Details

sample40.0ms

Algorithm

intervals

Results

15.0ms	255×	body	80	valid
5.0ms	7×	body	1280	valid
4.0ms	81×	body	80	overflowed
3.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	4×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

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)))

rewrite13.0ms

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)))

series125.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
59.0ms	(log (+ 1.0 (exp x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (56.0ms)

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

prune166.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

50×	`log-pow`
40×	`pow1`
37×	`*-un-lft-identity`
26×	`fma-neg` `prod-diff`
20×	`distribute-rgt-out`
19×	`add-sqr-sqrt` `add-cube-cbrt` `distribute-lft-out`
14×	`log-prod` `sqrt-pow1` `pow1/2`
9×	`add-log-exp`
8×	`log-div` `sqrt-div` `sqrt-prod`
6×	`add-exp-log`
5×	`flip3-+` `flip-+`
4×	`associate--l-` `expm1-log1p-u` `distribute-lft1-in` `distribute-rgt1-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def`
2×	`associate-+l-` `associate-+r-` `count-2` `diff-log` `rem-log-exp` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 133

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
66.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
3.0ms	(log (sqrt (+ 1.0 (exp x))))
4.0ms	(log (sqrt (+ 1.0 (exp x))))

series355.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (exp x))
145.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
101.0ms	(log (sqrt (+ 1.0 (exp x))))
102.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify46.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	360	1216
1	1267	981
2	5001	919

prune318.0ms

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))
6.3b	(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)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(- (log (fma 1/2 (pow x 2) (+ x 2.0))) (* x y))
17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
54.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify90.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (84.0ms)

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

prune147.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/2 (pow x 2) (+ x 2.0))
0.1b	(log (log (fma 1/2 (pow x 2) (+ x 2.0))))
0.3b	(exp (log (log (fma 1/2 (pow x 2) (+ x 2.0)))))
6.3b	(log (fma 1/2 (pow x 2) (+ x 2.0)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

11×	`log-prod`
9×	`pow1`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log`
5×	`log-pow`
4×	`expm1-log1p-u` `exp-prod` `exp-sum` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp`
1×	`fma-udef` `rem-exp-log`

Counts

4 → 57

Calls

4 calls:

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

series237.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(fma 1/2 (pow x 2) (+ x 2.0))
110.0ms	(log (log (fma 1/2 (pow x 2) (+ x 2.0))))
56.0ms	(exp (log (log (fma 1/2 (pow x 2) (+ x 2.0)))))
53.0ms	(log (fma 1/2 (pow x 2) (+ x 2.0)))

simplify133.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	275	542
1	1001	481
2	4777	458
3	5001	452

prune209.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes55.0ms

Accuracy

0% (0.3b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 0.6b

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

506.0ms	8439×	body	80	valid
137.0ms	2522×	body	80	overflowed
92.0ms	145×	body	1280	valid
86.0ms	256×	body	640	valid
37.0ms	170×	body	320	valid
15.0ms	111×	body	160	valid