Details

analyze873.0ms (6.7%)

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
0%	99.9%	0.1%	5
3.1%	96.8%	0.1%	6
15.6%	81.2%	3.2%	7
23.4%	72.6%	4%	8
32.4%	56.2%	11.4%	9
36.3%	51.7%	12%	10
40.7%	42.9%	16.4%	11
42.6%	40.3%	17.1%	12
44.5%	35.7%	19.8%	13
45.5%	34.4%	20.1%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample163.0ms (1.3%)

Algorithm

1×

intervals

Results

74.0ms	56×	body	2048	valid
50.0ms	93×	body	1024	valid
13.0ms	48×	body	512	valid
3.0ms	48×	body	128	valid
3.0ms	8×	body	512	invalid
2.0ms	21×	body	128	invalid
2.0ms	3×	body	1024	invalid
2.0ms	11×	body	256	valid
1.0ms	5×	body	256	invalid
1.0ms	1×	body	2048	invalid
1.0ms	13×	body	128	nan

Compiler

Compiled 37 to 25 computations (32.4% saved)

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-/r/_binary64`
484×	`associate-/r*_binary64`
474×	`associate-*l/_binary64`
421×	`associate-/l/_binary64`
396×	`associate-*r/_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	29	22
2	66	22
3	158	22
4	444	22
5	1676	22
6	4664	22
7	4987	22
8	4974	22
9	5036	22

prune2.0ms (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

50.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	50.2b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))

Compiler

Compiled 34 to 22 computations (35.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
1.1b	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
5.3b	(pow.f64 (+.f64 1 (/.f64 i n)) n)
9.7b	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))

rewrite679.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

50.0b

Rules

584×	`times-frac_binary64`
486×	`add-sqr-sqrt_binary64`
367×	`*-un-lft-identity_binary64`
225×	`add-cube-cbrt_binary64`
174×	`associate-r_binary64`

Counts

4 → 451

Calls

4 calls:

60.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
21.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
11.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
7.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 10984 to 6006 computations (45.3% saved)

series511.0ms (3.9%)

Error

3.3b

Counts

4 → 61

Calls

4 calls:

161.0ms	(*.f64 100 (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n)))
143.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 i n))
75.0ms	(-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1)
45.0ms	(pow.f64 (+.f64 1 (/.f64 i n)) n)

Compiler

Compiled 6857 to 4753 computations (30.7% saved)

simplify331.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

505×	`associate-/l*_binary64`
396×	`associate-/r/_binary64`
269×	`*-commutative_binary64`
217×	`times-frac_binary64`
197×	`associate-/l/_binary64`

Counts

512 → 488

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	874	19005
1	2533	18561
2	4968	18561

prune349.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	476	12	488
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	477	12	489

Error

0.6b

Counts

489 → 12

Alt Table

Status	Error	Program
	58.8b	(.f64 100 (-.f64 (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (log.f64 n) 4) (pow.f64 n 5)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5))) i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i)) (+.f64 (/.f64 (.f64 (log.f64 i) (pow.f64 n 4)) (.f64 i i)) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (log.f64 i) (pow.f64 n 4))) i) (/.f64 (.f64 (log.f64 n) (pow.f64 n 5)) (pow.f64 i 3)))) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (pow.f64 n 5)) (.f64 i i)) (/.f64 (pow.f64 n 5) (pow.f64 i 3)))) (+.f64 (.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5)) (.f64 i i))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i)) (/.f64 (.f64 (.f64 n n) (log.f64 i)) i))))))))))))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 n 3) (log.f64 i))) i) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 4))) i)) (+.f64 (.f64 1/6 (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 3) (pow.f64 n 5))) i) (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (log.f64 i) (pow.f64 n 5))) (.f64 i i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 i) (pow.f64 n 5)) (pow.f64 i 3))) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 n)) i) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 n) 3) (.f64 (log.f64 i) (pow.f64 n 5))) i)) (+.f64 (/.f64 (.f64 (log.f64 n) (pow.f64 n 4)) (.f64 i i)) (.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)))))))))))))
	50.2b	(/.f64 (*.f64 100 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1)) (/.f64 i n))
	55.6b	(.f64 100 (.f64 (/.f64 (*.f64 n n) i) (log.f64 (/.f64 i n))))
	50.1b	(*.f64 (/.f64 100 i) (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 1 n)))
	26.6b	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
	29.8b	(.f64 100 (-.f64 (+.f64 (.f64 1/2 (.f64 n i)) (+.f64 (.f64 1/3 (/.f64 (.f64 i i) n)) (+.f64 (.f64 1/6 (.f64 n (.f64 i i))) (+.f64 (.f64 11/24 (/.f64 (pow.f64 i 3) n)) (+.f64 n (.f64 1/24 (.f64 n (pow.f64 i 3)))))))) (+.f64 (.f64 1/4 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 1/2 (+.f64 i (*.f64 i i))))))
▶	26.3b	(.f64 100 (+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (*.f64 i i)))))
	47.0b	(*.f64 100 (/.f64 (+.f64 (exp.f64 i) -1) (/.f64 i n)))
	37.4b	(.f64 100 (/.f64 (+.f64 i (.f64 1/2 (-.f64 (.f64 i i) (/.f64 (.f64 i i) n)))) (/.f64 i n)))
	57.5b	(.f64 100 (/.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2))) (+.f64 (.f64 n (log.f64 i)) (+.f64 (/.f64 (.f64 n n) i) (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)))))) (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i))))) (/.f64 i n)))
	54.4b	(.f64 100 (/.f64 (.f64 n (log.f64 (/.f64 i n))) (/.f64 i n)))
	46.9b	(.f64 100 (/.f64 (.f64 n (+.f64 (exp.f64 i) -1)) i))

