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)

sample1.9s (37.5%)

Results

839.0ms	6206×	body	128	valid
473.0ms	1036×	body	1024	valid
206.0ms	605×	body	512	valid
60.0ms	319×	body	256	valid
40.0ms	90×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify206.0ms (4.1%)

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 (0.1%)

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)

series50.0ms (1%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(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))

rewrite66.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

74× egg-rr

Counts

2 → 74

Calls

2 calls:

63.0ms	((fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2) (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	261	30
2	3563	30
3	4908	30
0	0	0
1	0	0

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

935×	`times-frac_binary64`
498×	`cancel-sign-sub-inv_binary64`
367×	`sub-neg_binary64`
205×	`+-commutative_binary64`
189×	`associate-+r+_binary64`

Counts

122 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2358
1	749	2323
2	2913	2279
3	5252	2279

prune113.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	125	4	129

Error

0.0b

Counts

129 → 4

Alt Table

Status	Error	Program
	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 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))))))))))
▶	13.9b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)))
	47.9b	(/.f64 (+.f64 beta 1) alpha)

Compiler

Compiled 4063 to 2606 computations (35.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series220.0ms (4.4%)

Counts

4 → 96

Calls

4 calls:

135.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2))
34.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)
32.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)))
18.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))

rewrite137.0ms (2.7%)

Algorithm

2×	batch-egg-rewrite

Rules

302× egg-rr

Counts

4 → 302

Calls

2 calls:

123.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	274	66
2	3639	66
3	5349	66
0	0	0
1	0	0

simplify165.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

616×	`times-frac_binary64`
615×	`associate-/r*_binary64`
614×	`fma-def_binary64`
396×	`associate-/l*_binary64`
211×	`+-commutative_binary64`

Counts

398 → 370

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	581	7838
1	2089	7682
2	5645	7682

prune525.0ms (10.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	369	1	370
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	369	5	374

Error

0.0b

Counts

374 → 5

Alt Table

Status	Error	Program
▶	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 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))))))))))
	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 alpha beta) 2)) -1/2 1/2)))
	47.9b	(/.f64 (+.f64 beta 1) alpha)

Compiler

Compiled 25297 to 16217 computations (35.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series74.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

41.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2))
33.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)))

rewrite63.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

45× egg-rr

Counts

2 → 45

Calls

2 calls:

62.0ms	((log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2))) (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)) -1/2 1/2)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	36
1	274	36
2	3639	36
3	5349	36
0	0	0
1	0	0

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

360×	`sub-neg_binary64`
288×	`times-frac_binary64`
252×	`fma-def_binary64`
247×	`+-commutative_binary64`
244×	`associate-+r+_binary64`

Counts

93 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	327	3258
1	1048	3199
2	4469	3157
3	5036	3157

prune471.0ms (9.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	413	0	413
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	413	5	418

Error

0.0b

Counts

418 → 5

Alt Table

Status	Error	Program
✓	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 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))))))))))
	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 alpha beta) 2)) -1/2 1/2)))
▶	47.9b	(/.f64 (+.f64 beta 1) alpha)

Compiler

Compiled 23783 to 14917 computations (37.3% saved)

localize3.0ms (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)

rewrite42.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

36× egg-rr

Counts

1 → 36

Calls

2 calls:

41.0ms	((/.f64 (+.f64 beta 1) alpha))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	128	7
2	1621	7
3	5298	7
0	0	0
1	0	0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

48 → 39

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	102
1	10	102
2	9	102

prune27.0ms (0.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	39	0	39
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	39	5	44

Error

0.0b

Counts

44 → 5

Alt Table

Status	Error	Program
✓	13.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 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))))))))))
	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 alpha beta) 2)) -1/2 1/2)))
✓	47.9b	(/.f64 (+.f64 beta 1) alpha)

Compiler

Compiled 932 to 655 computations (29.7% saved)

regimes454.0ms (9%)

Accuracy

Total 0.0b remaining (38.5%)

Threshold costs 0.0b (38.5%)

Counts

50 → 2

Compiler

Compiled 8885 to 6696 computations (24.6% saved)

bsearch3.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-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	31	80
1	43	80
2	57	80
3	72	80
4	79	80
5	81	80
6	79	80

end341.0ms (6.7%)

Compiler: Compiled 643 to 436 computations (32.2% saved)

Details

analyze2.0ms (0%)

sample1.9s (37.5%)

simplify206.0ms (4.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series50.0ms (1%)

rewrite66.0ms (1.3%)

simplify66.0ms (1.3%)

prune113.0ms (2.2%)

localize9.0ms (0.2%)

series220.0ms (4.4%)

rewrite137.0ms (2.7%)

simplify165.0ms (3.3%)

prune525.0ms (10.4%)

localize11.0ms (0.2%)

series74.0ms (1.5%)

rewrite63.0ms (1.3%)

simplify83.0ms (1.6%)

prune471.0ms (9.3%)

localize3.0ms (0.1%)

series5.0ms (0.1%)

rewrite42.0ms (0.8%)

simplify7.0ms (0.1%)

prune27.0ms (0.5%)

regimes454.0ms (9%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end341.0ms (6.7%)

Profiling