Details

sample144.0ms

Algorithm

intervals

Results

54.0ms	113×	body	1280	valid
18.0ms	31×	body	10240	exit
16.0ms	45×	body	640	valid
10.0ms	24×	body	1280	nan
8.0ms	151×	body	80	valid
5.0ms	25×	body	320	valid
5.0ms	21×	body	640	nan
5.0ms	134×	body	80	nan
2.0ms	11×	body	320	nan
2.0ms	14×	body	160	valid
1.0ms	11×	body	160	nan

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	224	13
5	687	13
6	3439	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite63.0ms

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:

2.0ms	(pow x (/ 1.0 n))
8.0ms	(pow (+ x 1.0) (/ 1.0 n))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series493.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(pow x (/ 1.0 n))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify716.0ms

Counts

158 → 158

Iterations

Useful iterations: done (710.0ms)

Iter	Nodes	Cost
0	271	4785
1	626	3566
2	1852	3220
done	5000	3172

prune334.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 19.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

195×	`sqrt-prod`
129×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
110×	`prod-diff`
100×	`unpow-prod-down`
94×	`add-cube-cbrt`
39×	`pow-unpow`
33×	`sqr-pow`
27×	`times-frac`
16×	`difference-of-squares`
14×	`distribute-lft-out`
11×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 244

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
58.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series747.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow x (/ 1.0 n))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))
156.0ms	(pow (+ x 1.0) (/ 1.0 n))
377.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify730.0ms

Counts

256 → 256

Iterations

Useful iterations: done (720.0ms)

Iter	Nodes	Cost
0	338	9618
1	752	7067
2	2012	5790
done	5001	5768

prune862.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 19.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
98.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series755.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow x (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify743.0ms

Counts

249 → 249

Iterations

Useful iterations: done (734.0ms)

Iter	Nodes	Cost
0	430	9019
1	805	6371
2	2103	5670
done	5001	5574

prune523.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 19.3b

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

236×	`unpow-prod-down`
224×	`prod-diff`
206×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
128×	`log-prod`
122×	`cbrt-prod`
116×	`exp-sum`
74×	`sqr-pow`
32×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `sub-neg` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 334

Calls

4 calls:

47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
46.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
46.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

289.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
450.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
447.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify557.0ms

Counts

346 → 346

Iterations

Useful iterations: done (540.0ms)

Iter	Nodes	Cost
0	401	16714
1	636	12150
2	1489	9942
done	5001	9866

prune884.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 19.2b

regimes289.0ms

Accuracy

81.8% (1.5b remaining)

Error of 22.1b against oracle of 20.6b and baseline of 29.0b

bsearch209.0ms

Steps

Iters	Range		Point
10	0.11513722063736925	8521518135.486671	196016184.31866574
8	-2.2021465089483198e+21	-7.884632933156152e+16	-8.092517375237888e+16

simplify5.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	34	119
1	45	80
2	47	80
done	47	80

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	3210×	body	1280	valid
552.0ms	1581×	body	640	valid
443.0ms	1119×	body	10240	exit
320.0ms	660×	body	1280	nan
260.0ms	4726×	body	80	valid
213.0ms	676×	body	640	nan
187.0ms	848×	body	320	valid
183.0ms	4956×	body	80	nan
66.0ms	341×	body	320	nan
60.0ms	438×	body	160	valid
21.0ms	191×	body	160	nan