Compiler

Compiled 11509 to 6208 computations (46.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/3 (/.f64 (.f64 i i) n))
2.6b	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
2.8b	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
8.8b	(/.f64 (*.f64 i i) n)

rewrite220.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

23×	`associate-*r/_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-add_binary64`
18×	`flip3-+_binary64` `flip-+_binary64`
17×	`add-sqr-sqrt_binary64`
13×	`add-log-exp_binary64`

Counts

4 → 99

Calls

4 calls:

14.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
10.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
7.0ms	(.f64 1/3 (/.f64 (.f64 i i) n))
5.0ms	(/.f64 (*.f64 i i) n)

Compiler

Compiled 5626 to 2691 computations (52.2% saved)

series184.0ms (1.4%)

Error

0.6b

Counts

4 → 37

Calls

4 calls:

75.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (/.f64 (.f64 i i) n)))) (.f64 -1/2 (+.f64 i (.f64 i i))))
38.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
25.0ms	(.f64 1/3 (/.f64 (.f64 i i) n))
24.0ms	(/.f64 (*.f64 i i) n)

Compiler

Compiled 2262 to 1566 computations (30.8% saved)

simplify146.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

404×	`distribute-rgt-in_binary64`
393×	`associate-l_binary64`
387×	`distribute-lft-in_binary64`
383×	`associate-r_binary64`
102×	`*-commutative_binary64`

Counts

136 → 110

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	5412
1	971	4839
2	4823	4838
3	5013	4838

