Details

analyze227.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 42 to 27 computations (35.7% saved)

sample45.0ms (0.3%)

Algorithm

1×

intervals

Results

16.0ms	212×	body	128	valid
6.0ms	256×	pre	128	true
6.0ms	21×	body	1024	valid
3.0ms	15×	body	512	valid
1.0ms	6×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 77 to 50 computations (35.1% saved)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
576×	`sub-neg_binary64`
537×	`div-sub_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	43
2	106	43
3	409	43
4	1505	43
5	2316	43
6	3123	43
7	4954	43
8	4973	43
9	5371	43

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

23.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	23.3b	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Compiler

Compiled 96 to 60 computations (37.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

1.9b

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

19.7b

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

rewrite314.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Error

11.2b

Rules

54×	`times-frac_binary64`
47×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 111

Calls

3 calls:

26.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

19.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

13.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 4869 to 2450 computations (49.7% saved)

series492.0ms (3.6%)

Error

0.3b

Counts

3 → 60

Calls

3 calls:

228.0ms

(+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1)

163.0ms

(/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2))

48.0ms

(/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i)))

Compiler

Compiled 8610 to 6471 computations (24.8% saved)

simplify145.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

475×	`times-frac_binary64`
392×	`associate-/l*_binary64`
339×	`associate-/r*_binary64`
303×	`distribute-rgt-in_binary64`
289×	`distribute-lft-in_binary64`

Counts

171 → 146

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	488	9018
1	1556	8748
2	5026	8748

prune134.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	5	147

Error

0.0b

Counts

147 → 5

Alt Table

Status	Error	Program
▶	11.5b	(/.f64 (+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1) 2)
	11.6b	(/.f64 (+.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1) 2)
	51.2b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 12 (+.f64 (.f64 (/.f64 i alpha) (/.f64 i alpha)) (.f64 (/.f64 beta alpha) (/.f64 i alpha)))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))) 2)
	17.7b	(/.f64 (+.f64 (/.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))) 1) 2)
	50.4b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)

Compiler

Compiled 6062 to 3297 computations (45.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))
0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
1.8b	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
2.9b	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)

rewrite863.0ms (6.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

321×	`times-frac_binary64`
290×	`*-un-lft-identity_binary64`
211×	`add-sqr-sqrt_binary64`
140×	`add-cube-cbrt_binary64`
90×	`associate-r_binary64`

Counts

4 → 295

Calls

4 calls:

34.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
22.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
18.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 11516 to 6062 computations (47.4% saved)

series752.0ms (5.5%)

Error

0.0b

Counts

4 → 80

Calls

4 calls:

249.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
191.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
146.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
44.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 11960 to 8859 computations (25.9% saved)

simplify280.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

530×	`times-frac_binary64`
378×	`distribute-rgt-in_binary64`
360×	`distribute-lft-in_binary64`
197×	`*-commutative_binary64`
162×	`associate-*r/_binary64`

Counts

375 → 347

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	739	18632
1	2262	18202
2	5051	18202

prune364.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	346	1	347
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	348	4	352

Error

0.0b

Counts

352 → 4

Alt Table

Status	Error	Program
	11.6b	(/.f64 (+.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1) 2)
	51.2b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 12 (+.f64 (.f64 (/.f64 i alpha) (/.f64 i alpha)) (.f64 (/.f64 beta alpha) (/.f64 i alpha)))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))) 2)
▶	11.5b	(/.f64 (+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1) 2)
	50.4b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)

Compiler

Compiled 12667 to 6805 computations (46.3% saved)

localize62.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
0.3b	(/.f64 1 (/.f64 (+.f64 (*.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha)))
1.8b	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
2.9b	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)

rewrite1.2s (8.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1650×	`times-frac_binary64`
1106×	`*-un-lft-identity_binary64`
849×	`add-sqr-sqrt_binary64`
642×	`add-cube-cbrt_binary64`
278×	`associate-r_binary64`

Counts

4 → 800

Calls

4 calls:

105.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
62.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
36.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
11.0ms	(/.f64 1 (/.f64 (+.f64 (*.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha)))

Compiler

Compiled 32905 to 18772 computations (43% saved)

series648.0ms (4.8%)

Error

0.0b

Counts

4 → 80

Calls

4 calls:

230.0ms	(+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1)
174.0ms	(.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
139.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))
44.0ms	(/.f64 1 (/.f64 (+.f64 (*.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha)))

Compiler

Compiled 11960 to 8859 computations (25.9% saved)

simplify640.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

553×	`times-frac_binary64`
375×	`distribute-rgt-in_binary64`
364×	`distribute-lft-in_binary64`
202×	`*-commutative_binary64`
173×	`associate-*r/_binary64`

Counts

880 → 833

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	803	44452
1	2391	43572
2	5031	43572

prune492.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	833	0	833
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	833	4	837

