Details

sample1.6min

Algorithm

intervals

Results

25.0ms	369×	body	80	valid
5.0ms	115×	body	80	nan

simplify100.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (3.0ms)

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

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 1.6b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
14×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
6×	`prod-exp`
4×	`pow1` `unpow-prod-down` `div-exp` `sum-log`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 74

Calls

4 calls:

2.0ms	(+ 1.0 (* 10.0 k))
4.0ms	(* a (pow k m))
4.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
7.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ 1.0 (* 10.0 k))
14.0ms	(* a (pow k m))
2.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	471	611
1	2227	545
2	5002	538

prune108.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Merged error: 1.5b

Counts

87 → 5

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.4b	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
4.3b	(/ (+ 1.0 (* k (+ 10.0 k))) a)

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

910×	`times-frac`
415×	`add-sqr-sqrt` `*-un-lft-identity`
413×	`add-cube-cbrt`
156×	`unpow-prod-down`
98×	`associate-/r*`
56×	`add-exp-log`
52×	`sqr-pow`
42×	`div-exp`
34×	`div-inv`
16×	`add-cbrt-cube`
7×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `pow-to-exp` `pow-exp` `associate-/l*`
4×	`associate-r`
3×	`associate-l` `add-log-exp`
2×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+` `associate-/l/`
1×	`distribute-rgt-in` `pow-flip` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

3 → 472

Calls

3 calls:

6.0ms	(* k (+ 10.0 k))
19.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
6.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

series37.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* k (+ 10.0 k))
27.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
6.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

simplify100.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	2096	7320
1	5001	6925

prune656.0ms

Filtered

278 candidates to 481 candidates (-73.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	480	1	481
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	481	5	486

Merged error: 1.5b

Counts

486 → 5

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.4b	(/ 1 (/ (* (+ 1.0 (* k (+ 10.0 k))) (/ 1 a)) (pow k m)))
4.3b	(* (+ 1.0 (* k (+ 10.0 k))) (/ 1 a))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

153×	`add-exp-log`
97×	`div-exp`
72×	`times-frac`
46×	`add-sqr-sqrt`
41×	`prod-exp`
40×	`*-un-lft-identity`
37×	`add-cube-cbrt`
26×	`rec-exp` `1-exp`
24×	`add-cbrt-cube`
17×	`associate-r`
15×	`pow-to-exp` `pow-exp`
12×	`unpow-prod-down`
11×	`associate-/r*`
9×	`cbrt-undiv`
8×	`pow1`
6×	`associate-l` `div-inv`
5×	`cbrt-unprod`
4×	`unswap-sqr` `sqr-pow`
3×	`flip3-+` `associate-r/` `flip-+` `associate-/l` `add-log-exp`
2×	`frac-times` `pow-prod-down` `associate-l/` `-commutative`
1×	`distribute-rgt-in` `pow-flip` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r/` `un-div-inv` `distribute-lft-out` `inv-pow`

Counts

3 → 175

Calls

3 calls:

5.0ms	(* k (+ 10.0 k))
10.0ms	(/ 1 (/ (* (+ 1.0 (* k (+ 10.0 k))) (/ 1 a)) (pow k m)))
8.0ms	(* (+ 1.0 (* k (+ 10.0 k))) (/ 1 a))

series37.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* k (+ 10.0 k))
27.0ms	(/ 1 (/ (* (+ 1.0 (* k (+ 10.0 k))) (/ 1 a)) (pow k m)))
6.0ms	(* (+ 1.0 (* k (+ 10.0 k))) (/ 1 a))

simplify100.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	898	1720
1	4631	1530
2	5001	1518

prune150.0ms

Filtered

90 candidates to 184 candidates (-104.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	184	0	184
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	184	5	189

Merged error: 1.5b

Counts

189 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
13.1b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
13.1b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
66×	`sqrt-prod`
55×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
20×	`add-exp-log` `sqrt-div`
16×	`associate-/r/`
13×	`add-cbrt-cube`
12×	`associate-/l*`
11×	`flip3-+` `flip-+`
9×	`div-exp` `add-log-exp`
8×	`div-inv`
6×	`pow1` `associate-/r*`
5×	`cbrt-undiv`
3×	`prod-exp` `sum-log`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

4.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
3.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
3.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify80.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	738	3111
1	3265	2780
2	5002	2777

prune249.0ms

Filtered

102 candidates to 166 candidates (-62.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	166	5	171

Merged error: 1.5b

Counts

171 → 5

regimes209.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample51.9s

Algorithm

intervals

Results

Details

sample1.6min

simplify100.0ms

prune8.0ms

localize9.0ms

rewrite20.0ms

series51.0ms

simplify54.0ms

prune108.0ms

localize9.0ms

rewrite67.0ms

series37.0ms

simplify100.0ms

prune656.0ms

localize15.0ms

rewrite30.0ms

series37.0ms

simplify100.0ms

prune150.0ms

localize12.0ms

rewrite32.0ms

series41.0ms

simplify80.0ms

prune249.0ms

regimes209.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample51.9s

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