prune170.0ms (1.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	107	15	122

Error

0.5b

Counts

122 → 15

Alt Table

Status	Error	Program
	58.8b	(.f64 100 (-.f64 (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (log.f64 n) 4) (pow.f64 n 5)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5))) i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i)) (+.f64 (/.f64 (.f64 (log.f64 i) (pow.f64 n 4)) (.f64 i i)) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (log.f64 i) (pow.f64 n 4))) i) (/.f64 (.f64 (log.f64 n) (pow.f64 n 5)) (pow.f64 i 3)))) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (pow.f64 n 5)) (.f64 i i)) (/.f64 (pow.f64 n 5) (pow.f64 i 3)))) (+.f64 (.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5)) (.f64 i i))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i)) (/.f64 (.f64 (.f64 n n) (log.f64 i)) i))))))))))))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 n 3) (log.f64 i))) i) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 4))) i)) (+.f64 (.f64 1/6 (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 3) (pow.f64 n 5))) i) (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (log.f64 i) (pow.f64 n 5))) (.f64 i i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 i) (pow.f64 n 5)) (pow.f64 i 3))) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 n)) i) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 n) 3) (.f64 (log.f64 i) (pow.f64 n 5))) i)) (+.f64 (/.f64 (.f64 (log.f64 n) (pow.f64 n 4)) (.f64 i i)) (.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)))))))))))))
	50.2b	(/.f64 (*.f64 100 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1)) (/.f64 i n))
	55.6b	(.f64 100 (.f64 (/.f64 (*.f64 n n) i) (log.f64 (/.f64 i n))))
	50.1b	(*.f64 (/.f64 100 i) (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 1 n)))
	26.6b	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
	29.8b	(.f64 100 (-.f64 (+.f64 (.f64 1/2 (.f64 n i)) (+.f64 (.f64 1/3 (/.f64 (.f64 i i) n)) (+.f64 (.f64 1/6 (.f64 n (.f64 i i))) (+.f64 (.f64 11/24 (/.f64 (pow.f64 i 3) n)) (+.f64 n (.f64 1/24 (.f64 n (pow.f64 i 3)))))))) (+.f64 (.f64 1/4 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 1/2 (+.f64 i (*.f64 i i))))))
	49.2b	(.f64 100 (/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i))))) 3) (pow.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) 3)) (+.f64 (.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i))))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))))) (.f64 -1/2 (.f64 (+.f64 i (.f64 i i)) (-.f64 (-.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))) (.f64 n (.f64 i (+.f64 1/2 (*.f64 1/6 i))))))))))
	44.6b	(.f64 100 (.f64 (sqrt.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (.f64 1/2 (+.f64 i (.f64 i i)))))) (sqrt.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (.f64 1/2 (+.f64 i (.f64 i i))))))))
	47.0b	(*.f64 100 (/.f64 (+.f64 (exp.f64 i) -1) (/.f64 i n)))
	37.4b	(.f64 100 (/.f64 (+.f64 i (.f64 1/2 (-.f64 (.f64 i i) (/.f64 (.f64 i i) n)))) (/.f64 i n)))
	46.1b	(.f64 100 (/.f64 (+.f64 (.f64 (-.f64 i (.f64 i i)) (-.f64 (.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i))))) (.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))))) (.f64 (.f64 -1/2 (-.f64 (.f64 i i) (pow.f64 i 4))) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))))) (.f64 (-.f64 i (.f64 i i)) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))))))
▶	26.3b	(.f64 100 (+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (*.f64 i i)))))
	57.5b	(.f64 100 (/.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2))) (+.f64 (.f64 n (log.f64 i)) (+.f64 (/.f64 (.f64 n n) i) (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)))))) (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i))))) (/.f64 i n)))
	54.4b	(.f64 100 (/.f64 (.f64 n (log.f64 (/.f64 i n))) (/.f64 i n)))
	46.9b	(.f64 100 (/.f64 (.f64 n (+.f64 (exp.f64 i) -1)) i))

Compiler

Compiled 5515 to 3153 computations (42.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 1/6 (.f64 i i))
0.2b	(.f64 1/3 (.f64 i (/.f64 i n)))
2.6b	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
2.8b	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (.f64 i i))))

rewrite414.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

24×	`associate-*r/_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-add_binary64`
18×	`flip3-+_binary64` `flip-+_binary64`
16×	`pow1_binary64`
13×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

14.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (.f64 i i))))
7.0ms	(.f64 1/3 (.f64 i (/.f64 i n)))
6.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
6.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 5146 to 2497 computations (51.5% saved)

series167.0ms (1.3%)

Error

0.5b

Counts

4 → 34

Calls

4 calls:

74.0ms	(+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (.f64 i i))))
37.0ms	(.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i))))
25.0ms	(.f64 1/3 (.f64 i (/.f64 i n)))
9.0ms	(.f64 1/6 (.f64 i i))

Compiler

Compiled 2095 to 1473 computations (29.7% saved)

simplify145.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-l_binary64`
445×	`associate-r_binary64`
404×	`distribute-rgt-in_binary64`
387×	`distribute-lft-in_binary64`
109×	`*-commutative_binary64`

Counts

124 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	5210
1	974	4685
2	4823	4684
3	5025	4684

