Details

sample212.0ms

Algorithm

intervals

Results

74.0ms	115×	body	1280	valid
24.0ms	53×	body	640	valid
22.0ms	36×	body	10240	exit
14.0ms	23×	body	1280	nan
12.0ms	151×	body	80	valid
10.0ms	210×	body	80	nan
9.0ms	20×	body	640	nan
8.0ms	22×	body	320	valid
4.0ms	14×	body	320	nan
2.0ms	13×	body	160	nan
2.0ms	9×	body	160	valid

simplify3.0s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.0b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite159.0ms

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))
127.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series717.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(pow x (/ 1.0 n))
430.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
198.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.5s

Counts

158 → 158

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	271	4785
1	647	3566
2	1619	3020
done	5000	2646

prune503.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 21.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (log (pow x (/ 1.0 n)))))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.6b	(log (pow x (/ 1.0 n)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

94×	`*-un-lft-identity`
85×	`add-sqr-sqrt` `unpow-prod-down`
80×	`prod-diff`
72×	`log-prod`
68×	`add-cube-cbrt`
65×	`exp-sum`
29×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac`
12×	`distribute-lft-out` `difference-of-squares`
8×	`add-exp-log` `fma-neg`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `rem-log-exp` `pow-exp`
2×	`pow-pow` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `log-pow` `flip--` `distribute-lft-out--`

Counts

4 → 194

Calls

4 calls:

9.0ms	(pow x (/ 1.0 n))
151.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (log (pow x (/ 1.0 n)))))
13.0ms	(pow (+ x 1.0) (/ 1.0 n))
4.0ms	(log (pow x (/ 1.0 n)))

series769.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow x (/ 1.0 n))
364.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (exp (log (pow x (/ 1.0 n)))))
202.0ms	(pow (+ x 1.0) (/ 1.0 n))
121.0ms	(log (pow x (/ 1.0 n)))

simplify1.5s

Counts

206 → 206

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	349	7549
1	785	4797
2	1891	3845
done	5000	3264

prune621.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 18.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (log x)) (pow n 2))
0.5b	(/ 0.5 (* (pow x 2) n))
1.9b	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
10.2b	(* (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:

14.0ms	(/ (- (log x)) (pow n 2))
10.0ms	(/ 0.5 (* (pow x 2) n))
765.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
24.0ms	(* (pow x 2) n)

series327.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (log x)) (pow n 2))
30.0ms	(/ 0.5 (* (pow x 2) n))
184.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
19.0ms	(* (pow x 2) n)

simplify10.0s

Counts

2866 → 2866

Iterations

Useful iterations: done (9.7s)

Iter	Nodes	Cost
0	3603	192576
done	5001	173755

prune14.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 18.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 0.5 (log1p (expm1 (* (pow x 2) n))))
0.5b	(/ (- (log x)) (pow n 2))
1.9b	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
10.2b	(* (pow x 2) n)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

4439×	`times-frac`
2802×	`add-sqr-sqrt`
2769×	`*-un-lft-identity`
2750×	`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`
26×	`associate-r`
21×	`add-exp-log` `associate-l`
15×	`add-cbrt-cube` `associate-/l*` `difference-of-squares`
11×	`associate-/r*`
6×	`unswap-sqr`
5×	`div-exp` `prod-exp` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `neg-sub0` `frac-times` `div-sub` `associate-*r/` `cbrt-unprod`
2×	`pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `pow-exp` `clear-num` `*-commutative` `frac-sub` `flip--` `associate--r-`
1×	`distribute-frac-neg` `pow-prod-down` `associate-*l/`

Counts

4 → 2858

Calls

4 calls:

5.0ms	(/ 0.5 (log1p (expm1 (* (pow x 2) n))))
14.0ms	(/ (- (log x)) (pow n 2))
816.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
12.0ms	(* (pow x 2) n)

series430.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ 0.5 (log1p (expm1 (* (pow x 2) n))))
105.0ms	(/ (- (log x)) (pow n 2))
214.0ms	(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
34.0ms	(* (pow x 2) n)

simplify9.3s

Counts

2870 → 2870

Iterations

Useful iterations: done (8.5s)

Iter	Nodes	Cost
0	3618	192767
done	5000	173869

prune14.8s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 18.4b

regimes531.0ms

Accuracy

71.2% (3.3b remaining)

Error of 21.2b against oracle of 17.9b and baseline of 29.3b

bsearch982.0ms

Steps

Iters	Range		Point
11	0.007160366775085844	5.482779149720861e+18	117373745.42755693
10	9.822127780452029e-163	1.8051240975654942e-151	1.0126678986455559e-162
10	-1.9406440019384646e-302	3.066359621321708e-299	1.94201371468443e-310
9	-66911392.43097515	-2.284674362912159	-36780699.510345064

simplify12.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	49	112
1	56	111
done	56	111

end0.0ms

sample6.1s

Algorithm

intervals

Results

2.1s	3162×	body	1280	valid
769.0ms	1550×	body	640	valid
647.0ms	1100×	body	10240	exit
405.0ms	611×	body	1280	nan
360.0ms	4773×	body	80	valid
322.0ms	696×	body	640	nan
275.0ms	5097×	body	80	nan
266.0ms	835×	body	320	valid
100.0ms	358×	body	320	nan
87.0ms	461×	body	160	valid
32.0ms	197×	body	160	nan