Details

sample139.0ms

Algorithm

intervals

Results

89.0ms	171×	body	10240	exit
22.0ms	336×	body	80	valid
6.0ms	175×	body	80	nan

simplify107.0ms

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.3b	(* a (pow k m))
3.0b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

9.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
6.0ms	(* a (pow k m))
14.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
57.0ms	(* a (pow k m))
114.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify55.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	405	548
1	1965	482
2	5001	475

prune178.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* a (pow (sqrt k) m))
0.0b	(* (* a (pow (sqrt k) m)) (pow (sqrt k) m))
3.0b	(/ (* (* a (pow (sqrt k) m)) (pow (sqrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

9.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms	(* a (pow (sqrt k) m))
16.0ms	(* (* a (pow (sqrt k) m)) (pow (sqrt k) m))
26.0ms	(/ (* (* a (pow (sqrt k) m)) (pow (sqrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
154.0ms	(* a (pow (sqrt k) m))
188.0ms	(* (* a (pow (sqrt k) m)) (pow (sqrt k) m))
246.0ms	(/ (* (* a (pow (sqrt k) m)) (pow (sqrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify78.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	522	1100
1	2799	906
2	5001	876

prune268.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 3.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sqrt k))
0.6b	(cbrt (sqrt k))
0.6b	(cbrt (sqrt k))
3.0b	(/ (* (* (* a (pow (sqrt k) m)) (pow (* (cbrt (sqrt k)) (cbrt (sqrt k))) m)) (pow (cbrt (sqrt k)) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

214×	`add-exp-log`
147×	`prod-exp`
53×	`pow-exp`
52×	`div-exp`
41×	`pow-to-exp`
18×	`cbrt-prod` `add-cbrt-cube`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `add-log-exp`
3×	`times-frac` `pow1/3` `associate-/r*`
2×	`associate-/r/`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 117

Calls

4 calls:

1.0ms	(cbrt (sqrt k))
1.0ms	(cbrt (sqrt k))
1.0ms	(cbrt (sqrt k))
58.0ms	(/ (* (* (* a (pow (sqrt k) m)) (pow (* (cbrt (sqrt k)) (cbrt (sqrt k))) m)) (pow (cbrt (sqrt k)) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series1.1s

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (sqrt k))
151.0ms	(cbrt (sqrt k))
151.0ms	(cbrt (sqrt k))
665.0ms	(/ (* (* (* a (pow (sqrt k) m)) (pow (* (cbrt (sqrt k)) (cbrt (sqrt k))) m)) (pow (cbrt (sqrt k)) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify91.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	702	2038
1	3116	1835
2	5002	1773

prune337.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 3.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.3b	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
14.7b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
14.7b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
134×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
48×	`associate-r`
45×	`unpow-prod-down`
33×	`add-exp-log`
24×	`associate-l`
21×	`unswap-sqr`
19×	`sqr-pow`
18×	`add-cbrt-cube`
13×	`div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp`
7×	`associate-/l*`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 218

Calls

4 calls:

16.0ms	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
86.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
10.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
10.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
116.0ms	(* (/ a (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (/ (pow k m) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))))
53.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify105.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	899	3695
1	3999	3453
2	5002	3348

prune604.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 3.0b

regimes72.0ms

Accuracy

0% (0.0b remaining)

Error of 2.8b against oracle of 2.7b and baseline of 2.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	11
1	19	11

end0.0ms

sample4.1s

Algorithm

intervals

Results

2.6s	5092×	body	10240	exit
747.0ms	10678×	body	80	valid
205.0ms	5645×	body	80	nan