Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.7s (41%)

Results

717.0ms	6206×	body	128	valid
397.0ms	1036×	body	1024	valid
167.0ms	605×	body	512	valid
68.0ms	319×	body	256	valid
39.0ms	90×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify211.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series55.0ms (1.3%)

Counts

2 → 48

Calls

2 calls:

37.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
18.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite13.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify89.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
218×	`+-commutative_binary64`
206×	`fma-def_binary64`
194×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

112 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3790
1	962	3664
2	3486	3620
3	4984	3620

prune117.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Error

0.0b

Counts

143 → 4

Alt Table

Status	Error	Program
	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	47.9b	(/.f64 (+.f64 beta 1) alpha)
▶	13.9b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	50.1b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))

Compiler

Compiled 4453 to 2749 computations (38.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.1b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	1.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	2.0b	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

series169.0ms (4.2%)

Counts

2 → 48

Calls

2 calls:

136.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
32.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

1.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
1.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify95.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

594×	`times-frac_binary64`
585×	`associate-/r*_binary64`
539×	`fma-def_binary64`
383×	`associate-/l*_binary64`
182×	`+-commutative_binary64`

Counts

79 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	556	6288
1	1886	6047
2	5229	6047

prune293.0ms (7.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	258	5	263

Error

0.0b

Counts

263 → 5

Alt Table

Status	Error	Program
▶	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	47.9b	(/.f64 (+.f64 beta 1) alpha)
	51.4b	(exp.f64 (-.f64 (fma.f64 25 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (fma.f64 38 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2)))) (fma.f64 8 (/.f64 beta (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 28 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 8 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (/.f64 4 (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 5 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (log1p.f64 beta) (/.f64 8 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))))))) (log.f64 alpha))))))) (fma.f64 3 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 13/2 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 11 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 2 (.f64 alpha (+.f64 beta 1))) (fma.f64 6 (/.f64 beta (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (/.f64 8/3 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 21 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 1/2 (/.f64 (pow.f64 beta 4) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 1/3 (/.f64 (pow.f64 beta 6) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 7 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 8 (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 (.f64 beta beta) (.f64 alpha (+.f64 beta 1))) (fma.f64 3 (/.f64 beta (.f64 alpha (+.f64 beta 1))) (fma.f64 20 (/.f64 beta (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 22 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 3 (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 12 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 18 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (/.f64 2 (.f64 (*.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))))))))))))))))))))))))
✓	13.9b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	49.9b	(-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) (.f64 8 (/.f64 beta (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 13253 to 9151 computations (31% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
	1.6b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	1.6b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

series87.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

52.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
34.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`exp-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`log-prod_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
1.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

simplify101.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

363×	`sub-neg_binary64`
288×	`times-frac_binary64`
253×	`fma-def_binary64`
251×	`+-commutative_binary64`
247×	`associate-+r+_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	4045
1	1105	3894
2	4579	3852
3	5169	3852

prune254.0ms (6.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	255	5	260

Error

0.0b

Counts

260 → 5

Alt Table

Status	Error	Program
✓	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
▶	47.9b	(/.f64 (+.f64 beta 1) alpha)
	51.4b	(exp.f64 (-.f64 (fma.f64 25 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (fma.f64 38 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2)))) (fma.f64 8 (/.f64 beta (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 28 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 8 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (/.f64 4 (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 5 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (log1p.f64 beta) (/.f64 8 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))))))) (log.f64 alpha))))))) (fma.f64 3 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 13/2 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 11 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 2 (.f64 alpha (+.f64 beta 1))) (fma.f64 6 (/.f64 beta (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (/.f64 8/3 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 21 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 1/2 (/.f64 (pow.f64 beta 4) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 1/3 (/.f64 (pow.f64 beta 6) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 7 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 8 (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 (.f64 beta beta) (.f64 alpha (+.f64 beta 1))) (fma.f64 3 (/.f64 beta (.f64 alpha (+.f64 beta 1))) (fma.f64 20 (/.f64 beta (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 22 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 3 (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 12 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 18 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (/.f64 2 (.f64 (*.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))))))))))))))))))))))))
✓	13.9b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	49.9b	(-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) (.f64 8 (/.f64 beta (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 10123 to 6781 computations (33% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 beta 1) alpha)

series5.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

5.0ms

(/.f64 (+.f64 beta 1) alpha)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
4×	`associate-/l*_binary64`

