Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	79×	body	1280	valid
7.0ms	65×	body	10240	exit
5.0ms	53×	body	640	valid
2.0ms	98×	body	80	valid
1.0ms	12×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize4.0ms

Local error

Found 2 expressions with local error:

1.0b	(/ (exp x) (- (exp x) 1.0))
4.1b	(- (exp x) 1.0)

rewrite35.0ms

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:

21.0ms	(/ (exp x) (- (exp x) 1.0))
11.0ms	(- (exp x) 1.0)

series38.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(/ (exp x) (- (exp x) 1.0))
13.0ms	(- (exp x) 1.0)

simplify195.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (188.0ms)

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

prune145.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

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))

rewrite6.0ms

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:

5.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.0ms	(fma 1/12 x (/ 1 x))

series60.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
46.0ms	(fma 1/12 x (/ 1 x))

simplify38.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	90	129
1	306	121
2	1283	120
3	5001	119

prune64.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (exp x))
0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
4.1b	(- 1 (/ 1.0 (exp x)))

rewrite63.0ms

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:

6.0ms	(/ 1.0 (exp x))
30.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
20.0ms	(- 1 (/ 1.0 (exp x)))

series92.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ 1.0 (exp x))
44.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
36.0ms	(- 1 (/ 1.0 (exp x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (46.0ms)

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

prune179.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- 1 (cbrt (pow (/ 1.0 (exp x)) 3))))
0.0b	(pow (/ 1.0 (exp x)) 3)
0.0b	(cbrt (pow (/ 1.0 (exp x)) 3))
4.1b	(- 1 (cbrt (pow (/ 1.0 (exp x)) 3)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

256×	`add-sqr-sqrt`
188×	`cbrt-prod`
186×	`*-un-lft-identity`
164×	`times-frac`
141×	`add-cube-cbrt`
105×	`prod-diff`
85×	`unpow-prod-down` `cube-prod`
70×	`difference-of-squares`
18×	`associate-/r*`
15×	`sqr-pow`
11×	`div-inv`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`cube-mult` `unpow3` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `div-exp` `associate-/l*`
2×	`cbrt-undiv` `cube-div` `flip3--` `pow-exp` `associate-/r/` `flip--` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `rec-exp` `cbrt-div` `pow-flip` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `1-exp` `clear-num` `rem-cbrt-cube` `inv-pow`

Counts

4 → 324

Calls

4 calls:

84.0ms	(/ 1 (- 1 (cbrt (pow (/ 1.0 (exp x)) 3))))
8.0ms	(pow (/ 1.0 (exp x)) 3)
6.0ms	(cbrt (pow (/ 1.0 (exp x)) 3))
52.0ms	(- 1 (cbrt (pow (/ 1.0 (exp x)) 3)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1 (- 1 (cbrt (pow (/ 1.0 (exp x)) 3))))
42.0ms	(pow (/ 1.0 (exp x)) 3)
12.0ms	(cbrt (pow (/ 1.0 (exp x)) 3))
33.0ms	(- 1 (cbrt (pow (/ 1.0 (exp x)) 3)))

simplify119.0ms

Algorithm

egg-herbie

Counts

336 → 336

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	915	5233
1	3505	3165
2	5001	3075

prune314.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes43.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.0b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	20
1	33	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

378.0ms	2277×	body	1280	valid
265.0ms	2525×	body	10240	exit
181.0ms	1687×	body	640	valid
61.0ms	2833×	body	80	valid
54.0ms	806×	body	320	valid
17.0ms	399×	body	160	valid