Details

analyze244.0ms (0.7%)

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)

sample57.0ms (0.2%)

Algorithm

1×

intervals

Results

14.0ms	189×	body	128	valid
12.0ms	24×	body	512	valid
8.0ms	29×	body	1024	valid
7.0ms	256×	pre	128	true
2.0ms	14×	body	256	valid

Compiler

Compiled 77 to 50 computations (35.1% saved)

simplify74.0ms (0.2%)

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

prune3.0ms (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

30.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.6b	(/.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)

localize16.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b

(/.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))

2.6b

(+.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)

24.4b

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

rewrite243.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

16.8b

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:

27.0ms

(+.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)

18.0ms

(/.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))

12.0ms

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

Compiler

Compiled 4869 to 2450 computations (49.7% saved)

series860.0ms (2.4%)

Error

0.6b

Counts

3 → 71

Calls

3 calls:

397.0ms

(+.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)

314.0ms

(/.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))

46.0ms

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

Compiler

Compiled 14043 to 10677 computations (24% saved)

simplify651.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

722×	`associate-/l*_binary64`
308×	`distribute-rgt-in_binary64`
294×	`distribute-lft-in_binary64`
189×	`+-commutative_binary64`
178×	`*-commutative_binary64`

Counts

182 → 157

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	732	14408
1	2433	14108
2	5499	14108

prune220.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	152	5	157
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	5	158

Error

0.3b

Counts

158 → 5

Alt Table

Status	Error	Program
▶	17.2b	(/.f64 (+.f64 (/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 1) 2)
	51.2b	(/.f64 (-.f64 2 (+.f64 (.f64 4 (/.f64 i beta)) (+.f64 (/.f64 2 beta) (.f64 2 (/.f64 alpha beta))))) 2)
	51.0b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (+.f64 (.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i))) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3))) (+.f64 (.f64 4 (/.f64 i alpha)) (+.f64 (.f64 20 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 3))) (+.f64 (.f64 32 (/.f64 i (pow.f64 alpha 3))) (+.f64 (.f64 48 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (.f64 (/.f64 beta (pow.f64 alpha 3)) i))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))))))))) (+.f64 (.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (+.f64 (.f64 28 (.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) i)) (+.f64 (.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (+.f64 (.f64 80 (/.f64 i (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (.f64 (/.f64 beta (pow.f64 alpha 4)) (pow.f64 i 3)))) (+.f64 (.f64 12 (/.f64 beta (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (.f64 (/.f64 beta (pow.f64 alpha 4)) i)) (+.f64 (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))) (.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4))))))))))))))))))))))) 2)
	44.3b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)
	24.3b	(/.f64 (+.f64 (/.f64 (.f64 (/.f64 (+.f64 beta alpha) (sqrt.f64 (+.f64 (.f64 2 i) (+.f64 beta alpha)))) (/.f64 (-.f64 beta alpha) (sqrt.f64 (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (+.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) 2)) 1) 2)

Compiler

Compiled 9399 to 5509 computations (41.4% saved)

localize17.0ms (0%)

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 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
2.6b	(/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
2.6b	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 1)

rewrite2.8s (7.9%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

5126×	`times-frac_binary64`
3533×	`*-un-lft-identity_binary64`
2233×	`add-sqr-sqrt_binary64`
1787×	`add-cube-cbrt_binary64`
650×	`distribute-lft-out_binary64`

Counts

4 → 1734

Calls

4 calls:

412.0ms	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 1)
52.0ms	(/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
19.0ms	(/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 64630 to 35691 computations (44.8% saved)

series1.0s (2.9%)

Error

0.3b

Counts

4 → 115

Calls

4 calls:

391.0ms	(+.f64 (/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 1)
272.0ms	(/.f64 (/.f64 (+.f64 alpha beta) 1) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
127.0ms	(/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
76.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))

Compiler

Compiled 19485 to 14402 computations (26.1% saved)

simplify3.7s (10.6%)

Algorithm

1×	egg-herbie

Rules

759×	`associate-/r/_binary64`
333×	`associate-/l/_binary64`
305×	`associate-+r+_binary64`
220×	`*-commutative_binary64`
182×	`sub-neg_binary64`

Counts

1849 → 1745

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1823	138361
1	4545	137970
2	4835	137970
3	4995	137970
4	4774	137970

prune1.2s (3.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	1742	3	1745
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	1745	5	1750

