Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	68×	body	1280	valid
6.0ms	49×	body	640	valid
2.0ms	104×	body	80	valid
2.0ms	88×	body	80	overflowed
2.0ms	21×	body	320	valid
1.0ms	14×	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: 38.1b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite14.0ms

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)

series46.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify188.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (180.0ms)

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

prune319.0ms

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

localize11.0ms

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)
11.1b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite6.0ms

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))

series142.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
74.0ms	(fma 1/6 (pow x 3) x)
27.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify92.0ms

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

prune143.0ms

Filtered

58 candidates to 45 candidates (77.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	58	4	62

Merged error: 0.0b

Counts

62 → 4

localize5.0ms

Local error

Found 1 expressions with local error:

0.2b	(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))

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify60.0ms

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

prune22.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	13	4	17

Merged error: 0.0b

Counts

17 → 4

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
3.7b	(- 1 (/ 1.0 (exp x)))

rewrite27.0ms

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:

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

series102.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(/ 1.0 (exp x))
47.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
39.0ms	(- 1 (/ 1.0 (exp x)))

simplify63.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (47.0ms)

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

prune144.0ms

Filtered

154 candidates to 73 candidates (47.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	154	4	158

Merged error: 0.0b

Counts

158 → 4

regimes41.0ms

Accuracy

93.4% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 12.0b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms

sample975.0ms

Algorithm

intervals

Results

422.0ms	2253×	body	1280	valid
198.0ms	1579×	body	640	valid
68.0ms	2904×	body	80	valid
67.0ms	836×	body	320	valid
55.0ms	2509×	body	80	overflowed
25.0ms	430×	body	160	valid