Details

analyze108.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	14%	86%	0
0%	14%	86%	1
0%	14%	86%	2
0%	14%	86%	3
0%	14%	86%	4
0%	14%	86%	5
0%	14%	86%	6
8.1%	5.9%	86%	7
10.3%	3.7%	86%	8
12.6%	1.5%	86%	9
13.9%	0.1%	86%	10
14%	0%	86%	11
14%	0%	86%	12
14%	0%	86%	13
14%	0%	86%	14

Compiler

Compiled 67 to 35 computations (47.8% saved)

sample2.4s (7.4%)

Symmetry

(sort alpha beta)

Results

2.3s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify65.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

705×	`associate-+l+_binary64`
492×	`associate-l_binary64`
422×	`associate-r_binary64`
369×	`times-frac_binary64`
336×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	75
1	67	67
2	293	67
3	1612	67
4	4979	67
5	5035	67

prune4.0ms (0%)

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

55.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	55.5b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Status

Error

Program

▶

55.5b

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

Compiler

Compiled 203 to 89 computations (56.2% saved)

localize16.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 i (+.f64 i (+.f64 alpha beta)))
✓	0.1b	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	36.6b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	47.9b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))

series5.2s (15.9%)

Counts

4 → 144

Calls

4 calls:

4.8s	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
276.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
59.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
13.0ms	(*.f64 i (+.f64 i (+.f64 alpha beta)))

rewrite72.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-cbrt-cube_binary64`
61×	`add-exp-log_binary64`
22×	`*-un-lft-identity_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`

Counts

4 → 129

Calls

4 calls:

20.0ms	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
11.0ms	(*.f64 i (+.f64 i (+.f64 alpha beta)))
10.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
7.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

simplify456.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

731×	`fma-def_binary64`
507×	`associate-/l*_binary64`
344×	`times-frac_binary64`
54×	`sqr-pow_binary64`
54×	`sub-neg_binary64`

Counts

273 → 274

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2544	48017
1	5136	48017

prune2.2s (6.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	267	7	274
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	268	7	275

Error

14.6b

Counts

275 → 7

Alt Table

Status	Error	Program
▶	23.9b	1/16
	52.4b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.5b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	56.0b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
	58.3b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	40.2b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	47.1b	(/.f64 (-.f64 (fma.f64 1/4 (.f64 i alpha) (fma.f64 1/8 (.f64 beta alpha) (.f64 1/4 (+.f64 (.f64 i i) (.f64 beta i))))) (.f64 1/16 (+.f64 (.f64 alpha alpha) (.f64 beta beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 62122 to 36189 computations (41.7% saved)

localize0.0ms (0%)

prune34.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

14.6b

Counts

7 → 7

Alt Table

Status	Error	Program
✓	23.9b	1/16
	52.4b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.5b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	56.0b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
	58.3b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	40.2b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	47.1b	(/.f64 (-.f64 (fma.f64 1/4 (.f64 i alpha) (fma.f64 1/8 (.f64 beta alpha) (.f64 1/4 (+.f64 (.f64 i i) (.f64 beta i))))) (.f64 1/16 (+.f64 (.f64 alpha alpha) (.f64 beta beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 452 to 248 computations (45.1% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	8.5b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
✓	26.9b	(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	34.0b	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
✓	34.9b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

series7.0s (21.4%)

Counts

4 → 144

Calls

4 calls:

4.9s	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
1.9s	(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
115.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
81.0ms	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite141.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

159×	`times-frac_binary64`
102×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
93×	`add-cube-cbrt_binary64`
52×	`add-cbrt-cube_binary64`

Counts

4 → 211

Calls

4 calls:

57.0ms	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
11.0ms	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
8.0ms	(/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
4.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify1.1s (3.4%)

Algorithm

1×	egg-herbie

Rules

835×	`fma-def_binary64`
518×	`times-frac_binary64`
9×	`cube-mult_binary64`
9×	`unpow2_binary64`
9×	`unpow3_binary64`

Counts

355 → 390

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3290	67928
1	5077	67928

prune3.0s (9.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	386	4	390
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	389	8	397

Error

14.6b

Counts

397 → 8

Alt Table

Status	Error	Program
	41.5b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	40.3b	(.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))) (.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
✓	23.9b	1/16
	52.4b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	40.3b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (+.f64 (pow.f64 i 2) (.f64 beta i)) (+.f64 beta (.f64 2 i))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	58.3b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	40.2b	(.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (/.f64 1 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	40.9b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) 1) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))))))

Compiler

Compiled 88404 to 50571 computations (42.8% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(/.f64 1 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	34.0b	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
	34.9b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	36.2b	(.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (/.f64 1 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))

series5.5s (16.9%)

Counts

2 → 72

Calls

2 calls:

5.3s

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

225.0ms

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

rewrite98.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`add-exp-log_binary64`
69×	`add-cbrt-cube_binary64`
60×	`prod-exp_binary64`
44×	`div-exp_binary64`
30×	`cbrt-unprod_binary64`

Counts

2 → 109

Calls

2 calls:

28.0ms

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

5.0ms

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

simplify751.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

612×	`fma-def_binary64`
407×	`associate-/l*_binary64`
341×	`associate-/r*_binary64`
336×	`times-frac_binary64`
53×	`sqr-pow_binary64`

Counts

181 → 226

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2229	43434
1	5064	43434

prune2.4s (7.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	362	0	362
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	362	8	370

Error

14.6b

Counts

370 → 8

Alt Table

Status	Error	Program
	41.5b	(/.f64 (*.f64 1/4 (pow.f64 i 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	40.3b	(.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))) (.f64 (sqrt.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
✓	23.9b	1/16
	52.4b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	40.3b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (+.f64 (pow.f64 i 2) (.f64 beta i)) (+.f64 beta (.f64 2 i))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	58.3b	(/.f64 (/.f64 (.f64 i (.f64 (pow.f64 alpha 2) (+.f64 beta i))) (*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	40.2b	(.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (/.f64 1 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	40.9b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) 1) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))))))

Compiler

Compiled 68613 to 38650 computations (43.7% saved)

regimes1.7s (5.1%)

Accuracy

Total 2.5b remaining (19.6%)

Threshold costs 0b (0%)

Counts

127 → 2

Compiler

Compiled 25712 to 13293 computations (48.3% saved)

bsearch49.0ms (0.1%)

Steps

Iters	Range		Point
4	4.4481022267649774e+145	7.667337699967073e+145	4.860000921899335e+145

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	74
1	27	74
2	27	74

end302.0ms (0.9%)

Remove: (sort alpha beta)
Compiler: Compiled 541 to 261 computations (51.8% saved)

Details

analyze108.0ms (0.3%)

sample2.4s (7.4%)

simplify65.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0%)

series5.2s (15.9%)

rewrite72.0ms (0.2%)

simplify456.0ms (1.4%)

prune2.2s (6.8%)

localize0.0ms (0%)

prune34.0ms (0.1%)

localize40.0ms (0.1%)

series7.0s (21.4%)

rewrite141.0ms (0.4%)

simplify1.1s (3.4%)

prune3.0s (9.1%)

localize32.0ms (0.1%)

series5.5s (16.9%)

rewrite98.0ms (0.3%)

simplify751.0ms (2.3%)

prune2.4s (7.4%)

regimes1.7s (5.1%)

bsearch49.0ms (0.1%)

simplify6.0ms (0%)

end302.0ms (0.9%)

Profiling