Details

analyze51.0ms (0.6%)

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)

sample1.6s (19.1%)

Symmetry

(sort alpha beta)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify46.0ms (0.6%)

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 (0.1%)

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

55.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	55.1b	(/.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

▶

55.1b

(/.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)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	0.1b	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	36.9b	(/.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))
✓	47.0b	(/.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))))

series3.0s (36.7%)

Counts

4 → 144

Calls

4 calls:

2.7s	(/.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))
240.0ms	(/.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))))
48.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
15.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite111.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

113× egg-rr

Counts

4 → 113

Calls

2 calls:

107.0ms

((/.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)))) (/.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)) (*.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))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	131
1	381	131
2	4911	131
3	6081	131
0	0	0
1	0	0

simplify357.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

739×	`fma-def_binary64`
489×	`associate-/l*_binary64`
336×	`associate-/r*_binary64`
333×	`times-frac_binary64`
53×	`sqr-pow_binary64`

Counts

257 → 268

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2376	40163
1	5421	40163

prune1.1s (13.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	259	9	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	260	9	269

Error

7.4b

Counts

269 → 9

Alt Table

Status	Error	Program
▶	15.6b	1/16
	41.6b	(/.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))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	56.8b	(/.f64 (-.f64 (fma.f64 i alpha (.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (/.f64 (.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	21.1b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
	40.1b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) 2)
	40.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	55.2b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 59281 to 35652 computations (39.9% saved)

localize0.0ms (0%)

prune13.0ms (0.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

7.4b

Counts

9 → 9

Alt Table

Status	Error	Program
✓	15.6b	1/16
	41.6b	(/.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))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	56.8b	(/.f64 (-.f64 (fma.f64 i alpha (.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (/.f64 (.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	21.1b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
	40.1b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) 2)
	40.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	55.2b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 676 to 368 computations (45.6% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (*.f64 i i))
✓	1.8b	(/.f64 (.f64 alpha alpha) (.f64 i i))
✓	16.4b	(/.f64 (.f64 beta beta) (.f64 i i))

series63.0ms (0.8%)

Counts

3 → 60

Calls

3 calls:

30.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
29.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
3.0ms	(/.f64 1 (*.f64 i i))

rewrite62.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

108× egg-rr

Counts

3 → 108

Calls

2 calls:

60.0ms	((/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)) (/.f64 1 (*.f64 i i)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	236	18
2	2934	18
3	5370	18
0	0	0
1	0	0

simplify116.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

550×	`sqr-pow_binary64`
522×	`associate-/l*_binary64`
500×	`unswap-sqr_binary64`
463×	`*-commutative_binary64`
367×	`associate-/r*_binary64`

Counts

168 → 114

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	564
1	24	564
2	44	564
3	123	564
4	503	564
5	2533	564
6	3052	564
7	3286	564
8	3545	564
9	3852	564
10	4233	564
11	4694	564
12	4946	564

prune121.0ms (1.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	114	9	123

Error

7.4b

Counts

123 → 9

Alt Table

Status	Error	Program
✓	15.6b	1/16
	41.6b	(/.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))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	56.8b	(/.f64 (-.f64 (fma.f64 i alpha (.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (/.f64 (.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	16.3b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (+.f64 (pow.f64 (/.f64 beta i) 2) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
	40.1b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) 2)
	40.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	55.2b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 4071 to 2066 computations (49.3% saved)

localize48.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f64 (/.f64 beta i) 2)
	0.4b	(/.f64 1 (*.f64 i i))
	1.8b	(/.f64 (.f64 alpha alpha) (.f64 i i))

series10.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

10.0ms

(pow.f64 (/.f64 beta i) 2)

rewrite44.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

62× egg-rr

Counts

1 → 62

Calls

2 calls:

43.0ms	((pow.f64 (/.f64 beta i) 2))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	127	7
2	1435	7
3	5503	7
0	0	0
1	0	0

simplify268.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1209×	`associate-/r/_binary64`
570×	`unswap-sqr_binary64`
555×	`times-frac_binary64`
478×	`sqr-pow_binary64`
259×	`associate-/l*_binary64`

Counts

86 → 63

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	240
1	15	240
2	28	240
3	71	240
4	268	240
5	1715	240
6	2536	240
7	2652	240
8	2816	240
9	3030	240
10	3291	240
11	4574	240
12	4930	240
13	4994	240
14	4972	240

prune387.0ms (4.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	134	9	143

Error

7.4b

Counts

143 → 9

Alt Table

Status	Error	Program
✓	15.6b	1/16
	41.6b	(/.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))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	56.8b	(/.f64 (-.f64 (fma.f64 i alpha (.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (/.f64 (.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	16.3b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (.f64 1/32 (+.f64 (pow.f64 (/.f64 beta i) 2) (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
	40.1b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(pow.f64 (/.f64 (/.f64 (sqrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) 2)
	40.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) 1) (/.f64 (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	55.2b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (pow.f64 (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) 2)) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (cbrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 4278 to 2367 computations (44.7% saved)

regimes453.0ms (5.6%)

Accuracy

Total 2.4b remaining (18.7%)

Threshold costs 0b (0%)

Counts

53 → 2

Compiler

Compiled 12536 to 7365 computations (41.2% saved)

bsearch34.0ms (0.4%)

Steps

Iters	Range		Point
8	1.2605185829862502e+139	1.9231094843981654e+143	1.1792264146842992e+140

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	62
1	28	62
2	28	62

end263.0ms (3.2%)

Remove: (sort alpha beta)
Compiler: Compiled 522 to 287 computations (45% saved)

Details

analyze51.0ms (0.6%)

sample1.6s (19.1%)

simplify46.0ms (0.6%)

prune4.0ms (0.1%)

localize15.0ms (0.2%)

series3.0s (36.7%)

rewrite111.0ms (1.4%)

simplify357.0ms (4.4%)

prune1.1s (13.8%)

localize0.0ms (0%)

prune13.0ms (0.2%)

localize13.0ms (0.2%)

series63.0ms (0.8%)

rewrite62.0ms (0.8%)

simplify116.0ms (1.4%)

prune121.0ms (1.5%)

localize48.0ms (0.6%)

series10.0ms (0.1%)

rewrite44.0ms (0.5%)

simplify268.0ms (3.3%)

prune387.0ms (4.7%)

regimes453.0ms (5.6%)

bsearch34.0ms (0.4%)

simplify2.0ms (0%)

end263.0ms (3.2%)

Profiling