Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	371×	body	80	valid
5.0ms	147×	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

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite30.0ms

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

series194.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
116.0ms	(/ (* 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

prune180.0ms

Filtered

72 candidates to 53 candidates (73.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 3.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
30×	`prod-exp`
16×	`div-exp`
13×	`add-cbrt-cube`
11×	`pow-exp`
9×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow-to-exp`
4×	`pow1` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `pow1/3` `associate-/r*` `cbrt-unprod`
2×	`associate-/r/`
1×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 71

Calls

4 calls:

0.0ms	(cbrt k)
0.0ms	(cbrt k)
0.0ms	(cbrt k)
21.0ms	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series882.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt k)
169.0ms	(cbrt k)
171.0ms	(cbrt k)
372.0ms	(/ (* (* a (pow (* (cbrt k) (cbrt k)) m)) (pow (cbrt k) m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify64.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	506	882
1	2389	755
2	5001	731

prune252.0ms

Filtered

83 candidates to 57 candidates (68.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
12.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
12.9b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `flip-+`

Counts

4 → 52

Calls

4 calls:

0.0ms	(cbrt k)
0.0ms	(cbrt k)
13.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
10.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt k)
171.0ms	(cbrt k)
50.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))
47.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify64.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	179	366
1	588	352
2	2219	340
3	5002	338

prune265.0ms

Filtered

64 candidates to 54 candidates (84.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

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))
0.4b	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
5.0b	(/ (+ 1.0 (* k (+ 10.0 k))) a)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

1073×	`times-frac`
500×	`add-sqr-sqrt` `*-un-lft-identity`
498×	`add-cube-cbrt`
198×	`unpow-prod-down`
105×	`associate-/r*`
70×	`add-exp-log`
66×	`sqr-pow`
51×	`div-exp`
43×	`div-inv`
22×	`add-cbrt-cube`
19×	`associate-/l*`
10×	`cbrt-undiv`
8×	`pow-to-exp` `pow-exp`
7×	`pow1` `rec-exp` `1-exp`
4×	`associate-r` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `associate-/l/`
2×	`flip3-+` `associate-*r/` `flip-+`
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

4 → 602

Calls

4 calls:

15.0ms	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
10.0ms	(* k (+ 10.0 k))
26.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
9.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

series303.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m))
42.0ms	(* k (+ 10.0 k))
108.0ms	(/ 1 (/ (/ (+ 1.0 (* k (+ 10.0 k))) a) (pow k m)))
48.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) a)

simplify129.0ms

Algorithm

egg-herbie

Counts

614 → 614

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2178	9172
1	5002	8740

prune1.4s

Filtered

614 candidates to 381 candidates (62.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes69.0ms

Accuracy

94.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 2.2b

bsearch64.0ms

Steps

Iters	Range		Point
7	2.0033128006131575e+43	7.386370596371953e+44	1.4637587288026368e+44

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	54
1	58	54

end0.0ms

sample1.0s

Algorithm

intervals

Results

493.0ms	11895×	body	80	valid
143.0ms	4121×	body	80	nan