Details

sample65.0ms

Algorithm

intervals

Results

28.0ms	136×	body	5120	exit
11.0ms	207×	body	80	valid
4.0ms	122×	body	80	overflowed
2.0ms	22×	body	320	valid
2.0ms	10×	body	640	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	5002	8

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 10.9b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (/ x (+ wj 1)) (exp wj)) wj)
0.0b	(/ x (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
4.9b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
103×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
21×	`associate-/l*`
18×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-log-exp`
10×	`associate-/r/`
9×	`add-exp-log`
7×	`flip3-+` `associate-/r*` `flip-+`
6×	`div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `diff-log` `clear-num` `sum-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--` `associate-/l/`

Counts

4 → 155

Calls

4 calls:

23.0ms	(+ (/ (/ x (+ wj 1)) (exp wj)) wj)
5.0ms	(/ x (+ wj 1))
9.0ms	(/ (/ x (+ wj 1)) (exp wj))
28.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series162.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (/ (/ x (+ wj 1)) (exp wj)) wj)
21.0ms	(/ x (+ wj 1))
37.0ms	(/ (/ x (+ wj 1)) (exp wj))
56.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify71.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	674	1485
1	3058	1436
2	5002	1434

prune510.0ms

Filtered

167 candidates to 124 candidates (74.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	162	5	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	5	168

Merged error: 0.4b

Counts

168 → 5

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

series50.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(* 2 (* wj x))
31.0ms	(+ x (pow wj 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	149	122
1	551	108
2	2352	107
3	5001	107

prune105.0ms

Filtered

36 candidates to 21 candidates (58.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	32	9	41

Merged error: 0.4b

Counts

41 → 9

localize11.0ms

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)))

rewrite29.0ms

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:

14.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))
4.0ms	(cbrt (+ x (pow wj 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (cbrt (+ x (pow wj 2))) (cbrt (+ x (pow wj 2))))
313.0ms	(cbrt (+ x (pow wj 2)))
305.0ms	(cbrt (+ x (pow wj 2)))
305.0ms	(cbrt (+ x (pow wj 2)))

simplify165.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (155.0ms)

Iter	Nodes	Cost
0	252	878
1	944	827
2	4715	760
3	5001	749

prune371.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	108	8	116

Merged error: 0.4b

Counts

116 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

115×	`times-frac`
103×	`*-un-lft-identity`
69×	`add-sqr-sqrt`
64×	`add-cube-cbrt`
21×	`associate-/l*`
18×	`distribute-lft-out`
11×	`add-cbrt-cube` `add-log-exp`
10×	`associate-/r/`
9×	`add-exp-log`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`pow1` `cbrt-undiv` `div-exp`
2×	`sub-neg` `associate-+r+` `flip3--` `frac-2neg` `diff-log` `frac-add` `clear-num` `sum-log` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate-+r-` `associate-/l/`

Counts

4 → 157

Calls

4 calls:

36.0ms	(+ (/ (/ x (+ wj 1)) (exp wj)) (- wj (/ wj (+ wj 1))))
5.0ms	(/ x (+ wj 1))
9.0ms	(/ (/ x (+ wj 1)) (exp wj))
8.0ms	(- wj (/ wj (+ wj 1)))

series141.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (/ (/ x (+ wj 1)) (exp wj)) (- wj (/ wj (+ wj 1))))
27.0ms	(/ x (+ wj 1))
37.0ms	(/ (/ x (+ wj 1)) (exp wj))
25.0ms	(- wj (/ wj (+ wj 1)))

simplify75.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	688	1409
1	3015	1360
2	5001	1358

prune496.0ms

Filtered

169 candidates to 124 candidates (73.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	173	4	177

Merged error: 0.0b

Counts

177 → 4

regimes99.0ms

Accuracy

76% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 1.2b

bsearch45.0ms

Steps

Iters	Range		Point
9	1.8814443039852147e-08	45.05589645901405	0.00010020069437579795

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.8s

Algorithm

intervals

Results

812.0ms	3761×	body	5120	exit
219.0ms	6323×	body	80	valid
132.0ms	3806×	body	80	overflowed
86.0ms	783×	body	320	valid
74.0ms	439×	body	640	valid
39.0ms	548×	body	160	valid

Details

sample65.0ms

simplify45.0ms

prune8.0ms

localize9.0ms

rewrite71.0ms

series162.0ms

simplify71.0ms

prune510.0ms

localize7.0ms

rewrite9.0ms

series50.0ms

simplify68.0ms

prune105.0ms

localize11.0ms

rewrite29.0ms

series1.2s

simplify165.0ms

prune371.0ms

localize9.0ms

rewrite64.0ms

series141.0ms

simplify75.0ms

prune496.0ms

regimes99.0ms

bsearch45.0ms

simplify1.0ms

end0.0ms

sample1.8s

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