Details

sample126.0ms

Algorithm

intervals

Results

42.0ms	100×	body	1280	valid
14.0ms	42×	body	640	valid
12.0ms	16×	body	1280	nan
11.0ms	23×	body	10240	exit
8.0ms	166×	body	80	valid
6.0ms	19×	body	640	nan
6.0ms	152×	body	80	nan
4.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	8×	body	320	nan
0.0ms	4×	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: 26.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.1b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite117.0ms

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:

5.0ms	(pow x (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
94.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series461.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
138.0ms	(pow (+ x 1.0) (/ 1.0 n))
262.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify63.0ms

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637
done	5002	1637

prune326.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ (/ 1.0 n) 2))
1.1b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.1b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.2b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

7.0ms	(pow x (/ (/ 1.0 n) 2))
16.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
94.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow x (/ (/ 1.0 n) 2))
139.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
144.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
272.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify90.0ms

Counts

281 → 281

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	985	3525
1	3500	2856
2	5001	2853
done	5001	2853

prune858.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.2b

localize29.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
3.0b	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
9.3b	(* x (pow n 2))
11.2b	(* (pow x 2) n)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`associate-l`
16×	`add-exp-log`
14×	`associate-r`
12×	`add-cube-cbrt` `unpow-prod-down`
10×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`prod-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `unpow2` `add-log-exp` `sqr-pow`
3×	`*-commutative` `cbrt-unprod` `fma-udef`
2×	`pow-to-exp` `associate-*l/` `pow-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+`

Counts

4 → 95

Calls

4 calls:

0.0ms	(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
179.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
12.0ms	(* x (pow n 2))
12.0ms	(* (pow x 2) n)

series531.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
382.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
30.0ms	(* x (pow n 2))
23.0ms	(* (pow x 2) n)

simplify77.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	564	1277
1	2613	1122
2	5001	1121
done	5001	1121

prune476.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 20.1b

localize37.0ms

Local error

Found 4 expressions with local error:

1.8b	(fma (- 0.25) (+ (/ 1 (log1p (expm1 (* (pow x 2) n)))) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
3.0b	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (log1p (expm1 (* (pow x 2) n)))) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
9.3b	(* x (pow n 2))
11.2b	(* (pow x 2) n)

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
17×	`associate-l`
16×	`add-exp-log`
14×	`associate-r`
12×	`add-cube-cbrt` `unpow-prod-down`
10×	`add-cbrt-cube`
9×	`unswap-sqr`
7×	`prod-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out` `unpow2` `add-log-exp` `sqr-pow`
3×	`*-commutative` `cbrt-unprod` `fma-udef`
2×	`pow-to-exp` `associate-*l/` `pow-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+`

Counts

4 → 95

Calls

4 calls:

0.0ms	(fma (- 0.25) (+ (/ 1 (log1p (expm1 (* (pow x 2) n)))) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
179.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (log1p (expm1 (* (pow x 2) n)))) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
12.0ms	(* x (pow n 2))
12.0ms	(* (pow x 2) n)

series525.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(fma (- 0.25) (+ (/ 1 (log1p (expm1 (* (pow x 2) n)))) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
335.0ms	(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (fma (- 0.25) (+ (/ 1 (log1p (expm1 (* (pow x 2) n)))) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
29.0ms	(* x (pow n 2))
19.0ms	(* (pow x 2) n)

simplify78.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	583	1375
1	2711	1188
2	5001	1176
done	5001	1176

prune507.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 20.1b

regimes295.0ms

Accuracy

85% (1.3b remaining)

Error of 21.5b against oracle of 20.2b and baseline of 28.8b

bsearch2.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	69
1	57	69
done	57	69

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3166×	body	1280	valid
532.0ms	1599×	body	640	valid
433.0ms	1091×	body	10240	exit
292.0ms	639×	body	1280	nan
248.0ms	4738×	body	80	valid
212.0ms	655×	body	640	nan
184.0ms	830×	body	320	valid
181.0ms	5055×	body	80	nan
62.0ms	457×	body	160	valid
58.0ms	314×	body	320	nan
23.0ms	180×	body	160	nan