Details

sample1.5m

Algorithm

intervals

Results

24.0ms	360×	body	80	valid
6.0ms	149×	body	80	nan

simplify101.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

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

prune10.0ms

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: 2.8b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* a (pow k m))
0.0b	(+ 1.0 (* 10.0 k))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.8b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite23.0ms

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:

5.0ms	(* a (pow k m))
2.0ms	(+ 1.0 (* 10.0 k))
4.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (48.0ms)

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

prune100.0ms

Filtered

86 candidates to 63 candidates (26.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	86	2	88

Merged error: 2.8b

Counts

88 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* k (+ 10.0 k)) 1.0)
0.0b	(* k (+ 10.0 k))
0.2b	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
2.7b	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

6.0ms	(+ (* k (+ 10.0 k)) 1.0)
5.0ms	(* k (+ 10.0 k))
10.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
13.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

series51.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (* k (+ 10.0 k)) 1.0)
4.0ms	(* k (+ 10.0 k))
15.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
28.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

simplify70.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	637	1201
1	2651	1127
2	5001	1126

prune173.0ms

Filtered

145 candidates to 110 candidates (24.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	145	2	147

Merged error: 2.8b

Counts

147 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
17.8b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
17.8b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-sqr-sqrt`
92×	`times-frac`
52×	`sqrt-prod`
48×	`associate-r`
46×	`add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log`
24×	`unpow-prod-down` `associate-l`
21×	`unswap-sqr`
16×	`add-cbrt-cube`
12×	`sqr-pow`
10×	`div-exp`
9×	`add-log-exp`
8×	`pow1` `sqrt-div` `prod-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`sum-log`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `div-inv`
1×	`+-commutative` `frac-times` `associate-+l+` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 160

Calls

4 calls:

5.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
37.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (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)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
3.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
4.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify90.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	869	2737
1	3910	2557
2	5002	2443

prune272.0ms

Filtered

172 candidates to 112 candidates (34.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	172	2	174

Merged error: 2.8b

Counts

174 → 2

regimes120.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	6
1	15	6

end0.0ms

sample58.2s

Algorithm

intervals

Results

Details

sample1.5m

simplify101.0ms

prune10.0ms

localize10.0ms

rewrite23.0ms

series52.0ms

simplify55.0ms

prune100.0ms

localize9.0ms

rewrite39.0ms

series51.0ms

simplify70.0ms

prune173.0ms

localize13.0ms

rewrite57.0ms

series42.0ms

simplify90.0ms

prune272.0ms

regimes120.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample58.2s

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