Details

analyze168.0ms (1.2%)

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)

sample1.9s (13.2%)

Results

1.1s	6672×	body	128	valid
423.0ms	743×	body	1024	valid
210.0ms	478×	body	512	valid
94.0ms	322×	body	256	valid
27.0ms	41×	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

20.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	20.5b	(/.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)
	25.6b	(/.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)

Status

Error

Program

▶

20.5b

(/.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)

25.6b

(/.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 180 to 106 computations (41.1% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	12.2b	(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)
✓	20.1b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series902.0ms (6.2%)

Counts

3 → 108

Calls

3 calls:

571.0ms

(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)

309.0ms

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

21.0ms

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

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 67

Calls

3 calls:

9.0ms

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

8.0ms

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

simplify215.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

561×	`+-commutative_binary64`
490×	`fma-def_binary64`
487×	`associate-+r+_binary64`
392×	`*-commutative_binary64`
294×	`associate-*r/_binary64`

Counts

175 → 205

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1400	19973
1	5450	19973

prune993.0ms (6.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	199	6	205
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	201	6	207

Error

0.2b

Counts

207 → 6

Alt Table

Status	Error	Program
	46.1b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
	12.2b	(/.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)
	54.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (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 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
▶	12.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	48.2b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)

Compiler

Compiled 25261 to 16306 computations (35.4% saved)

localize47.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	12.2b	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series935.0ms (6.5%)

Counts

3 → 108

Calls

3 calls:

565.0ms

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

316.0ms

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

50.0ms

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

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
24×	`associate-/l*_binary64`

Counts

3 → 169

Calls

3 calls:

9.0ms

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

7.0ms

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

0.0ms

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

simplify305.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
477×	`associate-+r+_binary64`
326×	`associate-*r/_binary64`
177×	`associate-/l*_binary64`
171×	`associate-/r*_binary64`

Counts

277 → 297

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1591	25853
1	5046	25853

prune611.0ms (4.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	297	0	297
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	297	6	303

Error

0.2b

Counts

303 → 6

Alt Table

Status	Error	Program
	46.1b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
▶	12.2b	(/.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)
	54.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (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 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
✓	12.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	48.2b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)

Compiler

Compiled 30788 to 19077 computations (38% saved)

localize14.0ms (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)))))
✓	12.2b	(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)

series979.0ms (6.8%)

Counts

4 → 144

Calls

4 calls:

538.0ms	(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)
322.0ms	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
82.0ms	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
35.0ms	(/.f64 1 (fma.f64 2 i (+.f64 alpha beta)))

rewrite43.0ms (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:

16.0ms	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
7.0ms	(/.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)

simplify275.0ms (1.9%)

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

prune716.0ms (4.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	370	0	370
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	370	6	376

Error

0.2b

Counts

376 → 6

Alt Table

Status	Error	Program
▶	46.1b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
✓	12.2b	(/.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)
	54.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (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 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
✓	12.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	48.2b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)

Compiler

Compiled 35026 to 22005 computations (37.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓	0.1b	(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	9.1b	(fma.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
✓	9.7b	(/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))

series2.0s (13.8%)

Counts

4 → 64

Calls

4 calls:

668.0ms	(/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))
647.0ms	(fma.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
353.0ms	(/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
323.0ms	(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))

rewrite508.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

2365×	`times-frac_binary64`
2076×	`*-un-lft-identity_binary64`
1504×	`add-sqr-sqrt_binary64`
822×	`sqrt-prod_binary64`
760×	`add-cube-cbrt_binary64`

Counts

4 → 1078

Calls

4 calls:

45.0ms	(/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))
15.0ms	(/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
10.0ms	(/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
0.0ms	(fma.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)

simplify1.2s (8.3%)

Algorithm

1×	egg-herbie

Rules

450×	`associate-/r/_binary64`
313×	`+-commutative_binary64`
285×	`*-commutative_binary64`
277×	`fma-def_binary64`
260×	`associate-+r+_binary64`

Counts

1142 → 825

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1445	87119
1	4681	86511
2	5016	86511

prune1.3s (9.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	824	1	825
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	825	6	831

Error

0.2b

Counts

831 → 6

Alt Table

Status	Error	Program
✓	12.2b	(/.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)
	54.7b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 3)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 20 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 3)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 (.f64 i i) (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 240 (/.f64 (.f64 beta (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (fma.f64 40 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (+.f64 (/.f64 16 (pow.f64 alpha 4)) (fma.f64 28 (/.f64 (.f64 i (pow.f64 beta 3)) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (pow.f64 i 3) (pow.f64 alpha 4)) (fma.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 (.f64 beta beta) (.f64 i i)) (pow.f64 alpha 4)) (fma.f64 80 (/.f64 (pow.f64 i 4) (pow.f64 alpha 4)) (fma.f64 108 (/.f64 (.f64 i (.f64 beta beta)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (fma.f64 80 (/.f64 i (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i i) (pow.f64 alpha 4)) (fma.f64 160 (/.f64 (.f64 beta (pow.f64 i 3)) (pow.f64 alpha 4)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 160 (/.f64 (.f64 i beta) (pow.f64 alpha 4)) (fma.f64 36 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)))))))))))))))))))))))) 2)
✓	12.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	48.2b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
	46.0b	(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (+.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 (sqrt.f64 beta) (sqrt.f64 alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))) 1) 2)

Compiler

Compiled 58598 to 27242 computations (53.5% saved)

regimes913.0ms (6.3%)

Accuracy

Total 1.3b remaining (89.8%)

Threshold costs 0b (0%)

Counts

71 → 2

Compiler

Compiled 19966 to 13588 computations (31.9% saved)

bsearch5.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
4×	`*-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	30	96
1	42	96
2	46	96
3	48	96
4	49	96
5	48	96

end282.0ms (1.9%)

Compiler: Compiled 565 to 348 computations (38.4% saved)

Details

analyze168.0ms (1.2%)

sample1.9s (13.2%)

simplify44.0ms (0.3%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series902.0ms (6.2%)

rewrite21.0ms (0.1%)

simplify215.0ms (1.5%)

prune993.0ms (6.9%)

localize47.0ms (0.3%)

series935.0ms (6.5%)

rewrite42.0ms (0.3%)

simplify305.0ms (2.1%)

prune611.0ms (4.2%)

localize14.0ms (0.1%)

series979.0ms (6.8%)

rewrite43.0ms (0.3%)

simplify275.0ms (1.9%)

prune716.0ms (4.9%)

localize15.0ms (0.1%)

series2.0s (13.8%)

rewrite508.0ms (3.5%)

simplify1.2s (8.3%)

prune1.3s (9.1%)

regimes913.0ms (6.3%)

bsearch5.0ms (0%)

simplify4.0ms (0%)

end282.0ms (1.9%)

Profiling