Details

sample123.0ms

Algorithm

intervals

Results

71.0ms	383×	body	80	valid
26.0ms	174×	body	80	nan

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5006
6	2177
5	655
4	215
3	97
2	52
1	26
0	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1 (* 10 k))
0.0b	(+ (+ 1 (* 10 k)) (* k k))
0.0b	(* a (pow k m))
2.0b	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

rewrite445.0ms

Algorithm

rewrite-expression-head

Rules

396×	`*-un-lft-identity`
204×	`distribute-lft-out`
162×	`times-frac`
135×	`associate-l`
123×	`add-sqr-sqrt`
77×	`associate-r`
68×	`add-cube-cbrt`
44×	`unpow-prod-down`
33×	`unswap-sqr`
22×	`sqr-pow`
19×	`add-exp-log`
18×	`associate-/l*`
11×	`add-cbrt-cube` `*-commutative` `add-log-exp`
9×	`associate-/r*`
8×	`fma-def`
6×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `sum-log` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`+-commutative` `flip3-+` `flip-+`
2×	`pow-to-exp` `cbrt-undiv` `associate-+l+` `pow-exp` `associate-/r/` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `pow-prod-down` `div-inv`

Counts

4 → 286

Calls

4 calls:

15.0ms	(+ 1 (* 10 k))
125.0ms	(+ (+ 1 (* 10 k)) (* k k))
24.0ms	(* a (pow k m))
262.0ms	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ 1 (* 10 k))
19.0ms	(+ (+ 1 (* 10 k)) (* k k))
68.0ms	(* a (pow k m))
163.0ms	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

simplify2.2s

Counts

298 → 298

Iterations

Iter	Nodes
done	5008
2	2471
1	721
0	275

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 2.0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (fma (+ k 10) k 1) (pow k m))
2.0b	(/ a (/ (fma (+ k 10) k 1) (pow k m)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

180×	`times-frac`
103×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
51×	`unpow-prod-down`
39×	`associate-/r*`
17×	`add-exp-log` `sqr-pow`
13×	`associate-/r/`
10×	`div-exp`
9×	`add-cbrt-cube` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv`
3×	`clear-num` `frac-2neg`
2×	`expm1-log1p-u` `pow-to-exp` `pow1` `pow-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 183

Calls

2 calls:

9.0ms	(/ (fma (+ k 10) k 1) (pow k m))
21.0ms	(/ a (/ (fma (+ k 10) k 1) (pow k m)))

series275.0ms

Counts

2 → 6

Calls

2 calls:

121.0ms	(/ (fma (+ k 10) k 1) (pow k m))
154.0ms	(/ a (/ (fma (+ k 10) k 1) (pow k m)))

simplify2.4s

Counts

189 → 189

Iterations

Iter	Nodes
done	5002
2	3233
1	861
0	334

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.6b	(cbrt a)
6.4b	(sqrt (/ (fma (+ k 10) k 1) (pow k m)))
6.4b	(sqrt (/ (fma (+ k 10) k 1) (pow k m)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
50×	`sqrt-prod`
48×	`times-frac`
40×	`*-un-lft-identity` `add-cube-cbrt`
26×	`unpow-prod-down` `sqrt-div`
14×	`associate-/r*`
10×	`sqr-pow`
8×	`rem-sqrt-square`
6×	`cbrt-prod` `pow1` `associate-/l*`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow1/3` `div-inv`

Counts

4 → 136

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(cbrt a)
17.0ms	(sqrt (/ (fma (+ k 10) k 1) (pow k m)))
21.0ms	(sqrt (/ (fma (+ k 10) k 1) (pow k m)))

series1.3s

Counts

4 → 12

Calls

4 calls:

309.0ms	(cbrt a)
683.0ms	(cbrt a)
151.0ms	(sqrt (/ (fma (+ k 10) k 1) (pow k m)))
140.0ms	(sqrt (/ (fma (+ k 10) k 1) (pow k m)))

simplify1.7s

Counts

148 → 148

Iterations

Iter	Nodes
done	5000
3	1771
2	742
1	317
0	200

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize63.0ms

Local error

Found 4 expressions with local error:

2.0b	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))
6.2b	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))
6.2b	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))
6.2b	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))

rewrite861.0ms

Algorithm

rewrite-expression-head

Rules

1459×	`*-un-lft-identity`
760×	`distribute-lft-out`
648×	`times-frac`
504×	`cbrt-prod`
500×	`associate-l`
443×	`add-sqr-sqrt`
280×	`associate-r`
243×	`add-cube-cbrt`
160×	`unpow-prod-down`
120×	`unswap-sqr`
90×	`cbrt-div`
80×	`sqr-pow`
72×	`associate-/l*`
40×	`*-commutative`
36×	`associate-/r*`
14×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`associate-/r/`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `flip3-+` `div-exp` `flip-+` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow1/3` `prod-exp`
2×	`cbrt-undiv`
1×	`pow-to-exp` `pow-exp` `cbrt-unprod`

Counts

4 → 837

Calls

4 calls:

214.0ms	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))
181.0ms	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))
169.0ms	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))
223.0ms	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))

series990.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))
259.0ms	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))
302.0ms	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))
262.0ms	(cbrt (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))

simplify2.6s

Counts

849 → 849

Iterations

Iter	Nodes
done	5008
2	2677
1	877
0	421

prune3.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes227.0ms

Accuracy

98.7% (0.0b remaining)

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

bsearch61.0ms

Steps

Iters	Range		Point
6	1.0558091000171249e+107	4.3071813422759086e+107	3.050984953394394e+107

simplify24.0ms

Iterations

Iter	Nodes
done	57
4	57
3	55
2	50
1	43
0	31

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.2s	11968×	body	80	valid
649.0ms	4230×	body	80	nan