Details

sample383.0ms

Algorithm

intervals

Results

102.0ms	92×	body	1280	valid
55.0ms	50×	body	10240	exit
55.0ms	66×	body	640	valid
51.0ms	17×	body	640	nan
29.0ms	26×	body	1280	nan
23.0ms	146×	body	80	valid
16.0ms	144×	body	80	nan
15.0ms	27×	body	320	valid
6.0ms	9×	body	160	valid
4.0ms	9×	body	320	nan
2.0ms	6×	body	160	nan

simplify1.7s

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize30.0ms

Local error

Found 3 expressions with local error:

1.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.5b	(pow (+ x 1) (/ 1 n))
0.0b	(pow x (/ 1 n))

rewrite102.0ms

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` `insert-posit16` `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 → 152

Calls

3 calls:

Slowest

76.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
16.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(pow x (/ 1 n))

series772.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

577.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
116.0ms	(pow (+ x 1) (/ 1 n))
78.0ms	(pow x (/ 1 n))

simplify900.0ms

Counts: 161 → 161

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize22.0ms

Local error

Found 4 expressions with local error:

34.1b	(- (pow (+ x 1) (/ 1 n)) (expm1 (log1p (pow x (/ 1 n)))))
0.5b	(pow (+ x 1) (/ 1 n))
0.0b	(pow x (/ 1 n))
0.0b	(expm1 (log1p (pow x (/ 1 n))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
36×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`unpow-prod-down` `prod-diff`
18×	`times-frac`
8×	`fma-neg`
7×	`sqr-pow`
6×	`pow1` `add-exp-log` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `expm1-udef`
1×	`expm1-log1p` `sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `associate--r-`

Counts

4 → 125

Calls

4 calls:

Slowest

58.0ms	(- (pow (+ x 1) (/ 1 n)) (expm1 (log1p (pow x (/ 1 n)))))
7.0ms	(pow (+ x 1) (/ 1 n))
5.0ms	(pow x (/ 1 n))
0.0ms	(expm1 (log1p (pow x (/ 1 n))))

series585.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

311.0ms	(- (pow (+ x 1) (/ 1 n)) (expm1 (log1p (pow x (/ 1 n)))))
113.0ms	(pow (+ x 1) (/ 1 n))
102.0ms	(expm1 (log1p (pow x (/ 1 n))))
59.0ms	(pow x (/ 1 n))

simplify2.1s

Counts: 137 → 137

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize64.0ms

Local error

Found 4 expressions with local error:

34.1b	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
0.5b	(pow (+ x 1) (/ 1 n))
0.5b	(pow (+ x 1) (/ 1 n))
0.0b	(pow x (/ 1 n))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

101×	`sqrt-prod`
93×	`*-un-lft-identity`
85×	`add-sqr-sqrt`
71×	`add-cube-cbrt`
66×	`prod-diff`
41×	`unpow-prod-down`
39×	`pow-unpow`
27×	`times-frac`
12×	`sqr-pow`
11×	`fma-neg`
9×	`distribute-lft-out`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
2×	`distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 194

Calls

4 calls:

Slowest

75.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
7.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
3.0ms	(pow x (/ 1 n))

series737.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

449.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
114.0ms	(pow (+ x 1) (/ 1 n))
106.0ms	(pow (+ x 1) (/ 1 n))
67.0ms	(pow x (/ 1 n))

simplify727.0ms

Counts: 206 → 206

prune3.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.3b

localize90.0ms

Local error

Found 4 expressions with local error:

34.1b	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
34.1b	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
34.1b	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
0.5b	(pow (+ x 1) (/ 1 n))

rewrite289.0ms

Algorithm

rewrite-expression-head

Rules

303×	`sqrt-prod`
198×	`prod-diff`
197×	`*-un-lft-identity`
183×	`add-sqr-sqrt`
141×	`add-cube-cbrt`
94×	`unpow-prod-down`
33×	`fma-neg`
28×	`sqr-pow`
24×	`difference-of-squares`
22×	`distribute-lft-out`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 337

Calls

4 calls:

Slowest

91.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
86.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
86.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
13.0ms	(pow (+ x 1) (/ 1 n))

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

462.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
393.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
392.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (expm1 (log1p (pow x (/ 1 n))))))
140.0ms	(pow (+ x 1) (/ 1 n))

simplify1.7s

Counts: 349 → 349

prune8.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.3b

regimes440.0ms

Accuracy

86.6% (1.6b remaining)

Error of 19.4b against oracle of 17.8b and baseline of 29.5b

bsearch489.0ms

end0.0ms

sample11.0s

Algorithm

intervals

Results

3.8s	3208×	body	1280	valid
1.5s	1198×	body	10240	exit
1.3s	1660×	body	640	valid
886.0ms	858×	body	320	valid
774.0ms	4625×	body	80	valid
754.0ms	678×	body	1280	nan
607.0ms	5002×	body	80	nan
510.0ms	663×	body	640	nan
207.0ms	359×	body	320	nan
130.0ms	416×	body	160	valid
49.0ms	169×	body	160	nan