Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	377×	body	80	valid
5.0ms	145×	body	80	nan

simplify105.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k 10.0 1.0)
0.2b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.3b	(fma k k (fma k 10.0 1.0))
4.3b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
96×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`unpow-prod-down`
19×	`add-exp-log`
16×	`associate-/r*`
14×	`sqr-pow`
11×	`add-cbrt-cube`
10×	`div-exp` `div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef`
1×	`associate-/r/`

Counts

4 → 181

Calls

4 calls:

0.0ms	(fma k 10.0 1.0)
13.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.0ms	(fma k k (fma k 10.0 1.0))
5.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series195.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma k 10.0 1.0)
100.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
20.0ms	(fma k k (fma k 10.0 1.0))
41.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify89.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	715	1922
1	3280	1854
2	5002	1852

prune599.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.2b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.5b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`fma-def` `prod-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `div-exp` `sum-log` `log1p-expm1-u`
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 → 88

Calls

4 calls:

6.0ms	(+ 1.0 (* 10.0 k))
12.0ms	(* a (pow k m))
26.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
32.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ 1.0 (* 10.0 k))
57.0ms	(* a (pow k m))
16.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
106.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify59.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	477	629
1	2275	544
2	5001	524

prune288.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (fma k k (fma k 10.0 1.0)) a)
18.7b	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))
18.7b	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))
18.7b	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
36×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 101

Calls

4 calls:

5.0ms	(/ (fma k k (fma k 10.0 1.0)) a)
2.0ms	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))
2.0ms	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))
2.0ms	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))

series346.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ (fma k k (fma k 10.0 1.0)) a)
100.0ms	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))
100.0ms	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))
100.0ms	(cbrt (/ (fma k k (fma k 10.0 1.0)) a))

simplify82.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	250	1090
1	681	1034
2	2752	1001
3	5002	923

prune545.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma k k (fma k 10.0 1.0))
0.5b	(/ (pow k m) (/ (sqrt (fma k k (fma k 10.0 1.0))) a))
18.9b	(sqrt (fma k k (fma k 10.0 1.0)))
18.9b	(sqrt (fma k k (fma k 10.0 1.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

298×	`times-frac`
158×	`add-sqr-sqrt`
156×	`add-cube-cbrt` `*-un-lft-identity`
78×	`sqrt-prod`
69×	`unpow-prod-down`
23×	`sqr-pow`
22×	`associate-/r*`
17×	`add-exp-log`
9×	`div-exp` `add-cbrt-cube` `div-inv`
7×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv`
2×	`pow-to-exp` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp`
1×	`frac-2neg` `clear-num` `associate-/r/` `fma-udef`

Counts

4 → 244

Calls

4 calls:

0.0ms	(fma k k (fma k 10.0 1.0))
17.0ms	(/ (pow k m) (/ (sqrt (fma k k (fma k 10.0 1.0))) a))
1.0ms	(sqrt (fma k k (fma k 10.0 1.0)))
2.0ms	(sqrt (fma k k (fma k 10.0 1.0)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(fma k k (fma k 10.0 1.0))
188.0ms	(/ (pow k m) (/ (sqrt (fma k k (fma k 10.0 1.0))) a))
54.0ms	(sqrt (fma k k (fma k 10.0 1.0)))
54.0ms	(sqrt (fma k k (fma k 10.0 1.0)))

simplify109.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	929	3168
1	4194	3048
2	5002	3045

prune796.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes120.0ms

Accuracy

80.9% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 2.0b

bsearch68.0ms

Steps

Iters	Range		Point
9	32327.4576854492	306100497056.45215	105088950.88671507

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	50
1	55	50
2	55	50

end0.0ms

sample1.1s

Algorithm

intervals

Results

458.0ms	11891×	body	80	valid
142.0ms	4118×	body	80	nan