Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	56×	body	1280	valid
3.0ms	40×	body	640	valid
3.0ms	129×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	10×	body	160	valid

simplify21.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ x (+ x 1.0))
0.0b	(/ (+ x 1.0) (- x 1.0))
3.1b	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

981×	`*-un-lft-identity`
736×	`times-frac`
585×	`add-sqr-sqrt`
468×	`prod-diff`
419×	`add-cube-cbrt`
189×	`distribute-lft-out`
94×	`associate-/r/`
90×	`distribute-lft-out--`
81×	`difference-of-squares`
47×	`div-inv`
29×	`flip3-+` `flip-+`
20×	`flip3--` `flip--`
18×	`fma-neg`
9×	`associate-/r*`
7×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
1×	`sub-neg` `diff-log` `frac-sub`

Counts

3 → 596

Calls

3 calls:

5.0ms	(/ x (+ x 1.0))
13.0ms	(/ (+ x 1.0) (- x 1.0))
77.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ x (+ x 1.0))
40.0ms	(/ (+ x 1.0) (- x 1.0))
130.0ms	(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify201.0ms

Algorithm

egg-herbie

Counts

605 → 605

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1208	18366
1	3687	13388
2	5001	13292

prune717.0ms

Filtered

605 candidates to 217 candidates (35.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
30.1b	(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

series675.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt x)
177.0ms	(cbrt x)
185.0ms	(cbrt x)
134.0ms	(fma (/ (* (cbrt x) (cbrt x)) 1) (/ (cbrt x) (+ x 1.0)) (- (/ (+ x 1.0) (- x 1.0))))

simplify50.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	123	312
1	340	272
2	1569	258
3	5002	253

prune174.0ms

Filtered

61 candidates to 54 candidates (88.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
0.3b	(/ 1 (pow x 3))
0.7b	(/ (- 1.0) (pow x 2))
6.0b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
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 → 559

Calls

4 calls:

0.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
5.0ms	(/ 1 (pow x 3))
6.0ms	(/ (- 1.0) (pow x 2))
77.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

series181.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3))))
37.0ms	(/ 1 (pow x 3))
25.0ms	(/ (- 1.0) (pow x 2))
36.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 x) (* 3.0 (/ 1 (pow x 3)))))

simplify175.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	1159	12779
1	4167	7106
2	5001	7094

prune779.0ms

Filtered

571 candidates to 218 candidates (38.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
0.3b	(/ 1 (pow x 3))
0.7b	(/ (- 1.0) (pow x 2))
6.0b	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

440×	`times-frac`
354×	`add-sqr-sqrt`
344×	`*-un-lft-identity`
342×	`add-cube-cbrt`
252×	`prod-diff`
166×	`unpow-prod-down`
123×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
84×	`fma-neg`
56×	`sqr-pow`
52×	`unpow2`
41×	`neg-mul-1`
20×	`associate-/r*`
18×	`add-exp-log`
13×	`associate-/l*`
12×	`cube-prod`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`div-inv` `add-log-exp`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `cube-mult` `pow-to-exp` `unpow3` `pow-exp` `log1p-expm1-u`
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 → 559

Calls

4 calls:

0.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
5.0ms	(/ 1 (pow x 3))
8.0ms	(/ (- 1.0) (pow x 2))
76.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

series182.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x))
31.0ms	(/ 1 (pow x 3))
26.0ms	(/ (- 1.0) (pow x 2))
42.0ms	(- (/ (- 1.0) (pow x 2)) (fma 3.0 (/ 1 (pow x 3)) (/ 3.0 x)))

simplify169.0ms

Algorithm

egg-herbie

Counts

571 → 571

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	1162	11394
1	4062	6475
2	5001	6466

prune772.0ms

Filtered

571 candidates to 217 candidates (38.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch85.0ms

Steps

Iters	Range		Point
8	48.29475874355119	356290.51007653365	6807.567749486692
10	-204248214.92732975	-1.534026600097144e-05	-8055.654339134288

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	20
1	42	20
2	42	20

end0.0ms

sample523.0ms

Algorithm

intervals

Results

177.0ms	1660×	body	1280	valid
101.0ms	1240×	body	640	valid
98.0ms	4160×	body	80	valid
43.0ms	639×	body	320	valid
13.0ms	301×	body	160	valid

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6

Iter	Nodes	Cost
0	12	6
1	16	6
2	19	6
3	21	6
4	27	6
5	39	6
6	58	6
7	79	6
8	107	6
9	160	6
10	277	6
11	303	6
12	303	6