Details

analyze49.0ms (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)

sample1.5s (15.3%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 134 to 70 computations (47.8% saved)

preprocess35.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

915×	`distribute-rgt-in_binary64`
897×	`distribute-lft-in_binary64`
304×	`fma-def_binary64`
241×	`times-frac_binary64`
202×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	300
1	246	268
2	1026	268
0	3	3
1	3	3

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort alpha beta)

Compiler

Compiled 56 to 27 computations (51.8% saved)

simplify21.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

684×	`associate-+l+_binary64`
483×	`associate-l_binary64`
418×	`associate-r_binary64`
369×	`times-frac_binary64`
337×	`associate-/l*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	75
1	67	67
2	332	67
3	2169	67

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

47.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	47.4b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
	52.5b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 (+.f64 alpha beta) i)) (+.f64 (.f64 beta alpha) (.f64 i (+.f64 (+.f64 alpha beta) i)))) (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i)))) (-.f64 (.f64 (+.f64 (+.f64 alpha beta) (.f64 2 i)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) 1))

Status

Error

Program

▶

47.4b

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

52.5b

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

Compiler

Compiled 315 to 155 computations (50.8% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))
✓	0.3b	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))
✓	4.2b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))
✓	45.7b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))

series1.5s (15.4%)

Counts

4 → 144

Calls

36 calls:

337.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))	alpha
331.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))	beta
268.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1))))	i
134.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))	beta
119.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (.f64 (+.f64 alpha (fma.f64 i 2 beta)) (fma.f64 (+.f64 alpha (fma.f64 i 2 beta)) (+.f64 alpha (fma.f64 i 2 beta)) -1)))	alpha

rewrite48.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

211×	`add-sqr-sqrt_binary64`
200×	`add-cbrt-cube_binary64`
200×	`log1p-expm1-u_binary64`
200×	`expm1-log1p-u_binary64`
195×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	152
1	411	137

Stop Event

1×	node limit

Counts

4 → 98

simplify362.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-def_binary64`
570×	`associate-/l*_binary64`
511×	`times-frac_binary64`
69×	`sub-neg_binary64`
56×	`sqr-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2906	51644

Stop Event

1×	node limit

Counts

242 → 276

prune1.6s (16.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	270	6	276
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	272	6	278

Error

8.8b

Counts

278 → 6

Alt Table

Status	Error	Program
	38.4b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 alpha (fma.f64 i 2 beta)))))
	38.1b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
▶	17.8b	1/16
	54.2b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	43.3b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))

Compiler

Compiled 75136 to 46190 computations (38.5% saved)

localize0.0ms (0%)

prune7.0ms (0.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	0	0
Total	6	6

Error

8.8b

Counts

6 → 6

Alt Table

Status	Error	Program
	38.4b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta))) 2) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta))) (+.f64 alpha (fma.f64 i 2 beta)))))
▶	38.1b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓	17.8b	1/16
	54.2b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	43.3b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))

Compiler

Compiled 348 to 200 computations (42.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 1 (+.f64 alpha (fma.f64 i 2 beta)))
	0.3b	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))
✓	4.2b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
✓	38.5b	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))

series1.3s (13.7%)

Counts

3 → 108

Calls

27 calls:

374.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))	alpha
362.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))	beta
280.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))	i
74.0ms	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))	alpha
42.0ms	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))	beta

rewrite39.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

251×	`log1p-expm1-u_binary64`
251×	`expm1-log1p-u_binary64`
250×	`add-cbrt-cube_binary64`
242×	`add-log-exp_binary64`
241×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	103
1	543	103

Stop Event

1×	node limit

Counts

3 → 52

simplify276.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

703×	`fma-def_binary64`
447×	`associate-/l*_binary64`
336×	`associate-/r*_binary64`
333×	`times-frac_binary64`
59×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2396	40224

Stop Event

1×	node limit

Counts

160 → 192

prune1.3s (13%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	258	3	261
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	259	8	267

Error

4.6b

Counts

267 → 8

Alt Table

Status	Error	Program
▶	17.8b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
✓	17.8b	1/16
	38.4b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (*.f64 beta i)))) -1))))
✓	38.1b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	54.2b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	43.3b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))
	49.0b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (+.f64 i alpha) beta)))

