Details

sample42.0ms

Algorithm

intervals

Results

17.0ms	277×	body	80	valid
5.0ms	8×	body	1280	valid
5.0ms	88×	body	80	overflowed
3.0ms	8×	body	640	valid
2.0ms	8×	body	320	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize7.0ms

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:

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

series125.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+ 1.0 (exp x))
58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
60.0ms	(log (+ 1.0 (exp x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (55.0ms)

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

prune161.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (- (log (+ 1.0 (exp x))) (* x y)))
0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.7b	(log (+ 1.0 (exp x)))
0.9b	(expm1 (log1p (- (log (+ 1.0 (exp x))) (* x y))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

0.0ms	(log1p (- (log (+ 1.0 (exp x))) (* x y)))
6.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))
0.0ms	(expm1 (log1p (- (log (+ 1.0 (exp x))) (* x y))))

series749.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(log1p (- (log (+ 1.0 (exp x))) (* x y)))
63.0ms	(- (log (+ 1.0 (exp x))) (* x y))
64.0ms	(log (+ 1.0 (exp x)))
406.0ms	(expm1 (log1p (- (log (+ 1.0 (exp x))) (* x y))))

simplify45.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	462	699
1	1611	634
2	5001	629

prune229.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize14.0ms

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))
9.0b	(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)))

series150.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
23.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
51.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify94.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (83.0ms)

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

prune151.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes56.0ms

Accuracy

0% (0.3b 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	10	5
1	10	5

end0.0ms

sample1.1s

Algorithm

intervals

Results

513.0ms	8431×	body	80	valid
130.0ms	2407×	body	80	overflowed
92.0ms	255×	body	640	valid
76.0ms	124×	body	1280	valid
37.0ms	171×	body	320	valid
12.0ms	91×	body	160	valid