Details

sample40.0ms

Algorithm

intervals

Results

20.0ms	375×	body	80	valid
4.0ms	117×	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

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: 1.2b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
0.0b	(* a (pow k m))
1.2b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite20.0ms

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:

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

series199.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
63.0ms	(* a (pow k m))
118.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify57.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (50.0ms)

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

prune179.0ms

Filtered

72 candidates to 53 candidates (73.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Merged error: 1.2b

Counts

74 → 7

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* k (+ 10.0 k))
0.0b	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
1.2b	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

rewrite34.0ms

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:

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

series219.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* k (+ 10.0 k))
63.0ms	(/ (pow k m) (+ (* k (+ 10.0 k)) 1.0))
107.0ms	(* (/ (pow k m) (+ (* k (+ 10.0 k)) 1.0)) a)

simplify75.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (61.0ms)

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

prune307.0ms

Filtered

129 candidates to 98 candidates (76.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	126	3	129
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	131	5	136

Merged error: 1.2b

Counts

136 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
1.2b	(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
12.1b	(sqrt (+ (* k (+ 10.0 k)) 1.0))
12.1b	(sqrt (+ (* k (+ 10.0 k)) 1.0))

rewrite170.0ms

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:

27.0ms	(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
63.0ms	(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
6.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
6.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

series279.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0)))
105.0ms	(* (/ (/ (pow k m) (sqrt (+ (* k (+ 10.0 k)) 1.0))) (sqrt (+ (* k (+ 10.0 k)) 1.0))) a)
47.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))
56.0ms	(sqrt (+ (* k (+ 10.0 k)) 1.0))

simplify156.0ms

Algorithm

egg-herbie

Counts

733 → 733

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1754	13231
1	5002	11898

prune1.5s

Filtered

733 candidates to 399 candidates (54.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	733	0	733
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	733	5	738

Merged error: 1.2b

Counts

738 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b	(* (/ 1 (* (cbrt (+ (* k (+ 10.0 k)) 1.0)) (cbrt (+ (* k (+ 10.0 k)) 1.0)))) (* (/ (pow k m) (cbrt (+ (* k (+ 10.0 k)) 1.0))) a))
12.6b	(cbrt (+ (* k (+ 10.0 k)) 1.0))
12.6b	(cbrt (+ (* k (+ 10.0 k)) 1.0))
12.6b	(cbrt (+ (* k (+ 10.0 k)) 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

141×	`add-exp-log`
78×	`prod-exp`
41×	`div-exp`
31×	`add-cbrt-cube`
18×	`cbrt-div` `cbrt-unprod`
15×	`associate-l`
10×	`rec-exp` `1-exp`
9×	`pow1` `cbrt-undiv` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `flip-+`
8×	`associate-/r/`
7×	`pow-to-exp` `pow-exp`
5×	`frac-times` `associate-*l/`
4×	`add-log-exp`
3×	`times-frac` `pow1/3` `associate-*r/` `pow-prod-down`
1×	`associate-r` `*-commutative` `div-inv`

Counts

4 → 112

Calls

4 calls:

33.0ms	(* (/ 1 (* (cbrt (+ (* k (+ 10.0 k)) 1.0)) (cbrt (+ (* k (+ 10.0 k)) 1.0)))) (* (/ (pow k m) (cbrt (+ (* k (+ 10.0 k)) 1.0))) a))
6.0ms	(cbrt (+ (* k (+ 10.0 k)) 1.0))
6.0ms	(cbrt (+ (* k (+ 10.0 k)) 1.0))
6.0ms	(cbrt (+ (* k (+ 10.0 k)) 1.0))

series448.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (/ 1 (* (cbrt (+ (* k (+ 10.0 k)) 1.0)) (cbrt (+ (* k (+ 10.0 k)) 1.0)))) (* (/ (pow k m) (cbrt (+ (* k (+ 10.0 k)) 1.0))) a))
110.0ms	(cbrt (+ (* k (+ 10.0 k)) 1.0))
118.0ms	(cbrt (+ (* k (+ 10.0 k)) 1.0))
114.0ms	(cbrt (+ (* k (+ 10.0 k)) 1.0))

simplify82.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	692	2014
1	2890	1629
2	5001	1339

prune304.0ms

Filtered

124 candidates to 72 candidates (58.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	125	4	129

Merged error: 1.2b

Counts

129 → 4

regimes95.0ms

Accuracy

0% (0.0b remaining)

Error of 1.9b against oracle of 1.8b and baseline of 1.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

sample1.1s

Algorithm

intervals

Results

545.0ms	11957×	body	80	valid
158.0ms	4335×	body	80	nan