Details

analyze1.6s (7.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample506.0ms (2.3%)

Algorithm

1×

intervals

Results

138.0ms	53×	body	1024	nan
134.0ms	82×	body	1024	valid
64.0ms	61×	body	2048	valid
33.0ms	34×	body	512	nan
30.0ms	81×	body	128	overflowed
30.0ms	41×	body	512	valid
16.0ms	8×	body	1024	invalid
10.0ms	54×	body	128	valid
8.0ms	18×	body	256	valid
6.0ms	13×	body	256	nan
5.0ms	6×	body	512	invalid
3.0ms	30×	body	128	nan
2.0ms	4×	body	256	invalid
1.0ms	6×	body	128	invalid

Compiler

Compiled 33 to 25 computations (24.2% saved)

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

436×	`unswap-sqr_binary64`
377×	`fma-def_binary64`
359×	`sub-neg_binary64`
289×	`unsub-neg_binary64`
253×	`distribute-rgt-neg-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	41	19
3	102	19
4	248	19
5	790	19
6	2110	19
7	4405	19
8	5048	19

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

30.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	30.0b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
2.1b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite696.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

29.9b

Rules

78×	`*-un-lft-identity_binary64`
76×	`unpow-prod-down_binary64`
65×	`add-sqr-sqrt_binary64`
56×	`prod-diff_binary64`
53×	`add-cube-cbrt_binary64`

Counts

3 → 155

Calls

3 calls:

18.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
8.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
6.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 5061 to 3574 computations (29.4% saved)

series156.0ms (0.7%)

Error

0.6b

Counts

3 → 40

Calls

3 calls:

73.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
27.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
19.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 2546 to 1916 computations (24.7% saved)

simplify180.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

749×	`times-frac_binary64`
563×	`fma-neg_binary64`
368×	`cancel-sign-sub-inv_binary64`
175×	`unswap-sqr_binary64`
174×	`sub-neg_binary64`

Counts

195 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	319	7480
1	702	5904
2	2232	4066
3	4606	4066
4	4881	4066

prune154.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	5	164

Error

0.3b

Counts

164 → 5

Alt Table

Status	Error	Program
	29.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
▶	25.6b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n)))))
	29.6b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
	30.7b	(/.f64 (exp.f64 (/.f64 (+.f64 0 (log.f64 x)) n)) (*.f64 x n))
	41.0b	(-.f64 (fma.f64 11/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 n n) (pow.f64 x 4))) (fma.f64 1/3 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 3))) (fma.f64 1/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 4) (pow.f64 n 4))) (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x n) (.f64 x n))) (fma.f64 1/6 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 3) (pow.f64 n 3))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))))) (fma.f64 1/2 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (.f64 n (pow.f64 x 3))))) (.f64 1/4 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 4))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 n 3) (pow.f64 x 4)))))))

Compiler

Compiled 2336 to 1399 computations (40.1% saved)

localize42.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.8b	(/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4))
7.2b	(fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))
10.4b	(fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n))))
10.9b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n)))))

rewrite455.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

49×	`times-frac_binary64`
48×	`unpow-prod-down_binary64`
46×	`*-un-lft-identity_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64`

Counts

4 → 137

Calls

4 calls:

5.0ms	(/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4))
3.0ms	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n)))))
0.0ms	(fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))
0.0ms	(fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n))))

Compiler

Compiled 12499 to 6616 computations (47.1% saved)

series678.0ms (3.1%)

Error

0.2b

Counts

4 → 58

Calls

4 calls:

227.0ms	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n)))))
207.0ms	(fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))
109.0ms	(fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n))))
40.0ms	(/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4))

Compiler

Compiled 10662 to 7748 computations (27.3% saved)

simplify237.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

437×	`fma-def_binary64`
358×	`associate-/r*_binary64`
309×	`times-frac_binary64`
232×	`associate-/l*_binary64`
159×	`associate-r_binary64`

Counts

195 → 125

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	597	11766
1	1626	10842
2	4963	10842

prune189.0ms (0.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	123	7	130

Error

0.2b

Counts

130 → 7

Alt Table

Status	Error	Program
	30.7b	(/.f64 (exp.f64 (/.f64 (+.f64 0 (log.f64 x)) n)) (*.f64 x n))
	51.6b	(.f64 (+.f64 (sqrt.f64 (fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n))))) (sqrt.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))))) (-.f64 (sqrt.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n))))) (sqrt.f64 (fma.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3) (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (*.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)) (/.f64 (log.f64 x) n)))))))
	29.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
	29.6b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
	41.0b	(-.f64 (fma.f64 11/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 n n) (pow.f64 x 4))) (fma.f64 1/3 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 3))) (fma.f64 1/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 4) (pow.f64 n 4))) (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x n) (.f64 x n))) (fma.f64 1/6 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 3) (pow.f64 n 3))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))))) (fma.f64 1/2 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (.f64 n (pow.f64 x 3))))) (.f64 1/4 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 4))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 n 3) (pow.f64 x 4)))))))
▶	25.6b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))
	42.5b	(/.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 3)) (/.f64 1 n)) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 4)) (/.f64 (neg.f64 (log.f64 x)) (*.f64 n n)))) x)

