Details

sample38.0ms

Algorithm

intervals

Results

19.0ms	84×	body	1280	valid
4.0ms	41×	body	640	valid
3.0ms	158×	body	80	valid
2.0ms	30×	body	320	valid
1.0ms	17×	body	160	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1633	3
7	5002	3

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: 31.0b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.9b	(- (exp (* a x)) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt` `exp-prod`
9×	`prod-diff`
6×	`add-log-exp`
3×	`fma-neg` `associate-r` `associate-l`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `exp-to-pow` `diff-log` `*-commutative` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

2 → 51

Calls

2 calls:

4.0ms	(exp (* a x))
7.0ms	(- (exp (* a x)) 1.0)

series57.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1.0)

simplify101.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	208	321
1	654	240
2	3113	229
3	5001	202

prune103.0ms

Filtered

57 candidates to 37 candidates (64.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	50	7	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	7	58

Merged error: 9.2b

Counts

58 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
13.3b	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
14.9b	(* (pow a 2) (pow x 2))
16.1b	(* (pow a 3) (pow x 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
28×	`add-exp-log`
26×	`unpow-prod-down`
25×	`unswap-sqr`
20×	`*-un-lft-identity`
18×	`prod-exp` `sqr-pow`
16×	`add-cube-cbrt` `pow-unpow` `associate-r` `associate-l` `pow-prod-down`
12×	`pow1` `pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
2×	`unpow3` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 133

Calls

4 calls:

1.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
10.0ms	(* (pow a 2) (pow x 2))
10.0ms	(* (pow a 3) (pow x 3))

series350.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(fma 1/6 (* (pow a 3) (pow x 3)) (* a x))
119.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (fma 1/6 (* (pow a 3) (pow x 3)) (* a x)))
34.0ms	(* (pow a 2) (pow x 2))
77.0ms	(* (pow a 3) (pow x 3))

simplify68.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	411	767
1	1778	665
2	5001	653

prune336.0ms

Filtered

145 candidates to 85 candidates (58.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	140	5	145
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	141	11	152

Merged error: 4.8b

Counts

152 → 11

localize12.0ms

Local error

Found 2 expressions with local error:

4.6b	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
14.9b	(* (pow a 2) (pow x 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`add-exp-log` `unpow-prod-down`
10×	`*-un-lft-identity` `unpow2` `sqr-pow`
9×	`prod-exp`
8×	`add-cube-cbrt` `pow-unpow` `associate-r` `associate-l` `pow-prod-down`
6×	`pow1` `pow-to-exp` `pow-exp`
4×	`add-cbrt-cube`
2×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
1×	`*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 70

Calls

2 calls:

1.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
10.0ms	(* (pow a 2) (pow x 2))

series101.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(fma 1/2 (* (pow a 2) (pow x 2)) (* a x))
33.0ms	(* (pow a 2) (pow x 2))

simplify188.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	222	358
1	823	287
2	4849	283
3	5001	283

prune118.0ms

Filtered

76 candidates to 42 candidates (55.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	80	7	87

Merged error: 0.1b

Counts

87 → 7

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (fabs (* x a)) (fabs (* x a)))
4.6b	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

3.0ms	(* (fabs (* x a)) (fabs (* x a)))
1.0ms	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

series49.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(* (fabs (* x a)) (fabs (* x a)))
41.0ms	(fma 1/2 (* (fabs (* x a)) (fabs (* x a))) (* a x))

simplify52.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	87	278
1	336	224
2	1500	210
3	5002	204

prune64.0ms

Filtered

43 candidates to 28 candidates (65.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	43	7	50

Merged error: 0.1b

Counts

50 → 7

regimes223.0ms

Accuracy

95.9% (0.9b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 21.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	11
1	19	11
2	19	11

end0.0ms

sample920.0ms

Algorithm

intervals

Results

428.0ms	2752×	body	1280	valid
139.0ms	1354×	body	640	valid
104.0ms	5480×	body	80	valid
51.0ms	751×	body	320	valid
16.0ms	366×	body	160	valid