Details

sample40.0ms

Algorithm

intervals

Results

12.0ms	70×	body	1280	valid
9.0ms	87×	body	10240	exit
6.0ms	55×	body	640	valid
2.0ms	26×	body	320	valid
2.0ms	93×	body	80	valid
1.0ms	12×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 40.5b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.8b	(- (exp x) 1.0)

rewrite16.0ms

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)

series46.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
20.0ms	(- (exp x) 1.0)

simplify190.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (183.0ms)

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

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

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:

0.0ms

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

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

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

simplify64.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (4.0ms)

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

prune25.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp x) (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0)))
0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
3.8b	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

3.0ms	(/ (exp x) (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0)))
1.0ms	(sqrt (exp x))
2.0ms	(sqrt (exp x))
0.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

series143.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (exp x) (fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0)))
12.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
53.0ms	(fma (sqrt (exp x)) (sqrt (exp x)) (- 1.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	167	613
1	517	520
2	2463	509
3	5001	503

prune204.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp x))
0.0b	(sqrt (exp x))
0.0b	(* (sqrt (sqrt (exp x))) (sqrt (sqrt (exp x))))
3.8b	(fma (* (sqrt (sqrt (exp x))) (sqrt (sqrt (exp x)))) (sqrt (exp x)) (- 1.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

76×	`sqrt-pow1`
72×	`sqrt-prod`
58×	`add-sqr-sqrt`
29×	`pow1`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`exp-prod`
18×	`pow1/2`
15×	`swap-sqr`
12×	`pow-prod-up`
9×	`associate-r` `associate-l` `unswap-sqr`
8×	`pow-prod-down` `pow-sqr`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 132

Calls

4 calls:

1.0ms	(sqrt (exp x))
1.0ms	(sqrt (exp x))
23.0ms	(* (sqrt (sqrt (exp x))) (sqrt (sqrt (exp x))))
0.0ms	(fma (* (sqrt (sqrt (exp x))) (sqrt (sqrt (exp x)))) (sqrt (exp x)) (- 1.0))

series91.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
18.0ms	(* (sqrt (sqrt (exp x))) (sqrt (sqrt (exp x))))
49.0ms	(fma (* (sqrt (sqrt (exp x))) (sqrt (sqrt (exp x)))) (sqrt (exp x)) (- 1.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	230	638
1	894	556
2	5001	537

prune278.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 21.8b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	17
1	21	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

381.0ms	2201×	body	1280	valid
272.0ms	2461×	body	10240	exit
193.0ms	1644×	body	640	valid
60.0ms	839×	body	320	valid
58.0ms	2910×	body	80	valid
19.0ms	407×	body	160	valid