Details

sample86.0ms

Algorithm

intervals

Results

47.0ms	135×	body	10240	exit
10.0ms	201×	body	80	valid
6.0ms	133×	body	80	overflowed
4.0ms	24×	body	320	valid
4.0ms	15×	body	640	valid
2.0ms	18×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	21	9
1	52	9
2	113	9
3	240	8
4	1625	8
5	5001	8

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
0.0b	(/ x (+ wj 1))
5.4b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite480.0ms

Algorithm

rewrite-expression-head

Rules

231×	`*-un-lft-identity`
175×	`times-frac`
129×	`add-sqr-sqrt`
124×	`add-cube-cbrt`
72×	`prod-diff`
52×	`distribute-lft-out`
24×	`associate-/l*`
20×	`associate-/r/`
13×	`add-cbrt-cube`
11×	`add-exp-log` `flip3-+` `associate-/r*` `flip-+` `div-inv`
9×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 260

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
13.0ms	(/ (/ x (+ wj 1)) (exp wj))
5.0ms	(/ x (+ wj 1))
443.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series143.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ wj (+ wj 1))
42.0ms	(/ (/ x (+ wj 1)) (exp wj))
22.0ms	(/ x (+ wj 1))
59.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify122.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1015	4090
1	4555	3249
2	5001	3243

prune506.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (pow wj 2))
0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`fma-neg` `prod-diff`
3×	`expm1-log1p-u` `fma-def` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
2×	`diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate-r` `associate--l+` `*-commutative` `flip--` `flip-+`

Counts

3 → 61

Calls

3 calls:

5.0ms	(+ x (pow wj 2))
53.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
6.0ms	(* 2 (* wj x))

series80.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ x (pow wj 2))
32.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify36.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	237	340
1	926	292
2	5001	274

prune138.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify2.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune8.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
0.0b	(/ x (+ wj 1))
4.8b	(- wj (/ wj (+ wj 1)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

176×	`*-un-lft-identity`
163×	`times-frac`
121×	`add-sqr-sqrt`
116×	`add-cube-cbrt`
54×	`prod-diff`
29×	`distribute-lft-out`
24×	`associate-/l*`
18×	`associate-/r/`
13×	`add-cbrt-cube`
11×	`add-exp-log` `associate-/r*`
10×	`div-inv`
9×	`flip3-+` `flip-+`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`frac-2neg` `fma-neg` `clear-num`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate-/l/` `distribute-lft-out--`

Counts

4 → 236

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
16.0ms	(/ (/ x (+ wj 1)) (exp wj))
5.0ms	(/ x (+ wj 1))
17.0ms	(- wj (/ wj (+ wj 1)))

series111.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ wj (+ wj 1))
44.0ms	(/ (/ x (+ wj 1)) (exp wj))
22.0ms	(/ x (+ wj 1))
25.0ms	(- wj (/ wj (+ wj 1)))

simplify101.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	921	2790
1	4082	2167
2	5002	2164

prune501.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes47.0ms

Accuracy

76.4% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 1.0b

bsearch52.0ms

Steps

Iters	Range		Point
10	2.8000448109264612e-18	4.860543997610572e-08	4.811043021165421e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	3830×	body	10240	exit
334.0ms	6296×	body	80	valid
173.0ms	3809×	body	80	overflowed
127.0ms	791×	body	320	valid
103.0ms	431×	body	640	valid
57.0ms	543×	body	160	valid