Details

sample22.0ms

Algorithm

intervals

Results

7.0ms	64×	body	640	valid
3.0ms	45×	body	320	valid
3.0ms	122×	body	80	valid
1.0ms	25×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 16.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (+ x 1.0))
3.6b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

643×	`*-un-lft-identity`
574×	`times-frac`
477×	`add-sqr-sqrt`
378×	`prod-diff`
357×	`add-cube-cbrt`
84×	`associate-/r/`
76×	`distribute-lft-out`
75×	`distribute-lft-out--`
58×	`difference-of-squares`
43×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
20×	`flip--`
19×	`flip3--`
18×	`fma-neg`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `frac-sub`

Counts

2 → 465

Calls

2 calls:

5.0ms	(/ 1.0 (+ x 1.0))
39.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series200.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(/ 1.0 (+ x 1.0))
175.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify174.0ms

Algorithm

egg-herbie

Counts

471 → 471

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	1148	13140
1	3382	9415
2	5002	9365

prune538.0ms

Filtered

471 candidates to 177 candidates (37.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	469	2	471
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	470	2	472

Merged error: 0.2b

Counts

472 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (/ 1 (pow x 4)))
0.1b	(/ (- 2.0) (pow x 6))
0.2b	(/ 1 (pow x 2))
0.4b	(/ 1 (pow x 4))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
113×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
98×	`add-cube-cbrt`
68×	`unpow-prod-down`
47×	`add-exp-log`
25×	`associate-r`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqr-pow`
22×	`associate-/r*`
21×	`div-exp`
16×	`associate-/l*`
15×	`add-cbrt-cube`
10×	`pow-to-exp` `pow-exp` `prod-exp`
9×	`rec-exp` `1-exp`
8×	`neg-mul-1`
7×	`unswap-sqr`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `unpow2` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num`
2×	`pow-flip` `cbrt-unprod` `inv-pow`
1×	`neg-sub0` `div-sub` `associate-r/` `distribute-frac-neg` `pow-prod-down` `un-div-inv` `-commutative`

Counts

4 → 279

Calls

4 calls:

10.0ms	(* 2.0 (/ 1 (pow x 4)))
6.0ms	(/ (- 2.0) (pow x 6))
5.0ms	(/ 1 (pow x 2))
5.0ms	(/ 1 (pow x 4))

series130.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 2.0 (/ 1 (pow x 4)))
52.0ms	(/ (- 2.0) (pow x 6))
15.0ms	(/ 1 (pow x 2))
28.0ms	(/ 1 (pow x 4))

simplify93.0ms

Algorithm

egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	725	1547
1	3260	1256
2	5001	1204

prune490.0ms

Filtered

291 candidates to 145 candidates (49.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	290	1	291
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	291	2	293

Merged error: 0.0b

Counts

293 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
0.0b	(* 2.0 (/ 1 (pow x 4)))
0.1b	(/ (- 2.0) (pow x 6))
0.4b	(/ 1 (pow x 4))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
96×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
81×	`add-cube-cbrt`
56×	`unpow-prod-down`
38×	`add-exp-log`
25×	`associate-r`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
20×	`sqr-pow`
15×	`div-exp`
14×	`associate-/r*`
13×	`add-cbrt-cube` `associate-/l*`
10×	`prod-exp`
8×	`neg-mul-1`
7×	`pow-to-exp` `pow-exp` `unswap-sqr`
6×	`pow1` `rec-exp` `1-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-l` `div-inv`
2×	`frac-2neg` `clear-num` `cbrt-unprod`
1×	`neg-sub0` `pow-flip` `div-sub` `associate-r/` `distribute-frac-neg` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 230

Calls

4 calls:

1.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
11.0ms	(* 2.0 (/ 1 (pow x 4)))
6.0ms	(/ (- 2.0) (pow x 6))
5.0ms	(/ 1 (pow x 4))

series224.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
40.0ms	(* 2.0 (/ 1 (pow x 4)))
46.0ms	(/ (- 2.0) (pow x 6))
32.0ms	(/ 1 (pow x 4))

simplify76.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	631	1390
1	2864	1207
2	5001	1154

prune473.0ms

Filtered

242 candidates to 142 candidates (58.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	242	2	244

Merged error: 0.0b

Counts

244 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
0.2b	(/ 1.0 (- (* x x) (* 1.0 1.0)))
9.6b	(- (/ 1.0 (+ x 1.0)) (* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0)))))
16.2b	(* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

61×	`*-un-lft-identity` `times-frac`
52×	`add-sqr-sqrt`
47×	`add-cube-cbrt`
18×	`fma-neg` `associate-r` `prod-diff`
13×	`add-exp-log` `add-cbrt-cube`
11×	`difference-of-squares`
10×	`associate-/r/`
8×	`associate-/r*`
7×	`distribute-lft-out`
6×	`pow1` `flip3-+` `flip-+` `associate-/l*` `add-log-exp`
5×	`frac-sub` `div-inv`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-l` `associate-*l/` `flip--` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp`
2×	`frac-2neg` `associate-*r/` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative`

Counts

4 → 169

Calls

4 calls:

9.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
5.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
11.0ms	(- (/ 1.0 (+ x 1.0)) (* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0)))))
13.0ms	(* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
53.0ms	(/ 1.0 (- (* x x) (* 1.0 1.0)))
243.0ms	(- (/ 1.0 (+ x 1.0)) (* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0)))))
47.0ms	(* (+ x 1.0) (/ 1.0 (- (* x x) (* 1.0 1.0))))

simplify130.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (105.0ms)

Iter	Nodes	Cost
0	637	1899
1	3701	1689
2	5001	1668

prune385.0ms

Filtered

181 candidates to 148 candidates (81.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	181	2	183

Merged error: 0.0b

Counts

183 → 2

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch112.0ms

Steps

Iters	Range		Point
10	14.716166499582775	2.5158614700293387e+20	206.43994406203456
11	-2193661101726697.2	-1.4639597033977343e-08	-232.232226491263

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	29
1	52	29
2	52	29

end0.0ms

sample545.0ms

Algorithm

intervals

Results

193.0ms	1914×	body	640	valid
113.0ms	4188×	body	80	valid
103.0ms	1268×	body	320	valid
43.0ms	630×	body	160	valid