Details

analyze168.0ms (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)

sample1.9s (11.9%)

Results

1.1s	6653×	body	128	valid
396.0ms	692×	body	1024	valid
239.0ms	558×	body	512	valid
82.0ms	289×	body	256	valid
43.0ms	64×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify28.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
245×	`+-commutative_binary64`
193×	`associate-+l+_binary64`
184×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	112	37
3	520	37
4	2735	37
5	4514	37

Stop Event

1×	node limit

Counts

1 → 2

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

15.2b

Counts

3 → 2

Alt Table

Status	Error	Program
	23.6b	(/.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)
▶	15.2b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

Status

Error

Program

23.6b

(/.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)

▶

15.2b

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

Compiler

Compiled 180 to 109 computations (39.4% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
✓	1.7b	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

series235.0ms (1.4%)

Counts

3 → 108

Calls

3 calls:

145.0ms

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

55.0ms

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

34.0ms

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

rewrite46.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

180×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`
167×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	349	65

Stop Event

1×	node limit

Counts

3 → 89

Calls

3 calls:

44.0ms

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

44.0ms

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

44.0ms

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

simplify122.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-/l*_binary64`
365×	`+-commutative_binary64`
282×	`associate-+r+_binary64`
265×	`fma-def_binary64`
218×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	883	10939
1	3352	10904

Stop Event

1×	node limit

Counts

197 → 218

prune444.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	212	6	218
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	213	7	220

Error

0.2b

Counts

220 → 7

Alt Table

Status	Error	Program
	24.7b	(/.f64 (/.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1) (-.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)) 2)
	47.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 i (/.f64 alpha 4)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (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)
	15.4b	(/.f64 (expm1.f64 (log1p.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
▶	15.2b	(/.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
	46.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	15.2b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
	25.9b	(/.f64 (-.f64 (+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))))) (+.f64 (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (+.f64 beta (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (+.f64 beta (+.f64 2 (*.f64 2 i))))))) 2)

Compiler

Compiled 15699 to 9800 computations (37.6% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))
	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
✓	1.7b	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
✓	1.7b	(log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))

series546.0ms (3.3%)

Counts

3 → 108

Calls

3 calls:

259.0ms

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

147.0ms

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

138.0ms

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

rewrite42.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

203×	`add-sqr-sqrt_binary64`
194×	`log1p-expm1-u_binary64`
194×	`expm1-log1p-u_binary64`
192×	`add-cbrt-cube_binary64`
188×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	104
1	397	104

Stop Event

1×	node limit

Counts

3 → 59

Calls

3 calls:

40.0ms

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

40.0ms

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

40.0ms

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

simplify224.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

418×	`+-commutative_binary64`
370×	`*-commutative_binary64`
353×	`associate-+r+_binary64`
311×	`fma-def_binary64`
218×	`associate-*r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1186	23181
1	4788	23181

Stop Event

1×	node limit

Counts

167 → 133

prune656.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	212	6	218

Error

0.2b

Counts

218 → 6

Alt Table

Status	Error	Program
	24.7b	(/.f64 (/.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1) (-.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)) 2)
	47.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 i (/.f64 alpha 4)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (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)
▶	15.2b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))))) 2)
	46.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	15.2b	(/.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
	25.9b	(/.f64 (-.f64 (+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))))) (+.f64 (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (+.f64 beta (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (+.f64 beta (+.f64 2 (*.f64 2 i))))))) 2)

Compiler

Compiled 27551 to 18306 computations (33.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))
	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
	1.7b	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)
✓	1.7b	(log.f64 (sqrt.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))))

series373.0ms (2.3%)

Counts

1 → 36

Calls

1 calls:

373.0ms

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

rewrite30.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

219×	`add-sqr-sqrt_binary64`
208×	`log1p-expm1-u_binary64`
208×	`expm1-log1p-u_binary64`
207×	`add-cbrt-cube_binary64`
205×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	40
1	429	37

Stop Event

1×	node limit

Counts

1 → 18

Calls

1 calls:

30.0ms

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

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
626×	`associate-/l*_binary64`
618×	`associate-/r*_binary64`
184×	`+-commutative_binary64`
182×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	588	6610
1	2175	5778

Stop Event

1×	node limit

Counts

54 → 65

prune1.5s (9.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	422	0	422
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	422	6	428

