Details

sample239.0ms

Algorithm

intervals

Results

87.0ms	103×	body	1280	valid
27.0ms	29×	body	1280	nan
19.0ms	31×	body	640	valid
18.0ms	186×	body	80	valid
17.0ms	30×	body	10240	exit
12.0ms	30×	body	320	valid
11.0ms	164×	body	80	nan
10.0ms	16×	body	640	nan
4.0ms	10×	body	320	nan
2.0ms	11×	body	160	valid
1.0ms	7×	body	160	nan

simplify1.7s

Counts

1 → 1

Iterations

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite142.0ms

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:

6.0ms	(pow x (/ 1.0 n))
15.0ms	(pow (+ x 1.0) (/ 1.0 n))
113.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series682.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(pow x (/ 1.0 n))
198.0ms	(pow (+ x 1.0) (/ 1.0 n))
420.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.9s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	2866
1	738
0	270

prune804.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.4b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite408.0ms

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:

3.0ms	(pow x (/ 1.0 n))
9.0ms	(pow (+ x 1.0) (/ 1.0 n))
273.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
112.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow x (/ 1.0 n))
205.0ms	(pow (+ x 1.0) (/ 1.0 n))
375.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
385.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.3s

Counts

249 → 249

Iterations

Iter	Nodes
done	5000
2	3271
1	927
0	429

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.4b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite551.0ms

Algorithm

rewrite-expression-head

Rules

260×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
87×	`sqr-pow`
61×	`log-prod`
58×	`exp-sum`
36×	`difference-of-squares`
35×	`distribute-lft-out`
24×	`fma-neg`
16×	`log-pow`
15×	`exp-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 358

Calls

4 calls:

247.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
86.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.6s

Counts

4 → 12

Calls

4 calls:

422.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
381.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
427.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
368.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.0s

Counts

370 → 370

Iterations

Iter	Nodes
done	5003
2	1780
1	613
0	344

prune3.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.4b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite620.0ms

Algorithm

rewrite-expression-head

Rules

198×	`unpow-prod-down`
169×	`*-un-lft-identity`
168×	`prod-diff`
136×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
66×	`sqr-pow`
27×	`distribute-lft-out` `difference-of-squares`
24×	`fma-neg`
12×	`pow1`
10×	`add-log-exp`
9×	`log-pow` `distribute-lft-out--`
7×	`add-exp-log`
6×	`pow1/3`
4×	`expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `exp-diff` `log1p-expm1-u`
3×	`log-div` `sub-neg` `flip3--` `diff-log` `flip--`
2×	`rem-log-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `log-prod` `pow-plus` `associate-l/` `prod-exp` `associate-r/`

Counts

4 → 294

Calls

4 calls:

111.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
104.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
106.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

series2.1s

Counts

4 → 12

Calls

4 calls:

362.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
417.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
419.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
866.0ms	(log (* (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))) (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))))

simplify1.9s

Counts

306 → 306

Iterations

Iter	Nodes
done	5001
2	1789
1	530
0	229

prune2.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 14.4b

regimes718.0ms

Accuracy

85.5% (1.3b remaining)

Error of 22.0b against oracle of 20.7b and baseline of 29.6b

bsearch307.0ms

Steps

Iters	Range		Point
10	5.808149794101367e-16	1126.7541422477805	1096.3579088579716
8	-118939140946.09552	-31677438.02179023	-47651231.91183168

simplify12.0ms

Iterations

Iter	Nodes
done	39
1	39
0	31

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.9s	3133×	body	1280	valid
1.4s	1656×	body	640	valid
1.0s	1146×	body	10240	exit
593.0ms	4662×	body	80	valid
536.0ms	629×	body	1280	nan
400.0ms	631×	body	640	nan
374.0ms	884×	body	320	valid
357.0ms	5035×	body	80	nan
200.0ms	453×	body	160	valid
182.0ms	397×	body	320	nan
33.0ms	171×	body	160	nan