Details

sample33.0ms

Algorithm

intervals

Results

14.0ms	79×	body	1280	valid
6.0ms	56×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	80×	body	80	valid
1.0ms	62×	body	80	overflowed
1.0ms	15×	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: 43.9b

localize4.0ms

Local error

Found 2 expressions with local error:

0.5b	(/ (exp x) (- (exp x) 1.0))
3.6b	(- (exp x) 1.0)

rewrite15.0ms

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:

8.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series44.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
18.0ms	(- (exp x) 1.0)

simplify183.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (177.0ms)

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

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

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)))
0.0b	(fma 1/6 (pow x 3) x)
9.0b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite4.0ms

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:

3.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series141.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(/ (exp x) (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
68.0ms	(fma 1/6 (pow x 3) x)
29.0ms	(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

prune173.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (/ 1 (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))))
0.0b	(/ 1 (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0b	(fma 1/6 (pow x 3) x)
9.0b	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log` `associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `fma-udef` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 91

Calls

4 calls:

10.0ms	(* (exp x) (/ 1 (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))))
2.0ms	(/ 1 (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
0.0ms	(fma 1/6 (pow x 3) x)
0.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

series180.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (exp x) (/ 1 (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))))
34.0ms	(/ 1 (fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x)))
73.0ms	(fma 1/6 (pow x 3) x)
30.0ms	(fma 1/2 (pow x 2) (fma 1/6 (pow x 3) x))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	308	803
1	1359	699
2	5001	671

prune253.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize5.0ms

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:

0.0ms

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

series47.0ms

Counts

1 → 3

Calls

1 calls:

47.0ms

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

simplify59.0ms

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

prune21.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

93.3% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 11.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	22
1	26	22

end0.0ms

sample887.0ms

Algorithm

intervals

Results

390.0ms	2259×	body	1280	valid
171.0ms	1561×	body	640	valid
68.0ms	877×	body	320	valid
58.0ms	2871×	body	80	valid
44.0ms	2488×	body	80	overflowed
20.0ms	432×	body	160	valid