Details

analyze50.0ms (0.4%)

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 (12.2%)

Symmetry

(sort alpha beta)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify38.0ms (0.3%)

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

54.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	54.3b	(/.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

▶

54.3b

(/.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)))
✓	36.1b	(/.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))
✓	46.6b	(/.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))))

series1.4s (11.3%)

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))
130.0ms	(/.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)))

rewrite96.0ms (0.8%)

Algorithm

2×	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 → 116

Calls

4 calls:

90.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
90.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
90.0ms	(/.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))
90.0ms	(/.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
0	0	0
1	0	0

simplify395.0ms (3.1%)

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

260 → 271

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2376	40163
1	5421	40163

prune1.0s (8.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	263	8	271
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	264	8	272

Error

11.2b

Counts

272 → 8

Alt Table

Status	Error	Program
	50.1b	(.f64 (/.f64 i (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	58.4b	(/.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))
	55.7b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
▶	19.3b	1/16
	54.3b	(/.f64 (.f64 (/.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))) (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	39.2b	(/.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))
	61.5b	(/.f64 (/.f64 (.f64 (pow.f64 beta 2) (.f64 (+.f64 i alpha) 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))

Compiler

Compiled 59304 to 35625 computations (39.9% saved)

localize0.0ms (0%)

prune12.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

11.2b

Counts

8 → 8

Alt Table

Status	Error	Program
	50.1b	(.f64 (/.f64 i (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	58.4b	(/.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))
	55.7b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
✓	19.3b	1/16
	54.3b	(/.f64 (.f64 (/.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))) (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	39.2b	(/.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))
	61.5b	(/.f64 (/.f64 (.f64 (pow.f64 beta 2) (.f64 (+.f64 i alpha) 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))

Compiler

Compiled 572 to 304 computations (46.9% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
✓	3.8b	(.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)))))
✓	36.1b	(/.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))
✓	40.3b	(/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

series1.5s (11.9%)

Counts

4 → 144

Calls

4 calls:

1.1s	(/.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))
182.0ms	(.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)))))
135.0ms	(/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
135.0ms	(/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))

rewrite91.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

255×	`prod-diff_binary64`
205×	`add-sqr-sqrt_binary64`
195×	`log1p-expm1-u_binary64`
195×	`expm1-log1p-u_binary64`
190×	`add-cbrt-cube_binary64`

Counts

4 → 125

Calls

4 calls:

86.0ms	(/.f64 1 (/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
86.0ms	(.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)))))
86.0ms	(/.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))
86.0ms	(/.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	151
1	420	148
2	4761	148
3	5211	148
0	0	0
1	0	0

simplify440.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

954×	`fma-def_binary64`
361×	`times-frac_binary64`
76×	`sub-neg_binary64`
67×	`sqr-pow_binary64`
13×	`unpow2_binary64`

Counts

269 → 313

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3163	49600
1	5099	49600

prune1.9s (14.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	311	2	313
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	312	9	321

Error

11.2b

Counts

321 → 9

Alt Table

Status	Error	Program
	50.1b	(.f64 (/.f64 i (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
✓	39.2b	(/.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))
	39.3b	(.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))) (/.f64 1 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	58.4b	(/.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))
	55.7b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
✓	19.3b	1/16
	54.3b	(/.f64 (.f64 (/.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))) (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	39.2b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 72323 to 43157 computations (40.3% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
✓	3.8b	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2)))
✓	33.5b	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	36.1b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

series1.5s (11.9%)

Counts

4 → 112

Calls

4 calls:

1.0s	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
257.0ms	(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
143.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2)))
103.0ms	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

rewrite83.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

252×	`prod-diff_binary64`
213×	`add-sqr-sqrt_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`
198×	`add-cbrt-cube_binary64`

Counts

4 → 109

Calls

4 calls:

80.0ms	(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
80.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2)))
80.0ms	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
80.0ms	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	145
1	440	136
2	4917	136
3	5328	136
0	0	0
1	0	0

simplify367.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

856×	`fma-def_binary64`
493×	`associate-/l*_binary64`
333×	`times-frac_binary64`
63×	`sub-neg_binary64`
61×	`sqr-pow_binary64`

Counts

221 → 280

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2822	42697
1	5484	42697

prune1.2s (9.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	280	0	280
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	280	9	289

Error

11.2b

Counts

289 → 9

Alt Table

Status	Error	Program
	50.1b	(.f64 (/.f64 i (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)) (/.f64 (.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2)))
	55.0b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
✓	39.2b	(/.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))
	39.3b	(.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))) (/.f64 1 (+.f64 (pow.f64 (fma.f64 i 2 (+.f64 alpha beta)) 2) -1)))
	58.4b	(/.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))
	55.7b	(-.f64 (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (/.f64 (.f64 i alpha) (.f64 beta beta))) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (*.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))
✓	19.3b	1/16
	54.3b	(/.f64 (.f64 (/.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))) (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	39.2b	(/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 1 (pow.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) 2))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 65277 to 39673 computations (39.2% saved)

regimes510.0ms (4%)

Accuracy

Total 4.6b remaining (31.1%)

Threshold costs 0b (0%)

Counts

67 → 4

Compiler

Compiled 12904 to 6985 computations (45.9% saved)

bsearch63.0ms (0.5%)

Steps

Iters	Range		Point
5	2.2103164570154006e+104	4.91789605599852e+104	2.2365987727338013e+104
4	5.769104402683842e+80	9.045710042806379e+80	5.87149832893767e+80
6	5.553915828965183e+63	2.5180090088112775e+64	2.4951242434289404e+64

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	148
1	55	148
2	54	148

end332.0ms (2.6%)

Compiler: Compiled 758 to 395 computations (47.9% saved)

Details

analyze50.0ms (0.4%)

sample1.6s (12.2%)

simplify38.0ms (0.3%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series1.4s (11.3%)

rewrite96.0ms (0.8%)

simplify395.0ms (3.1%)

prune1.0s (8.2%)

localize0.0ms (0%)

prune12.0ms (0.1%)

localize16.0ms (0.1%)

series1.5s (11.9%)

rewrite91.0ms (0.7%)

simplify440.0ms (3.5%)

prune1.9s (14.8%)

localize18.0ms (0.1%)

series1.5s (11.9%)

rewrite83.0ms (0.7%)

simplify367.0ms (2.9%)

prune1.2s (9.8%)

regimes510.0ms (4%)

bsearch63.0ms (0.5%)

simplify4.0ms (0%)

end332.0ms (2.6%)

Profiling