Details

sample36.0ms

Algorithm

intervals

Results

13.0ms	94×	body	1280	valid
7.0ms	82×	body	640	valid
3.0ms	363×	pre	80	true
2.0ms	46×	body	320	valid
1.0ms	117×	body	80	valid
1.0ms	24×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	6	2
1	7	2
2	7	2

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.6b

localize3.0ms

Local error

Found 1 expressions with local error:

6.7b	(- (exp x) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 28

Calls

1 calls:

5.0ms

(- (exp x) 1.0)

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	140	205
1	403	130
2	2063	120
3	5003	90

prune60.0ms

Filtered

31 candidates to 18 candidates (58.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1/6 (pow x 3) x)
0.0b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series107.0ms

Counts

2 → 6

Calls

2 calls:

76.0ms	(fma 1/6 (pow x 3) x)
31.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify41.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	55	118
1	186	104
2	1137	104
3	5001	104

prune77.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (pow x 3) x)
0.0b	(fma 1/6 (pow x 3) x)
0.0b	(fma 1/2 (pow x 2) (* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x))))
0.2b	(* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1`
18×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`sqrt-pow1` `pow1/2` `swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr` `fma-udef`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x))))
7.0ms	(* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma 1/6 (pow x 3) x)
75.0ms	(fma 1/6 (pow x 3) x)
32.0ms	(fma 1/2 (pow x 2) (* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x))))
76.0ms	(* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x)))

simplify178.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	137	463
1	559	393
2	3899	377
3	5001	377

prune204.0ms

Filtered

93 candidates to 51 candidates (54.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (fma 1/6 (pow x 3) x)))
0.1b	(sqrt (sqrt (fma 1/6 (pow x 3) x)))
0.2b	(* (pow (sqrt (sqrt (fma 1/6 (pow x 3) x))) 3) (sqrt (sqrt (fma 1/6 (pow x 3) x))))
0.4b	(pow (sqrt (sqrt (fma 1/6 (pow x 3) x))) 3)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

107×	`sqrt-prod`
74×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l` `unswap-sqr`
12×	`pow1` `sqrt-pow1`
10×	`add-exp-log`
9×	`associate-r`
7×	`add-cbrt-cube`
6×	`pow1/2`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `rem-sqrt-square` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `prod-exp`
2×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp`
1×	`pow-plus` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 157

Calls

4 calls:

1.0ms	(sqrt (sqrt (fma 1/6 (pow x 3) x)))
1.0ms	(sqrt (sqrt (fma 1/6 (pow x 3) x)))
19.0ms	(* (pow (sqrt (sqrt (fma 1/6 (pow x 3) x))) 3) (sqrt (sqrt (fma 1/6 (pow x 3) x))))
3.0ms	(pow (sqrt (sqrt (fma 1/6 (pow x 3) x))) 3)

series466.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sqrt (sqrt (fma 1/6 (pow x 3) x)))
122.0ms	(sqrt (sqrt (fma 1/6 (pow x 3) x)))
75.0ms	(* (pow (sqrt (sqrt (fma 1/6 (pow x 3) x))) 3) (sqrt (sqrt (fma 1/6 (pow x 3) x))))
153.0ms	(pow (sqrt (sqrt (fma 1/6 (pow x 3) x))) 3)

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	425	1517
1	1903	1284
2	5001	1127

prune382.0ms

Filtered

169 candidates to 83 candidates (49.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes47.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4

end0.0ms

sample1.1s

Algorithm

intervals

Results

476.0ms	3364×	body	1280	valid
204.0ms	2490×	body	640	valid
97.0ms	11963×	pre	80	true
70.0ms	1303×	body	320	valid
46.0ms	4138×	body	80	valid
21.0ms	668×	body	160	valid