Details

sample91.0ms

Algorithm

intervals

Results

36.0ms	388×	body	80	valid
12.0ms	148×	body	80	nan

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	12	15
1	24	15
2	53	13
3	107	12
4	254	12
5	735	12
6	2729	12
done	5001	12

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (fma k (+ 10.0 k) 1.0) (pow k m))
0.0b	(fma k (+ 10.0 k) 1.0)
2.3b	(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 179

Calls

3 calls:

10.0ms	(/ (fma k (+ 10.0 k) 1.0) (pow k m))
0.0ms	(fma k (+ 10.0 k) 1.0)
15.0ms	(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

series311.0ms

Counts

3 → 9

Calls

3 calls:

111.0ms	(/ (fma k (+ 10.0 k) 1.0) (pow k m))
28.0ms	(fma k (+ 10.0 k) 1.0)
173.0ms	(/ a (/ (fma k (+ 10.0 k) 1.0) (pow k m)))

simplify1.9s

Counts

188 → 188

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	337	4223
1	724	4006
2	2408	3857
done	5001	3812

prune778.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.3b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-exp-log`
7×	`add-cbrt-cube` `add-log-exp`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`div-exp`
3×	`fma-def` `times-frac` `prod-exp` `associate-/r*` `sum-log`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 45

Calls

2 calls:

35.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
39.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series240.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
209.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.2s

Counts

51 → 51

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	129	955
1	358	809
2	1334	660
done	5000	616

prune257.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
0.3b	(/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0)))
14.4b	(sqrt (fma k (+ 10.0 k) 1.0))
14.4b	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
66×	`sqrt-prod`
56×	`add-sqr-sqrt`
53×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-exp-log`
18×	`add-cbrt-cube`
13×	`div-exp`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`div-inv`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `pow-exp` `clear-num` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`hypot-def` `associate-/l/`

Counts

4 → 163

Calls

4 calls:

43.0ms	(/ (/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
23.0ms	(/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0)))
3.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
61.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ (/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0))) (sqrt (+ (+ 1.0 (* 10.0 k)) (* k k))))
284.0ms	(/ (* a (pow k m)) (sqrt (fma k (+ 10.0 k) 1.0)))
71.0ms	(sqrt (fma k (+ 10.0 k) 1.0))
64.0ms	(sqrt (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify1.5s

Counts

175 → 175

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	295	5389
1	759	4930
2	2306	3921
done	5000	3805

prune727.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma k (+ 10.0 k) 1.0)
0.2b	(/ 1 (fma k (+ 10.0 k) 1.0))
2.4b	(* (* a (pow k m)) (/ 1 (fma k (+ 10.0 k) 1.0)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log`
28×	`prod-exp`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
17×	`add-cbrt-cube`
13×	`associate-r`
10×	`div-exp`
6×	`pow1` `cbrt-unprod`
5×	`rec-exp` `1-exp`
4×	`pow-to-exp` `pow-exp`
3×	`cbrt-undiv` `expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `associate-l` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 90

Calls

3 calls:

1.0ms	(fma k (+ 10.0 k) 1.0)
11.0ms	(/ 1 (fma k (+ 10.0 k) 1.0))
58.0ms	(* (* a (pow k m)) (/ 1 (fma k (+ 10.0 k) 1.0)))

series265.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(fma k (+ 10.0 k) 1.0)
60.0ms	(/ 1 (fma k (+ 10.0 k) 1.0))
184.0ms	(* (* a (pow k m)) (/ 1 (fma k (+ 10.0 k) 1.0)))

simplify1.9s

Counts

99 → 99

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	170	1588
1	424	1373
2	1360	1193
done	5000	1162

prune321.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

96.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch69.0ms

Steps

Iters	Range		Point
7	2.5061009111116397e+147	1.9462919806934515e+149	8.644575216938256e+148

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	51
1	36	51
done	36	51

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.6s	11952×	body	80	valid
299.0ms	4230×	body	80	nan