Details

analyze156.0ms (1.3%)

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)

sample79.0ms (0.7%)

Algorithm

1×

intervals

Results

16.0ms	212×	body	128	valid
7.0ms	21×	body	1024	valid
6.0ms	256×	pre	128	true
2.0ms	13×	body	256	valid
1.0ms	7×	body	512	valid
1.0ms	3×	body	2048	valid

Compiler

Compiled 78 to 51 computations (34.6% saved)

simplify44.0ms (0.4%)

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

19.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.0b	(/.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)
	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)

Status

Error

Program

▶

19.0b

(/.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)

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 180 to 106 computations (41.1% saved)

localize14.0ms (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))))
✓	12.1b	(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)
✓	17.3b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series883.0ms (7.5%)

Counts

3 → 108

Calls

3 calls:

547.0ms

(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)

313.0ms

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

22.0ms

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

rewrite17.0ms (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:

8.0ms

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

4.0ms

(*.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)

simplify617.0ms (5.3%)

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

prune523.0ms (4.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	203	4	207

Error

0.2b

Counts

207 → 4

Alt Table

Status	Error	Program
	12.1b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
	53.7b	(/.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)
▶	12.1b	(/.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)
	49.8b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 25147 to 16234 computations (35.4% saved)

localize13.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.0b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	12.1b	(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)

series1.0s (8.6%)

Counts

3 → 108

Calls

3 calls:

590.0ms

(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)

337.0ms

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

76.0ms

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

rewrite42.0ms (0.4%)

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:

12.0ms

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

5.0ms

(/.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)

simplify297.0ms (2.5%)

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 → 298

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1591	25853
1	5046	25853

prune614.0ms (5.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	297	1	298
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	298	4	302

Error

0.2b

Counts

302 → 4

Alt Table

Status	Error	Program
	12.1b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
▶	11.9b	(/.f64 (+.f64 (*.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)
	53.7b	(/.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)
	49.8b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 30733 to 19037 computations (38.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
	0.0b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	2.5b	(*.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)))))
✓	4.7b	(+.f64 (*.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)

series941.0ms (8%)

Counts

2 → 72

Calls

2 calls:

624.0ms

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

rewrite67.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`times-frac_binary64`
123×	`*-un-lft-identity_binary64`
92×	`add-sqr-sqrt_binary64`
82×	`associate-r_binary64`
59×	`add-cube-cbrt_binary64`

Counts

2 → 125

Calls

2 calls:

26.0ms

(*.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)))))

15.0ms

(+.f64 (*.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)

simplify289.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

404×	`+-commutative_binary64`
361×	`*-commutative_binary64`
354×	`fma-def_binary64`
349×	`associate-+r+_binary64`
271×	`associate-*r/_binary64`

Counts

197 → 265

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1236	21338
1	4728	21233
2	5013	21233

prune975.0ms (8.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	506	1	507
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	507	4	511

Error

0.2b

Counts

511 → 4

Alt Table

Status	Error	Program
▶	12.0b	(/.f64 (+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	53.7b	(/.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)
✓	11.9b	(/.f64 (+.f64 (*.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)
	49.8b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 49090 to 30070 computations (38.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 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 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))))
✓	3.0b	(+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series887.0ms (7.6%)

Counts

3 → 108

Calls

3 calls:

532.0ms

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

305.0ms

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

49.0ms

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

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
19×	`associate-r_binary64`
17×	`add-cbrt-cube_binary64`

Counts

3 → 103

Calls

3 calls:

15.0ms

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

12.0ms

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

11.0ms

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

simplify215.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

462×	`+-commutative_binary64`
394×	`fma-def_binary64`
387×	`associate-+r+_binary64`
364×	`*-commutative_binary64`
265×	`associate-*r/_binary64`

Counts

211 → 302

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1336	21970
1	5061	21970

prune683.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	385	0	385
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	385	4	389

Error

0.2b

Counts

389 → 4

Alt Table

Status	Error	Program
✓	12.0b	(/.f64 (+.f64 (/.f64 (*.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	53.7b	(/.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)
✓	11.9b	(/.f64 (+.f64 (*.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)
	49.8b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 34345 to 21127 computations (38.5% saved)

regimes1.3s (11%)

Accuracy

Total 1.8b remaining (93.5%)

Threshold costs 0b (0%)

Counts

101 → 2

Compiler

Compiled 25396 to 17625 computations (30.6% saved)

bsearch6.0ms (0.1%)

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

simplify5.0ms (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	48	98
3	50	98
4	51	98
5	50	98

end1.0ms (0%)

Compiler: Compiled 70 to 41 computations (41.4% saved)

sample2.0s (16.9%)

Algorithm

1×

intervals

Results

680.0ms	6500×	body	128	valid
320.0ms	655×	body	1024	valid
211.0ms	8000×	pre	128	true
112.0ms	481×	body	512	valid
45.0ms	301×	body	256	valid
22.0ms	63×	body	2048	valid

Compiler

Compiled 485 to 303 computations (37.5% saved)

Details

analyze156.0ms (1.3%)

sample79.0ms (0.7%)

simplify44.0ms (0.4%)

prune5.0ms (0%)

localize14.0ms (0.1%)

series883.0ms (7.5%)

rewrite17.0ms (0.1%)

simplify617.0ms (5.3%)

prune523.0ms (4.5%)

localize13.0ms (0.1%)

series1.0s (8.6%)

rewrite42.0ms (0.4%)

simplify297.0ms (2.5%)

prune614.0ms (5.2%)

localize13.0ms (0.1%)

series941.0ms (8%)

rewrite67.0ms (0.6%)

simplify289.0ms (2.5%)

prune975.0ms (8.3%)

localize14.0ms (0.1%)

series887.0ms (7.6%)

rewrite49.0ms (0.4%)

simplify215.0ms (1.8%)

prune683.0ms (5.8%)

regimes1.3s (11%)

bsearch6.0ms (0.1%)

simplify5.0ms (0%)

end1.0ms (0%)

sample2.0s (16.9%)

Profiling