Details

analyze161.0ms (1.1%)

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 43 to 28 computations (34.9% saved)

sample2.1s (14.2%)

Results

1.2s	6630×	body	128	valid
348.0ms	671×	body	1024	valid
225.0ms	568×	body	512	valid
206.0ms	335×	body	256	valid
35.0ms	52×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify44.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	110	37
3	435	37
4	1672	37
5	2494	37
6	3358	37
7	5392	37

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

22.6b

Counts

3 → 2

Alt Table

Status	Error	Program
	26.0b	(/.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)
▶	22.7b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

Status

Error

Program

26.0b

(/.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)

▶

22.7b

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

Compiler

Compiled 180 to 106 computations (41.1% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
✓	0.0b	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	15.0b	(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
✓	18.7b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series1.3s (8.8%)

Counts

4 → 144

Calls

4 calls:

719.0ms	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
551.0ms	(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
20.0ms	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
9.0ms	(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 85

Calls

4 calls:

9.0ms	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
7.0ms	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
2.0ms	(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
0.0ms	(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify290.0ms (2%)

Algorithm

1×	egg-herbie

Rules

563×	`+-commutative_binary64`
490×	`fma-def_binary64`
488×	`associate-+r+_binary64`
393×	`*-commutative_binary64`
294×	`associate-*r/_binary64`

Counts

229 → 235

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1410	20564
1	5474	20564

prune600.0ms (4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	229	6	235
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	231	6	237

Error

0.2b

Counts

237 → 6

Alt Table

Status	Error	Program
	21.9b	(/.f64 (-.f64 (+.f64 1 (/.f64 beta (+.f64 beta (+.f64 2 alpha)))) (/.f64 alpha (+.f64 beta (+.f64 2 alpha)))) 2)
	49.5b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
	46.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	51.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)
	22.7b	(/.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
▶	14.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

Compiler

Compiled 25886 to 16588 computations (35.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓	15.0b	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series842.0ms (5.7%)

Counts

4 → 144

Calls

4 calls:

469.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
272.0ms	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
70.0ms	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
30.0ms	(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
65×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`

Counts

4 → 162

Calls

4 calls:

14.0ms	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
6.0ms	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
2.0ms	(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))
0.0ms	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

simplify240.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

579×	`fma-def_binary64`
560×	`associate-+r+_binary64`
386×	`associate-*r/_binary64`
174×	`associate-/l*_binary64`
155×	`associate-/r*_binary64`

Counts

306 → 370

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1717	26289
1	5484	26289

prune836.0ms (5.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	366	4	370
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	370	6	376

Error

0.2b

Counts

376 → 6

Alt Table

Status	Error	Program
	46.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	14.8b	(/.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) 2)
▶	14.7b	(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	51.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)
	14.8b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	16.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))) 1) 2)

Compiler

Compiled 34812 to 21865 computations (37.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))
✓	1.1b	(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))))
✓	2.6b	(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1)

series1.1s (7.7%)

Counts

3 → 108

Calls

3 calls:

511.0ms

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

326.0ms

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

307.0ms

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

rewrite126.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

299×	`times-frac_binary64`
256×	`*-un-lft-identity_binary64`
193×	`add-sqr-sqrt_binary64`
128×	`add-cube-cbrt_binary64`
82×	`associate-r_binary64`

Counts

3 → 250

Calls

3 calls:

33.0ms

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

16.0ms

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

14.0ms

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

simplify541.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-def_binary64`
555×	`associate-+r+_binary64`
405×	`associate-*r/_binary64`
204×	`associate-/r*_binary64`
200×	`associate-/l*_binary64`

Counts

358 → 402

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1802	35564
1	5760	35564

prune1.5s (10.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	488	3	491
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	490	7	497

Error

0.2b

Counts

497 → 7

Alt Table

Status	Error	Program
	46.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	14.8b	(/.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) 2)
	15.1b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1)) (cbrt.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1))) (cbrt.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1))) 2)
▶	14.7b	(/.f64 (+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) (fma.f64 2 i (+.f64 alpha beta))) 1) 2)
✓	14.7b	(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	51.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)
	16.1b	(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 2 alpha))) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)

Compiler

Compiled 49747 to 30725 computations (38.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓	1.4b	(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) (fma.f64 2 i (+.f64 alpha beta))) 1)
✓	1.9b	(/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) (fma.f64 2 i (+.f64 alpha beta)))

series1.3s (8.6%)

Counts

3 → 108

Calls

3 calls:

600.0ms

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

493.0ms

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

186.0ms

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

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
27×	`times-frac_binary64`
26×	`associate-r_binary64`
18×	`add-cube-cbrt_binary64`

Counts

3 → 103

Calls

3 calls:

15.0ms

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

13.0ms

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

11.0ms

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

simplify279.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

473×	`fma-def_binary64`
465×	`associate-+r+_binary64`
402×	`*-commutative_binary64`
303×	`associate-*r/_binary64`
188×	`associate-/l*_binary64`

Counts

211 → 262

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1460	23616
1	5083	23616

prune917.0ms (6.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	347	4	351
Fresh	2	3	5
Picked	1	0	1
Done	1	0	1
Total	351	7	358

Error

0.2b

Counts

358 → 7

Alt Table

Status	Error	Program
	46.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	14.8b	(/.f64 (log.f64 (exp.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))) 1))) 2)
	16.1b	(/.f64 (+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 2 alpha)))) (fma.f64 2 i (+.f64 alpha beta))) 1) 2)
	14.7b	(/.f64 (+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (log1p.f64 (expm1.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) (fma.f64 2 i (+.f64 alpha beta))) 1) 2)
	51.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i beta) (pow.f64 alpha 3)) (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)
	14.8b	(/.f64 (fma.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) 1) 2)
	17.9b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (sqrt.f64 (fma.f64 2 i (+.f64 alpha beta)))) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (sqrt.f64 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)

Compiler

Compiled 36346 to 22861 computations (37.1% saved)

regimes2.2s (14.9%)

Accuracy

Total 1.3b remaining (93%)

Threshold costs 0b (0%)

Counts

175 → 2

Compiler

Compiled 43419 to 28055 computations (35.4% saved)

bsearch10.0ms (0.1%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-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	31	98
1	45	98
2	49	98
3	51	98
4	52	98
5	51	98

end226.0ms (1.5%)

Compiler: Compiled 468 to 284 computations (39.3% saved)

Details

analyze161.0ms (1.1%)

sample2.1s (14.2%)

simplify44.0ms (0.3%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series1.3s (8.8%)

rewrite23.0ms (0.2%)

simplify290.0ms (2%)

prune600.0ms (4%)

localize13.0ms (0.1%)

series842.0ms (5.7%)

rewrite38.0ms (0.3%)

simplify240.0ms (1.6%)

prune836.0ms (5.6%)

localize14.0ms (0.1%)

series1.1s (7.7%)

rewrite126.0ms (0.8%)

simplify541.0ms (3.6%)

prune1.5s (10.2%)

localize14.0ms (0.1%)

series1.3s (8.6%)

rewrite48.0ms (0.3%)

simplify279.0ms (1.9%)

prune917.0ms (6.2%)

regimes2.2s (14.9%)

bsearch10.0ms (0.1%)

simplify4.0ms (0%)

end226.0ms (1.5%)

Profiling