Details

sample257.0ms

Algorithm

intervals

Results

90.0ms	109×	body	1280	valid
33.0ms	35×	body	10240	exit
30.0ms	47×	body	640	valid
21.0ms	24×	body	1280	nan
13.0ms	129×	body	80	valid
11.0ms	162×	body	80	nan
11.0ms	17×	body	640	nan
8.0ms	19×	body	320	valid
4.0ms	14×	body	160	valid
4.0ms	11×	body	320	nan
2.0ms	8×	body	160	nan

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	245	13
5	730	13
6	3688	13
done	5000	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite165.0ms

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:

4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
143.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series673.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(pow x (/ 1.0 n))
213.0ms	(pow (+ x 1.0) (/ 1.0 n))
375.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

158 → 158

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	271	4785
1	647	3566
2	1620	3020
done	5000	2646

prune509.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow x (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
1.0b	(pow (+ x 1.0) (/ 1.0 n))
5.5b	(fma (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n))) (- (pow x (/ 1.0 n))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
32×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
11×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `sqr-pow`
2×	`distribute-lft-out`
1×	`fma-udef`

Counts

4 → 99

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
23.0ms	(pow (+ x 1.0) (/ 1.0 n))
22.0ms	(pow (+ x 1.0) (/ 1.0 n))
1.0ms	(fma (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n))) (- (pow x (/ 1.0 n))))

series1.3s

Counts

4 → 12

Calls

4 calls:

107.0ms	(pow x (/ 1.0 n))
234.0ms	(pow (+ x 1.0) (/ 1.0 n))
251.0ms	(pow (+ x 1.0) (/ 1.0 n))
745.0ms	(fma (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow (+ x 1.0) (/ 1.0 n))) (- (pow x (/ 1.0 n))))

simplify2.6s

Counts

111 → 111

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	169	1454
1	423	1245
2	1123	1172
3	3511	1147
done	5000	1142

prune672.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (log x)) (pow n 2))
0.6b	(/ 0.5 (* (pow x 2) n))
1.6b	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
7.8b	(* (pow x 2) n)

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

4433×	`times-frac`
2796×	`add-sqr-sqrt`
2763×	`*-un-lft-identity`
2744×	`add-cube-cbrt`
2600×	`prod-diff`
1303×	`distribute-rgt-in` `distribute-lft-in`
982×	`unpow-prod-down`
870×	`distribute-rgt-neg-in`
868×	`distribute-lft-neg-in`
441×	`pow1`
435×	`log-pow`
330×	`unpow2` `sqr-pow`
230×	`div-inv`
217×	`neg-mul-1`
29×	`add-exp-log`
26×	`associate-r`
21×	`associate-l`
18×	`add-cbrt-cube`
15×	`associate-/l*` `difference-of-squares`
9×	`associate-/r*`
8×	`div-exp` `prod-exp`
6×	`unswap-sqr`
5×	`distribute-lft-out--`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`neg-sub0` `frac-times` `pow-to-exp` `div-sub` `associate-*r/` `pow-exp`
2×	`sub-neg` `flip3--` `frac-2neg` `clear-num` `*-commutative` `frac-sub` `flip--` `associate--r-`
1×	`distribute-frac-neg` `pow-prod-down` `associate-*l/`

Counts

4 → 2854

Calls

4 calls:

18.0ms	(/ (- (log x)) (pow n 2))
18.0ms	(/ 0.5 (* (pow x 2) n))
770.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
17.0ms	(* (pow x 2) n)

series360.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- (log x)) (pow n 2))
33.0ms	(/ 0.5 (* (pow x 2) n))
194.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
33.0ms	(* (pow x 2) n)

simplify9.9s

Counts

2866 → 2866

Iterations

Useful iterations: done (9.6s)

Iter	Nodes	Cost
0	3603	192576
done	5001	173755

prune15.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (* (pow x 2) n)))
0.5b	(/ (- (log x)) (pow n 2))
1.6b	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
7.8b	(* (pow x 2) n)

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

4430×	`times-frac`
2794×	`add-sqr-sqrt`
2761×	`*-un-lft-identity`
2742×	`add-cube-cbrt`
2600×	`prod-diff`
1303×	`distribute-rgt-in` `distribute-lft-in`
982×	`unpow-prod-down`
870×	`distribute-rgt-neg-in`
868×	`distribute-lft-neg-in`
441×	`pow1`
435×	`log-pow`
330×	`unpow2` `sqr-pow`
229×	`div-inv`
217×	`neg-mul-1`
26×	`associate-r`
21×	`associate-l`
19×	`add-exp-log`
15×	`difference-of-squares`
13×	`add-cbrt-cube`
12×	`associate-/l*`
8×	`associate-/r*`
6×	`unswap-sqr`
5×	`prod-exp` `distribute-lft-out--`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`neg-sub0` `frac-times` `div-sub` `associate-*r/` `cbrt-unprod`
2×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `pow-exp` `*-commutative` `frac-sub` `flip--` `associate--r-`
1×	`log1p-udef` `frac-2neg` `log1p-expm1` `distribute-frac-neg` `pow-prod-down` `associate-*l/` `clear-num`

Counts

4 → 2840

Calls

4 calls:

0.0ms	(log1p (expm1 (* (pow x 2) n)))
15.0ms	(/ (- (log x)) (pow n 2))
746.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
13.0ms	(* (pow x 2) n)

series376.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(log1p (expm1 (* (pow x 2) n)))
112.0ms	(/ (- (log x)) (pow n 2))
195.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
22.0ms	(* (pow x 2) n)

simplify8.5s

Counts

2852 → 2852

Iterations

Useful iterations: done (8.2s)

Iter	Nodes	Cost
0	3579	192400
done	5000	173562

prune17.0s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 18.2b

regimes584.0ms

Accuracy

81.1% (1.6b remaining)

Error of 22.4b against oracle of 20.7b and baseline of 29.4b

bsearch212.0ms

Steps

Iters	Range		Point
8	0.9435061171835805	249.10217458544693	247.0873999593015
5	-873354922362061.5	-351616126183326.2	-380251775535541.94

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	120
1	51	120
done	51	120

end0.0ms

sample9.2s

Algorithm

intervals

Results

3.1s	3122×	body	1280	valid
1.0s	1180×	body	10240	exit
936.0ms	1620×	body	640	valid
708.0ms	4668×	body	80	valid
648.0ms	702×	body	1280	nan
583.0ms	465×	body	160	valid
424.0ms	5103×	body	80	nan
409.0ms	834×	body	320	valid
399.0ms	661×	body	640	nan
121.0ms	357×	body	320	nan
38.0ms	179×	body	160	nan