Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	400×	body	80	valid
5.0ms	152×	body	80	nan

simplify111.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma k 10.0 1.0)
0.1b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.3b	(fma k k (fma k 10.0 1.0))
2.9b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite18.0ms

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)
8.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.0ms	(fma k k (fma k 10.0 1.0))
2.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series214.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(fma k 10.0 1.0)
109.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
22.0ms	(fma k k (fma k 10.0 1.0))
51.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify99.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (71.0ms)

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

prune565.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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))
1.4b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite34.0ms

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:

2.0ms	(+ 1.0 (* 10.0 k))
5.0ms	(* a (pow k m))
10.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
14.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (* 10.0 k))
56.0ms	(* a (pow k m))
24.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
114.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify60.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (52.0ms)

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

prune270.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma k k (fma k 10.0 1.0))
0.3b	(fma k k (fma k 10.0 1.0))
14.0b	(sqrt (fma k k (fma k 10.0 1.0)))
14.0b	(sqrt (fma k k (fma k 10.0 1.0)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 50

Calls

4 calls:

4.0ms	(fma k k (fma k 10.0 1.0))
0.0ms	(fma k k (fma k 10.0 1.0))
1.0ms	(sqrt (fma k k (fma k 10.0 1.0)))
1.0ms	(sqrt (fma k k (fma k 10.0 1.0)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(fma k k (fma k 10.0 1.0))
22.0ms	(fma k k (fma k 10.0 1.0))
59.0ms	(sqrt (fma k k (fma k 10.0 1.0)))
53.0ms	(sqrt (fma k k (fma k 10.0 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	109	266
1	309	244
2	1228	236
3	5001	232

prune232.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.3b	(fma k k (fma k 10.0 1.0))
2.9b	(/ (fma k k (fma k 10.0 1.0)) a)
13.2b	(cbrt (pow (/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a)) 3))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
249×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
216×	`unpow-prod-down`
198×	`cbrt-prod`
96×	`cube-prod`
41×	`sqr-pow`
26×	`div-inv`
19×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
10×	`div-exp` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r/`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num`
1×	`cube-div` `cube-mult` `cbrt-div` `pow1/3` `unpow3` `rem-cbrt-cube` `fma-udef`

Counts

4 → 381

Calls

4 calls:

8.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
0.0ms	(fma k k (fma k 10.0 1.0))
2.0ms	(/ (fma k k (fma k 10.0 1.0)) a)
26.0ms	(cbrt (pow (/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a)) 3))

series319.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
23.0ms	(fma k k (fma k 10.0 1.0))
51.0ms	(/ (fma k k (fma k 10.0 1.0)) a)
135.0ms	(cbrt (pow (/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a)) 3))

simplify96.0ms

Algorithm

egg-herbie

Counts

393 → 393

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2082	4764
1	5001	4722

prune975.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes114.0ms

Accuracy

95.8% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.3b

bsearch59.0ms

Steps

Iters	Range		Point
8	18294.474683640892	423887742.1010123	1484471.4191297374

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	32
1	48	32
2	48	32

end0.0ms

sample955.0ms

Algorithm

intervals

Results

467.0ms	11931×	body	80	valid
142.0ms	4177×	body	80	nan