Details

sample51.0ms

Algorithm

intervals

Results

23.0ms	57×	body	10240	exit
10.0ms	277×	body	80	valid
5.0ms	4×	body	1280	valid
2.0ms	8×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (log (+ 1.0 (exp x))) (* x y))
0.0b	(+ 1.0 (exp x))
0.3b	(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

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

series130.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(- (log (+ 1.0 (exp x))) (* x y))
8.0ms	(+ 1.0 (exp x))
64.0ms	(log (+ 1.0 (exp x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	207	322
1	584	301
2	1729	298
3	5001	297

prune120.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`log-prod`
8×	`pow1` `add-sqr-sqrt` `add-cube-cbrt` `sqrt-prod` `add-log-exp`
6×	`add-exp-log` `log-pow`
4×	`log-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `distribute-lft-out`
2×	`+-commutative` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log`

Counts

4 → 64

Calls

4 calls:

5.0ms	(+ 1.0 (exp x))
5.0ms	(+ 1.0 (exp x))
6.0ms	(log (sqrt (+ 1.0 (exp x))))
6.0ms	(log (sqrt (+ 1.0 (exp x))))

series231.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ 1.0 (exp x))
8.0ms	(+ 1.0 (exp x))
106.0ms	(log (sqrt (+ 1.0 (exp x))))
109.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	155	476
1	390	434
2	1073	422
3	5002	414

prune201.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
7.1b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-exp-log` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r`
6×	`log-prod` `add-cbrt-cube`
5×	`pow1`
4×	`unpow-prod-down` `log-div` `unswap-sqr`
3×	`flip3-+` `associate-l` `prod-exp` `associate--l+` `sum-log` `flip-+`
2×	`associate--l-` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+r+` `flip3--` `diff-log` `rem-log-exp` `pow-exp` `log-pow` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 71

Calls

4 calls:

11.0ms	(* 1/2 (pow x 2))
16.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
10.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
8.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 1/2 (pow x 2))
17.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
80.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
65.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	371	575
1	1439	529
2	5001	520

prune203.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2))))
7.1b	(log (+ (* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2)))) (+ x 2.0)))
26.7b	(sqrt (* 1/2 (pow x 2)))
26.7b	(sqrt (* 1/2 (pow x 2)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1`
11×	`add-sqr-sqrt`
10×	`sqrt-pow1` `pow1/2`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`add-exp-log`
6×	`sqrt-prod` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
3×	`log-prod` `pow-prod-down` `pow-sqr`
2×	`log-div`
1×	`pow2` `flip3-+` `pow-plus` `sqrt-unprod` `rem-log-exp` `prod-exp` `rem-square-sqrt` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

16.0ms	(* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2))))
25.0ms	(log (+ (* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2)))) (+ x 2.0)))
2.0ms	(sqrt (* 1/2 (pow x 2)))
2.0ms	(sqrt (* 1/2 (pow x 2)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2))))
128.0ms	(log (+ (* (sqrt (* 1/2 (pow x 2))) (sqrt (* 1/2 (pow x 2)))) (+ x 2.0)))
39.0ms	(sqrt (* 1/2 (pow x 2)))
35.0ms	(sqrt (* 1/2 (pow x 2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	272	585
1	1370	480
2	5001	465

prune217.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes35.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.4b 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

sample1.7s

Algorithm

intervals

Results

971.0ms	2455×	body	10240	exit
312.0ms	8483×	body	80	valid
62.0ms	225×	body	640	valid
56.0ms	116×	body	1280	valid
28.0ms	181×	body	320	valid
9.0ms	99×	body	160	valid