Details

sample51.0ms

Algorithm

intervals

Results

25.0ms	62×	body	10240	exit
9.0ms	259×	body	80	valid
3.0ms	5×	body	1280	valid
2.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

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: 0.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.5b	(log (+ 1.0 (exp x)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 62

Calls

3 calls:

3.0ms	(+ 1.0 (exp x))
6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series129.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
59.0ms	(- (log (+ 1.0 (exp x))) (* x y))
62.0ms	(log (+ 1.0 (exp x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	236	404
1	702	369
2	2284	367
3	5002	340

prune175.0ms

Filtered

71 candidates to 54 candidates (76.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
0.0b	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
1.2b	(log (sqrt (+ 1.0 (exp x))))
1.2b	(log (sqrt (+ 1.0 (exp x))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

35×	`log-prod`
31×	`*-un-lft-identity`
20×	`sqrt-prod`
19×	`log-pow`
18×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`pow1`
15×	`associate-+r+`
14×	`associate--l+`
12×	`prod-diff`
8×	`log-div` `sqrt-div`
7×	`associate-+l+` `distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `fma-def` `sqrt-pow1` `pow1/2` `fma-neg`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`associate--l-` `associate-+l-` `sub-neg` `diff-log` `rem-log-exp` `sum-log`
1×	`+-commutative` `associate-+r-` `flip3--` `flip--`

Counts

4 → 126

Calls

4 calls:

19.0ms	(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
9.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
3.0ms	(log (sqrt (+ 1.0 (exp x))))
6.0ms	(log (sqrt (+ 1.0 (exp x))))

series478.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
129.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
101.0ms	(log (sqrt (+ 1.0 (exp x))))
103.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify127.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	359	1212
1	1168	1104
2	4337	1034
3	5001	1024

prune402.0ms

Filtered

138 candidates to 103 candidates (74.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
8.5b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `log-prod`
4×	`add-exp-log` `fma-neg` `prod-diff` `add-log-exp`
3×	`expm1-log1p-u` `associate--l+` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `fma-udef`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
7.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series143.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
76.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
51.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	229	423
1	763	380
2	3267	376
3	5001	356

prune149.0ms

Filtered

58 candidates to 46 candidates (79.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow x 2) (pow 2.0 2))
0.0b	(* 1/2 (/ (pow x 2) (pow 2.0 2)))
0.0b	(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
8.8b	(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
110×	`add-sqr-sqrt` `unpow-prod-down`
76×	`add-cube-cbrt` `*-un-lft-identity`
68×	`associate-r`
42×	`unpow2` `sqr-pow`
39×	`add-exp-log`
18×	`div-exp`
17×	`unswap-sqr`
12×	`pow-to-exp` `pow-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
8×	`associate-/r` `associate-/l`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `associate-l` `prod-diff`
2×	`cbrt-undiv` `cbrt-unprod` `fma-udef` `div-inv`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `-commutative` `flip--`

Counts

4 → 245

Calls

4 calls:

6.0ms	(/ (pow x 2) (pow 2.0 2))
25.0ms	(* 1/2 (/ (pow x 2) (pow 2.0 2)))
3.0ms	(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
0.0ms	(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (pow x 2) (pow 2.0 2))
52.0ms	(* 1/2 (/ (pow x 2) (pow 2.0 2)))
75.0ms	(- (fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2))))) (* x y))
61.0ms	(fma x (+ (* 0.25 x) 0.5) (- (log 2.0) (* 1/2 (/ (pow x 2) (pow 2.0 2)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

257 → 257

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	714	1754
1	3098	1441
2	5002	1430

prune805.0ms

Filtered

257 candidates to 151 candidates (58.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes34.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms

sample1.6s

Algorithm

intervals

Results

955.0ms	2449×	body	10240	exit
310.0ms	8350×	body	80	valid
67.0ms	259×	body	640	valid
56.0ms	113×	body	1280	valid
32.0ms	210×	body	320	valid
9.0ms	96×	body	160	valid