Details

sample60.0ms

Algorithm

intervals

Results

26.0ms	125×	body	5120	exit
7.0ms	215×	body	80	valid
4.0ms	121×	body	80	overflowed
3.0ms	14×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid

simplify48.0ms

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	5002	8

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 9.7b

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))
3.1b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite61.0ms

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))
31.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ wj (+ wj 1))
6.0ms	(/ x (+ wj 1))
14.0ms	(/ (/ x (+ wj 1)) (exp wj))
16.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify82.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	721	1524
1	3303	1471
2	5002	1469

prune258.0ms

Filtered

188 candidates to 138 candidates (26.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	185	5	190

Merged error: 0.3b

Counts

190 → 5

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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:

5.0ms	(* 2 (* wj x))
4.0ms	(+ x (pow wj 2))
8.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))

series20.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 2 (* wj x))
9.0ms	(+ x (pow wj 2))
7.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))

simplify135.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	202	245
1	794	228
2	4221	225
3	5001	225

prune77.0ms

Filtered

53 candidates to 32 candidates (39.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	51	7	58

Merged error: 0.3b

Counts

58 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))
0.6b	(cbrt (+ x (pow wj 2)))

rewrite30.0ms

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×	`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 → 95

Calls

4 calls:

13.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
5.0ms	(cbrt (+ x (pow wj 2)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
54.0ms	(cbrt (+ x (pow wj 2)))
56.0ms	(cbrt (+ x (pow wj 2)))
57.0ms	(cbrt (+ x (pow wj 2)))

simplify136.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	286	944
1	927	893
2	4130	787
3	5001	764

prune275.0ms

Filtered

107 candidates to 72 candidates (32.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	106	8	114

Merged error: 0.3b

Counts

114 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cbrt-prod`
19×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `distribute-lft-out` `add-log-exp`
3×	`pow-unpow` `flip3-+` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

4.0ms	(cbrt (+ x (pow wj 2)))
5.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
8.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

series251.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (+ x (pow wj 2)))
54.0ms	(cbrt (+ x (pow wj 2)))
57.0ms	(cbrt (+ x (pow wj 2)))
84.0ms	(pow (cbrt (cbrt (+ x (pow wj 2)))) 4)

simplify104.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (96.0ms)

Iter	Nodes	Cost
0	295	638
1	851	597
2	3181	545
3	5001	519

prune275.0ms

Filtered

79 candidates to 57 candidates (27.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	79	8	87

Merged error: 0.3b

Counts

87 → 8

regimes232.0ms

Accuracy

97.1% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 2.0b

bsearch40.0ms

Steps

Iters	Range		Point
8	3.469362278490668e-12	4.9301397366023513e-08	9.022428011286162e-09
9	-0.05940270564741191	-1.0623176005719452e-10	-1.4120689286568841e-08

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	22
1	36	22

end0.0ms

sample1.8s

Algorithm

intervals

Results

826.0ms	3815×	body	5120	exit
225.0ms	6244×	body	80	valid
123.0ms	3775×	body	80	overflowed
94.0ms	814×	body	320	valid
80.0ms	445×	body	640	valid
42.0ms	580×	body	160	valid

Details

sample60.0ms

simplify48.0ms

prune13.0ms

localize9.0ms

rewrite61.0ms

series39.0ms

simplify82.0ms

prune258.0ms

localize7.0ms

rewrite18.0ms

series20.0ms

simplify135.0ms

prune77.0ms

localize12.0ms

rewrite30.0ms

series230.0ms

simplify136.0ms

prune275.0ms

localize17.0ms

rewrite23.0ms

series251.0ms

simplify104.0ms

prune275.0ms

regimes232.0ms

bsearch40.0ms

simplify1.0ms

end0.0ms

sample1.8s

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