Error

0.3b

Counts

1750 → 5

Alt Table

Status	Error	Program
	51.0b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (+.f64 (.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i))) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3))) (+.f64 (.f64 4 (/.f64 i alpha)) (+.f64 (.f64 20 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 3))) (+.f64 (.f64 32 (/.f64 i (pow.f64 alpha 3))) (+.f64 (.f64 48 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (.f64 (/.f64 beta (pow.f64 alpha 3)) i))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))))))))) (+.f64 (.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (+.f64 (.f64 28 (.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) i)) (+.f64 (.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (+.f64 (.f64 80 (/.f64 i (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (.f64 (/.f64 beta (pow.f64 alpha 4)) (pow.f64 i 3)))) (+.f64 (.f64 12 (/.f64 beta (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (.f64 (/.f64 beta (pow.f64 alpha 4)) i)) (+.f64 (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))) (.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4))))))))))))))))))))))) 2)
	44.3b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)
▶	17.2b	(/.f64 (+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) 1) 2)
	28.9b	(/.f64 (/.f64 (+.f64 (.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) -1) (+.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) -1)) 2)
	17.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 3) 1) (+.f64 (.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) (-.f64 1 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))))) 2)

Compiler

Compiled 27947 to 14957 computations (46.5% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))
2.6b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
2.6b	(+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) 1)
3.4b	(log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))))

rewrite1.6s (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

2167×	`times-frac_binary64`
1804×	`*-un-lft-identity_binary64`
1021×	`add-sqr-sqrt_binary64`
775×	`add-cube-cbrt_binary64`
392×	`distribute-lft-out_binary64`

Counts

4 → 983

Calls

4 calls:

142.0ms	(+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) 1)
90.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
80.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))))
23.0ms	(/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))

Compiler

Compiled 34038 to 17987 computations (47.2% saved)

series1.6s (4.6%)

Error

0.3b

Counts

4 → 112

Calls

4 calls:

492.0ms	(+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) 1)
483.0ms	(log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))))
257.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
200.0ms	(/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))

Compiler

Compiled 20961 to 15770 computations (24.8% saved)

simplify1.2s (3.3%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-/r/_binary64`
325×	`+-commutative_binary64`
273×	`associate-+r+_binary64`
182×	`*-commutative_binary64`
174×	`rem-log-exp_binary64`

Counts

1095 → 1023

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1683	68449
1	4248	68033
2	5083	68033

prune1.2s (3.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1023	0	1023
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	1023	5	1028

Error

0.3b

Counts

1028 → 5

Alt Table

Status	Error	Program
	51.0b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (+.f64 (.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i))) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3))) (+.f64 (.f64 4 (/.f64 i alpha)) (+.f64 (.f64 20 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 3))) (+.f64 (.f64 32 (/.f64 i (pow.f64 alpha 3))) (+.f64 (.f64 48 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (.f64 (/.f64 beta (pow.f64 alpha 3)) i))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))))))))) (+.f64 (.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (+.f64 (.f64 28 (.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) i)) (+.f64 (.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (+.f64 (.f64 80 (/.f64 i (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (.f64 (/.f64 beta (pow.f64 alpha 4)) (pow.f64 i 3)))) (+.f64 (.f64 12 (/.f64 beta (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (.f64 (/.f64 beta (pow.f64 alpha 4)) i)) (+.f64 (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))) (.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4))))))))))))))))))))))) 2)
	44.3b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)
✓	17.2b	(/.f64 (+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) 1) 2)
	28.9b	(/.f64 (/.f64 (+.f64 (.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) -1) (+.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha))))) -1)) 2)
▶	17.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 3) 1) (+.f64 (.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) (-.f64 1 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (*.f64 2 i) (+.f64 beta alpha)))))))) 2)

Compiler

Compiled 36643 to 19458 computations (46.9% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
2.6b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
2.6b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
2.6b	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))

rewrite5.3s (15%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

4304×	`times-frac_binary64`
3564×	`*-un-lft-identity_binary64`
2004×	`add-sqr-sqrt_binary64`
1524×	`add-cube-cbrt_binary64`
780×	`distribute-lft-out_binary64`

Counts

4 → 1872

Calls

4 calls:

46.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
40.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
37.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
33.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))

Compiler

Compiled 146011 to 72615 computations (50.3% saved)

series1.4s (4.1%)

Error

0.3b

Counts

4 → 110

Calls

4 calls:

300.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
299.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
291.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))
291.0ms	(/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))

Compiler

Compiled 39377 to 26117 computations (33.7% saved)

simplify2.6s (7.4%)

Algorithm

1×	egg-herbie

Rules

852×	`times-frac_binary64`
438×	`associate-/r/_binary64`
265×	`distribute-rgt-in_binary64`
253×	`distribute-lft-in_binary64`
127×	`*-commutative_binary64`

Counts

1982 → 1950

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	966	145346
1	2717	143846
2	5373	143846

prune4.0s (11.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	1948	2	1950
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	1950	5	1955