Compiler

Compiled 7313 to 4088 computations (44.1% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.8b	(/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4))
7.2b	(fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))
10.4b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n)))
11.2b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))

rewrite569.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

76×	`*-un-lft-identity_binary64`
73×	`add-sqr-sqrt_binary64`
61×	`add-cube-cbrt_binary64`
49×	`times-frac_binary64`
48×	`unpow-prod-down_binary64`

Counts

4 → 183

Calls

4 calls:

8.0ms	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))
5.0ms	(/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4))
3.0ms	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n)))
0.0ms	(fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))

Compiler

Compiled 19538 to 10688 computations (45.3% saved)

series1.2s (5.4%)

Error

0.2b

Counts

4 → 58

Calls

4 calls:

483.0ms	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))
269.0ms	(fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))
242.0ms	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n)))
76.0ms	(/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4))

Compiler

Compiled 10907 to 7978 computations (26.9% saved)

simplify372.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

463×	`fma-def_binary64`
358×	`associate-/r*_binary64`
332×	`times-frac_binary64`
245×	`associate-/l*_binary64`
148×	`+-commutative_binary64`

Counts

241 → 185

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	670	20821
1	1781	16192
2	4955	16192

prune565.0ms (2.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	182	3	185
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	183	9	192

Error

0.1b

Counts

192 → 9

Alt Table

Status	Error	Program
▶	29.6b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
	38.2b	(.f64 (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n))))) (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (*.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n))))))
	47.4b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (.f64 (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n)))) (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n))))))
	42.5b	(/.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 3)) (/.f64 1 n)) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 4)) (/.f64 (neg.f64 (log.f64 x)) (*.f64 n n)))) x)
	29.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
	30.7b	(/.f64 (exp.f64 (/.f64 (+.f64 0 (log.f64 x)) n)) (*.f64 x n))
	41.0b	(-.f64 (fma.f64 11/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 n n) (pow.f64 x 4))) (fma.f64 1/3 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 3))) (fma.f64 1/24 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 4) (pow.f64 n 4))) (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x n) (.f64 x n))) (fma.f64 1/6 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 x 3) (pow.f64 n 3))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))))) (fma.f64 1/2 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (.f64 n (pow.f64 x 3))))) (.f64 1/4 (+.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 n (pow.f64 x 4))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (pow.f64 n 3) (pow.f64 x 4)))))))
	51.7b	(-.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n)))) (fma.f64 (neg.f64 (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n)))) (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))) (*.f64 (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))) (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))))
✓	25.6b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))

Compiler

Compiled 11532 to 6567 computations (43.1% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (/.f64 (log1p.f64 x) n))
0.0b	(pow.f64 x (/.f64 1 n))
0.1b	(/.f64 (log1p.f64 x) n)
2.4b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))

rewrite215.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

48×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
43×	`add-cube-cbrt_binary64`
27×	`times-frac_binary64`
21×	`prod-diff_binary64`

Counts

4 → 129

Calls

4 calls:

7.0ms	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
3.0ms	(exp.f64 (/.f64 (log1p.f64 x) n))
2.0ms	(pow.f64 x (/.f64 1 n))
2.0ms	(/.f64 (log1p.f64 x) n)

Compiler

Compiled 3139 to 1506 computations (52% saved)

series147.0ms (0.7%)

Error

0.1b

Counts

4 → 49

Calls

4 calls:

48.0ms	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
22.0ms	(exp.f64 (/.f64 (log1p.f64 x) n))
21.0ms	(/.f64 (log1p.f64 x) n)
20.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 2862 to 2105 computations (26.5% saved)

simplify222.0ms (1%)

Algorithm

1×	egg-herbie

Rules

801×	`times-frac_binary64`
797×	`fma-def_binary64`
419×	`fma-neg_binary64`
161×	`sub-neg_binary64`
150×	`unswap-sqr_binary64`

