Details

sample11.0ms

Algorithm

intervals

Results

6.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	3
1	6	3

prune1.0ms

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: 14.3b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

14.3b

(/ x (+ (* x x) 1.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
3×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
2×	`associate-/r/`
1×	`pow1` `cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `add-log-exp`

Counts

1 → 29

Calls

1 calls:

5.0ms

(/ x (+ (* x x) 1.0))

series60.0ms

Counts

1 → 3

Calls

1 calls:

60.0ms

(/ x (+ (* x x) 1.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	165	210
1	555	195
2	1839	192
3	5001	192

prune60.0ms

Filtered

32 candidates to 26 candidates (81.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	4	33

Merged error: 0b

Counts

33 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
0.0b	(/ x (sqrt (+ (* x x) 1.0)))
14.3b	(sqrt (+ (* x x) 1.0))
14.3b	(sqrt (+ (* x x) 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`associate-/r*`
11×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/l/`

Counts

4 → 262

Calls

4 calls:

15.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
6.0ms	(/ x (sqrt (+ (* x x) 1.0)))
4.0ms	(sqrt (+ (* x x) 1.0))
4.0ms	(sqrt (+ (* x x) 1.0))

series269.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (/ x (sqrt (+ (* x x) 1.0))) (sqrt (+ (* x x) 1.0)))
120.0ms	(/ x (sqrt (+ (* x x) 1.0)))
49.0ms	(sqrt (+ (* x x) 1.0))
44.0ms	(sqrt (+ (* x x) 1.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

274 → 274

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	774	3878
1	2962	3482
2	5001	3411

prune326.0ms

Filtered

274 candidates to 146 candidates (53.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	274	0	274
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	274	4	278

Merged error: 0b

Counts

278 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1 (pow x 5))
0.1b	(/ 1 (pow x 3))
22.4b	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

195×	`add-sqr-sqrt`
173×	`times-frac`
111×	`*-un-lft-identity`
63×	`difference-of-squares`
56×	`unpow-prod-down`
46×	`add-cube-cbrt`
40×	`sqr-pow`
26×	`cube-prod`
21×	`add-exp-log`
19×	`associate-/r*`
12×	`div-exp`
7×	`add-cbrt-cube` `distribute-lft-out--`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `div-inv` `associate-/l*`
5×	`add-log-exp`
4×	`cube-mult` `unpow3`
3×	`pow1`
2×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `inv-pow`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--`

Counts

3 → 209

Calls

3 calls:

5.0ms	(/ 1 (pow x 5))
5.0ms	(/ 1 (pow x 3))
43.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series165.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ 1 (pow x 5))
31.0ms	(/ 1 (pow x 3))
91.0ms	(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify61.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	546	1643
1	2035	1390
2	5001	1390

prune199.0ms

Filtered

218 candidates to 76 candidates (34.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	218	4	222

Merged error: 0b

Counts

222 → 4

localize6.0ms

Local error

Found 2 expressions with local error:

2.7b	(/ (sqrt x) (+ (* x x) 1.0))
4.2b	(* (sqrt x) (/ (sqrt x) (+ (* x x) 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
29×	`sqrt-prod`
24×	`associate-r`
9×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`pow1` `associate-/r/`
3×	`associate-/r*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 91

Calls

2 calls:

6.0ms	(/ (sqrt x) (+ (* x x) 1.0))
13.0ms	(* (sqrt x) (/ (sqrt x) (+ (* x x) 1.0)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(/ (sqrt x) (+ (* x x) 1.0))
57.0ms	(* (sqrt x) (/ (sqrt x) (+ (* x x) 1.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	374	834
1	1666	727
2	5001	703

prune134.0ms

Filtered

97 candidates to 65 candidates (67.0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	97	4	101

Merged error: 0b

Counts

101 → 4

regimes47.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.6b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	22
1	33	22

end0.0ms

sample269.0ms

Algorithm

intervals

Results

176.0ms

8000×

body

valid