Details

analyze65.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

sample25.0ms

Algorithm

intervals

Results

11.0ms	238×	body	80	valid
3.0ms	5×	body	1280	valid
1.0ms	5×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	1×	body	5120	exit
0.0ms	2×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5973	9

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.3b

Counts

2 → 1

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)))

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 → 44

Calls

3 calls:

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

series21.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(- (log (+ 1.0 (exp x))) (* x y))
2.0ms	(+ 1.0 (exp x))
10.0ms	(log (+ 1.0 (exp x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4843	504
1	4843	504

prune83.0ms

Filtered

39 candidates to 53 candidates (-35.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	49	4	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	4	54

Merged error: 0.2b

Counts

54 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (+ 1.0 (exp x)))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(sqrt (log (+ 1.0 (exp x))))
0.7b	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

3.0ms	(log (+ 1.0 (exp x)))
1.0ms	(sqrt (log (+ 1.0 (exp x))))
1.0ms	(sqrt (log (+ 1.0 (exp x))))
7.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(log (+ 1.0 (exp x)))
12.0ms	(sqrt (log (+ 1.0 (exp x))))
12.0ms	(sqrt (log (+ 1.0 (exp x))))
10.0ms	(* (sqrt (log (+ 1.0 (exp x)))) (sqrt (log (+ 1.0 (exp x)))))

simplify41.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5045	845

prune129.0ms

Filtered

54 candidates to 109 candidates (-101.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	109	4	113

Merged error: 0.2b

Counts

113 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ 2.0 (* x (* x 1/2))))
0.0b	(- (log (+ x (+ 2.0 (* x (* x 1/2))))) (* x y))
8.0b	(log (+ x (+ 2.0 (* x (* x 1/2)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

5.0ms	(+ x (+ 2.0 (* x (* x 1/2))))
6.0ms	(- (log (+ x (+ 2.0 (* x (* x 1/2))))) (* x y))
4.0ms	(log (+ x (+ 2.0 (* x (* x 1/2)))))

series16.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(+ x (+ 2.0 (* x (* x 1/2))))
9.0ms	(- (log (+ x (+ 2.0 (* x (* x 1/2))))) (* x y))
4.0ms	(log (+ x (+ 2.0 (* x (* x 1/2)))))

simplify44.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5025	866

prune91.0ms

Filtered

43 candidates to 55 candidates (-27.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	54	5	59

Merged error: 0.2b

Counts

59 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0)))))
0.0b	(* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))))
0.0b	(- (+ (log 2.0) (+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0)))))) (* x y))
0.0b	(+ (log 2.0) (+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
7×	`sum-log`
6×	`add-cube-cbrt` `associate-r`
5×	`sub-neg`
3×	`associate-+l+` `associate-+r+` `log-prod` `diff-log` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `distribute-rgt-in` `flip3--` `distribute-lft-in` `flip3-+` `associate-*r/` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`
1×	`times-frac` `associate-l` `associate--l+` `log-pow` `*-commutative` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

6.0ms	(+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0)))))
10.0ms	(* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))))
9.0ms	(- (+ (log 2.0) (+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0)))))) (* x y))
6.0ms	(+ (log 2.0) (+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))))))

series20.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0)))))
3.0ms	(* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))))
7.0ms	(- (+ (log 2.0) (+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0)))))) (* x y))
4.0ms	(+ (log 2.0) (+ (* x 0.5) (* (* x x) (- 0.25 (/ 1/2 (* 2.0 2.0))))))

simplify27.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4991	1354
1	4991	1354

prune120.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	83	5	88

Merged error: 0.2b

Counts

88 → 5

regimes95.0ms

Accuracy

0% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

end0.0ms

sample682.0ms

Algorithm

intervals

Results

350.0ms	7379×	body	80	valid
71.0ms	233×	body	640	valid
63.0ms	115×	body	1280	valid
34.0ms	178×	body	320	valid
11.0ms	95×	body	160	valid
3.0ms	7×	body	5120	exit
3.0ms	45×	body	80	invalid

Details

analyze65.0ms

sample25.0ms

simplify67.0ms

prune7.0ms

localize7.0ms

rewrite12.0ms

series21.0ms

simplify65.0ms

prune83.0ms

localize10.0ms

rewrite15.0ms

series45.0ms

simplify41.0ms

prune129.0ms

localize10.0ms

rewrite17.0ms

series16.0ms

simplify44.0ms

prune91.0ms

localize14.0ms

rewrite34.0ms

series20.0ms

simplify27.0ms

prune120.0ms

regimes95.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample682.0ms

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