Counts

178 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	4678
1	727	3912
2	2245	3131
3	4650	3131
4	4911	3131

prune78.0ms (0.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	107	9	116

Error

0.1b

Counts

116 → 9

Alt Table

Status	Error	Program
	29.6b	(-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))
	38.2b	(.f64 (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n))))) (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (*.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n))))))
	47.4b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (.f64 (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n)))) (sqrt.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n))))))
	42.5b	(/.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (pow.f64 n 3)) (/.f64 1 n)) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 4)) (/.f64 (neg.f64 (log.f64 x)) (*.f64 n n)))) x)
	29.6b	(.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n))))) (cbrt.f64 (-.f64 (exp.f64 (/.f64 (log1p.f64 x) n)) (pow.f64 x (/.f64 1 n)))))
	30.7b	(/.f64 (exp.f64 (/.f64 (+.f64 0 (log.f64 x)) n)) (*.f64 x n))
	51.7b	(-.f64 (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (-.f64 (.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3))) (/.f64 (log.f64 x) n)))) (fma.f64 (neg.f64 (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n)))) (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))) (*.f64 (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))) (sqrt.f64 (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))))
	25.6b	(-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log1p.f64 x) 2) (.f64 n n)) (fma.f64 1/24 (/.f64 (pow.f64 (log1p.f64 x) 4) (pow.f64 n 4)) (fma.f64 1/6 (pow.f64 (/.f64 (log1p.f64 x) n) 3) (/.f64 (log1p.f64 x) n)))) (-.f64 (fma.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)) (*.f64 1/24 (/.f64 (pow.f64 (log.f64 x) 4) (pow.f64 n 4)))) (fma.f64 1/6 (/.f64 (pow.f64 (neg.f64 (log.f64 x)) 3) (pow.f64 n 3)) (/.f64 (neg.f64 (log.f64 x)) n))))
	32.5b	(fma.f64 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x (.f64 x n))) -1/2 (fma.f64 1/2 (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 (.f64 x n) (.f64 x n))) (/.f64 (pow.f64 x (/.f64 1 n)) (.f64 x n))))

Compiler

Compiled 1859 to 976 computations (47.5% saved)

regimes2.5s (11.1%)

Accuracy

Total 11.6b remaining (98.1%)

Threshold costs 0b (0%)

Compiler

Compiled 56537 to 36706 computations (35.1% saved)

bsearch21.0ms (0.1%)

Compiler: Compiled 5 to 4 computations (20% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
13×	`+-commutative_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`
9×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	210
1	82	210
2	104	210
3	124	208
4	139	208
5	144	208
6	149	208
7	154	208
8	156	208
9	152	208

end3.0ms (0%)

Compiler: Compiled 139 to 86 computations (38.1% saved)

sample11.2s (50.7%)

Algorithm

1×

intervals

Results

2.7s	2666×	body	1024	valid
2.2s	1730×	body	2048	valid
1.8s	1400×	body	1024	nan
804.0ms	2596×	body	128	overflowed
670.0ms	1246×	body	512	valid
480.0ms	647×	body	512	nan
281.0ms	203×	body	1024	invalid
272.0ms	1780×	body	128	valid
197.0ms	578×	body	256	valid
175.0ms	238×	body	512	invalid
134.0ms	335×	body	256	nan
79.0ms	798×	body	128	nan
64.0ms	161×	body	256	invalid
49.0ms	260×	body	128	invalid
15.0ms	8×	body	2048	nan

Compiler

Compiled 771 to 470 computations (39% saved)

Iter	Nodes	Cost
0	63	210
1	82	210
2	104	210
3	124	208
4	139	208
5	144	208
6	149	208
7	154	208
8	156	208
9	152	208

Iter	Nodes	Cost
0	63	210
1	82	210
2	104	210
3	124	208
4	139	208
5	144	208
6	149	208
7	154	208
8	156	208
9	152	208

Details

analyze1.6s (7.2%)

sample506.0ms (2.3%)

simplify81.0ms (0.4%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite696.0ms (3.2%)

series156.0ms (0.7%)

simplify180.0ms (0.8%)

prune154.0ms (0.7%)

localize42.0ms (0.2%)

rewrite455.0ms (2.1%)

series678.0ms (3.1%)

simplify237.0ms (1.1%)

prune189.0ms (0.9%)

localize43.0ms (0.2%)

rewrite569.0ms (2.6%)

series1.2s (5.4%)

simplify372.0ms (1.7%)

prune565.0ms (2.6%)

localize8.0ms (0%)

rewrite215.0ms (1%)

series147.0ms (0.7%)

simplify222.0ms (1%)

prune78.0ms (0.4%)

regimes2.5s (11.1%)

bsearch21.0ms (0.1%)

simplify13.0ms (0.1%)

end3.0ms (0%)

sample11.2s (50.7%)

Profiling

Iter	Nodes	Cost
0	63	210
1	82	210
2	104	210
3	124	208
4	139	208
5	144	208
6	149	208
7	154	208
8	156	208
9	152	208