Details

sample33.0ms

Algorithm

intervals

Results

12.0ms	58×	body	1280	valid
6.0ms	49×	body	640	valid
3.0ms	111×	body	80	valid
2.0ms	84×	body	80	overflowed
2.0ms	21×	body	320	valid
1.0ms	17×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

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: 36.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.9b	(- (exp x) 1.0)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

7.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series45.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify190.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (182.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune128.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 0.0b

Counts

74 → 4

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.1b	(fma 1/6 (pow x 3) x)
11.6b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

4.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
1.0ms	(fma 1/6 (pow x 3) x)
1.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series144.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
75.0ms	(fma 1/6 (pow x 3) x)
26.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify93.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	178	458
1	614	416
2	3125	414
3	5002	414

prune146.0ms

Filtered

58 candidates to 45 candidates (77.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	57	5	62

Merged error: 0b

Counts

62 → 5

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/12 x (/ 1 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`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

1 → 10

Calls

1 calls:

1.0ms

(fma 1/12 x (/ 1 x))

series43.0ms

Counts

1 → 3

Calls

1 calls:

43.0ms

(fma 1/12 x (/ 1 x))

simplify64.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	43
1	49	38
2	150	38
3	482	38
4	2338	38
5	5002	38

prune24.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	13	5	18

Merged error: 0b

Counts

18 → 5

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
3.9b	(- 1 (/ 1.0 (exp x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

99×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
70×	`times-frac`
59×	`add-cube-cbrt`
39×	`prod-diff`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `fma-neg` `div-exp` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 145

Calls

3 calls:

9.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
4.0ms	(/ 1.0 (exp x))
8.0ms	(- 1 (/ 1.0 (exp x)))

series100.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
14.0ms	(/ 1.0 (exp x))
39.0ms	(- 1 (/ 1.0 (exp x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	552	1839
1	2298	1281
2	5001	1188

prune141.0ms

Filtered

154 candidates to 73 candidates (47.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	154	5	159

Merged error: 0b

Counts

159 → 5

regimes58.0ms

Accuracy

91% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 7.6b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	15
1	20	15

end0.0ms

sample1.0s

Algorithm

intervals

Results

440.0ms	2252×	body	1280	valid
215.0ms	1618×	body	640	valid
72.0ms	828×	body	320	valid
70.0ms	2864×	body	80	valid
56.0ms	2559×	body	80	overflowed
25.0ms	439×	body	160	valid

Details

sample33.0ms

simplify5.0ms

prune2.0ms

localize4.0ms

rewrite13.0ms

series45.0ms

simplify190.0ms

prune128.0ms

localize12.0ms

rewrite7.0ms

series144.0ms

simplify93.0ms

prune146.0ms

localize6.0ms

rewrite1.0ms

series43.0ms

simplify64.0ms

prune24.0ms

localize5.0ms

rewrite28.0ms

series100.0ms

simplify67.0ms

prune141.0ms

regimes58.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample1.0s

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