Details

sample38.0ms

Algorithm

intervals

Results

13.0ms	76×	body	1280	valid
9.0ms	82×	body	10240	exit
6.0ms	55×	body	640	valid
2.0ms	92×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	18×	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: 40.4b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
4.6b	(- (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×	`add-exp-log` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `div-exp` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

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

series47.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ (exp x) (- (exp x) 1.0))
16.0ms	(- (exp x) 1.0)

simplify176.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (170.0ms)

Iter	Nodes	Cost
0	236	523
1	784	433
2	4452	420
3	5001	408

prune117.0ms

Filtered

74 candidates to 50 candidates (67.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Merged error: 0.0b

Counts

75 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

3.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
1.0ms	(fma 1/12 x (/ 1 x))

series63.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
45.0ms	(fma 1/12 x (/ 1 x))

simplify38.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	89	126
1	305	119
2	1283	117
3	5001	116

prune54.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Merged error: 0.0b

Counts

37 → 4

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
4.6b	(- 1 (/ 1.0 (exp x)))

rewrite30.0ms

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*`
10×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`div-inv` `distribute-lft-out--` `add-log-exp`
4×	`pow1` `div-exp`
3×	`expm1-log1p-u` `fma-neg` `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 → 146

Calls

3 calls:

10.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
4.0ms	(/ 1.0 (exp x))
10.0ms	(- 1 (/ 1.0 (exp x)))

series102.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
13.0ms	(/ 1.0 (exp x))
40.0ms	(- 1 (/ 1.0 (exp x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	550	1840
1	2288	1283
2	5001	1190

prune141.0ms

Filtered

155 candidates to 73 candidates (47.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	155	4	159

Merged error: 0.0b

Counts

159 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- 1 (/ 1.0 (exp x))))
4.6b	(- 1 (/ 1.0 (exp x)))
4.6b	(- 1 (/ 1.0 (exp x)))
4.6b	(- 1 (/ 1.0 (exp x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

142×	`add-sqr-sqrt`
126×	`*-un-lft-identity`
117×	`prod-diff`
110×	`add-cube-cbrt`
89×	`times-frac`
16×	`difference-of-squares`
10×	`add-log-exp`
9×	`fma-neg` `div-inv`
8×	`cbrt-prod`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 203

Calls

4 calls:

7.0ms	(cbrt (- 1 (/ 1.0 (exp x))))
9.0ms	(- 1 (/ 1.0 (exp x)))
9.0ms	(- 1 (/ 1.0 (exp x)))
9.0ms	(- 1 (/ 1.0 (exp x)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- 1 (/ 1.0 (exp x))))
39.0ms	(- 1 (/ 1.0 (exp x)))
36.0ms	(- 1 (/ 1.0 (exp x)))
42.0ms	(- 1 (/ 1.0 (exp x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	472	3900
1	1677	2456
2	5002	2173

prune217.0ms

Filtered

215 candidates to 79 candidates (36.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	215	4	219

Merged error: 0.0b

Counts

219 → 4

regimes43.0ms

Accuracy

97.1% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 20.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	19
1	21	19

end0.0ms

sample1.1s

Algorithm

intervals

Results

375.0ms	2185×	body	1280	valid
275.0ms	2540×	body	10240	exit
185.0ms	1692×	body	640	valid
63.0ms	874×	body	320	valid
53.0ms	2795×	body	80	valid
20.0ms	455×	body	160	valid