Counts

1 → 35

Calls

1 calls:

4.0ms

(/.f64 (+.f64 beta 1) alpha)

simplify77.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

657×	`distribute-rgt-in_binary64`
554×	`distribute-lft-in_binary64`
413×	`associate-+l+_binary64`
338×	`unsub-neg_binary64`
305×	`associate-+r+_binary64`

Counts

47 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	63	585
1	134	551
2	294	551
3	688	518
4	1731	518
5	3257	518
6	4763	518
7	5090	518

prune34.0ms (0.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	57	5	62

Error

0.0b

Counts

62 → 5

Alt Table

Status	Error	Program
✓	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	47.9b	(/.f64 (+.f64 beta 1) alpha)
	51.4b	(exp.f64 (-.f64 (fma.f64 25 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (fma.f64 38 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2)))) (fma.f64 8 (/.f64 beta (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 28 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 8 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))) (-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (/.f64 4 (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (fma.f64 5 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (+.f64 beta 1))) (+.f64 (log1p.f64 beta) (/.f64 8 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 2))))))) (log.f64 alpha))))))) (fma.f64 3 (/.f64 (pow.f64 beta 3) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 13/2 (/.f64 (.f64 beta beta) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 11 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 2 (.f64 alpha (+.f64 beta 1))) (fma.f64 6 (/.f64 beta (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (+.f64 (/.f64 8/3 (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (+.f64 (/.f64 (pow.f64 beta 4) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 21 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 1/2 (/.f64 (pow.f64 beta 4) (.f64 (.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))) (fma.f64 1/3 (/.f64 (pow.f64 beta 6) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 7 (/.f64 (pow.f64 beta 3) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 8 (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (+.f64 (/.f64 (.f64 beta beta) (.f64 alpha (+.f64 beta 1))) (fma.f64 3 (/.f64 beta (.f64 alpha (+.f64 beta 1))) (fma.f64 20 (/.f64 beta (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (fma.f64 22 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 3 (/.f64 (pow.f64 beta 5) (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 12 (/.f64 beta (.f64 (pow.f64 alpha 3) (pow.f64 (+.f64 beta 1) 3))) (fma.f64 18 (/.f64 (.f64 beta beta) (.f64 (pow.f64 alpha 3) (+.f64 beta 1))) (/.f64 2 (.f64 (*.f64 alpha alpha) (pow.f64 (+.f64 beta 1) 2))))))))))))))))))))))))
✓	13.9b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	49.9b	(-.f64 (+.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) (.f64 8 (/.f64 beta (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 1164 to 778 computations (33.2% saved)

regimes457.0ms (11.2%)

Accuracy

Total 0.0b remaining (43%)

Threshold costs 0.0b (43%)

Counts

49 → 2

Compiler

Compiled 8925 to 6721 computations (24.7% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	43	80
2	57	80
3	72	80
4	79	80
5	81	80
6	79	80

end284.0ms (7%)

Compiler: Compiled 606 to 411 computations (32.2% saved)

Details

analyze2.0ms (0%)

sample1.7s (41%)

simplify211.0ms (5.2%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series55.0ms (1.3%)

rewrite13.0ms (0.3%)

simplify89.0ms (2.2%)

prune117.0ms (2.9%)

localize10.0ms (0.3%)

series169.0ms (4.2%)

rewrite4.0ms (0.1%)

simplify95.0ms (2.3%)

prune293.0ms (7.2%)

localize11.0ms (0.3%)

series87.0ms (2.1%)

rewrite4.0ms (0.1%)

simplify101.0ms (2.5%)

prune254.0ms (6.3%)

localize4.0ms (0.1%)

series5.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify77.0ms (1.9%)

prune34.0ms (0.8%)

regimes457.0ms (11.2%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end284.0ms (7%)

Profiling