Details

sample79.0ms

Algorithm

intervals

Results

34.0ms	371×	body	80	valid
10.0ms	122×	body	80	nan

simplify5.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2300
5	662
4	213
3	94
2	50
1	24
0	12

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize38.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (/ a (fma k (+ 10.0 k) 1.0)) (pow k m))
4.4b	(/ a (fma k (+ 10.0 k) 1.0))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
21×	`times-frac`
19×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
13×	`associate-l`
9×	`add-cbrt-cube`
7×	`associate-r`
6×	`prod-exp` `unswap-sqr`
5×	`unpow-prod-down`
4×	`div-exp`
3×	`associate-/r` `associate-/l` `sqr-pow`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `pow-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

2 → 74

Calls

2 calls:

44.0ms	(* (/ a (fma k (+ 10.0 k) 1.0)) (pow k m))
11.0ms	(/ a (fma k (+ 10.0 k) 1.0))

series344.0ms

Counts

2 → 6

Calls

2 calls:

218.0ms	(* (/ a (fma k (+ 10.0 k) 1.0)) (pow k m))
125.0ms	(/ a (fma k (+ 10.0 k) 1.0))

simplify2.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1374
1	419
0	168

prune808.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (pow k m) (fma (+ 10.0 k) k 1.0))
2.0b	(* a (/ (pow k m) (fma (+ 10.0 k) k 1.0)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
43×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
25×	`associate-r`
22×	`unpow-prod-down`
17×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`sqr-pow`
7×	`associate-/l*`
6×	`div-exp`
4×	`pow1` `prod-exp` `unswap-sqr`
3×	`associate-l` `associate-/r*`
2×	`cbrt-undiv` `expm1-log1p-u` `pow-to-exp` `pow-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

2 → 97

Calls

2 calls:

17.0ms	(/ (pow k m) (fma (+ 10.0 k) k 1.0))
41.0ms	(* a (/ (pow k m) (fma (+ 10.0 k) k 1.0)))

series352.0ms

Counts

2 → 6

Calls

2 calls:

143.0ms	(/ (pow k m) (fma (+ 10.0 k) k 1.0))
209.0ms	(* a (/ (pow k m) (fma (+ 10.0 k) k 1.0)))

simplify2.7s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1597
1	491
0	203

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))) (pow k m))
0.1b	(/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0)))
14.0b	(sqrt (fma k (+ 10.0 k) 1.0))
14.0b	(sqrt (fma k (+ 10.0 k) 1.0))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

528×	`times-frac`
335×	`add-sqr-sqrt`
273×	`sqrt-prod`
268×	`add-cube-cbrt` `*-un-lft-identity`
136×	`associate-l`
33×	`add-exp-log`
22×	`associate-/l*`
21×	`unswap-sqr`
18×	`add-cbrt-cube`
15×	`div-inv`
12×	`div-exp`
10×	`unpow-prod-down`
9×	`prod-exp`
8×	`sqr-pow`
7×	`associate-r`
6×	`pow1` `cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 394

Calls

4 calls:

157.0ms	(* (/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))) (pow k m))
29.0ms	(/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0)))
3.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
4.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

series577.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0))) (pow k m))
128.0ms	(/ (/ a (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (fma k (+ 10.0 k) 1.0)))
93.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
137.0ms	(sqrt (fma k (+ 10.0 k) 1.0))

simplify3.7s

Counts

406 → 406

Iterations

Iter	Nodes
done	5034
2	3406
1	1112
0	434

prune3.7s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ 1 (/ (fma k (+ 10.0 k) 1.0) a)) (pow k m))
0.3b	(/ 1 (/ (fma k (+ 10.0 k) 1.0) a))
4.3b	(/ (fma k (+ 10.0 k) 1.0) a)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
127×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
90×	`add-cube-cbrt`
66×	`add-exp-log`
44×	`associate-l`
29×	`div-exp`
21×	`prod-exp`
19×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`unswap-sqr`
10×	`div-inv`
8×	`unpow-prod-down` `rec-exp` `1-exp`
7×	`cbrt-undiv` `pow-to-exp` `associate-r` `pow-exp`
6×	`associate-/l*` `sqr-pow`
4×	`pow1`
3×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`pow-flip` `associate-l/` `-commutative` `inv-pow`

Counts

3 → 208

Calls

3 calls:

79.0ms	(* (/ 1 (/ (fma k (+ 10.0 k) 1.0) a)) (pow k m))
25.0ms	(/ 1 (/ (fma k (+ 10.0 k) 1.0) a))
7.0ms	(/ (fma k (+ 10.0 k) 1.0) a)

series396.0ms

Counts

3 → 9

Calls

3 calls:

242.0ms	(* (/ 1 (/ (fma k (+ 10.0 k) 1.0) a)) (pow k m))
71.0ms	(/ 1 (/ (fma k (+ 10.0 k) 1.0) a))
83.0ms	(/ (fma k (+ 10.0 k) 1.0) a)

simplify3.3s

Counts

217 → 217

Iterations

Iter	Nodes
done	5001
2	2234
1	866
0	320

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes341.0ms

Accuracy

98.5% (0.0b remaining)

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

bsearch50.0ms

Steps

Iters	Range		Point
4	1.5762529458040165e+25	2.8848106960954074e+25	2.7285682477325216e+25

simplify9.0ms

Iterations

Iter	Nodes
done	28
1	28
0	24

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.0s	11787×	body	80	valid
459.0ms	4210×	body	80	nan