Details

analyze61.0ms (0.8%)

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 (20.8%)

Symmetry

(sort alpha beta)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify41.0ms (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

53.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	53.5b	(/.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

▶

53.5b

(/.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)

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)))
✓	38.1b	(/.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))
✓	45.7b	(/.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))))

series1.5s (18.8%)

Counts

4 → 144

Calls

4 calls:

1.3s	(/.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))
134.0ms	(/.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))))
35.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
13.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite93.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

582×	`prod-diff_binary64`
192×	`add-sqr-sqrt_binary64`
182×	`log1p-expm1-u_binary64`
182×	`expm1-log1p-u_binary64`
178×	`add-cbrt-cube_binary64`

Counts

4 → 113

Calls

4 calls:

89.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
89.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
89.0ms	(/.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))
89.0ms	(/.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))))

Iterations

Useful iterations: 0 (0.0ms)

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

simplify382.0ms (4.8%)

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

prune1.6s (20.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	258	10	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	259	10	269

Error

11.8b

Counts

269 → 10

Alt Table

Status	Error	Program
	59.0b	(/.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))
	41.4b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) 1) (/.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))
▶	19.4b	1/16
	56.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	41.4b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (/.f64 (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))))
	53.7b	(/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) 2) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (cbrt.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)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	23.0b	(-.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)))))
	41.4b	(/.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))
	27.7b	(-.f64 (+.f64 1/16 (fma.f64 1/64 (/.f64 1 (.f64 i i)) (fma.f64 1/32 (/.f64 (pow.f64 beta 3) (pow.f64 i 3)) (fma.f64 1/32 (/.f64 (pow.f64 alpha 3) (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (/.f64 (pow.f64 i 3) alpha)) (/.f64 (.f64 beta (.f64 alpha alpha)) (pow.f64 i 3)))))))) (fma.f64 1/64 (/.f64 beta (pow.f64 i 3)) (fma.f64 1/64 (/.f64 alpha (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))))))
	53.6b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 59501 to 35756 computations (39.9% saved)

localize0.0ms (0%)

prune29.0ms (0.4%)

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

11.8b

Counts

10 → 10

Alt Table

Status	Error	Program
	59.0b	(/.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))
	41.4b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) 1) (/.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))
✓	19.4b	1/16
	56.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	41.4b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (/.f64 (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))))
	53.7b	(/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) 2) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (cbrt.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)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	23.0b	(-.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)))))
	41.4b	(/.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))
	27.7b	(-.f64 (+.f64 1/16 (fma.f64 1/64 (/.f64 1 (.f64 i i)) (fma.f64 1/32 (/.f64 (pow.f64 beta 3) (pow.f64 i 3)) (fma.f64 1/32 (/.f64 (pow.f64 alpha 3) (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (/.f64 (pow.f64 i 3) alpha)) (/.f64 (.f64 beta (.f64 alpha alpha)) (pow.f64 i 3)))))))) (fma.f64 1/64 (/.f64 beta (pow.f64 i 3)) (fma.f64 1/64 (/.f64 alpha (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))))))
	53.6b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 896 to 472 computations (47.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (*.f64 i i))))
✓	0.9b	(/.f64 1 (*.f64 i i))
✓	2.3b	(/.f64 (.f64 alpha alpha) (.f64 i i))
✓	20.3b	(/.f64 (.f64 beta beta) (.f64 i i))

series151.0ms (1.9%)

Counts

4 → 96

Calls

4 calls:

87.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (*.f64 i i))))
31.0ms	(/.f64 (.f64 beta beta) (.f64 i i))
30.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
2.0ms	(/.f64 1 (*.f64 i i))

rewrite98.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

262×	`expm1-udef_binary64`
262×	`log1p-udef_binary64`
156×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Counts

4 → 121

Calls

4 calls:

94.0ms	(.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (*.f64 i i))))
94.0ms	(/.f64 1 (*.f64 i i))
94.0ms	(/.f64 (.f64 alpha alpha) (.f64 i i))
94.0ms	(/.f64 (.f64 beta beta) (.f64 i i))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	52
1	318	34
2	4488	34
3	5170	34

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

756×	`associate-/l/_binary64`
610×	`associate-*l/_binary64`
594×	`fma-def_binary64`
561×	`associate-l_binary64`
479×	`unswap-sqr_binary64`