Error

0.2b

Counts

428 → 6

Alt Table

Status	Error	Program
▶	24.7b	(/.f64 (/.f64 (-.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1) (-.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)) 2)
	47.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 i (/.f64 alpha 4)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (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)
✓	15.2b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))))) 2)
	46.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	15.2b	(/.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
	25.9b	(/.f64 (-.f64 (+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))))) (+.f64 (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (+.f64 beta (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (+.f64 beta (+.f64 2 (*.f64 2 i))))))) 2)

Compiler

Compiled 67284 to 43933 computations (34.7% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))))
✓	0.1b	(*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))
✓	1.1b	(-.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)
✓	2.7b	(-.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1)

series4.4s (26.6%)

Counts

4 → 144

Calls

4 calls:

2.7s	(-.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1)
1.2s	(.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))))
246.0ms	(-.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)
156.0ms	(*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))

rewrite46.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

240×	`add-sqr-sqrt_binary64`
231×	`log1p-expm1-u_binary64`
231×	`expm1-log1p-u_binary64`
230×	`add-cbrt-cube_binary64`
224×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	142
1	469	142

Stop Event

1×	node limit

Counts

4 → 76

Calls

4 calls:

44.0ms	(.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))))
44.0ms	(*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))
44.0ms	(-.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)
44.0ms	(-.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) 1)

simplify511.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
10×	`unpow2_binary64`
9×	`cube-mult_binary64`
9×	`unpow3_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4115	80403

Stop Event

1×	node limit

Counts

220 → 252

prune3.3s (20%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	368	2	370
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	369	7	376

Error

0.2b

Counts

376 → 7

Alt Table

Status	Error	Program
	47.4b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 i (/.f64 alpha 4)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (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)
	24.7b	(/.f64 (/.f64 (/.f64 (-.f64 (pow.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 4) 1) (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 2) 1)) (-.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)) 2)
✓	15.2b	(/.f64 (+.f64 (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)))) (log.f64 (sqrt.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))))) 2)
	46.6b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	15.2b	(/.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1))) 2)
	33.7b	(/.f64 (/.f64 (-.f64 (/.f64 (pow.f64 alpha 4) (.f64 (pow.f64 (+.f64 (.f64 2 i) alpha) 2) (pow.f64 (+.f64 2 (+.f64 (.f64 2 i) alpha)) 2))) 1) (-.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)) 2)
	25.9b	(/.f64 (-.f64 (+.f64 1 (/.f64 (pow.f64 beta 2) (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (.f64 2 i)))))) (+.f64 (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (+.f64 beta (.f64 2 i)) (pow.f64 (+.f64 beta (+.f64 2 (.f64 2 i))) 2))) (/.f64 (.f64 (pow.f64 beta 2) alpha) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (+.f64 beta (+.f64 2 (*.f64 2 i))))))) 2)

Compiler

Compiled 139574 to 96051 computations (31.2% saved)

regimes1.4s (8.7%)

Accuracy

Total 1.5b remaining (92.4%)

Threshold costs 0b (0%)

Counts

136 → 2

Compiler

Compiled 42997 to 29400 computations (31.6% saved)

bsearch9.0ms (0.1%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

9×	`+-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	38	105
1	52	105
2	56	105
3	58	105
4	59	105

Stop Event

1×

saturated

end222.0ms (1.4%)

Compiler: Compiled 529 to 344 computations (35% saved)

Details

analyze168.0ms (1%)

sample1.9s (11.9%)

simplify28.0ms (0.2%)

prune5.0ms (0%)

localize16.0ms (0.1%)

series235.0ms (1.4%)

rewrite46.0ms (0.3%)

simplify122.0ms (0.7%)

prune444.0ms (2.7%)

localize19.0ms (0.1%)

series546.0ms (3.3%)

rewrite42.0ms (0.3%)

simplify224.0ms (1.4%)

prune656.0ms (4%)

localize22.0ms (0.1%)

series373.0ms (2.3%)

rewrite30.0ms (0.2%)

simplify87.0ms (0.5%)

prune1.5s (9.2%)

localize20.0ms (0.1%)

series4.4s (26.6%)

rewrite46.0ms (0.3%)

simplify511.0ms (3.1%)

prune3.3s (20%)

regimes1.4s (8.7%)

bsearch9.0ms (0.1%)

simplify4.0ms (0%)

end222.0ms (1.4%)

Profiling