Details

sample76.0ms

Algorithm

intervals

Results

36.0ms	55×	body	10240	exit
16.0ms	265×	body	80	valid
3.0ms	4×	body	1280	valid
3.0ms	7×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp x))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.7b	(log (+ 1.0 (exp x)))

rewrite17.0ms

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))
8.0ms	(- (log (+ 1.0 (exp x))) (* x y))
5.0ms	(log (+ 1.0 (exp x)))

series128.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
61.0ms	(- (log (+ 1.0 (exp x))) (* x y))
59.0ms	(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

prune170.0ms

Pruning

4 alts after pruning (3 fresh and 1 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))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite38.0ms

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)))
8.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
3.0ms	(log (sqrt (+ 1.0 (exp x))))
3.0ms	(log (sqrt (+ 1.0 (exp x))))

series486.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
127.0ms	(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
101.0ms	(log (sqrt (+ 1.0 (exp x))))
109.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify125.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (114.0ms)

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

prune374.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x))))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))
1.4b	(log (sqrt (+ 1.0 (exp x))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

21×	`log-prod`
16×	`*-un-lft-identity`
12×	`sqrt-prod`
10×	`pow1` `add-sqr-sqrt` `add-cube-cbrt`
9×	`log-pow`
7×	`add-exp-log`
6×	`log-div` `sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 76

Calls

4 calls:

0.0ms	(fma (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x))))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
3.0ms	(log (sqrt (+ 1.0 (exp x))))
3.0ms	(log (sqrt (+ 1.0 (exp x))))
3.0ms	(log (sqrt (+ 1.0 (exp x))))

series720.0ms

Counts

4 → 12

Calls

4 calls:

405.0ms	(fma (sqrt (log (sqrt (+ 1.0 (exp x))))) (sqrt (log (sqrt (+ 1.0 (exp x))))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
102.0ms	(log (sqrt (+ 1.0 (exp x))))
110.0ms	(log (sqrt (+ 1.0 (exp x))))
104.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	179	814
1	490	723
2	1607	692
3	5002	669

prune276.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
7.5b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite6.0ms

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:

4.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
0.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
1.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

series149.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
55.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (82.0ms)

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

prune154.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes57.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

end0.0ms

sample1.6s

Algorithm

intervals

Results

919.0ms	2274×	body	10240	exit
317.0ms	8417×	body	80	valid
68.0ms	258×	body	640	valid
58.0ms	116×	body	1280	valid
32.0ms	205×	body	320	valid
11.0ms	112×	body	160	valid