Details

sample57.0ms

Algorithm

intervals

Results

30.0ms	75×	body	10240	exit
10.0ms	272×	body	80	valid
2.0ms	9×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	19	5
2	23	5
3	23	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp x))
1.0b	(log (+ 1.0 (exp x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

8×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `add-log-exp`
3×	`pow1` `add-exp-log` `fma-def`
2×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
1×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

2 → 34

Calls

2 calls:

3.0ms	(+ 1.0 (exp x))
3.0ms	(log (+ 1.0 (exp x)))

series74.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(+ 1.0 (exp x))
66.0ms	(log (+ 1.0 (exp x)))

simplify101.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 4 (97.0ms)

Iter	Nodes	Cost
0	137	181
1	364	163
2	1024	163
3	3614	161
4	5001	159

prune100.0ms

Filtered

40 candidates to 31 candidates (77.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(expm1 (log1p (log (+ 1.0 (exp x)))))
1.0b	(log (+ 1.0 (exp x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
0.0ms	(expm1 (log1p (log (+ 1.0 (exp x)))))
3.0ms	(log (+ 1.0 (exp x)))

series302.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
231.0ms	(expm1 (log1p (log (+ 1.0 (exp x)))))
63.0ms	(log (+ 1.0 (exp x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	205	271
1	631	245
2	2368	240
3	5002	240

prune147.0ms

Filtered

54 candidates to 40 candidates (74.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
0.0b	(log1p (log (fma 1/2 (pow x 2) (+ x 2.0))))
0.4b	(expm1 (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))
6.6b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `rem-log-exp` `log-pow` `fma-udef` `expm1-udef`

Counts

4 → 46

Calls

4 calls:

0.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
0.0ms	(log1p (log (fma 1/2 (pow x 2) (+ x 2.0))))
0.0ms	(expm1 (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
127.0ms	(log1p (log (fma 1/2 (pow x 2) (+ x 2.0))))
187.0ms	(expm1 (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))
51.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify36.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	313	486
1	1232	431
2	5001	409

prune209.0ms

Filtered

58 candidates to 48 candidates (82.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.4b	(expm1 (* (* (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0))))) (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))) (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))))
6.6b	(log (fma 1/2 (pow x 2) (+ x 2.0)))
6.6b	(log (fma 1/2 (pow x 2) (+ x 2.0)))
6.6b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`log-prod`
7×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp` `log-pow`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 53

Calls

4 calls:

0.0ms	(expm1 (* (* (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0))))) (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))) (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(expm1 (* (* (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0))))) (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))) (cbrt (log1p (log (fma 1/2 (pow x 2) (+ x 2.0)))))))
51.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
57.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))
56.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	178	718
1	597	603
2	2622	590
3	5002	418

prune284.0ms

Filtered

65 candidates to 54 candidates (83.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

regimes51.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

941.0ms	2372×	body	10240	exit
307.0ms	8418×	body	80	valid
74.0ms	275×	body	640	valid
48.0ms	99×	body	1280	valid
29.0ms	190×	body	320	valid
10.0ms	106×	body	160	valid