Details

analyze1.9s (0.6%)

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 14 to 12 computations (14.3% saved)

sample338.0ms (0.1%)

Algorithm

1×

intervals

Results

86.0ms	80×	body	1024	valid
65.0ms	65×	body	2048	valid
52.0ms	36×	body	1024	nan
28.0ms	89×	body	128	overflowed
26.0ms	38×	body	512	valid
20.0ms	24×	body	512	nan
9.0ms	54×	body	128	valid
8.0ms	19×	body	256	valid
6.0ms	15×	body	256	nan
4.0ms	3×	body	1024	invalid
3.0ms	23×	body	128	nan
2.0ms	10×	body	128	invalid
2.0ms	4×	body	256	invalid
2.0ms	2×	body	512	invalid
1.0ms	1×	body	2048	nan

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify226.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4831	19
1	4831	19

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

31.0b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
0.2b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.2b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
2.4b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_93`
21×	`*-un-lft-identity_binary64_71`
17×	`unpow-prod-down_binary64_150`
13×	`pow-unpow_binary64_148`
12×	`add-cube-cbrt_binary64_106`
9×	`difference-of-squares_binary64_40` `times-frac_binary64_77`
8×	`sqr-pow_binary64_43`
7×	`cancel-sign-sub-inv_binary64_37`
4×	`add-log-exp_binary64_110`
3×	`add-exp-log_binary64_109` `distribute-lft-out--_binary64_23` `pow1_binary64_132`
2×	`add-cbrt-cube_binary64_107` `distribute-lft-out_binary64_22`
1×	`pow-exp_binary64_139` `pow-to-exp_binary64_140` `flip--_binary64_46` `pow-pow_binary64_143` `div-inv_binary64_68` `flip3--_binary64_75` `diff-log_binary64_163` `sub-neg_binary64_64`

Counts

2 → 58

Calls

4 calls:

20.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
11.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

series640.0ms (0.2%)

Counts

2 → 30

Calls

2 calls:

493.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
147.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

Compiler

Compiled 1316 to 1068 computations (18.8% saved)

simplify138.0ms (0%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4971	2424
1	4971	2424

prune382.0ms (0.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Error

0.6b

Counts

89 → 5

Compiler

Compiled 2345 to 1507 computations (35.7% saved)

localize89.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n)))
0.0b	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n))) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))))
0.0b	(+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))))
0.0b	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
1.7b	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
6.0b	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3))))
7.8b	(+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
12.0b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n))) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))

rewrite272.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-log-exp_binary64_110`
52×	`sum-log_binary64_162`
36×	`frac-add_binary64_79`
28×	`flip-+_binary64_45` `flip3-+_binary64_74`
24×	`frac-sub_binary64_80`
20×	`associate-*r/_binary64_13`
17×	`add-exp-log_binary64_109`
16×	`*-un-lft-identity_binary64_71` `diff-log_binary64_163`
11×	`add-sqr-sqrt_binary64_93`
9×	`add-cbrt-cube_binary64_107` `associate-/l*_binary64_16` `add-cube-cbrt_binary64_106` `times-frac_binary64_77`
8×	`unpow-prod-down_binary64_150`
6×	`div-exp_binary64_122` `associate-+r-_binary64_5` `pow1_binary64_132`
4×	`log-div_binary64_158` `div-sub_binary64_76` `cancel-sign-sub-inv_binary64_37` `associate-+l-_binary64_6`
3×	`prod-exp_binary64_120`
2×	`pow-exp_binary64_139` `pow-to-exp_binary64_140` `+-commutative_binary64_1` `associate--l-_binary64_9` `sqr-pow_binary64_43` `distribute-lft-out_binary64_22` `unpow2_binary64_136` `log-pow_binary64_160` `cbrt-undiv_binary64_105` `distribute-lft-out--_binary64_23`
1×	`flip--_binary64_46` `associate-/r*_binary64_15` `associate--r+_binary64_7` `associate--l+_binary64_8` `clear-num_binary64_70` `div-inv_binary64_68` `flip3--_binary64_75` `associate-+r+_binary64_3` `difference-of-squares_binary64_40` `cbrt-unprod_binary64_104` `frac-2neg_binary64_82` `sub-neg_binary64_64`

Counts

4 → 124

Calls

8 calls:

112.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n))) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
31.0ms	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3))))
21.0ms	(+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
13.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))
0.0ms	(+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))

series5.5s (1.8%)

Counts

4 → 52

Calls

4 calls:

2.3s	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (.f64 n n))) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
1.6s	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3))))
1.3s	(+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
297.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 x 1)) 2) (*.f64 n n))

Compiler

Compiled 6412 to 4931 computations (23.1% saved)

simplify382.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5447	22689

prune2.7s (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	171	5	176
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	171	10	181

