Details

sample52.0ms

Algorithm

intervals

Results

29.0ms	379×	body	80	valid
6.0ms	137×	body	80	nan

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	24	7
1	48	7
2	96	6
3	256	6
4	891	6
5	3963	6
6	5002	6

prune7.0ms

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: 1.7b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
1.7b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-exp-log`
10×	`add-log-exp`
8×	`add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp` `sum-log`
3×	`pow1` `flip3-+` `times-frac` `prod-exp` `associate-/r*` `flip-+`
2×	`cbrt-undiv` `+-commutative` `associate-/r/`
1×	`pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

3 → 49

Calls

3 calls:

2.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series164.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ 1.0 (* 10.0 k))
22.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
111.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify46.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	404	484
1	1787	427
2	5001	418

prune114.0ms

Filtered

58 candidates to 41 candidates (70.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	56	2	58
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	56	4	60

Merged error: 1.7b

Counts

60 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.1b	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
1.6b	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`times-frac`
38×	`*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`associate-l`
22×	`unpow-prod-down`
20×	`add-exp-log`
12×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`pow1` `associate-r` `associate-/l*`
6×	`div-exp`
5×	`prod-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`flip3-+` `associate-/r*` `cbrt-unprod` `flip-+` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `associate-r/` `pow-prod-down` `pow-exp` `-commutative` `div-inv`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `associate-*l/` `clear-num` `distribute-lft-out`

Counts

3 → 120

Calls

3 calls:

9.0ms	(* k (+ 10.0 k))
9.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
13.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

series209.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* k (+ 10.0 k))
61.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
101.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

simplify70.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	608	1105
1	2523	1041
2	5001	1035

prune263.0ms

Filtered

129 candidates to 98 candidates (76.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	129	4	133

Merged error: 1.7b

Counts

133 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ a (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
15.2b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.2b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.2b	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-div`
9×	`add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
8×	`associate-/r/`
7×	`add-cbrt-cube`
4×	`pow1` `frac-times` `add-log-exp`
3×	`times-frac` `pow1/3` `associate-/l*`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 68

Calls

4 calls:

13.0ms	(/ a (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
4.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(/ a (* (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k))) (cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
108.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
104.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
104.0ms	(cbrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify121.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	374	1027
1	1215	931
2	4304	905
3	5002	905

prune264.0ms

Filtered

80 candidates to 72 candidates (90.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	80	4	84

Merged error: 1.7b

Counts

84 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
1.6b	(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
14.6b	(sqrt (+ (* k (+ 10.0 k)) 1.0))
14.6b	(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

1148×	`times-frac`
607×	`add-sqr-sqrt`
583×	`sqrt-prod`
553×	`add-cube-cbrt` `*-un-lft-identity`
294×	`associate-l`
238×	`unpow-prod-down`
82×	`sqr-pow`
48×	`associate-/l*`
34×	`sqrt-div`
30×	`add-exp-log` `associate-/r/`
18×	`add-cbrt-cube`
17×	`flip3-+` `flip-+`
15×	`div-inv` `unswap-sqr`
14×	`div-exp`
8×	`pow1`
6×	`cbrt-undiv` `associate-/r*`
5×	`prod-exp`
4×	`add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 721

Calls

4 calls:

28.0ms	(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
57.0ms	(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
9.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
6.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

series280.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
110.0ms	(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
58.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
46.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify145.0ms

Algorithm

egg-herbie

Counts

733 → 733

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1754	13231
1	5002	11898

prune1.4s

Filtered

733 candidates to 399 candidates (54.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	733	0	733
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	733	4	737

Merged error: 1.7b

Counts

737 → 4

regimes89.0ms

Accuracy

0% (0.0b remaining)

Error of 2.1b against oracle of 2.0b and baseline of 2.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample1.4s

Algorithm

intervals

Results

822.0ms	11952×	body	80	valid
184.0ms	4215×	body	80	nan

Details

sample52.0ms

simplify111.0ms

prune7.0ms

localize10.0ms

rewrite16.0ms

series164.0ms

simplify46.0ms

prune114.0ms

localize9.0ms

rewrite35.0ms

series209.0ms

simplify70.0ms

prune263.0ms

localize18.0ms

rewrite27.0ms

series503.0ms

simplify121.0ms

prune264.0ms

localize11.0ms

rewrite159.0ms

series280.0ms

simplify145.0ms

prune1.4s

regimes89.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

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