Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	111×	body	1280	valid
7.0ms	80×	body	640	valid
3.0ms	381×	pre	80	true
2.0ms	40×	body	320	valid
2.0ms	130×	body	80	valid
1.0ms	20×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 59.3b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

5.8b	(- (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)

simplify59.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	137	205
1	379	130
2	1905	120
3	5001	90

prune42.0ms

Filtered

31 candidates to 18 candidates (58.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	30	1	31
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	30	2	32

Merged error: 0.0b

Counts

32 → 2

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))

rewrite2.0ms

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:

1.0ms	(fma 1/6 (pow x 3) x)
1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(fma 1/6 (pow x 3) x)
28.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify38.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	54	118
1	180	104
2	1078	104
3	5001	104

prune59.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	24	4	28

Merged error: 0.0b

Counts

28 → 4

localize13.0ms

Local error

Found 4 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))
0.0b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
0.3b	(* (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))) (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))))

rewrite11.0ms

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:

1.0ms	(fma 1/6 (pow x 3) x)
1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
7.0ms	(* (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))) (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))))

series174.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma 1/6 (pow x 3) x)
33.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
30.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
31.0ms	(* (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))) (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))))

simplify214.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	136	581
1	578	505
2	4575	479
3	5001	479

prune166.0ms

Filtered

93 candidates to 52 candidates (55.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	94	3	97

Merged error: 0.0b

Counts

97 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma 1/6 (pow x 3) x))
0.0b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
0.3b	(* (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))) (sqrt (fma 1/2 (pow x 2) (* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x))))))
0.3b	(* (sqrt (fma 1/6 (pow x 3) x)) (sqrt (fma 1/6 (pow x 3) x)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

2.0ms	(sqrt (fma 1/6 (pow x 3) x))
1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
6.0ms	(* (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))) (sqrt (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)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(sqrt (fma 1/6 (pow x 3) x))
27.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))
33.0ms	(* (sqrt (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))) (sqrt (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)))

simplify46.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	255	857
1	982	629
2	5001	579

prune250.0ms

Filtered

120 candidates to 68 candidates (56.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

regimes47.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

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

501.0ms	3444×	body	1280	valid
221.0ms	2488×	body	640	valid
100.0ms	12082×	pre	80	true
69.0ms	1263×	body	320	valid
50.0ms	4268×	body	80	valid
24.0ms	619×	body	160	valid