prune176.0ms (1.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	109	15	124

Error

0.5b

Counts

124 → 15

Alt Table

Status	Error	Program
	58.8b	(.f64 100 (-.f64 (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (log.f64 n) 4) (pow.f64 n 5)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5))) i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i)) (+.f64 (/.f64 (.f64 (log.f64 i) (pow.f64 n 4)) (.f64 i i)) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (log.f64 i) (pow.f64 n 4))) i) (/.f64 (.f64 (log.f64 n) (pow.f64 n 5)) (pow.f64 i 3)))) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (pow.f64 n 5)) (.f64 i i)) (/.f64 (pow.f64 n 5) (pow.f64 i 3)))) (+.f64 (.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5)) (.f64 i i))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i)) (/.f64 (.f64 (.f64 n n) (log.f64 i)) i))))))))))))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 n 3) (log.f64 i))) i) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 4))) i)) (+.f64 (.f64 1/6 (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 3) (pow.f64 n 5))) i) (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (log.f64 i) (pow.f64 n 5))) (.f64 i i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 i) (pow.f64 n 5)) (pow.f64 i 3))) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 n)) i) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 n) 3) (.f64 (log.f64 i) (pow.f64 n 5))) i)) (+.f64 (/.f64 (.f64 (log.f64 n) (pow.f64 n 4)) (.f64 i i)) (.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)))))))))))))
	50.2b	(/.f64 (*.f64 100 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1)) (/.f64 i n))
	55.6b	(.f64 100 (.f64 (/.f64 (*.f64 n n) i) (log.f64 (/.f64 i n))))
	50.1b	(*.f64 (/.f64 100 i) (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 1 n)))
▶	26.6b	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
	29.8b	(.f64 100 (-.f64 (+.f64 (.f64 1/2 (.f64 n i)) (+.f64 (.f64 1/3 (/.f64 (.f64 i i) n)) (+.f64 (.f64 1/6 (.f64 n (.f64 i i))) (+.f64 (.f64 11/24 (/.f64 (pow.f64 i 3) n)) (+.f64 n (.f64 1/24 (.f64 n (pow.f64 i 3)))))))) (+.f64 (.f64 1/4 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 1/2 (+.f64 i (*.f64 i i))))))
	49.2b	(.f64 100 (/.f64 (+.f64 (pow.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i))))) 3) (pow.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) 3)) (+.f64 (.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i))))) (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))))) (.f64 -1/2 (.f64 (+.f64 i (.f64 i i)) (-.f64 (-.f64 (.f64 -1/2 (+.f64 i (.f64 i i))) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))) (.f64 n (.f64 i (+.f64 1/2 (*.f64 1/6 i))))))))))
	44.6b	(.f64 100 (.f64 (sqrt.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (.f64 1/2 (+.f64 i (.f64 i i)))))) (sqrt.f64 (+.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (.f64 1/2 (+.f64 i (.f64 i i))))))))
	47.0b	(*.f64 100 (/.f64 (+.f64 (exp.f64 i) -1) (/.f64 i n)))
	37.4b	(.f64 100 (/.f64 (+.f64 i (.f64 1/2 (-.f64 (.f64 i i) (/.f64 (.f64 i i) n)))) (/.f64 i n)))
	46.1b	(.f64 100 (/.f64 (+.f64 (.f64 (-.f64 i (.f64 i i)) (-.f64 (.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i))))) (.f64 (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3)) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))))) (.f64 (.f64 -1/2 (-.f64 (.f64 i i) (pow.f64 i 4))) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))))) (.f64 (-.f64 i (.f64 i i)) (-.f64 (.f64 n (.f64 i (+.f64 1/2 (.f64 1/6 i)))) (+.f64 n (.f64 (/.f64 (.f64 i i) n) 1/3))))))
✓	26.3b	(.f64 100 (+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (*.f64 i i)))))
	57.5b	(.f64 100 (/.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2))) (+.f64 (.f64 n (log.f64 i)) (+.f64 (/.f64 (.f64 n n) i) (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)))))) (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i))))) (/.f64 i n)))
	54.4b	(.f64 100 (/.f64 (.f64 n (log.f64 (/.f64 i n))) (/.f64 i n)))
	46.9b	(.f64 100 (/.f64 (.f64 n (+.f64 (exp.f64 i) -1)) i))

Compiler

Compiled 5561 to 3167 computations (43% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 100 (*.f64 i 50))
0.0b	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
0.3b	(.f64 n (+.f64 100 (.f64 i 50)))

rewrite78.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

7×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
3×	`associate-l_binary64` `associate-r_binary64`
2×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64` `flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

3 → 47

Calls

3 calls:

6.0ms	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
5.0ms	(.f64 n (+.f64 100 (.f64 i 50)))
3.0ms	(+.f64 100 (*.f64 i 50))

Compiler

Compiled 885 to 674 computations (23.8% saved)

series77.0ms (0.6%)

Error

0.5b

Counts

3 → 27

Calls

3 calls:

34.0ms	(-.f64 (.f64 n (+.f64 100 (.f64 i 50))) (*.f64 i 50))
21.0ms	(.f64 n (+.f64 100 (.f64 i 50)))
10.0ms	(+.f64 100 (*.f64 i 50))

