Details

sample81.0ms

Algorithm

intervals

Results

42.0ms	376×	body	80	valid
15.0ms	136×	body	80	nan

simplify9.1s

Counts

1 → 1

Iterations

Iter	Nodes
7	7970
6	1954
5	624
4	202
3	85
2	45
1	24
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize19.0ms

Local error

Found 1 expressions with local error:

1.5b	(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
6×	`add-cbrt-cube`
4×	`div-exp`
3×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `prod-exp` `add-cube-cbrt`
2×	`cbrt-undiv` `associate-/r/`
1×	`pow-to-exp` `pow1` `clear-num` `frac-2neg` `flip3-+` `pow-exp` `cbrt-unprod` `flip-+` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`

Counts

1 → 26

Calls

1 calls:

36.0ms

(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))

series150.0ms

Counts

1 → 3

Calls

1 calls:

150.0ms

(/ (* (pow k m) a) (+ (* k (+ k 10)) 1))

simplify2.7s

Counts

29 → 29

Iterations

Iter	Nodes
3	5750
2	1068
1	304
0	107

prune306.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (pow k m) (/ (+ (* k (+ k 10)) 1) a))
2.4b	(/ (+ (* k (+ k 10)) 1) a)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
94×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
42×	`unpow-prod-down`
17×	`add-exp-log`
16×	`associate-/r*`
14×	`sqr-pow`
10×	`div-exp` `div-inv` `associate-/l*`
9×	`add-cbrt-cube`
4×	`cbrt-undiv`
2×	`pow-to-exp` `pow1` `clear-num` `frac-2neg` `pow-exp` `insert-posit16` `add-log-exp` `associate-/l/`
1×	`flip3-+` `associate-/r/` `flip-+`

Counts

2 → 161

Calls

2 calls:

17.0ms	(/ (pow k m) (/ (+ (* k (+ k 10)) 1) a))
34.0ms	(/ (+ (* k (+ k 10)) 1) a)

series213.0ms

Counts

2 → 6

Calls

2 calls:

133.0ms	(/ (pow k m) (/ (+ (* k (+ k 10)) 1) a))
79.0ms	(/ (+ (* k (+ k 10)) 1) a)

simplify2.1s

Counts

167 → 167

Iterations

Iter	Nodes
2	2497
1	816
0	319

prune1.8s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sqrt (+ (* k (+ k 10)) 1)) 1) (/ (sqrt (+ (* k (+ k 10)) 1)) a))
0.1b	(/ (pow k m) (* (/ (sqrt (+ (* k (+ k 10)) 1)) 1) (/ (sqrt (+ (* k (+ k 10)) 1)) a)))
17.2b	(sqrt (+ (* k (+ k 10)) 1))
17.2b	(sqrt (+ (* k (+ k 10)) 1))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

89×	`add-exp-log`
84×	`add-sqr-sqrt`
65×	`times-frac`
49×	`div-exp`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
35×	`sqrt-prod`
34×	`add-cbrt-cube`
24×	`prod-exp`
22×	`associate-r` `associate-l`
15×	`unswap-sqr`
13×	`cbrt-undiv`
8×	`pow1` `1-exp` `cbrt-unprod`
7×	`pow-to-exp` `pow-exp` `associate-/l*`
6×	`unpow-prod-down`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-/r/` `div-inv`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-l/` `associate-r/` `flip-+` `sqr-pow`
1×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative`

Counts

4 → 169

Calls

4 calls:

58.0ms	(* (/ (sqrt (+ (* k (+ k 10)) 1)) 1) (/ (sqrt (+ (* k (+ k 10)) 1)) a))
45.0ms	(/ (pow k m) (* (/ (sqrt (+ (* k (+ k 10)) 1)) 1) (/ (sqrt (+ (* k (+ k 10)) 1)) a)))
23.0ms	(sqrt (+ (* k (+ k 10)) 1))
20.0ms	(sqrt (+ (* k (+ k 10)) 1))

series339.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (/ (sqrt (+ (* k (+ k 10)) 1)) 1) (/ (sqrt (+ (* k (+ k 10)) 1)) a))
197.0ms	(/ (pow k m) (* (/ (sqrt (+ (* k (+ k 10)) 1)) 1) (/ (sqrt (+ (* k (+ k 10)) 1)) a)))
45.0ms	(sqrt (+ (* k (+ k 10)) 1))
49.0ms	(sqrt (+ (* k (+ k 10)) 1))

simplify902.0ms

Counts

181 → 181

Iterations

Iter	Nodes
2	2302
1	819
0	281

prune1.6s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.2b	(* m (+ 0 (log k)))
2.6b	(* (/ (exp (* m (+ 0 (log k)))) k) (/ a k))
2.6b	(* (/ (exp (* m (+ 0 (log k)))) k) (/ a k))
3.7b	(* (* (/ (exp (* m (+ 0 (log k)))) k) (/ a k)) (- (/ (/ 99 k) k) (/ 10 k)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
71×	`times-frac`
52×	`*-un-lft-identity`
48×	`add-cbrt-cube`
45×	`associate-r`
42×	`associate-l` `add-exp-log`
41×	`add-cube-cbrt`
19×	`frac-times`
18×	`prod-exp` `cbrt-unprod`
16×	`pow1`
13×	`associate-*r/`
12×	`cbrt-undiv` `div-exp` `exp-sum`
10×	`associate-*l/`
9×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
6×	`pow-prod-down` `div-inv` `difference-of-squares`
4×	`flip3--` `*-commutative` `frac-sub` `insert-posit16` `flip--` `distribute-lft-out--` `sub-div` `add-log-exp`
2×	`sub-neg` `distribute-lft-out`
1×	`flip3-+` `distribute-rgt-out--` `log-pow` `flip-+`

Counts

4 → 198

Calls

4 calls:

26.0ms	(* m (+ 0 (log k)))
24.0ms	(* (/ (exp (* m (+ 0 (log k)))) k) (/ a k))
30.0ms	(* (/ (exp (* m (+ 0 (log k)))) k) (/ a k))
124.0ms	(* (* (/ (exp (* m (+ 0 (log k)))) k) (/ a k)) (- (/ (/ 99 k) k) (/ 10 k)))

series660.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* m (+ 0 (log k)))
144.0ms	(* (/ (exp (* m (+ 0 (log k)))) k) (/ a k))
160.0ms	(* (/ (exp (* m (+ 0 (log k)))) k) (/ a k))
276.0ms	(* (* (/ (exp (* m (+ 0 (log k)))) k) (/ a k)) (- (/ (/ 99 k) k) (/ 10 k)))

simplify1.8s

Counts

210 → 210

Iterations

Iter	Nodes
2	3772
1	963
0	314

prune3.5s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes145.0ms

Accuracy

98% (0.0b remaining)

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

bsearch96.0ms

Steps

Iters	Range		Point
6	8.86859371011129e+141	6.252259408663382e+142	6.144520496396345e+142

simplify7.0ms

Iterations

Iter	Nodes
2	45
1	45
0	34

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	11929×	body	80	valid
604.0ms	4259×	body	80	nan