Error

0.3b

Counts

1955 → 5

Alt Table

Status	Error	Program
	44.3b	(/.f64 (/.f64 (+.f64 (.f64 beta 2) (+.f64 2 (.f64 i 4))) alpha) 2)
	60.0b	(/.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 3) 1) (+.f64 (.f64 (-.f64 (+.f64 (/.f64 2 alpha) (+.f64 (.f64 4 (/.f64 i alpha)) (.f64 2 (/.f64 beta alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (.f64 12 (.f64 (/.f64 i alpha) (/.f64 i alpha))) (+.f64 1 (+.f64 (.f64 12 (.f64 (/.f64 i alpha) (/.f64 beta 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)))))))))) (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) (-.f64 1 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))))) 2)
	51.0b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (/.f64 2 alpha) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (+.f64 (.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i))) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (+.f64 (.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3))) (+.f64 (.f64 4 (/.f64 i alpha)) (+.f64 (.f64 20 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 3))) (+.f64 (.f64 32 (/.f64 i (pow.f64 alpha 3))) (+.f64 (.f64 48 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (.f64 (/.f64 beta (pow.f64 alpha 3)) i))) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))))))))) (+.f64 (.f64 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (.f64 alpha alpha))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (+.f64 (.f64 28 (.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) i)) (+.f64 (.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4))) (+.f64 (.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4))) (+.f64 (.f64 108 (/.f64 (.f64 (.f64 beta beta) i) (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (.f64 alpha alpha))) (+.f64 (.f64 80 (/.f64 i (pow.f64 alpha 4))) (+.f64 (.f64 12 (/.f64 i (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (+.f64 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (.f64 (/.f64 beta (pow.f64 alpha 4)) (pow.f64 i 3)))) (+.f64 (.f64 12 (/.f64 beta (/.f64 (.f64 alpha alpha) i))) (+.f64 (.f64 160 (.f64 (/.f64 beta (pow.f64 alpha 4)) i)) (+.f64 (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))) (.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4))))))))))))))))))))))) 2)
	17.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) 3) 1) (+.f64 (.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 beta alpha)) (cbrt.f64 (+.f64 beta alpha))) (.f64 (cbrt.f64 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))) (cbrt.f64 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) (/.f64 (cbrt.f64 (+.f64 beta alpha)) (cbrt.f64 (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))) (-.f64 1 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha)))))))) 2)
	17.2b	(/.f64 (+.f64 (log.f64 (exp.f64 (/.f64 (+.f64 alpha beta) (/.f64 (+.f64 2 (+.f64 (.f64 2 i) (+.f64 beta alpha))) (/.f64 (-.f64 beta alpha) (+.f64 (.f64 2 i) (+.f64 beta alpha))))))) 1) 2)

Compiler

Compiled 144671 to 72204 computations (50.1% saved)

regimes3.2s (9.2%)

Accuracy

Total 1.3b remaining (89.9%)

Threshold costs 0b (0%)

Compiler

Compiled 90425 to 55329 computations (38.8% saved)

bsearch23.0ms (0.1%)

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
5×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	108
1	46	108
2	50	108
3	52	108
4	53	108
5	52	108

end1.0ms (0%)

Compiler: Compiled 75 to 46 computations (38.7% saved)

sample2.1s (5.9%)

Algorithm

1×

intervals

Results

628.0ms	6482×	body	128	valid
284.0ms	8000×	pre	128	true
217.0ms	687×	body	1024	valid
137.0ms	510×	body	512	valid
48.0ms	274×	body	256	valid
17.0ms	47×	body	2048	valid

Compiler

Compiled 818 to 497 computations (39.2% saved)

Details

analyze244.0ms (0.7%)

sample57.0ms (0.2%)

simplify74.0ms (0.2%)

prune3.0ms (0%)

localize16.0ms (0%)

rewrite243.0ms (0.7%)

series860.0ms (2.4%)

simplify651.0ms (1.9%)

prune220.0ms (0.6%)

localize17.0ms (0%)

rewrite2.8s (7.9%)

series1.0s (2.9%)

simplify3.7s (10.6%)

prune1.2s (3.3%)

localize21.0ms (0.1%)

rewrite1.6s (4.4%)

series1.6s (4.6%)

simplify1.2s (3.3%)

prune1.2s (3.3%)

localize26.0ms (0.1%)

rewrite5.3s (15%)

series1.4s (4.1%)

simplify2.6s (7.4%)

prune4.0s (11.3%)

regimes3.2s (9.2%)

bsearch23.0ms (0.1%)

simplify6.0ms (0%)

end1.0ms (0%)

sample2.1s (5.9%)

Profiling