Details

sample206.0ms

Algorithm

intervals

Results

56.0ms	84×	body	1280	valid
31.0ms	21×	body	1280	nan
27.0ms	53×	body	640	valid
13.0ms	41×	body	320	valid
13.0ms	144×	body	80	valid
13.0ms	28×	body	10240	exit
12.0ms	22×	body	640	nan
11.0ms	176×	body	80	nan
4.0ms	18×	body	160	valid
3.0ms	13×	body	320	nan
1.0ms	4×	body	160	nan

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1264
4	252
3	86
2	35
1	17
0	8

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.4b

localize15.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.1b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
93.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series765.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms	(pow x (/ 1.0 n))
184.0ms	(pow (+ x 1.0) (/ 1.0 n))
461.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.5s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	2866
1	738
0	270

prune724.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 (* 2 n)))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.6b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ 1.0 (* 2 n))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
83×	`unpow-prod-down`
77×	`prod-diff`
73×	`sqrt-prod`
69×	`add-cube-cbrt`
33×	`pow-unpow`
29×	`sqr-pow`
21×	`times-frac`
12×	`difference-of-squares`
11×	`fma-neg`
10×	`distribute-lft-out`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 198

Calls

4 calls:

3.0ms	(pow x (/ 1.0 (* 2 n)))
8.0ms	(pow (+ x 1.0) (/ 1.0 n))
8.0ms	(pow (+ x 1.0) (/ 1.0 n))
104.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ 1.0 (* 2 n))))

series1.1s

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow x (/ 1.0 (* 2 n)))
188.0ms	(pow (+ x 1.0) (/ 1.0 n))
194.0ms	(pow (+ x 1.0) (/ 1.0 n))
605.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ 1.0 (* 2 n))))

simplify1.5s

Counts

210 → 210

Iterations

Iter	Nodes
done	5001
2	3087
1	812
0	309

prune1.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 (* 2 n)))
0.5b	(pow x (/ 1.0 (* 2 n)))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
3.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ 1.0 (* 2 n))) (pow x (/ 1.0 (* 2 n)))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
27×	`pow-unpow`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
19×	`unpow-prod-down`
15×	`times-frac`
8×	`fma-neg` `prod-diff`
7×	`pow1` `add-exp-log`
6×	`add-log-exp` `sqr-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow x (/ 1.0 (* 2 n)))
4.0ms	(pow x (/ 1.0 (* 2 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
94.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ 1.0 (* 2 n))) (pow x (/ 1.0 (* 2 n)))))

series877.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow x (/ 1.0 (* 2 n)))
103.0ms	(pow x (/ 1.0 (* 2 n)))
215.0ms	(pow (+ x 1.0) (/ 1.0 n))
486.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (* (pow x (/ 1.0 (* 2 n))) (pow x (/ 1.0 (* 2 n)))))

simplify1.4s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	2440
1	593
0	205

prune850.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.2b

localize74.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ 1.0 (* 2 n)))) (- (/ (/ 0.5 n) x) (fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n))))
3.0b	(- (/ (/ 0.5 n) x) (fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n)))
3.1b	(fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n))
9.5b	(/ (/ 0.25 (pow x 2)) n)

rewrite533.0ms

Algorithm

rewrite-expression-head

Rules

846×	`times-frac`
594×	`add-sqr-sqrt`
580×	`*-un-lft-identity`
574×	`add-cube-cbrt`
387×	`prod-diff`
131×	`distribute-rgt-in` `distribute-lft-in`
45×	`div-inv`
43×	`fma-neg`
36×	`unpow-prod-down`
28×	`associate-/l*`
16×	`add-exp-log`
12×	`unpow2` `sqr-pow`
11×	`add-cbrt-cube`
7×	`div-exp` `associate-r`
6×	`pow1` `add-log-exp` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `flip3--` `associate-l` `log1p-expm1-u` `flip--`
3×	`cbrt-undiv` `associate-/r*` `sub-neg` `flip3-+` `flip-+`
2×	`associate-l/` `associate-r/` `fma-udef` `distribute-lft-out--`
1×	`pow-to-exp` `clear-num` `frac-2neg` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `associate--r+` `unswap-sqr` `associate-/l/`

Counts

4 → 630

Calls

4 calls:

365.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ 1.0 (* 2 n)))) (- (/ (/ 0.5 n) x) (fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n))))
71.0ms	(- (/ (/ 0.5 n) x) (fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n)))
0.0ms	(fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n))
15.0ms	(/ (/ 0.25 (pow x 2)) n)

series1.0s

Counts

4 → 12

Calls

4 calls:

758.0ms	(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ 1.0 (* 2 n)))) (- (/ (/ 0.5 n) x) (fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n))))
92.0ms	(- (/ (/ 0.5 n) x) (fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n)))
131.0ms	(fma (/ 0.25 (pow n 2)) (/ (- (log x)) x) (/ (/ 0.25 (pow x 2)) n))
29.0ms	(/ (/ 0.25 (pow x 2)) n)

simplify1.8s

Counts

642 → 642

Iterations

Iter	Nodes
done	5002
1	2966
0	955

prune4.9s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 22.1b

regimes601.0ms

Accuracy

81.8% (1.6b remaining)

Error of 22.2b against oracle of 20.6b and baseline of 29.3b

bsearch280.0ms

Steps

Iters	Range		Point
7	5787.9300826946865	383123.6636286385	251407.49747499867
9	-2.8555728020291845e+22	-83422883652835.42	-100941949052182.52

simplify13.0ms

Iterations

Iter	Nodes
done	58
2	58
1	56
0	46

end0.0ms

sample8.2s

Algorithm

intervals

Results

2.9s	3177×	body	1280	valid
1.3s	1663×	body	640	valid
832.0ms	1190×	body	10240	exit
606.0ms	698×	body	1280	nan
477.0ms	4583×	body	80	valid
398.0ms	5086×	body	80	nan
337.0ms	639×	body	640	nan
288.0ms	827×	body	320	valid
189.0ms	346×	body	320	nan
143.0ms	447×	body	160	valid
34.0ms	189×	body	160	nan