Details

sample74.0ms

Algorithm

intervals

Results

48.0ms	230×	body	10240	exit
6.0ms	185×	body	80	valid
3.0ms	35×	body	320	valid
3.0ms	19×	body	640	valid
1.0ms	18×	body	160	valid

simplify48.0ms

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

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: 16.9b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.2b	(/ (/ x (+ wj 1)) (exp wj))
6.2b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite68.0ms

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:

8.0ms	(/ wj (+ wj 1))
5.0ms	(/ x (+ wj 1))
10.0ms	(/ (/ x (+ wj 1)) (exp wj))
31.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ wj (+ wj 1))
21.0ms	(/ x (+ wj 1))
44.0ms	(/ (/ x (+ wj 1)) (exp wj))
53.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify131.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (92.0ms)

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

prune443.0ms

Filtered

272 candidates to 165 candidates (60.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	269	3	272
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	271	3	274

Merged error: 0.1b

Counts

274 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 37

Calls

2 calls:

5.0ms	(+ x (pow wj 2))
5.0ms	(* 2 (* wj x))

series47.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify70.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	156	140
1	573	114
2	2424	114
3	5002	113

prune73.0ms

Filtered

43 candidates to 30 candidates (69.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Merged error: 0.1b

Counts

46 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(cbrt (+ x (pow wj 2)))
0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
12.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))

series1.2s

Counts

4 → 12

Calls

4 calls:

319.0ms	(cbrt (+ x (pow wj 2)))
321.0ms	(cbrt (+ x (pow wj 2)))
318.0ms	(cbrt (+ x (pow wj 2)))
269.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))

simplify172.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	259	918
1	995	867
2	4922	790
3	5001	790

prune277.0ms

Filtered

115 candidates to 86 candidates (74.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	114	6	120

Merged error: 0.1b

Counts

120 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
0.5b	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
0.5b	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
0.5b	(* (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))) (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

420×	`cbrt-div`
148×	`frac-times`
126×	`flip3-+` `flip-+`
50×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
11×	`pow1` `cbrt-prod`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 173

Calls

4 calls:

11.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
11.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
11.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
10.0ms	(* (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))) (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

455.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
279.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
276.0ms	(cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2)))))
302.0ms	(* (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))) (cbrt (* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))))

simplify163.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	378	4841
1	1044	4705
2	4268	4621
3	5001	4617

prune454.0ms

Filtered

185 candidates to 101 candidates (54.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	184	7	191

Merged error: 0.1b

Counts

191 → 7

regimes63.0ms

Accuracy

69.1% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 2.0b

bsearch40.0ms

Steps

Iters	Range		Point
9	1.2261953182377537e-15	1.3201210546183864e-08	4.794595763324104e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	29	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.5s	7538×	body	10240	exit
199.0ms	6294×	body	80	valid
73.0ms	738×	body	320	valid
72.0ms	467×	body	640	valid
37.0ms	566×	body	160	valid