Compiler

Compiled 647 to 479 computations (26% saved)

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

359×	`distribute-rgt-in_binary64`
348×	`distribute-lft-in_binary64`
293×	`distribute-neg-in_binary64`
286×	`unswap-sqr_binary64`
270×	`sub-neg_binary64`

Counts

74 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	95	1015
1	243	967
2	775	955
3	2153	955
4	3110	955
5	5161	955

prune67.0ms (0.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	4	9	13
Picked	1	0	1
Done	0	1	1
Total	54	12	66

Error

0.5b

Counts

66 → 12

Alt Table

Status	Error	Program
	58.8b	(.f64 100 (-.f64 (+.f64 (/.f64 (pow.f64 n 3) (.f64 i i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 (log.f64 n) 4) (pow.f64 n 5)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 n) 2)) i)) (+.f64 (.f64 1/4 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5))) i)) (+.f64 (.f64 1/24 (/.f64 (.f64 (pow.f64 n 5) (pow.f64 (log.f64 i) 4)) i)) (+.f64 (/.f64 (.f64 (log.f64 i) (pow.f64 n 4)) (.f64 i i)) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (.f64 (log.f64 i) (pow.f64 n 4))) i) (/.f64 (.f64 (log.f64 n) (pow.f64 n 5)) (pow.f64 i 3)))) (+.f64 (.f64 1/2 (+.f64 (/.f64 (.f64 (pow.f64 (log.f64 n) 2) (pow.f64 n 5)) (.f64 i i)) (/.f64 (pow.f64 n 5) (pow.f64 i 3)))) (+.f64 (.f64 1/3 (/.f64 (pow.f64 n 5) (pow.f64 i 4))) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 5)) (.f64 i i))) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 i) 3)) i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 n 3) (pow.f64 (log.f64 i) 2)) i)) (/.f64 (.f64 (.f64 n n) (log.f64 i)) i))))))))))))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 n 3) (log.f64 i))) i) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 2) (pow.f64 n 4))) i)) (+.f64 (.f64 1/6 (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (pow.f64 (log.f64 i) 3) (pow.f64 n 5))) i) (/.f64 (.f64 (pow.f64 n 4) (pow.f64 (log.f64 n) 3)) i))) (+.f64 (/.f64 (.f64 (log.f64 n) (.f64 (log.f64 i) (pow.f64 n 5))) (.f64 i i)) (+.f64 (.f64 1/2 (/.f64 (.f64 (log.f64 i) (pow.f64 n 5)) (pow.f64 i 3))) (+.f64 (/.f64 (.f64 (.f64 n n) (log.f64 n)) i) (+.f64 (.f64 1/6 (/.f64 (.f64 (pow.f64 (log.f64 n) 3) (.f64 (log.f64 i) (pow.f64 n 5))) i)) (+.f64 (/.f64 (.f64 (log.f64 n) (pow.f64 n 4)) (.f64 i i)) (.f64 1/2 (/.f64 (pow.f64 n 4) (pow.f64 i 3)))))))))))))
	50.2b	(/.f64 (*.f64 100 (+.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) -1)) (/.f64 i n))
	55.6b	(.f64 100 (.f64 (/.f64 (*.f64 n n) i) (log.f64 (/.f64 i n))))
	50.1b	(*.f64 (/.f64 100 i) (/.f64 (-.f64 (pow.f64 (+.f64 1 (/.f64 i n)) n) 1) (/.f64 1 n)))
	29.8b	(.f64 100 (-.f64 (+.f64 (.f64 1/2 (.f64 n i)) (+.f64 (.f64 1/3 (/.f64 (.f64 i i) n)) (+.f64 (.f64 1/6 (.f64 n (.f64 i i))) (+.f64 (.f64 11/24 (/.f64 (pow.f64 i 3) n)) (+.f64 n (.f64 1/24 (.f64 n (pow.f64 i 3)))))))) (+.f64 (.f64 1/4 (+.f64 (pow.f64 i 3) (/.f64 (pow.f64 i 3) (.f64 n n)))) (.f64 1/2 (+.f64 i (*.f64 i i))))))
	48.9b	(-.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 (.f64 50 i) 100) n) 3)) (*.f64 i 50))
	26.9b	(-.f64 (/.f64 (.f64 n (-.f64 10000 (.f64 i (.f64 i 2500)))) (-.f64 100 (.f64 i 50))) (*.f64 i 50))
	47.0b	(*.f64 100 (/.f64 (+.f64 (exp.f64 i) -1) (/.f64 i n)))
	26.3b	(.f64 100 (+.f64 (+.f64 (.f64 n (+.f64 (.f64 1/2 i) (.f64 1/6 (.f64 i i)))) (+.f64 n (.f64 1/3 (.f64 i (/.f64 i n))))) (.f64 -1/2 (+.f64 i (*.f64 i i)))))
	57.5b	(.f64 100 (/.f64 (-.f64 (+.f64 (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 n) 2))) (+.f64 (.f64 n (log.f64 i)) (+.f64 (/.f64 (.f64 n n) i) (.f64 1/2 (.f64 (.f64 n n) (pow.f64 (log.f64 i) 2)))))) (.f64 (log.f64 n) (+.f64 n (.f64 (.f64 n n) (log.f64 i))))) (/.f64 i n)))
	54.4b	(.f64 100 (/.f64 (.f64 n (log.f64 (/.f64 i n))) (/.f64 i n)))
	46.9b	(.f64 100 (/.f64 (.f64 n (+.f64 (exp.f64 i) -1)) i))

