Details

sample42.0ms

Algorithm

intervals

Results

18.0ms	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

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: 0.5b

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)))

rewrite12.0ms

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:

3.0ms	(+ 1.0 (exp x))
5.0ms	(- (log (+ 1.0 (exp x))) (* x y))
3.0ms	(log (+ 1.0 (exp x)))

series129.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ 1.0 (exp x))
56.0ms	(- (log (+ 1.0 (exp x))) (* x y))
65.0ms	(log (+ 1.0 (exp x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 3 (46.0ms)

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

prune133.0ms

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))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

3.0ms	(+ 1.0 (exp x))
51.0ms	(- (+ (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))))

series345.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+ 1.0 (exp x))
142.0ms	(- (+ (log (sqrt (+ 1.0 (exp x)))) (log (sqrt (+ 1.0 (exp x))))) (* x y))
98.0ms	(log (sqrt (+ 1.0 (exp x))))
98.0ms	(log (sqrt (+ 1.0 (exp x))))

simplify87.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (81.0ms)

Iter	Nodes	Cost
0	272	721
1	917	619
2	3302	584
3	5002	576

prune210.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (pow x 2))
0.0b	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
0.0b	(+ (* 1/2 (pow x 2)) (+ x 2.0))
6.3b	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite36.0ms

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:

5.0ms	(* 1/2 (pow x 2))
10.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
8.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
11.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 1/2 (pow x 2))
83.0ms	(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
17.0ms	(+ (* 1/2 (pow x 2)) (+ x 2.0))
54.0ms	(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (42.0ms)

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

prune207.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
6.3b	(log (+ (* (* 1/2 (pow (* (cbrt x) (cbrt x)) 2)) (pow (cbrt x) 2)) (+ x 2.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`log-prod` `pow1/3`
2×	`log-div`
1×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 47

Calls

4 calls:

0.0ms	(cbrt x)
0.0ms	(cbrt x)
0.0ms	(cbrt x)
16.0ms	(log (+ (* (* 1/2 (pow (* (cbrt x) (cbrt x)) 2)) (pow (cbrt x) 2)) (+ x 2.0)))

series580.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt x)
174.0ms	(cbrt x)
170.0ms	(cbrt x)
66.0ms	(log (+ (* (* 1/2 (pow (* (cbrt x) (cbrt x)) 2)) (pow (cbrt x) 2)) (+ x 2.0)))

simplify188.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (183.0ms)

Iter	Nodes	Cost
0	213	429
1	786	384
2	4218	372
3	5002	369

prune199.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes70.0ms

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

497.0ms	8439×	body	80	valid
132.0ms	2522×	body	80	overflowed
83.0ms	145×	body	1280	valid
83.0ms	256×	body	640	valid
35.0ms	170×	body	320	valid
14.0ms	111×	body	160	valid