Details

sample107.0ms

Algorithm

intervals

Results

59.0ms	384×	body	80	valid
20.0ms	136×	body	80	nan

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2047
6	2047
5	655
4	215
3	97
2	52
1	26
0	12

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ 1 (* 10 k)) (* k k))
0.0b	(* a (pow k m))
1.2b	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log`
14×	`add-sqr-sqrt`
10×	`add-cbrt-cube`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-log-exp`
7×	`associate-r`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `sum-log` `fma-def` `times-frac` `associate-l*` `insert-posit16` `log1p-expm1-u` `unswap-sqr`
2×	`pow-to-exp` `cbrt-undiv` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`+-commutative` `associate-+l+` `clear-num` `frac-2neg` `-commutative` `div-inv` `associate-/l`

Counts

3 → 75

Calls

3 calls:

39.0ms	(+ (+ 1 (* 10 k)) (* k k))
18.0ms	(* a (pow k m))
45.0ms	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ (+ 1 (* 10 k)) (* k k))
78.0ms	(* a (pow k m))
145.0ms	(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

simplify1.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	2024
3	2024
2	1531
1	421
0	159

prune850.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
14.0b	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
14.0b	(sqrt (+ (+ 1 (* 10 k)) (* k k)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
72×	`sqrt-prod`
61×	`add-sqr-sqrt`
57×	`*-un-lft-identity` `add-cube-cbrt`
30×	`add-exp-log`
22×	`sqrt-div`
18×	`add-cbrt-cube` `associate-/r/`
13×	`div-exp` `associate-/l*`
12×	`associate-/r*`
11×	`flip3-+` `flip-+`
9×	`div-inv`
7×	`cbrt-undiv`
6×	`pow1` `prod-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-exp` `cbrt-unprod` `hypot-def`
1×	`associate-/l/`

Counts

4 → 186

Calls

4 calls:

26.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
58.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
25.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
17.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))

series435.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
160.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (+ (+ 1 (* 10 k)) (* k k))))
47.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
44.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))

simplify1.1s

Counts

198 → 198

Iterations

Iter	Nodes
done	2000
2	2000
1	724
0	280

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (sqrt (+ (+ 1 (* 10 k)) (* k k)))))
14.0b	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
14.0b	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
14.0b	(sqrt (+ (+ 1 (* 10 k)) (* k k)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
156×	`sqrt-prod`
82×	`add-sqr-sqrt`
76×	`*-un-lft-identity` `add-cube-cbrt`
30×	`sqrt-div`
22×	`associate-/r/`
20×	`add-exp-log`
14×	`flip3-+` `flip-+`
13×	`add-cbrt-cube`
12×	`associate-/l*`
11×	`div-inv`
9×	`associate-/r*` `div-exp`
7×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `prod-exp` `hypot-def`
1×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp` `cbrt-unprod` `associate-/l/`

Counts

4 → 210

Calls

4 calls:

68.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (sqrt (+ (+ 1 (* 10 k)) (* k k)))))
16.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
16.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
19.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(/ (/ (* a (pow k m)) (sqrt (+ (+ 1 (* 10 k)) (* k k)))) (sqrt (sqrt (+ (+ 1 (* 10 k)) (* k k)))))
36.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
50.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))
50.0ms	(sqrt (+ (+ 1 (* 10 k)) (* k k)))

simplify1.3s

Counts

222 → 222

Iterations

Iter	Nodes
done	2001
2	2001
1	805
0	319

prune3.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (* (pow k m) a) (fma k (+ k 10) 1))
1.2b	(/ (* (pow k m) a) (fma k (+ k 10) 1))
1.2b	(/ (* (pow k m) a) (fma k (+ k 10) 1))
14.6b	(cbrt (* (* (/ (* (pow k m) a) (fma k (+ k 10) 1)) (/ (* (pow k m) a) (fma k (+ k 10) 1))) (/ (* (pow k m) a) (fma k (+ k 10) 1))))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
19×	`add-cbrt-cube`
12×	`div-exp`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`associate-/r*` `times-frac` `prod-exp`
7×	`cbrt-div`
6×	`cbrt-undiv`
5×	`frac-times` `associate-*l/`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp` `associate-r/` `cbrt-unprod` `div-inv` `associate-/l`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 98

Calls

4 calls:

10.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))
16.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))
10.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))
87.0ms	(cbrt (* (* (/ (* (pow k m) a) (fma k (+ k 10) 1)) (/ (* (pow k m) a) (fma k (+ k 10) 1))) (/ (* (pow k m) a) (fma k (+ k 10) 1))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))
146.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))
135.0ms	(/ (* (pow k m) a) (fma k (+ k 10) 1))
161.0ms	(cbrt (* (* (/ (* (pow k m) a) (fma k (+ k 10) 1)) (/ (* (pow k m) a) (fma k (+ k 10) 1))) (/ (* (pow k m) a) (fma k (+ k 10) 1))))

simplify1.2s

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
3	2000
2	1167
1	363
0	139

prune1.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes316.0ms

Accuracy

92.1% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 2.0b

bsearch96.0ms

Steps

Iters	Range		Point
8	1.3481016745397874e+138	8.814273209687855e+141	8.663816625552649e+141

simplify10.0ms

Iterations

Iter	Nodes
done	55
3	55
2	50
1	43
0	32

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.8s	11956×	body	80	valid
600.0ms	4252×	body	80	nan