Details

sample39.0ms

Algorithm

intervals

Results

17.0ms	394×	body	80	valid
6.0ms	160×	body	80	nan

simplify126.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	24	7
1	48	7
2	96	6
3	256	6
4	891	6
5	3954	6
6	5002	6

prune9.0ms

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

385×	`*-un-lft-identity`
200×	`distribute-lft-out`
162×	`times-frac`
133×	`associate-l`
120×	`add-sqr-sqrt`
77×	`associate-r`
65×	`add-cube-cbrt`
44×	`unpow-prod-down`
33×	`unswap-sqr`
22×	`sqr-pow`
18×	`add-exp-log` `associate-/l*`
11×	`*-commutative`
10×	`add-cbrt-cube`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`prod-exp`
5×	`pow1`
4×	`div-exp`
3×	`sum-log`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`frac-2neg` `pow-prod-down` `clear-num` `div-inv`

Counts

3 → 253

Calls

3 calls:

6.0ms	(* a (pow k m))
12.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
22.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series204.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(* a (pow k m))
20.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
121.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify110.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	628	2627
1	3024	2476
2	5001	2464

prune292.0ms

Filtered

262 candidates to 112 candidates (42.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	260	4	264

Merged error: 1.2b

Counts

264 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
0.0b	(* k (+ 10.0 k))
0.1b	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
2.9b	(/ (+ 1.0 (* k (+ 10.0 k))) a)

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

1646×	`times-frac`
1165×	`*-un-lft-identity`
691×	`add-sqr-sqrt`
689×	`add-cube-cbrt`
291×	`unpow-prod-down`
237×	`distribute-lft-out`
160×	`associate-/r*`
121×	`associate-l`
97×	`sqr-pow`
70×	`add-exp-log`
60×	`associate-/l*`
51×	`div-exp`
44×	`div-inv`
42×	`associate-/r/`
36×	`associate-/l/`
22×	`add-cbrt-cube`
10×	`cbrt-undiv`
8×	`pow-to-exp` `pow-exp` `clear-num`
7×	`pow1` `rec-exp` `1-exp`
6×	`frac-2neg` `remove-double-div`
4×	`flip3-+` `associate-r` `flip-+` `add-log-exp`
2×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `associate-*r/`
1×	`pow-flip` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 887

Calls

4 calls:

18.0ms	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
6.0ms	(* k (+ 10.0 k))
43.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
11.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

series316.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
49.0ms	(* k (+ 10.0 k))
109.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
49.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

simplify183.0ms

Algorithm

egg-herbie

Counts

899 → 899

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	2235	12116
1	5001	11598

prune1.2s

Filtered

899 candidates to 419 candidates (46.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	898	1	899
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	899	4	903

Merged error: 1.2b

Counts

903 → 4

localize13.0ms

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))))
13.5b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
13.5b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite595.0ms

Algorithm

rewrite-expression-head

Rules

8939×	`*-un-lft-identity`
5472×	`times-frac`
4610×	`distribute-lft-out`
4140×	`sqrt-prod`
2776×	`associate-l`
2350×	`add-sqr-sqrt`
1563×	`add-cube-cbrt`
1099×	`associate-r`
628×	`unpow-prod-down`
471×	`unswap-sqr`
314×	`sqr-pow`
240×	`associate-/l*`
157×	`*-commutative`
33×	`associate-/l/`
32×	`sqrt-div`
28×	`associate-/r/`
24×	`associate-/r*`
20×	`add-exp-log`
17×	`flip3-+` `flip-+`
14×	`div-inv`
13×	`add-cbrt-cube`
9×	`div-exp` `add-log-exp`
6×	`pow1`
5×	`cbrt-undiv`
3×	`prod-exp` `sum-log`
2×	`+-commutative` `rem-sqrt-square` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`pow-to-exp` `pow-exp` `cbrt-unprod`

Counts

4 → 3013

Calls

4 calls:

12.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
118.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
12.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
15.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
125.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
49.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
60.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify654.0ms

Algorithm

egg-herbie

Counts

3025 → 3025

Iterations

Useful iterations: 1 (75.0ms)

Iter	Nodes	Cost
0	2603	62717
1	5001	55531

prune1.3s

Filtered

3025 candidates to 387 candidates (12.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	3025	0	3025
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	3025	4	3029

Merged error: 1.2b

Counts

3029 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* 1.0 (* a (* m (log k)))) (* 1.0 a)) (* 10.0 (* k a)))
0.2b	(* m (log k))
0.2b	(* 10.0 (* k a))
0.4b	(* a (* m (log k)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
53×	`add-sqr-sqrt`
51×	`distribute-rgt-in` `distribute-lft-in`
42×	`log-prod`
36×	`associate-r`
28×	`add-cube-cbrt` `associate-l`
26×	`associate--l+`
24×	`associate-+l+`
18×	`pow1`
16×	`add-exp-log` `add-cbrt-cube`
12×	`unswap-sqr`
10×	`distribute-lft-out--`
9×	`add-log-exp`
8×	`distribute-lft-out`
7×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`*-commutative`
3×	`difference-of-squares`
2×	`diff-log` `log-pow`
1×	`+-commutative` `sub-neg` `flip3--` `sum-log` `flip--`

Counts

4 → 152

Calls

4 calls:

57.0ms	(- (+ (* 1.0 (* a (* m (log k)))) (* 1.0 a)) (* 10.0 (* k a)))
4.0ms	(* m (log k))
7.0ms	(* 10.0 (* k a))
9.0ms	(* a (* m (log k)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (+ (* 1.0 (* a (* m (log k)))) (* 1.0 a)) (* 10.0 (* k a)))
44.0ms	(* m (log k))
22.0ms	(* 10.0 (* k a))
46.0ms	(* a (* m (log k)))

simplify88.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	704	1113
1	2899	998
2	5002	932

prune257.0ms

Filtered

164 candidates to 105 candidates (64.0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	164	4	168

Merged error: 1.2b

Counts

168 → 4

regimes82.0ms

Accuracy

0% (0.1b remaining)

Error of 1.9b against oracle of 1.9b 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

536.0ms	12067×	body	80	valid
156.0ms	4358×	body	80	nan