Details

sample157.0ms

Algorithm

intervals

Results

55.0ms	118×	body	1280	valid
28.0ms	50×	body	10240	exit
17.0ms	50×	body	640	valid
8.0ms	149×	body	80	valid
7.0ms	25×	body	640	nan
5.0ms	157×	body	80	nan
5.0ms	28×	body	320	valid
5.0ms	12×	body	1280	nan
2.0ms	12×	body	320	nan
2.0ms	13×	body	160	valid
1.0ms	6×	body	160	nan

simplify34.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6
done	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

70×	`unpow-prod-down`
67×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

2 → 120

Calls

2 calls:

12.0ms	(pow (+ x 1.0) (/ 1.0 n))
106.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series415.0ms

Counts

2 → 6

Calls

2 calls:

141.0ms	(pow (+ x 1.0) (/ 1.0 n))
274.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify62.0ms

Counts

126 → 126

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	542	2011
1	1694	1489
2	5001	1488
done	5001	1488

prune258.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (pow (+ x 1.0) (/ 1.0 n))))
0.0b	(exp (pow (+ x 1.0) (/ 1.0 n)))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (log (exp (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

91×	`*-un-lft-identity`
84×	`prod-diff`
82×	`log-pow`
81×	`unpow-prod-down`
80×	`exp-prod`
71×	`add-sqr-sqrt`
66×	`add-cube-cbrt`
24×	`sqr-pow`
15×	`pow1`
13×	`pow-unpow`
12×	`fma-neg`
11×	`distribute-lft-out`
9×	`times-frac`
6×	`log-prod` `add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`associate--l+` `difference-of-squares`
2×	`distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `rem-log-exp` `pow-exp` `flip--` `div-inv` `rem-exp-log`

Counts

4 → 188

Calls

4 calls:

33.0ms	(log (exp (pow (+ x 1.0) (/ 1.0 n))))
36.0ms	(exp (pow (+ x 1.0) (/ 1.0 n)))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
310.0ms	(- (log (exp (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

series875.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(log (exp (pow (+ x 1.0) (/ 1.0 n))))
294.0ms	(exp (pow (+ x 1.0) (/ 1.0 n)))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))
281.0ms	(- (log (exp (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify68.0ms

Counts

200 → 200

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	667	3178
1	2033	2043
2	5001	1999
done	5001	1999

prune395.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
1.1b	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
37.3b	(- (+ (* 2 (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
42×	`prod-diff`
39×	`add-sqr-sqrt`
34×	`add-cube-cbrt`
23×	`unpow-prod-down`
16×	`distribute-rgt-out`
13×	`pow1` `pow-unpow`
9×	`times-frac`
8×	`distribute-lft1-in` `log-pow` `add-log-exp` `sqr-pow`
6×	`cbrt-prod` `fma-neg`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`pow1/3` `diff-log`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `pow-exp` `associate--l+` `sum-log` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 124

Calls

4 calls:

12.0ms	(pow (+ x 1.0) (/ 1.0 n))
32.0ms	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
34.0ms	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
95.0ms	(- (+ (* 2 (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

series1.3s

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow (+ x 1.0) (/ 1.0 n))
371.0ms	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
366.0ms	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
435.0ms	(- (+ (* 2 (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

simplify68.0ms

Counts

136 → 136

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	599	2619
1	1993	1953
2	5001	1942
done	5001	1942

prune447.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (+ x 1.0) (/ 1.0 n))
0.7b	(pow (+ x 1.0) (/ 1.0 n))
1.1b	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
37.3b	(- (+ (* 2 (log (pow (exp (pow (+ x 1.0) (/ 1.0 n))) 1/3))) (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
35×	`add-cube-cbrt`
26×	`pow-unpow`
21×	`prod-diff`
18×	`unpow-prod-down` `times-frac`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `sqr-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `fma-neg` `difference-of-squares`
2×	`pow-to-exp` `pow-pow` `diff-log` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `pow1/3` `associate--l+` `sum-log` `flip--` `distribute-lft-out--`

Counts

4 → 117

Calls

4 calls:

12.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
33.0ms	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
88.0ms	(- (+ (* 2 (log (pow (exp (pow (+ x 1.0) (/ 1.0 n))) 1/3))) (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
146.0ms	(pow (+ x 1.0) (/ 1.0 n))
373.0ms	(cbrt (exp (pow (+ x 1.0) (/ 1.0 n))))
444.0ms	(- (+ (* 2 (log (pow (exp (pow (+ x 1.0) (/ 1.0 n))) 1/3))) (log (cbrt (exp (pow (+ x 1.0) (/ 1.0 n)))))) (pow x (/ 1.0 n)))

simplify63.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	572	2106
1	1958	1637
2	5001	1560
done	5001	1560

prune526.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.0b

regimes184.0ms

Accuracy

90.2% (1.8b remaining)

Error of 22.7b against oracle of 21.0b and baseline of 38.9b

bsearch285.0ms

Steps

Iters	Range		Point
11	2.142008608447194e-19	60.065953071798994	59.53547333114815
9	-1.3392188720065574e+27	-9.230054167364397e+20	-9.348333424414554e+20

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	24
1	48	24
done	48	24

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3183×	body	1280	valid
499.0ms	1514×	body	640	valid
496.0ms	1188×	body	10240	exit
271.0ms	620×	body	1280	nan
239.0ms	4681×	body	80	valid
203.0ms	655×	body	640	nan
197.0ms	914×	body	320	valid
171.0ms	4913×	body	80	nan
72.0ms	360×	body	320	nan
60.0ms	435×	body	160	valid
21.0ms	194×	body	160	nan