Compiler

Compiled 62142 to 38316 computations (38.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta)))
	0.2b	(/.f64 1 (+.f64 alpha (fma.f64 i 2 beta)))
✓	0.2b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
	0.3b	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))

series133.0ms (1.4%)

Counts

2 → 72

Calls

18 calls:

25.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))	beta	0
21.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))	alpha	0
13.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))	i	0
10.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))	beta	inf
10.0ms	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))	i	inf

rewrite42.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

182×	`add-sqr-sqrt_binary64`
177×	`log1p-expm1-u_binary64`
177×	`expm1-log1p-u_binary64`
176×	`add-cbrt-cube_binary64`
171×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	53
1	369	46

Stop Event

1×	node limit

Counts

2 → 78

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

656×	`times-frac_binary64`
613×	`associate-/l*_binary64`
522×	`fma-def_binary64`
420×	`associate-/r*_binary64`
190×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	589	6080
1	1994	5928

Stop Event

1×	node limit

Counts

150 → 167

prune360.0ms (3.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	295	3	298
Fresh	0	5	5
Picked	1	0	1
Done	1	1	2
Total	297	9	306

Error

4.6b

Counts

306 → 9

Alt Table

Status	Error	Program
	54.7b	(/.f64 (*.f64 (+.f64 i alpha) i) (pow.f64 beta 2))
	18.5b	(-.f64 1/16 (fma.f64 1/32 (.f64 (/.f64 alpha i) (/.f64 beta i)) (.f64 1/64 (+.f64 (.f64 (/.f64 beta i) (/.f64 beta i)) (.f64 (/.f64 alpha i) (/.f64 alpha i))))))
	49.0b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (+.f64 i alpha) beta)))
	17.8b	(.f64 (.f64 1/2 i) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
	38.4b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (*.f64 beta i)))) -1))))
✓	38.1b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))))
	54.2b	(/.f64 (+.f64 i alpha) (/.f64 (*.f64 beta beta) i))
	18.8b	(.f64 (.f64 (-.f64 1/2 (.f64 1/4 (+.f64 (/.f64 beta i) (/.f64 alpha i)))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
	43.3b	(.f64 (/.f64 (fma.f64 i alpha (.f64 i i)) (+.f64 (fma.f64 4 (.f64 i alpha) (+.f64 (.f64 alpha alpha) (.f64 4 (.f64 i i)))) -1)) (/.f64 (*.f64 i (+.f64 i alpha)) (pow.f64 (fma.f64 2 i alpha) 2)))

Compiler

Compiled 15641 to 9226 computations (41% saved)

regimes641.0ms (6.6%)

Accuracy

Total 7.7b remaining (59.6%)

Threshold costs 0b (0%)

Counts

86 → 3

Compiler

Compiled 13108 to 7981 computations (39.1% saved)

bsearch27.0ms (0.3%)

Algorithm

2×	binary-search

Calls

2 calls:

10.0ms	i
10.0ms	i

Steps

Iters	Point		Range
1.5892825401447096e+139	∈ [	2.0525073019388938e+138	,	2.0921160253234758e+139	]
5.9527315014016644e+60	∈ [	5.1721186770306776e+60	,	6.004772356359731e+60	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	98
1	51	98

Stop Event

1×

saturated

end312.0ms (3.2%)

Stop Event

1×

fuel

Compiler

Compiled 556 to 342 computations (38.5% saved)

Details

analyze49.0ms (0.5%)

sample1.5s (15.3%)

preprocess35.0ms (0.4%)

simplify21.0ms (0.2%)

prune5.0ms (0.1%)

localize15.0ms (0.2%)

series1.5s (15.4%)

rewrite48.0ms (0.5%)

simplify362.0ms (3.8%)

prune1.6s (16.8%)

localize0.0ms (0%)

prune7.0ms (0.1%)

localize23.0ms (0.2%)

series1.3s (13.7%)

rewrite39.0ms (0.4%)

simplify276.0ms (2.9%)

prune1.3s (13%)

localize12.0ms (0.1%)

series133.0ms (1.4%)

rewrite42.0ms (0.4%)

simplify78.0ms (0.8%)

prune360.0ms (3.7%)

regimes641.0ms (6.6%)

bsearch27.0ms (0.3%)

simplify4.0ms (0%)

end312.0ms (3.2%)

Profiling