Details

analyze51.0ms (0.5%)

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 (15.1%)

Symmetry

(sort alpha beta)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify54.0ms (0.5%)

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

55.1b

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)

localize16.0ms (0.1%)

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))))

series4.1s (38.6%)

Counts

4 → 144

Calls

4 calls:

3.3s	(/.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))
301.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
236.0ms	(/.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))))
223.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite359.0ms (3.4%)

Algorithm

4×	egg-rewrite

Rules

74×	`egg`
67×	`egg`
56×	`egg`
25×	`egg`

Counts

4 → 222

Calls

4 calls:

101.0ms	(/.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))
92.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
86.0ms	(/.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))))
72.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	318	39
2	4547	39
3	4979	39
0	17	55
1	381	55
2	4911	55
3	6081	55
0	10	26
1	224	26
2	3100	26
3	5016	26
0	8	11
1	169	11
2	1990	11
3	5777	11

simplify665.0ms (6.3%)

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

366 → 374

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2376	40163
1	5421	40163

prune1.8s (16.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	364	10	374
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	365	10	375

Error

7.4b

Counts

375 → 10

Alt Table

Status	Error	Program
	40.1b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.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))
	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)))))
	40.2b	(.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)))
	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 (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)))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	15.6b	1/16
	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))))
	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))
	40.4b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) 2) (/.f64 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (cbrt.f64 (*.f64 i (+.f64 i (+.f64 alpha beta)))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 64918 to 37312 computations (42.5% saved)

localize0.0ms (0%)

prune15.0ms (0.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	9	9
Picked	1	1
Done	0	0
Total	10	10

Error

7.4b

Counts

10 → 10

Alt Table

Status	Error	Program
	40.1b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.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))
▶	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)))))
	40.2b	(.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)))
	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 (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)))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	15.6b	1/16
	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))))
	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))
	40.4b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) 2) (/.f64 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (cbrt.f64 (*.f64 i (+.f64 i (+.f64 alpha beta)))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 790 to 410 computations (48.1% saved)

localize14.0ms (0.1%)

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))

series138.0ms (1.3%)

Counts

3 → 60

Calls

3 calls:

76.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
59.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite208.0ms (2%)

Algorithm

3×	egg-rewrite

Rules

67×	`egg`
59×	`egg`
59×	`egg`

Counts

3 → 185

Calls

3 calls:

90.0ms	(/.f64 1 (*.f64 i i))
63.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
52.0ms	(/.f64 (.f64 beta beta) (.f64 i i))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	129	7
2	1647	7
3	5252	7
0	6	10
1	129	7
2	1647	7
3	5252	7
0	5	7
1	100	4
2	1021	4
3	4826	4
4	5107	4

simplify143.0ms (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

245 → 188

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

prune228.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	188	10	198

Error

7.4b

Counts

198 → 10

Alt Table

Status	Error	Program
	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)))
	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 (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)))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2))) (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)))))
	40.4b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) 2) (/.f64 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (cbrt.f64 (*.f64 i (+.f64 i (+.f64 alpha beta)))))) (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 (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))
✓	15.6b	1/16
	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))))
	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))

Compiler

Compiled 6366 to 3010 computations (52.7% saved)

localize14.0ms (0.1%)

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)

rewrite51.0ms (0.5%)

Algorithm

1×	egg-rewrite

Rules

67× egg

Counts

1 → 67

Calls

1 calls:

50.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

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

simplify144.0ms (1.4%)

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

91 → 68

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

prune268.0ms (2.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	196	0	196
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	196	10	206

Error

7.4b

Counts

206 → 10

Alt Table

Status	Error	Program
	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)))
	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 (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)))
	40.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2))) (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)))))
	40.4b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 i (+.f64 i (+.f64 alpha beta)))) 2) (/.f64 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (cbrt.f64 (*.f64 i (+.f64 i (+.f64 alpha beta)))))) (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 (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))
✓	15.6b	1/16
	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))))
	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))

Compiler

Compiled 6039 to 3306 computations (45.3% saved)

regimes503.0ms (4.8%)

Accuracy

Total 2.4b remaining (18.7%)

Threshold costs 0b (0%)

Counts

67 → 2

Compiler

Compiled 14832 to 8605 computations (42% saved)

bsearch36.0ms (0.3%)

Steps

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

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	67
1	26	67
2	26	67

end212.0ms (2%)

Remove: (sort alpha beta)
Compiler: Compiled 595 to 308 computations (48.2% saved)

Details

analyze51.0ms (0.5%)

sample1.6s (15.1%)

simplify54.0ms (0.5%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series4.1s (38.6%)

rewrite359.0ms (3.4%)

simplify665.0ms (6.3%)

prune1.8s (16.6%)

localize0.0ms (0%)

prune15.0ms (0.1%)

localize14.0ms (0.1%)

series138.0ms (1.3%)

rewrite208.0ms (2%)

simplify143.0ms (1.4%)

prune228.0ms (2.2%)

localize14.0ms (0.1%)

series10.0ms (0.1%)

rewrite51.0ms (0.5%)

simplify144.0ms (1.4%)

prune268.0ms (2.5%)

regimes503.0ms (4.8%)

bsearch36.0ms (0.3%)

simplify3.0ms (0%)

end212.0ms (2%)

Profiling