Error

0.3b

Counts

181 → 10

Compiler

Compiled 21926 to 14451 computations (34.1% saved)

localize130.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))))
0.0b	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
0.0b	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
0.0b	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
13.7b	(-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
18.6b	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
18.6b	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
18.6b	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))

rewrite439.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-log-exp_binary64_110`
30×	`sum-log_binary64_162`
15×	`*-un-lft-identity_binary64_71`
12×	`flip-+_binary64_45` `diff-log_binary64_163` `flip3-+_binary64_74`
10×	`add-sqr-sqrt_binary64_93`
9×	`cbrt-prod_binary64_102`
8×	`add-cube-cbrt_binary64_106` `frac-sub_binary64_80`
6×	`cbrt-div_binary64_103`
4×	`add-cbrt-cube_binary64_107` `add-exp-log_binary64_109` `frac-add_binary64_79` `pow1_binary64_132` `cancel-sign-sub-inv_binary64_37`
3×	`pow1/3_binary64_153`
2×	`log-div_binary64_158` `associate-+r-_binary64_5` `associate--l-_binary64_9` `distribute-lft-out_binary64_22` `div-sub_binary64_76` `distribute-lft-out--_binary64_23` `associate-+l-_binary64_6`
1×	`flip--_binary64_46` `associate--r+_binary64_7` `associate--l+_binary64_8` `flip3--_binary64_75` `difference-of-squares_binary64_40` `sub-neg_binary64_64`

Counts

4 → 80

Calls

8 calls:

91.0ms	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
89.0ms	(-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
78.0ms	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
72.0ms	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
0.0ms	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))

series1.8min (34.3%)

Counts

4 → 52

Calls

4 calls:

36.0s	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
34.4s	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
33.8s	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
2.0s	(-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))

Compiler

Compiled 61944 to 49410 computations (20.2% saved)

simplify528.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5038	35843

prune5.9s (1.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	129	13	142

Error

0.3b

Counts

142 → 13

Compiler

Compiled 45725 to 29661 computations (35.1% saved)

localize200.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
0.0b	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
0.0b	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
0.0b	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))
18.6b	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
18.6b	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
18.6b	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
18.6b	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))

rewrite439.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_102`
8×	`*-un-lft-identity_binary64_71` `cbrt-div_binary64_103` `add-cube-cbrt_binary64_106` `add-sqr-sqrt_binary64_93`
4×	`add-cbrt-cube_binary64_107` `pow1/3_binary64_153` `add-log-exp_binary64_110` `add-exp-log_binary64_109` `flip-+_binary64_45` `pow1_binary64_132` `flip3-+_binary64_74`

Counts

4 → 52

Calls

8 calls:

94.0ms	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
90.0ms	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
81.0ms	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
73.0ms	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
0.0ms	(+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (*.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))

series2.4min (45.9%)

Counts

4 → 44

Calls

4 calls:

35.9s	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
35.4s	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
35.3s	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))
35.3s	(cbrt.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (-.f64 (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))))

Compiler

Compiled 86316 to 68108 computations (21.1% saved)

simplify525.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4981	36764
1	4981	36764

prune7.5s (2.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	10	10
Picked	1	0	1
Done	0	2	2
Total	96	13	109

Error

0.3b

Counts

109 → 13

Compiler

Compiled 52468 to 33333 computations (36.5% saved)

simplify177.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	1113	7206
1	1113	7206

regimes1.8s (0.6%)

Accuracy

Total 6.7b remaining (96.7%)

Threshold costs 0b (0%)

Compiler

Compiled 14095 to 9747 computations (30.8% saved)

bsearch126.0ms (0%)

Steps

Iters	Range		Point
9	6261.4083718037355	1099091900.3719664	67572.21162884781

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	81	102
1	81	102

end0.0ms (0%)

sample30.8s (10%)

Algorithm

1×

intervals

Results

2.9s	2731×	body	1024	valid
2.1s	1438×	body	1024	nan
1.9s	1715×	body	2048	valid
933.0ms	2593×	body	128	overflowed
815.0ms	1190×	body	512	valid
634.0ms	713×	body	512	nan
316.0ms	1798×	body	128	valid
303.0ms	176×	body	1024	invalid
234.0ms	566×	body	256	valid
201.0ms	216×	body	512	invalid
180.0ms	397×	body	256	nan
92.0ms	798×	body	128	nan
71.0ms	140×	body	256	invalid
62.0ms	259×	body	128	invalid
9.0ms	5×	body	2048	nan

Compiler

Compiled 14063 to 9689 computations (31.1% saved)

Pareto

-0.03735580441079173

Details

analyze1.9s (0.6%)

sample338.0ms (0.1%)

simplify226.0ms (0.1%)

prune4.0ms (0%)

localize14.0ms (0%)

rewrite41.0ms (0%)

series640.0ms (0.2%)

simplify138.0ms (0%)

prune382.0ms (0.1%)

localize89.0ms (0%)

rewrite272.0ms (0.1%)

series5.5s (1.8%)

simplify382.0ms (0.1%)

prune2.7s (0.9%)

localize130.0ms (0%)

rewrite439.0ms (0.1%)

series1.8min (34.3%)

simplify528.0ms (0.2%)

prune5.9s (1.9%)

localize200.0ms (0.1%)

rewrite439.0ms (0.1%)

series2.4min (45.9%)

simplify525.0ms (0.2%)

prune7.5s (2.4%)

simplify177.0ms (0.1%)

regimes1.8s (0.6%)

bsearch126.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample30.8s (10%)

Profiling