Details

analyze191.0ms (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)

sample1.9s (12.7%)

Results

1.1s	6625×	body	128	valid
393.0ms	714×	body	1024	valid
235.0ms	534×	body	512	valid
101.0ms	328×	body	256	valid
44.0ms	55×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify47.0ms (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

23.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	28.0b	(/.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)
▶	23.3b	(/.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

28.0b

(/.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)

▶

23.3b

(/.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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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))))
✓	15.4b	(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)
✓	21.4b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series1.3s (8.5%)

Counts

4 → 144

Calls

4 calls:

922.0ms	(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)
268.0ms	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
60.0ms	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
5.0ms	(fma.f64 2 i (+.f64 alpha beta))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 77

Calls

4 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 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)

simplify208.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

562×	`+-commutative_binary64`
490×	`fma-def_binary64`
488×	`associate-+r+_binary64`
392×	`*-commutative_binary64`
294×	`associate-*r/_binary64`

Counts

221 → 227

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1405	20324
1	5456	20324

prune609.0ms (4.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	244	5	249
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	246	5	251

Error

0.0b

Counts

251 → 5

Alt Table

Status	Error	Program
▶	15.3b	(/.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)
	49.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i 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)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
	32.8b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 (sqrt.f64 (-.f64 beta alpha)) (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (sqrt.f64 (-.f64 beta alpha)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
	46.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	51.3b	(/.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)

Compiler

Compiled 26221 to 16726 computations (36.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 2 i (+.f64 alpha beta))
✓	0.0b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	15.4b	(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)

series827.0ms (5.6%)

Counts

3 → 108

Calls

3 calls:

494.0ms

(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)

287.0ms

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

43.0ms

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

rewrite41.0ms (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))))

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)

simplify241.0ms (1.6%)

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

prune668.0ms (4.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	339	2	341
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	341	5	346

Error

0.0b

Counts

346 → 5

Alt Table

Status	Error	Program
	15.3b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
▶	15.2b	(/.f64 (log.f64 (exp.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)
	46.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	51.3b	(/.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)
	49.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i 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)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)

Compiler

Compiled 31773 to 19517 computations (38.6% saved)

localize15.0ms (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)))
	0.0b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	3.6b	(log.f64 (exp.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)))
	15.4b	(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)

series473.0ms (3.2%)

Counts

1 → 36

Calls

1 calls:

473.0ms

(log.f64 (exp.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)))

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log-prod_binary64`
4×	`log-pow_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`exp-prod_binary64`

Counts

1 → 18

Calls

1 calls:

2.0ms

(log.f64 (exp.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)))

simplify131.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

894×	`fma-def_binary64`
441×	`associate-*l/_binary64`
266×	`+-commutative_binary64`
241×	`*-commutative_binary64`
229×	`associate-+r+_binary64`

Counts

54 → 77

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	795	9427
1	3051	9078
2	5369	9078

prune862.0ms (5.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	372	2	374
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	373	6	379

Error

0.0b

Counts

379 → 6

Alt Table

Status	Error	Program
▶	15.3b	(/.f64 (exp.f64 (log.f64 (log.f64 (exp.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)
	46.6b	(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
	15.3b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
✓	15.2b	(/.f64 (log.f64 (exp.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)
	51.3b	(/.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)
	49.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i 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)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)

Compiler

Compiled 42607 to 27018 computations (36.6% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(exp.f64 (log.f64 (log.f64 (exp.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)))))
	3.6b	(log.f64 (exp.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)))
✓	3.8b	(log.f64 (log.f64 (exp.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))))
	15.4b	(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)

series3.3s (22.2%)

Counts

2 → 72

Calls

2 calls:

2.8s

(log.f64 (log.f64 (exp.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))))

472.0ms

(exp.f64 (log.f64 (log.f64 (exp.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)))))

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-prod_binary64`
10×	`exp-prod_binary64`
10×	`log-pow_binary64`
7×	`exp-sum_binary64`
7×	`*-un-lft-identity_binary64`

Counts

2 → 39

Calls

2 calls:

2.0ms

(exp.f64 (log.f64 (log.f64 (exp.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)))))

2.0ms

(log.f64 (log.f64 (exp.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))))

simplify477.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

826×	`fma-def_binary64`
426×	`associate-/r*_binary64`
392×	`associate-/l*_binary64`
362×	`times-frac_binary64`
59×	`sqr-pow_binary64`

Counts

111 → 161

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2411	42080
1	5517	42080

prune1.6s (10.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	293	1	294
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	294	6	300

Error

0.0b

Counts

300 → 6

Alt Table

Status	Error	Program
	51.3b	(/.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)
	15.6b	(/.f64 (.f64 (exp.f64 (log.f64 (.f64 (cbrt.f64 (log.f64 (exp.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)))) (cbrt.f64 (log.f64 (exp.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))))))) (exp.f64 (log.f64 (cbrt.f64 (log.f64 (exp.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)
	46.6b	(/.f64 (/.f64 (fma.f64 beta 2 (fma.f64 i 4 2)) alpha) 2)
	15.3b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (-.f64 beta alpha))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
✓	15.2b	(/.f64 (log.f64 (exp.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)
	49.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i 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)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)

Compiler

Compiled 79180 to 54342 computations (31.4% saved)

regimes1.7s (11.3%)

Accuracy

Total 1.3b remaining (92.6%)

Threshold costs 0b (0%)

Counts

156 → 2

Compiler

Compiled 32228 to 22381 computations (30.6% saved)

bsearch7.0ms (0%)

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-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	97
1	40	97
2	44	97
3	46	97
4	47	97
5	46	97

end223.0ms (1.5%)

Compiler: Compiled 529 to 313 computations (40.8% saved)

Details

analyze191.0ms (1.3%)

sample1.9s (12.7%)

simplify47.0ms (0.3%)

prune5.0ms (0%)

localize12.0ms (0.1%)

series1.3s (8.5%)

rewrite19.0ms (0.1%)

simplify208.0ms (1.4%)

prune609.0ms (4.1%)

localize13.0ms (0.1%)

series827.0ms (5.6%)

rewrite41.0ms (0.3%)

simplify241.0ms (1.6%)

prune668.0ms (4.5%)

localize15.0ms (0.1%)

series473.0ms (3.2%)

rewrite3.0ms (0%)

simplify131.0ms (0.9%)

prune862.0ms (5.8%)

localize16.0ms (0.1%)

series3.3s (22.2%)

rewrite10.0ms (0.1%)

simplify477.0ms (3.2%)

prune1.6s (10.7%)

regimes1.7s (11.3%)

bsearch7.0ms (0%)

simplify10.0ms (0.1%)

end223.0ms (1.5%)

Profiling