Details

sample61.0ms

Algorithm

intervals

Results

30.0ms	387×	body	80	valid
7.0ms	122×	body	80	nan

simplify1.4s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.5b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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

series300.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(/ (fma k (+ k 10.0) 1.0) (pow k m))
177.0ms	(/ a (/ (fma k (+ k 10.0) 1.0) (pow k m)))

simplify493.0ms

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
1	874
0	331

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt k)
0.5b	(cbrt k)
0.5b	(cbrt k)
2.5b	(/ (* a (pow (* (cbrt k) (cbrt k)) m)) (/ (fma k (+ k 10.0) 1.0) (pow (cbrt k) m)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

94×	`times-frac`
70×	`add-exp-log`
47×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
36×	`unpow-prod-down`
35×	`div-exp`
34×	`associate-/r*`
27×	`cbrt-prod`
20×	`prod-exp`
16×	`add-cbrt-cube`
13×	`pow-exp`
9×	`pow-to-exp`
6×	`cbrt-undiv` `sqr-pow`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-inv`
2×	`cbrt-unprod`
1×	`clear-num` `frac-2neg` `associate-/r/` `associate-/l*`

Counts

4 → 145

Calls

4 calls:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

276.0ms	(cbrt k)
312.0ms	(cbrt k)
300.0ms	(cbrt k)
590.0ms	(/ (* a (pow (* (cbrt k) (cbrt k)) m)) (/ (fma k (+ k 10.0) 1.0) (pow (cbrt k) m)))

simplify561.0ms

Counts

157 → 157

Iterations

Iter	Nodes
done	5001
1	862
0	308

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (* 1 (pow k m)) (fma k (+ k 10.0) 1.0))
2.5b	(* a (/ (* 1 (pow k m)) (fma k (+ k 10.0) 1.0)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 62

Calls

2 calls:

9.0ms	(/ (* 1 (pow k m)) (fma k (+ k 10.0) 1.0))
21.0ms	(* a (/ (* 1 (pow k m)) (fma k (+ k 10.0) 1.0)))

series307.0ms

Counts

2 → 6

Calls

2 calls:

123.0ms	(/ (* 1 (pow k m)) (fma k (+ k 10.0) 1.0))
184.0ms	(* a (/ (* 1 (pow k m)) (fma k (+ k 10.0) 1.0)))

simplify857.0ms

Counts

68 → 68

Iterations

Iter	Nodes
done	5000
2	2080
1	435
0	159

prune412.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m))))
0.1b	(/ (/ a (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))) (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m))))
10.1b	(sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))
10.1b	(sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))

rewrite673.0ms

Algorithm

rewrite-expression-head

Rules

8861×	`times-frac`
4575×	`sqrt-prod`
3629×	`add-sqr-sqrt`
3617×	`*-un-lft-identity` `add-cube-cbrt`
1649×	`unpow-prod-down`
551×	`sqr-pow`
214×	`div-inv`
92×	`associate-/l*`
56×	`associate-/r*`
33×	`sqrt-div`
31×	`associate-/r/`
11×	`add-cbrt-cube` `add-exp-log`
8×	`rem-sqrt-square`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`
1×	`associate-/l/`

Counts

4 → 2839

Calls

4 calls:

20.0ms	(/ a (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m))))
149.0ms	(/ (/ a (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))) (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m))))
13.0ms	(sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))
13.0ms	(sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))

series1.1s

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ a (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m))))
566.0ms	(/ (/ a (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))) (sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m))))
143.0ms	(sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))
131.0ms	(sqrt (/ (fma k (+ k 10.0) 1.0) (pow k m)))

simplify2.2s

Counts

2851 → 2851

Iterations

Iter	Nodes
done	5001
0	4296

prune25.8s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

98.1% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch75.0ms

Steps

Iters	Range		Point
6	3.4349050748812333e+109	1.905314630223606e+110	3.8998864630604305e+109

simplify1.6s

Iterations

Iter	Nodes
done	5000
6	2022
5	706
4	265
3	100
2	57
1	47
0	37

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.5s	12002×	body	80	valid
358.0ms	4131×	body	80	nan