Details

sample254.0ms

Algorithm

intervals

Results

78.0ms	99×	body	1280	valid
30.0ms	173×	body	80	nan
28.0ms	52×	body	640	valid
20.0ms	23×	body	1280	nan
16.0ms	30×	body	640	nan
14.0ms	28×	body	10240	exit
14.0ms	144×	body	80	valid
11.0ms	34×	body	320	valid
4.0ms	10×	body	320	nan
3.0ms	12×	body	160	valid
1.0ms	4×	body	160	nan

simplify1.6s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize27.0ms

Local error

Found 3 expressions with local error:

0.8b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite105.0ms

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:

3.0ms	(pow x (/ 1.0 n))
8.0ms	(pow (+ x 1.0) (/ 1.0 n))
87.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series713.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(pow x (/ 1.0 n))
219.0ms	(pow (+ x 1.0) (/ 1.0 n))
416.0ms	(- (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

prune944.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.2b

localize56.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
3.4b	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
56×	`pow-unpow`
50×	`*-un-lft-identity`
48×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`unpow-prod-down`
6×	`pow1` `add-exp-log`
5×	`div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `sqr-pow`
1×	`distribute-lft-out`

Counts

4 → 109

Calls

4 calls:

6.0ms	(pow x (/ (/ 1.0 n) 2))
13.0ms	(pow (+ x 1.0) (/ 1.0 n))
0.0ms	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
0.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow x (/ (/ 1.0 n) 2))
214.0ms	(pow (+ x 1.0) (/ 1.0 n))
532.0ms	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
498.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

simplify2.6s

Counts

121 → 121

Iterations

Iter	Nodes
done	5002
2	3703
1	842
0	264

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.2b

localize127.0ms

Local error

Found 4 expressions with local error:

3.2b	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
3.4b	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
3.4b	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
3.4b	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

0.0ms	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
0.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
0.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
1.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

148.0ms	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
485.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
461.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
477.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

simplify1.9s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	3353
2	583
1	162
0	73

prune461.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 20.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
3.2b	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
3.4b	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
56×	`pow-unpow`
50×	`*-un-lft-identity`
48×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`unpow-prod-down`
6×	`pow1` `add-exp-log`
5×	`div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-pow` `pow-exp` `fma-udef` `sqr-pow`
1×	`distribute-lft-out`

Counts

4 → 109

Calls

4 calls:

6.0ms	(pow x (/ (/ 1.0 n) 2))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
0.0ms	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
0.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

series956.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(pow x (/ (/ 1.0 n) 2))
228.0ms	(pow (+ x 1.0) (/ 1.0 n))
165.0ms	(fma (- (pow x (/ (/ 1.0 n) 2))) (pow x (/ (/ 1.0 n) 2)) (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
485.0ms	(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (pow x (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))

simplify2.7s

Counts

121 → 121

Iterations

Iter	Nodes
done	5002
2	3703
1	842
0	264

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 20.2b

regimes418.0ms

Accuracy

80.6% (1.7b remaining)

Error of 22.1b against oracle of 20.4b and baseline of 29.2b

bsearch2.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	55
2	55
1	53
0	43

end0.0ms

sample8.5s

Algorithm

intervals

Results

2.5s	3156×	body	1280	valid
1.0s	1213×	body	10240	exit
932.0ms	1585×	body	640	valid
874.0ms	5247×	body	80	nan
754.0ms	4883×	body	80	valid
573.0ms	641×	body	1280	nan
370.0ms	677×	body	640	nan
348.0ms	837×	body	320	valid
150.0ms	467×	body	160	valid
124.0ms	378×	body	320	nan
38.0ms	204×	body	160	nan