Compiler

Compiled 1255 to 881 computations (29.8% saved)

regimes2.7s (20.7%)

Accuracy

Total 11.1b remaining (95.8%)

Threshold costs 0b (0%)

Compiler

Compiled 35071 to 22424 computations (36.1% saved)

bsearch182.0ms (1.4%)

Steps

Iters	Range		Point
11	9.7351817396008e-05	5.266892532455959e+29	0.000957179281730772
9	-3.2443052991874786	-1.4950945909021711e-05	-0.00016572415090070473

Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

27×	`*-commutative_binary64`
21×	`+-commutative_binary64`
12×	`sub-neg_binary64`
10×	`neg-mul-1_binary64` `neg-sub0_binary64`
6×	`distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	65	177
1	98	177
2	106	177
3	118	177
4	138	177
5	156	177
6	168	177
7	175	177
8	177	177
9	175	177

end3.0ms (0%)

Compiler: Compiled 118 to 78 computations (33.9% saved)

sample5.2s (39.8%)

Algorithm

1×

intervals

Results

2.1s	1700×	body	2048	valid
1.4s	2663×	body	1024	valid
292.0ms	1204×	body	512	valid
120.0ms	1832×	body	128	valid
112.0ms	174×	body	1024	invalid
76.0ms	566×	body	256	valid
76.0ms	35×	body	4096	valid
72.0ms	200×	body	512	invalid
45.0ms	470×	body	128	invalid
31.0ms	143×	body	256	invalid
17.0ms	19×	body	2048	invalid
15.0ms	329×	body	128	nan

Compiler

Compiled 730 to 472 computations (35.3% saved)

Iter	Nodes	Cost
0	65	177
1	98	177
2	106	177
3	118	177
4	138	177
5	156	177
6	168	177
7	175	177
8	177	177
9	175	177

Iter	Nodes	Cost
0	65	177
1	98	177
2	106	177
3	118	177
4	138	177
5	156	177
6	168	177
7	175	177
8	177	177
9	175	177

Details

analyze873.0ms (6.7%)

sample163.0ms (1.3%)

simplify76.0ms (0.6%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite679.0ms (5.2%)

series511.0ms (3.9%)

simplify331.0ms (2.5%)

prune349.0ms (2.7%)

localize17.0ms (0.1%)

rewrite220.0ms (1.7%)

series184.0ms (1.4%)

simplify146.0ms (1.1%)

prune170.0ms (1.3%)

localize19.0ms (0.1%)

rewrite414.0ms (3.2%)

series167.0ms (1.3%)

simplify145.0ms (1.1%)

prune176.0ms (1.3%)

localize6.0ms (0%)

rewrite78.0ms (0.6%)

series77.0ms (0.6%)

simplify80.0ms (0.6%)

prune67.0ms (0.5%)

regimes2.7s (20.7%)

bsearch182.0ms (1.4%)

simplify11.0ms (0.1%)

end3.0ms (0%)

sample5.2s (39.8%)

Profiling

Iter	Nodes	Cost
0	65	177
1	98	177
2	106	177
3	118	177
4	138	177
5	156	177
6	168	177
7	175	177
8	177	177
9	175	177