Details

sample38.0ms

Algorithm

intervals

Results

14.0ms	369×	body	80	valid
4.0ms	130×	body	80	nan

simplify102.0ms

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
done	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma k 10.0 1.0)
0.3b	(fma k k (fma k 10.0 1.0))
0.3b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
8.2b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite26.0ms

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

series221.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(fma k 10.0 1.0)
23.0ms	(fma k k (fma k 10.0 1.0))
114.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
52.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify88.0ms

Counts

193 → 193

Iterations

Useful iterations: 2 (65.0ms)

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

prune567.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma k 10.0 1.0)
0.1b	(/ (pow k (/ m 2)) (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k (/ m 2))))
0.3b	(fma k k (fma k 10.0 1.0))
8.2b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

1906×	`times-frac`
812×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
600×	`unpow-prod-down`
200×	`sqr-pow`
98×	`associate-/r*`
66×	`div-inv`
62×	`add-exp-log`
49×	`div-exp`
15×	`add-cbrt-cube`
13×	`pow-to-exp` `pow-exp`
10×	`associate-/l*`
7×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef`
1×	`associate-/r/`

Counts

4 → 853

Calls

4 calls:

0.0ms	(fma k 10.0 1.0)
39.0ms	(/ (pow k (/ m 2)) (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k (/ m 2))))
0.0ms	(fma k k (fma k 10.0 1.0))
8.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series244.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma k 10.0 1.0)
143.0ms	(/ (pow k (/ m 2)) (/ (/ (fma k k (fma k 10.0 1.0)) a) (pow k (/ m 2))))
23.0ms	(fma k k (fma k 10.0 1.0))
46.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify210.0ms

Counts

865 → 865

Iterations

Useful iterations: 1 (58.0ms)

Iter	Nodes	Cost
0	3409	17568
1	5001	17388
done	5001	17388

prune2.8s

Pruning

5 alts after pruning (4 fresh and 1 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))
0.3b	(fma k k (fma k 10.0 1.0))
17.4b	(sqrt (fma k k (fma k 10.0 1.0)))
17.4b	(sqrt (fma k k (fma k 10.0 1.0)))

rewrite4.0ms

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:

0.0ms	(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)))
2.0ms	(sqrt (fma k k (fma k 10.0 1.0)))

series166.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(fma k k (fma k 10.0 1.0))
23.0ms	(fma k k (fma k 10.0 1.0))
53.0ms	(sqrt (fma k k (fma k 10.0 1.0)))
60.0ms	(sqrt (fma k k (fma k 10.0 1.0)))

simplify39.0ms

Counts

62 → 62

Iterations

Useful iterations: 3 (35.0ms)

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

prune243.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* a (pow k m))
0.2b	(+ (+ 1.0 (* 10.0 k)) (* k k))
4.5b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
14×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
7×	`associate-r`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`pow1` `expm1-log1p-u` `fma-def` `times-frac` `associate-l` `associate-/r*` `sum-log` `log1p-expm1-u` `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 → 72

Calls

3 calls:

11.0ms	(* a (pow k m))
23.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
35.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series202.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
125.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify54.0ms

Counts

81 → 81

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	419	575
1	2040	495
2	5002	476
done	5002	476

prune220.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

93.9% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 2.2b

bsearch38.0ms

Steps

Iters	Range		Point
5	1.0832224429018907e+39	3.9386002373957546e+39	1.1029498973414345e+39

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	51	36
2	51	36
done	51	36

end0.0ms

sample1.1s

Algorithm

intervals

Results

469.0ms	11967×	body	80	valid
133.0ms	4304×	body	80	nan