Details

sample72.0ms

Algorithm

intervals

Results

48.0ms	252×	body	10240	exit
6.0ms	206×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	19×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	20	9
1	48	9
2	107	9
3	224	8
4	1514	8
5	5001	8

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 12.6b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
5.0b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
118×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
24×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`add-exp-log` `associate-/r*`
9×	`add-log-exp`
7×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
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 → 176

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
8.0ms	(/ x (+ wj 1))
9.0ms	(/ (/ x (+ wj 1)) (exp wj))
30.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ wj (+ wj 1))
23.0ms	(/ x (+ wj 1))
46.0ms	(/ (/ x (+ wj 1)) (exp wj))
55.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify85.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	721	1524
1	3303	1471
2	5001	1469

prune434.0ms

Filtered

188 candidates to 138 candidates (73.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	182	6	188
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	184	6	190

Merged error: 0.2b

Counts

190 → 6

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))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 44

Calls

3 calls:

4.0ms	(+ x (pow wj 2))
7.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
5.0ms	(* 2 (* wj x))

series82.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ x (pow wj 2))
30.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify127.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	202	247
1	793	231
2	4232	228
3	5001	228

prune102.0ms

Filtered

53 candidates to 32 candidates (60.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	52	7	59

Merged error: 0.2b

Counts

59 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp wj) (- wj 1))
0.0b	(/ x (- (* wj wj) (* 1 1)))
0.0b	(/ wj (+ wj 1))
5.0b	(- (+ (/ (/ x (- (* wj wj) (* 1 1))) (/ (exp wj) (- wj 1))) wj) (/ wj (+ wj 1)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
55×	`add-sqr-sqrt`
46×	`times-frac`
34×	`add-cube-cbrt`
15×	`associate-/r*`
14×	`difference-of-squares`
10×	`add-cbrt-cube`
9×	`add-exp-log` `associate-/l*` `add-log-exp`
6×	`associate-/r/` `distribute-lft-out--`
5×	`distribute-lft-out`
4×	`pow1` `difference-of-sqr-1`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `diff-log` `frac-sub` `flip-+`
1×	`sub-neg` `associate--l+` `sum-log`

Counts

4 → 131

Calls

4 calls:

7.0ms	(/ (exp wj) (- wj 1))
5.0ms	(/ x (- (* wj wj) (* 1 1)))
5.0ms	(/ wj (+ wj 1))
141.0ms	(- (+ (/ (/ x (- (* wj wj) (* 1 1))) (/ (exp wj) (- wj 1))) wj) (/ wj (+ wj 1)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (exp wj) (- wj 1))
63.0ms	(/ x (- (* wj wj) (* 1 1)))
21.0ms	(/ wj (+ wj 1))
120.0ms	(- (+ (/ (/ x (- (* wj wj) (* 1 1))) (/ (exp wj) (- wj 1))) wj) (/ wj (+ wj 1)))

simplify62.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	598	1227
1	2539	1158
2	5002	1146

prune375.0ms

Filtered

143 candidates to 103 candidates (72.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	144	6	150

Merged error: 0.2b

Counts

150 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (exp wj) (- wj 1))
0.0b	(/ x (- (* wj wj) (* 1 1)))
0.0b	(/ (/ wj (sqrt (+ wj 1))) (sqrt (+ wj 1)))
5.0b	(- (+ (/ (/ x (- (* wj wj) (* 1 1))) (/ (exp wj) (- wj 1))) wj) (/ (/ wj (sqrt (+ wj 1))) (sqrt (+ wj 1))))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

400×	`times-frac`
314×	`*-un-lft-identity`
233×	`add-sqr-sqrt`
213×	`sqrt-prod`
193×	`add-cube-cbrt`
53×	`distribute-lft-out`
33×	`associate-/l*`
22×	`associate-/r/`
19×	`difference-of-squares`
18×	`sqrt-div` `associate-/r*`
13×	`add-cbrt-cube`
12×	`add-exp-log`
11×	`div-inv`
10×	`flip3-+` `flip-+`
9×	`add-log-exp`
6×	`distribute-lft-out--`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `difference-of-sqr-1`
3×	`flip3--` `frac-2neg` `clear-num` `flip--`
2×	`diff-log` `frac-sub`
1×	`sub-neg` `associate--l+` `sum-log` `associate-/l/`

Counts

4 → 343

Calls

4 calls:

9.0ms	(/ (exp wj) (- wj 1))
5.0ms	(/ x (- (* wj wj) (* 1 1)))
16.0ms	(/ (/ wj (sqrt (+ wj 1))) (sqrt (+ wj 1)))
383.0ms	(- (+ (/ (/ x (- (* wj wj) (* 1 1))) (/ (exp wj) (- wj 1))) wj) (/ (/ wj (sqrt (+ wj 1))) (sqrt (+ wj 1))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (exp wj) (- wj 1))
63.0ms	(/ x (- (* wj wj) (* 1 1)))
21.0ms	(/ (/ wj (sqrt (+ wj 1))) (sqrt (+ wj 1)))
118.0ms	(- (+ (/ (/ x (- (* wj wj) (* 1 1))) (/ (exp wj) (- wj 1))) wj) (/ (/ wj (sqrt (+ wj 1))) (sqrt (+ wj 1))))

simplify127.0ms

Algorithm

egg-herbie

Counts

355 → 355

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1087	4485
1	4890	3952
2	5001	3952

prune679.0ms

Filtered

355 candidates to 167 candidates (47.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	353	2	355
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	355	6	361

Merged error: 0.1b

Counts

361 → 6

regimes70.0ms

Accuracy

65.7% (0.6b remaining)

Error of 0.9b against oracle of 0.3b and baseline of 2.1b

bsearch41.0ms

Steps

Iters	Range		Point
8	2.2008713026740717e-11	7.826288469630172e-07	1.3121422791952024e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	55
1	36	55

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.5s	7827×	body	10240	exit
196.0ms	6325×	body	80	valid
74.0ms	753×	body	320	valid
63.0ms	432×	body	640	valid
35.0ms	567×	body	160	valid