Details

sample211.0ms

Algorithm

intervals

Results

79.0ms	115×	body	1280	valid
22.0ms	38×	body	320	valid
22.0ms	34×	body	10240	exit
19.0ms	37×	body	640	valid
12.0ms	131×	body	80	valid
9.0ms	146×	body	80	nan
8.0ms	17×	body	640	nan
7.0ms	12×	body	1280	nan
3.0ms	11×	body	320	nan
3.0ms	15×	body	160	valid
0.0ms	3×	body	160	nan

simplify1.3s

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	252	13
5	1266	13
done	5000	13

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite180.0ms

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:

8.0ms	(pow x (/ 1.0 n))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))
138.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series762.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(pow x (/ 1.0 n))
236.0ms	(pow (+ x 1.0) (/ 1.0 n))
448.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.8s

Counts

158 → 158

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	271	4785
1	740	3759
2	2874	3021
done	5002	2906

prune558.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.6b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow x (/ 1.0 n)) 3)
0.2b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

rewrite260.0ms

Algorithm

rewrite-expression-head

Rules

244×	`unpow-prod-down`
184×	`cbrt-prod` `prod-diff`
173×	`*-un-lft-identity`
157×	`add-sqr-sqrt`
121×	`add-cube-cbrt`
72×	`cube-prod`
71×	`sqr-pow`
29×	`pow-unpow`
27×	`difference-of-squares`
25×	`distribute-lft-out`
18×	`times-frac`
9×	`cube-mult` `unpow3`
8×	`add-exp-log` `fma-neg`
6×	`pow1` `pow-exp` `add-log-exp`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `pow-to-exp` `log1p-expm1-u`
3×	`pow-pow`
2×	`div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 328

Calls

4 calls:

5.0ms	(pow (pow x (/ 1.0 n)) 3)
4.0ms	(pow x (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
198.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

series867.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(pow (pow x (/ 1.0 n)) 3)
100.0ms	(pow x (/ 1.0 n))
218.0ms	(pow (+ x 1.0) (/ 1.0 n))
438.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (cbrt (pow (pow x (/ 1.0 n)) 3)))

simplify4.0s

Counts

340 → 340

Iterations

Useful iterations: 2 (1.5s)

Iter	Nodes	Cost
0	451	17024
1	1194	11664
2	4924	8971
done	5000	8971

prune841.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.6b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow x (* 2 (/ 1.0 n)))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(fma (- (cbrt (pow x (* 2 (/ 1.0 n))))) (cbrt (pow x (/ 1.0 n))) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

73×	`unpow-prod-down`
70×	`*-un-lft-identity`
57×	`add-sqr-sqrt`
56×	`prod-diff`
45×	`add-cube-cbrt`
24×	`sqr-pow`
14×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `div-inv`

Counts

4 → 147

Calls

4 calls:

3.0ms	(pow x (* 2 (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
0.0ms	(fma (- (cbrt (pow x (* 2 (/ 1.0 n))))) (cbrt (pow x (/ 1.0 n))) (pow x (/ 1.0 n)))
164.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.1s

Counts

4 → 12

Calls

4 calls:

74.0ms	(pow x (* 2 (/ 1.0 n)))
214.0ms	(pow (+ x 1.0) (/ 1.0 n))
370.0ms	(fma (- (cbrt (pow x (* 2 (/ 1.0 n))))) (cbrt (pow x (/ 1.0 n))) (pow x (/ 1.0 n)))
474.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.3s

Counts

159 → 159

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	300	5041
1	795	4026
2	3087	3227
done	5002	3109

prune879.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(fma (- (cbrt (pow (pow x 2) (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n))) (pow x (/ 1.0 n)))
2.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
17.7b	(pow (pow x 2) (/ 1.0 n))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

81×	`unpow-prod-down`
78×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
56×	`prod-diff`
53×	`add-cube-cbrt`
26×	`pow-unpow`
25×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`add-exp-log`
6×	`add-log-exp`
5×	`pow1` `pow-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `distribute-lft-out--`
2×	`pow-pow` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `unpow2`

Counts

4 → 166

Calls

4 calls:

22.0ms	(pow (+ x 1.0) (/ 1.0 n))
1.0ms	(fma (- (cbrt (pow (pow x 2) (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n))) (pow x (/ 1.0 n)))
176.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
13.0ms	(pow (pow x 2) (/ 1.0 n))

series1.5s

Counts

4 → 12

Calls

4 calls:

180.0ms	(pow (+ x 1.0) (/ 1.0 n))
431.0ms	(fma (- (cbrt (pow (pow x 2) (/ 1.0 n)))) (cbrt (pow x (/ 1.0 n))) (pow x (/ 1.0 n)))
794.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
81.0ms	(pow (pow x 2) (/ 1.0 n))

simplify2.7s

Counts

178 → 178

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	342	5294
1	934	4237
2	3698	3435
done	5000	3434

prune977.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 21.6b

regimes281.0ms

Accuracy

82.4% (2.8b remaining)

Error of 23.5b against oracle of 20.8b and baseline of 36.5b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	40	102
1	49	102
done	49	102

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.8s	3137×	body	1280	valid
1.0s	4763×	body	80	valid
879.0ms	1544×	body	640	valid
823.0ms	1192×	body	10240	exit
792.0ms	4986×	body	80	nan
532.0ms	658×	body	1280	nan
386.0ms	692×	body	640	nan
345.0ms	831×	body	320	valid
124.0ms	375×	body	320	nan
99.0ms	449×	body	160	valid
45.0ms	181×	body	160	nan