Error

0.0b

Counts

837 → 4

Alt Table

Status	Error	Program
▶	11.6b	(/.f64 (+.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1) 2)
	51.2b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 12 (+.f64 (.f64 (/.f64 i alpha) (/.f64 i alpha)) (.f64 (/.f64 beta alpha) (/.f64 i alpha)))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))) 2)
✓	11.5b	(/.f64 (+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1) 2)
	50.4b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)

Compiler

Compiled 22169 to 12224 computations (44.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))))
0.3b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
0.4b	(/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))
6.8b	(+.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1)

rewrite750.0ms (5.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

603×	`times-frac_binary64`
484×	`*-un-lft-identity_binary64`
408×	`add-sqr-sqrt_binary64`
260×	`add-cube-cbrt_binary64`
219×	`sqrt-prod_binary64`

Counts

4 → 485

Calls

4 calls:

96.0ms	(.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))))
34.0ms	(+.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1)
20.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
11.0ms	(/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))

Compiler

Compiled 21820 to 12309 computations (43.6% saved)

series610.0ms (4.5%)

Error

0.0b

Counts

4 → 66

Calls

4 calls:

237.0ms	(+.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1)
169.0ms	(.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))))
84.0ms	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
69.0ms	(/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))

Compiler

Compiled 11027 to 8138 computations (26.2% saved)

simplify462.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

465×	`times-frac_binary64`
369×	`associate-/l/_binary64`
231×	`*-commutative_binary64`
217×	`distribute-rgt-in_binary64`
202×	`distribute-lft-in_binary64`

Counts

551 → 528

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	809	32671
1	2521	31299
2	5016	31299

prune374.0ms (2.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	528	0	528
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	528	4	532

Error

0.0b

Counts

532 → 4

Alt Table

Status	Error	Program
	11.6b	(/.f64 (+.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))) (sqrt.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) 1) 2)
	51.2b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 12 (+.f64 (.f64 (/.f64 i alpha) (/.f64 i alpha)) (.f64 (/.f64 beta alpha) (/.f64 i alpha)))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (.f64 2 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))))) 2)
	11.5b	(/.f64 (+.f64 (.f64 (+.f64 beta alpha) (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 2 i) (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) 1) 2)
	50.4b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)

Compiler

Compiled 18138 to 10230 computations (43.6% saved)

regimes3.1s (22.6%)

Accuracy

Total 1.4b remaining (94.9%)

Threshold costs 0b (0%)

Compiler

Compiled 70478 to 46692 computations (33.7% saved)

bsearch17.0ms (0.1%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

35×	`+-commutative_binary64`
30×	`*-commutative_binary64`
22×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	188
1	80	188
2	91	188
3	108	188
4	131	188
5	160	188
6	204	188
7	233	188
8	250	188
9	257	188
10	258	188
11	253	188

end1.0ms (0%)

Compiler: Compiled 129 to 70 computations (45.7% saved)

sample1.5s (11.2%)

Algorithm

1×

intervals

Results

503.0ms	6530×	body	128	valid
201.0ms	626×	body	1024	valid
198.0ms	8000×	pre	128	true
101.0ms	490×	body	512	valid
54.0ms	307×	body	256	valid
16.0ms	47×	body	2048	valid

Compiler

Compiled 338 to 201 computations (40.5% saved)

Iter	Nodes	Cost
0	57	188
1	80	188
2	91	188
3	108	188
4	131	188
5	160	188
6	204	188
7	233	188
8	250	188
9	257	188
10	258	188
11	253	188

Iter	Nodes	Cost
0	57	188
1	80	188
2	91	188
3	108	188
4	131	188
5	160	188
6	204	188
7	233	188
8	250	188
9	257	188
10	258	188
11	253	188

Details

analyze227.0ms (1.7%)

sample45.0ms (0.3%)

simplify72.0ms (0.5%)

prune2.0ms (0%)

localize12.0ms (0.1%)

rewrite314.0ms (2.3%)

series492.0ms (3.6%)

simplify145.0ms (1.1%)

prune134.0ms (1%)

localize13.0ms (0.1%)

rewrite863.0ms (6.4%)

series752.0ms (5.5%)

simplify280.0ms (2.1%)

prune364.0ms (2.7%)

localize62.0ms (0.5%)

rewrite1.2s (8.7%)

series648.0ms (4.8%)

simplify640.0ms (4.7%)

prune492.0ms (3.6%)

localize17.0ms (0.1%)

rewrite750.0ms (5.5%)

series610.0ms (4.5%)

simplify462.0ms (3.4%)

prune374.0ms (2.8%)

regimes3.1s (22.6%)

bsearch17.0ms (0.1%)

simplify13.0ms (0.1%)

end1.0ms (0%)

sample1.5s (11.2%)

Profiling

Iter	Nodes	Cost
0	57	188
1	80	188
2	91	188
3	108	188
4	131	188
5	160	188
6	204	188
7	233	188
8	250	188
9	257	188
10	258	188
11	253	188