Counts

217 → 134

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	1392
1	45	1392
2	99	1302
3	294	1152
4	1252	1152
5	4266	1152
6	5486	1152

prune197.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	134	10	144

Error

11.7b

Counts

144 → 10

Alt Table

Status	Error	Program
	59.0b	(/.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))
	41.4b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) 1) (/.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))
✓	19.4b	1/16
	56.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
▶	19.6b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (pow.f64 (*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i))) 2))
	41.4b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (/.f64 (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))))
	53.7b	(/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) 2) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (cbrt.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)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.4b	(/.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))
	27.7b	(-.f64 (+.f64 1/16 (fma.f64 1/64 (/.f64 1 (.f64 i i)) (fma.f64 1/32 (/.f64 (pow.f64 beta 3) (pow.f64 i 3)) (fma.f64 1/32 (/.f64 (pow.f64 alpha 3) (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (/.f64 (pow.f64 i 3) alpha)) (/.f64 (.f64 beta (.f64 alpha alpha)) (pow.f64 i 3)))))))) (fma.f64 1/64 (/.f64 beta (pow.f64 i 3)) (fma.f64 1/64 (/.f64 alpha (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))))))
	53.6b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 4794 to 2530 computations (47.2% saved)

localize31.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (/.f64 beta i) (/.f64 alpha i))
✓	0.2b	(pow.f64 (*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i))) 2)
✓	0.4b	(*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))
	0.9b	(/.f64 1 (*.f64 i i))

series215.0ms (2.7%)

Counts

3 → 108

Calls

3 calls:

143.0ms	(pow.f64 (*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i))) 2)
44.0ms	(*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))
27.0ms	(hypot.f64 (/.f64 beta i) (/.f64 alpha i))

rewrite60.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

574×	`log-prod_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
191×	`log-pow_binary64`
138×	`prod-diff_binary64`

Counts

3 → 69

Calls

3 calls:

58.0ms	(hypot.f64 (/.f64 beta i) (/.f64 alpha i))
58.0ms	(pow.f64 (*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i))) 2)
58.0ms	(*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	254	41
2	2870	41
3	5152	41

simplify90.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

707×	`associate-/l*_binary64`
557×	`associate-/r*_binary64`
349×	`fma-def_binary64`
342×	`fma-neg_binary64`
314×	`associate-*l/_binary64`

Counts

177 → 146

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	3194
1	408	2630
2	1431	2454
3	4984	2454
4	5114	2454

prune301.0ms (3.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	170	11	181

Error

11.7b

Counts

181 → 11

Alt Table

Status	Error	Program
	59.0b	(/.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))
	41.4b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) 1) (/.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))
	19.9b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 1/32) (pow.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) 2))) (cbrt.f64 (pow.f64 (exp.f64 1/32) (pow.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 1/32) (pow.f64 (hypot.f64 (/.f64 beta i) (/.f64 alpha i)) 2))))))
✓	19.4b	1/16
	56.6b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
✓	19.6b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (pow.f64 (*.f64 (sqrt.f64 1/32) (hypot.f64 (/.f64 beta i) (/.f64 alpha i))) 2))
	41.4b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (/.f64 (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))))
	53.7b	(/.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) 2) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (cbrt.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)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	41.4b	(/.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))
	27.7b	(-.f64 (+.f64 1/16 (fma.f64 1/64 (/.f64 1 (.f64 i i)) (fma.f64 1/32 (/.f64 (pow.f64 beta 3) (pow.f64 i 3)) (fma.f64 1/32 (/.f64 (pow.f64 alpha 3) (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (/.f64 (pow.f64 i 3) alpha)) (/.f64 (.f64 beta (.f64 alpha alpha)) (pow.f64 i 3)))))))) (fma.f64 1/64 (/.f64 beta (pow.f64 i 3)) (fma.f64 1/64 (/.f64 alpha (pow.f64 i 3)) (.f64 1/32 (+.f64 (/.f64 (.f64 beta beta) (.f64 i i)) (/.f64 (.f64 alpha alpha) (.f64 i i)))))))
	53.6b	(.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))) (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) -2) (sqrt.f64 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1))))

Compiler

Compiled 5698 to 3536 computations (37.9% saved)

regimes954.0ms (12%)

Accuracy

Total 1.6b remaining (12.4%)

Threshold costs 0b (0%)

Counts

113 → 3

Compiler

Compiled 21552 to 12469 computations (42.1% saved)

bsearch63.0ms (0.8%)

Steps

Iters	Range		Point
8	4.7035865401146843e+123	2.4753143962637755e+126	2.4513853694972384e+126
6	1.9300181125297583e+84	1.1396334000464876e+85	1.0643669320506455e+85

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	101
1	39	101
2	38	101

end257.0ms (3.2%)

Remove: (sort alpha beta)
Compiler: Compiled 797 to 431 computations (45.9% saved)

Details

analyze61.0ms (0.8%)

sample1.6s (20.8%)

simplify41.0ms (0.5%)

prune4.0ms (0%)

localize15.0ms (0.2%)

series1.5s (18.8%)

rewrite93.0ms (1.2%)

simplify382.0ms (4.8%)

prune1.6s (20.7%)

localize0.0ms (0%)

prune29.0ms (0.4%)

localize18.0ms (0.2%)

series151.0ms (1.9%)

rewrite98.0ms (1.2%)

simplify88.0ms (1.1%)

prune197.0ms (2.5%)

localize31.0ms (0.4%)

series215.0ms (2.7%)

rewrite60.0ms (0.8%)

simplify90.0ms (1.1%)

prune301.0ms (3.8%)

regimes954.0ms (12%)

bsearch63.0ms (0.8%)

simplify3.0ms (0%)

end257.0ms (3.2%)

Profiling