def` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`
1×	`+-commutative` `neg-sub0` `associate-+r-` `neg-mul-1` `sub-neg` `flip3--` `div-sub` `distribute-frac-neg` `associate-/r` `sum-cubes` `flip--` `fma-udef` `associate-/l`

Counts

4 → 27

Calls

4 calls:

3.0ms	(/ (- 1.0) (- x 1.0))
10.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
4.0ms	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
1.0ms	(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (/ (- 1.0) (- x 1.0)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 1.0) (- x 1.0))
21.0ms	(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
72.0ms	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
203.0ms	(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (/ (- 1.0) (- x 1.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	291	213
1	1144	186
2	5002	172

prune115.0ms

Filtered

39 candidates to 30 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	38	3	41

Merged error: 0.0b

Counts

41 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (/ (- 2.0) (pow x 6)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 4)))
0.1b	(/ (/ 2.0 x) x)
0.2b	(/ (- 2.0) (pow x 6))
0.2b	(/ 2.0 (pow x 4))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

288×	`frac-sub`
109×	`frac-2neg` `clear-num`
69×	`sqr-pow`
67×	`associate-/r*`
63×	`associate-/l/`
50×	`associate-/l*`
31×	`neg-mul-1`
27×	`div-inv`
5×	`flip3--` `flip--`
4×	`associate--l+`
3×	`associate--l-`
2×	`neg-sub0` `sub-neg` `times-frac` `div-sub` `prod-diff`
1×	`distribute-frac-neg`

Counts

4 → 177

Calls

4 calls:

18.0ms	(- (- (/ (- 2.0) (pow x 6)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 4)))
3.0ms	(/ (/ 2.0 x) x)
3.0ms	(/ (- 2.0) (pow x 6))
2.0ms	(/ 2.0 (pow x 4))

series175.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (- (/ (- 2.0) (pow x 6)) (/ (/ 2.0 x) x)) (/ 2.0 (pow x 4)))
25.0ms	(/ (/ 2.0 x) x)
52.0ms	(/ (- 2.0) (pow x 6))
39.0ms	(/ 2.0 (pow x 4))

simplify92.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	2636	3800
1	5001	3429

prune469.0ms

Filtered

189 candidates to 119 candidates (63.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	185	4	189
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	186	6	192

Merged error: 0.0b

Counts

192 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (/ (- 2.0) (pow x 6)) (/ 1 (* x (/ x 2.0)))) (/ 2.0 (pow x 4)))
0.2b	(/ (- 2.0) (pow x 6))
0.2b	(/ 2.0 (pow x 4))
0.4b	(/ 1 (* x (/ x 2.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

248×	`frac-sub`
121×	`associate-/r*`
85×	`clear-num`
82×	`frac-2neg`
64×	`sqr-pow`
31×	`neg-mul-1` `div-inv`
25×	`associate-/l*`
21×	`associate-r` `*-commutative`
12×	`associate--l+` `associate-/r/`
10×	`prod-diff`
9×	`associate-*r/`
6×	`times-frac`
5×	`flip3--` `flip--`
3×	`associate--l-` `un-div-inv`
2×	`neg-sub0` `sub-neg` `div-sub`
1×	`distribute-frac-neg` `inv-pow`

Counts

4 → 169

Calls

4 calls:

19.0ms	(- (- (/ (- 2.0) (pow x 6)) (/ 1 (* x (/ x 2.0)))) (/ 2.0 (pow x 4)))
3.0ms	(/ (- 2.0) (pow x 6))
2.0ms	(/ 2.0 (pow x 4))
4.0ms	(/ 1 (* x (/ x 2.0)))

series174.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(- (- (/ (- 2.0) (pow x 6)) (/ 1 (* x (/ x 2.0)))) (/ 2.0 (pow x 4)))
53.0ms	(/ (- 2.0) (pow x 6))
36.0ms	(/ 2.0 (pow x 4))
30.0ms	(/ 1 (* x (/ x 2.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2366	3567
1	5002	3275

prune544.0ms

Filtered

181 candidates to 139 candidates (76.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	2	1	3
Picked	0	1	1
Done	0	2	2
Total	181	6	187

Merged error: 0.0b

Counts

187 → 6

regimes47.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 30.4b

bsearch100.0ms

Steps

Iters	Range		Point
9	0.09117784756913819	2697524.489058797	234.24057061613541
10	-1421.6155834850151	-1.485944467815708e-07	-207.4990042199672

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	22
1	44	22

end0.0ms

sample453.0ms

Algorithm

intervals

Results

158.0ms	1925×	body	640	valid
101.0ms	4194×	body	80	valid
73.0ms	1204×	body	320	valid
32.0ms	677×	body	160	valid