Details

sample22.0ms

Algorithm

intervals

Results

5.0ms	191×	body	80	valid
5.0ms	15×	body	1280	valid
2.0ms	18×	body	640	valid
1.0ms	21×	body	320	valid
1.0ms	11×	body	160	valid

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (17.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.6b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

6.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ y (+ y 1.0))
67.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify116.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	203	263
1	708	238
2	3148	232
3	5002	228

prune164.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
11.1b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series396.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (+ y 1.0))
112.0ms	(cbrt (+ y 1.0))
109.0ms	(cbrt (+ y 1.0))
66.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify91.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	235	565
1	699	515
2	2697	493
3	5001	461

prune297.0ms

Filtered

70 candidates to 62 candidates (88.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
10.4b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 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 y)
1.0ms	(cbrt y)
1.0ms	(cbrt y)
1.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

series712.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(cbrt y)
210.0ms	(cbrt y)
204.0ms	(cbrt y)
86.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	104	277
1	278	244
2	1012	231
3	5002	227

prune245.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
11.6b	(fma (/ (* (* (cbrt (* (cbrt y) (cbrt y))) (cbrt (cbrt y))) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 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:

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

series722.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(cbrt y)
209.0ms	(cbrt y)
209.0ms	(cbrt y)
85.0ms	(fma (/ (* (* (cbrt (* (cbrt y) (cbrt y))) (cbrt (cbrt y))) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify60.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	110	355
1	316	312
2	1251	301
3	5002	297

prune252.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.7b

regimes141.0ms

Accuracy

94% (0.5b remaining)

Error of 7.7b against oracle of 7.2b and baseline of 15.1b

bsearch125.0ms

Steps

Iters	Range		Point
7	1.2015983211331527e+60	8.871827210666939e+61	1.2211508164976468e+60
11	-5.005393495068343e+122	-2.3865927448386626e+86	-2.4231983371330456e+86

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample456.0ms

Algorithm

intervals

Results

151.0ms	6101×	body	80	valid
70.0ms	723×	body	640	valid
45.0ms	363×	body	1280	valid
38.0ms	512×	body	320	valid
14.0ms	301×	body	160	valid