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

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: 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)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

662×	`*-un-lft-identity`
589×	`times-frac`
496×	`add-sqr-sqrt`
378×	`prod-diff`
368×	`add-cube-cbrt`
86×	`associate-/r/`
79×	`distribute-lft-out--`
76×	`distribute-lft-out`
62×	`difference-of-squares`
44×	`div-inv`
24×	`flip-+`
23×	`flip3-+`
21×	`flip--`
20×	`flip3--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 504

Calls

3 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
42.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series238.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ 1.0 (- x 1.0))
26.0ms	(/ 1.0 (+ x 1.0))
184.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify180.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1200	13350
1	3593	9620
2	5001	9568

prune882.0ms

Filtered

513 candidates to 209 candidates (40.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	511	2	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	512	2	514

Merged error: 0.4b

Counts

514 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
0.0b	(fma 1.0 (- 1.0 x) (pow x 2))
0.0b	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
28.3b	(fma (fma 1.0 (- 1.0 x) (pow x 2)) (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (/ (- (pow (cbrt 1.0) 3)) (- x 1.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

247×	`*-un-lft-identity`
227×	`times-frac`
207×	`add-sqr-sqrt`
125×	`add-cube-cbrt`
108×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
88×	`unpow-prod-down` `cube-prod`
72×	`cbrt-prod`
43×	`associate-/l*`
41×	`distribute-lft-out--` `difference-of-squares`
20×	`distribute-lft-out`
14×	`associate-/r*`
12×	`cube-mult` `unpow3` `sqr-pow`
8×	`add-exp-log` `add-cbrt-cube`
6×	`neg-mul-1`
4×	`pow1` `expm1-log1p-u` `associate-/r/` `sum-cubes` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`
1×	`neg-sub0` `flip3--` `flip3-+` `div-sub` `distribute-frac-neg` `flip--` `flip-+`

Counts

4 → 338

Calls

4 calls:

19.0ms	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
1.0ms	(fma 1.0 (- 1.0 x) (pow x 2))
14.0ms	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
1.0ms	(fma (fma 1.0 (- 1.0 x) (pow x 2)) (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (/ (- (pow (cbrt 1.0) 3)) (- x 1.0)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- (pow (cbrt 1.0) 3)) (- x 1.0))
23.0ms	(fma 1.0 (- 1.0 x) (pow x 2))
66.0ms	(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
195.0ms	(fma (fma 1.0 (- 1.0 x) (pow x 2)) (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (/ (- (pow (cbrt 1.0) 3)) (- x 1.0)))

simplify160.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	883	3078
1	4786	2802
2	5001	2802

prune914.0ms

Filtered

350 candidates to 163 candidates (46.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	350	0	350
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	350	2	352

Merged error: 0.4b

Counts

352 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

398×	`times-frac`
335×	`add-sqr-sqrt`
327×	`*-un-lft-identity`
325×	`add-cube-cbrt`
222×	`prod-diff`
178×	`unpow-prod-down`
108×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
74×	`fma-neg`
60×	`sqr-pow`
36×	`neg-mul-1`
27×	`add-exp-log`
22×	`associate-/r*`
16×	`associate-/l*`
15×	`div-exp`
10×	`add-cbrt-cube`
7×	`pow-to-exp` `pow-exp` `div-inv`
6×	`rec-exp` `1-exp` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `unpow2` `difference-of-squares`
3×	`cbrt-undiv` `frac-2neg` `clear-num`
2×	`neg-sub0` `pow-flip` `div-sub` `inv-pow`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `distribute-frac-neg` `flip--` `fma-udef` `associate--r+` `distribute-lft-out--`

Counts

4 → 536

Calls

4 calls:

41.0ms	(- (/ (- 2.0) (pow x 6)) (fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4)))))
7.0ms	(/ (- 2.0) (pow x 6))
5.0ms	(/ 1 (pow x 4))
5.0ms	(/ 1 (pow x 2))

series153.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- (/ (- 2.0) (pow x 6)) (fma 2.0 (/ 1 (pow x 2)) (* 2.0 (/ 1 (pow x 4)))))
45.0ms	(/ (- 2.0) (pow x 6))
33.0ms	(/ 1 (pow x 4))
16.0ms	(/ 1 (pow x 2))

simplify191.0ms

Algorithm

egg-herbie

Counts

548 → 548

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1155	12881
1	3830	7373
2	5002	7324

prune997.0ms

Filtered

548 candidates to 234 candidates (42.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	546	2	548
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	547	3	550

Merged error: 0.0b

Counts

550 → 3

localize19.0ms

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) (pow x 6)) (fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4)))))
0.2b	(/ (- 2.0) (pow x 6))
0.2b	(/ 1 (pow x 4))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

374×	`times-frac`
318×	`add-sqr-sqrt`
310×	`*-un-lft-identity`
308×	`add-cube-cbrt`
222×	`prod-diff`
166×	`unpow-prod-down`
108×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
74×	`fma-neg`
56×	`sqr-pow`
36×	`neg-mul-1`
18×	`add-exp-log`
14×	`associate-/r*`
13×	`associate-/l*`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `pow-exp` `log1p-expm1-u` `difference-of-squares`
3×	`rec-exp` `1-exp`
2×	`cbrt-undiv` `neg-sub0` `frac-2neg` `div-sub` `clear-num` `fma-udef`
1×	`associate--l-` `sub-neg` `flip3--` `pow-flip` `diff-log` `distribute-frac-neg` `flip--` `associate--r+` `distribute-lft-out--` `inv-pow`

Counts

4 → 487

Calls

4 calls:

1.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
36.0ms	(- (/ (- 2.0) (pow x 6)) (fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4)))))
7.0ms	(/ (- 2.0) (pow x 6))
5.0ms	(/ 1 (pow x 4))

series257.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4))))
72.0ms	(- (/ (- 2.0) (pow x 6)) (fma 2.0 (pow x (- 2)) (* 2.0 (/ 1 (pow x 4)))))
53.0ms	(/ (- 2.0) (pow x 6))
26.0ms	(/ 1 (pow x 4))

simplify176.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1046	12714
1	3327	7377
2	5002	7208

prune930.0ms

Filtered

499 candidates to 220 candidates (44.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	499	0	499
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	499	3	502

Merged error: 0.0b

Counts

502 → 3

regimes31.0ms

Accuracy

100% (0.0b remaining)

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

bsearch119.0ms

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	55	35
1	60	35
2	60	35

end0.0ms

sample449.0ms

Algorithm

intervals

Results

153.0ms	1925×	body	640	valid
101.0ms	4194×	body	80	valid
78.0ms	1204×	body	320	valid
28.0ms	677×	body	160	valid