Details

sample78.0ms

Algorithm

intervals

Results

51.0ms	235×	body	10240	exit
7.0ms	213×	body	80	valid
3.0ms	29×	body	320	valid
1.0ms	9×	body	640	valid
1.0ms	13×	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

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: 11.4b

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))
4.1b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite60.0ms

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))
5.0ms	(/ x (+ wj 1))
10.0ms	(/ (/ x (+ wj 1)) (exp wj))
33.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series140.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ wj (+ wj 1))
22.0ms	(/ x (+ wj 1))
38.0ms	(/ (/ x (+ wj 1)) (exp wj))
57.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify80.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (64.0ms)

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

prune424.0ms

Filtered

188 candidates to 138 candidates (73.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	183	5	188
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	185	5	190

Merged error: 0.1b

Counts

190 → 5

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

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

series51.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify113.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	162	196
1	645	179
2	3837	177
3	5001	177

prune66.0ms

Filtered

38 candidates to 22 candidates (57.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	37	6	43

Merged error: 0.1b

Counts

43 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3--` `pow1/3` `flip--`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `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 → 87

Calls

4 calls:

17.0ms	(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
7.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
9.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
7.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

series1.1s

Counts

4 → 12

Calls

4 calls:

301.0ms	(* (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))) (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
264.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
263.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))
260.0ms	(cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	315	1593
1	1201	1500
2	5001	1416

prune278.0ms

Filtered

99 candidates to 75 candidates (75.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	99	6	105

Merged error: 0.1b

Counts

105 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.6b	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.6b	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
0.9b	(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-div`
9×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `flip3--` `flip--`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

7.0ms	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
7.0ms	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
7.0ms	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
10.0ms	(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

series944.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
273.0ms	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
276.0ms	(cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x)))))
125.0ms	(pow (cbrt (cbrt (- (+ x (pow wj 2)) (* 2 (* wj x))))) 4)

simplify51.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	395	1260
1	1423	1191
2	5001	1170

prune322.0ms

Filtered

84 candidates to 67 candidates (79.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 0.1b

Counts

90 → 7

regimes74.0ms

Accuracy

60.6% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.1b

bsearch34.0ms

Steps

Iters	Range		Point
8	4.278730963433957e-11	2.0940920541712224e-07	8.741130488109898e-09

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	16
1	31	16

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.5s	7551×	body	10240	exit
203.0ms	6295×	body	80	valid
80.0ms	770×	body	320	valid
72.0ms	484×	body	640	valid
35.0ms	553×	body	160	valid