Details

sample70.0ms

Algorithm

intervals

Results

28.0ms	365×	body	80	valid
11.0ms	156×	body	80	nan

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1475
4	274
3	108
2	53
1	24
0	12

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (fma k (+ k 10.0) 1.0) (pow k m))
2.4b	(/ a (/ (fma k (+ k 10.0) 1.0) (pow k m)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
100×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`unpow-prod-down`
32×	`associate-/r*`
17×	`add-exp-log`
16×	`sqr-pow`
10×	`div-exp`
9×	`add-cbrt-cube`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv`
2×	`expm1-log1p-u` `pow-to-exp` `pow1` `clear-num` `frac-2neg` `pow-exp` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/`

Counts

2 → 169

Calls

2 calls:

6.0ms	(/ (fma k (+ k 10.0) 1.0) (pow k m))
14.0ms	(/ a (/ (fma k (+ k 10.0) 1.0) (pow k m)))

series313.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(/ (fma k (+ k 10.0) 1.0) (pow k m))
189.0ms	(/ a (/ (fma k (+ k 10.0) 1.0) (pow k m)))

simplify445.0ms

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
1	874
0	331

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
18.4b	(sqrt (fma k (+ k 10.0) 1.0))
18.4b	(sqrt (fma k (+ k 10.0) 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt k)
1.0ms	(cbrt k)
1.0ms	(sqrt (fma k (+ k 10.0) 1.0))
1.0ms	(sqrt (fma k (+ k 10.0) 1.0))

series743.0ms

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt k)
279.0ms	(cbrt k)
71.0ms	(sqrt (fma k (+ k 10.0) 1.0))
92.0ms	(sqrt (fma k (+ k 10.0) 1.0))

simplify909.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	5001
3	1540
2	398
1	135
0	68

prune584.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt (fma k (+ k 10.0) 1.0)) (pow k m))
0.1b	(/ (/ a (sqrt (fma k (+ k 10.0) 1.0))) (/ (sqrt (fma k (+ k 10.0) 1.0)) (pow k m)))
18.4b	(sqrt (fma k (+ k 10.0) 1.0))
18.4b	(sqrt (fma k (+ k 10.0) 1.0))

rewrite267.0ms

Algorithm

rewrite-expression-head

Rules

2866×	`times-frac`
1270×	`add-sqr-sqrt`
1268×	`*-un-lft-identity` `add-cube-cbrt`
936×	`sqrt-prod`
435×	`unpow-prod-down`
145×	`sqr-pow`
72×	`div-inv`
53×	`associate-/r*`
33×	`add-exp-log`
28×	`associate-/l*`
21×	`div-exp`
18×	`add-cbrt-cube`
9×	`cbrt-undiv`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-exp`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 1207

Calls

4 calls:

15.0ms	(/ (sqrt (fma k (+ k 10.0) 1.0)) (pow k m))
61.0ms	(/ (/ a (sqrt (fma k (+ k 10.0) 1.0))) (/ (sqrt (fma k (+ k 10.0) 1.0)) (pow k m)))
2.0ms	(sqrt (fma k (+ k 10.0) 1.0))
3.0ms	(sqrt (fma k (+ k 10.0) 1.0))

series545.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (sqrt (fma k (+ k 10.0) 1.0)) (pow k m))
208.0ms	(/ (/ a (sqrt (fma k (+ k 10.0) 1.0))) (/ (sqrt (fma k (+ k 10.0) 1.0)) (pow k m)))
99.0ms	(sqrt (fma k (+ k 10.0) 1.0))
90.0ms	(sqrt (fma k (+ k 10.0) 1.0))

simplify932.0ms

Counts

1219 → 1219

Iterations

Iter	Nodes
done	5000
0	1451

prune7.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* a (pow k m))
0.1b	(/ 1 (/ (fma k (+ k 10.0) 1.0) (* a (pow k m))))
2.4b	(/ (fma k (+ k 10.0) 1.0) (* a (pow k m)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
36×	`times-frac`
29×	`add-sqr-sqrt`
26×	`div-exp`
24×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube`
15×	`prod-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `associate-r`
6×	`div-inv` `associate-/l*`
5×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`pow1` `unpow-prod-down`
3×	`expm1-log1p-u` `associate-l` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `sqr-pow`
1×	`associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

3 → 116

Calls

3 calls:

18.0ms	(* a (pow k m))
31.0ms	(/ 1 (/ (fma k (+ k 10.0) 1.0) (* a (pow k m))))
12.0ms	(/ (fma k (+ k 10.0) 1.0) (* a (pow k m)))

series392.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(* a (pow k m))
125.0ms	(/ 1 (/ (fma k (+ k 10.0) 1.0) (* a (pow k m))))
156.0ms	(/ (fma k (+ k 10.0) 1.0) (* a (pow k m)))

simplify1.2s

Counts

125 → 125

Iterations

Iter	Nodes
done	5000
2	2773
1	587
0	230

prune502.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.0b

regimes293.0ms

Accuracy

94.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.1b

bsearch77.0ms

Steps

Iters	Range		Point
7	257785.57693934403	20118063.614914328	6372440.7964035785

simplify7.0ms

Iterations

Iter	Nodes
done	46
2	46
1	40
0	34

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	11951×	body	80	valid
298.0ms	4190×	body	80	nan