Details

analyze54.0ms (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 (13.7%)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 134 to 70 computations (47.8% saved)

preprocess31.0ms (0.3%)

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)

simplify19.0ms (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%)

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

48.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	54.3b	(/.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))
▶	48.9b	(.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))))

Status

Error

Program

54.3b

(/.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))

▶

48.9b

(*.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))))

Compiler

Compiled 315 to 155 computations (50.8% saved)

localize15.0ms (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)))
✓	0.1b	(*.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))
✓	7.1b	(.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))))
✓	46.8b	(/.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)))

series1.4s (13.2%)

Counts

4 → 144

Calls

36 calls:

317.0ms	(.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
315.0ms	(.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
260.0ms	(.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
127.0ms	(/.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

rewrite53.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

216×	`add-sqr-sqrt_binary64`
212×	`*-un-lft-identity_binary64`
212×	`pow1_binary64`
200×	`add-cbrt-cube_binary64`
200×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	161
1	411	146

Stop Event

1×	node limit

Counts

4 → 105

simplify368.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-def_binary64`
511×	`times-frac_binary64`
68×	`sub-neg_binary64`
56×	`sqr-pow_binary64`
12×	`distribute-lft-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2952	51722

Stop Event

1×	node limit

Counts

249 → 281

prune1.5s (13.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	273	8	281
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	275	8	283

Error

14.0b

Counts

283 → 8

Alt Table

Status	Error	Program
	45.3b	(.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)))
	42.1b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (exp.f64 (log.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))))
▶	22.2b	1/16
	40.5b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta)))))
	40.5b	(.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))))
	59.3b	(-.f64 (fma.f64 6 (/.f64 (.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (fma.f64 50 (/.f64 (.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (fma.f64 196 (/.f64 (.f64 (pow.f64 i 3) (.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 220 (/.f64 (.f64 (pow.f64 i 4) alpha) (pow.f64 beta 5)) (fma.f64 74 (/.f64 (.f64 (.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 5)) (fma.f64 15 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 5)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (fma.f64 5 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 88 (/.f64 (pow.f64 i 5) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (pow.f64 i 3) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (.f64 i (pow.f64 alpha 4)) (pow.f64 beta 5)) (.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))))))))))
	40.6b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
	55.0b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))

Compiler

Compiled 76266 to 46840 computations (38.6% saved)

localize0.0ms (0%)

prune19.0ms (0.2%)

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

14.0b

Counts

8 → 8

Alt Table

Status	Error	Program
	45.3b	(.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)))
	42.1b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (exp.f64 (log.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)))))
✓	22.2b	1/16
	40.5b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1)) (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta)))))
▶	40.5b	(.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))))
	59.3b	(-.f64 (fma.f64 6 (/.f64 (.f64 i (pow.f64 alpha 3)) (pow.f64 beta 4)) (fma.f64 25 (/.f64 (pow.f64 i 4) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i i) (.f64 beta beta)) (fma.f64 50 (/.f64 (.f64 (pow.f64 i 3) alpha) (pow.f64 beta 4)) (fma.f64 31 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (pow.f64 beta 4)) (+.f64 (/.f64 (.f64 i alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (fma.f64 196 (/.f64 (.f64 (pow.f64 i 3) (.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 220 (/.f64 (.f64 (pow.f64 i 4) alpha) (pow.f64 beta 5)) (fma.f64 74 (/.f64 (.f64 (.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 5)) (fma.f64 15 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 5)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) alpha) (pow.f64 beta 3)) (fma.f64 5 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 5)) (fma.f64 3 (/.f64 (.f64 i (.f64 alpha alpha)) (pow.f64 beta 3)) (fma.f64 88 (/.f64 (pow.f64 i 5) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (pow.f64 i 3) (pow.f64 beta 5)) (fma.f64 10 (/.f64 (.f64 i (pow.f64 alpha 4)) (pow.f64 beta 5)) (.f64 6 (/.f64 (pow.f64 i 3) (pow.f64 beta 3))))))))))))))
	40.6b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
	55.0b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (/.f64 (+.f64 i alpha) (pow.f64 beta 2)))

Compiler

Compiled 914 to 560 computations (38.7% saved)

localize24.0ms (0.2%)

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)))
✓	0.1b	(.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)))
✓	7.1b	(.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))))
✓	41.2b	(/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))

series1.7s (16%)

Counts

3 → 108

Calls

27 calls:

373.0ms	(.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
373.0ms	(.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
325.0ms	(.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
133.0ms	(.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
128.0ms	(.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

rewrite40.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

270×	`add-sqr-sqrt_binary64`
266×	`pow1_binary64`
265×	`*-un-lft-identity_binary64`
251×	`add-cbrt-cube_binary64`
251×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	132
1	543	132

Stop Event

1×	node limit

Counts

3 → 31

simplify392.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-def_binary64`
511×	`times-frac_binary64`
9×	`cube-mult_binary64`
9×	`unpow2_binary64`
9×	`unpow3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3152	55872

Stop Event

1×	node limit

Counts

139 → 176

prune1.4s (13.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	243	7	250
Fresh	5	1	6
Picked	1	0	1
Done	0	1	1
Total	249	9	258

Error

7.1b

Counts

258 → 9

Alt Table

Status	Error	Program
	40.5b	(.f64 (/.f64 (.f64 i (+.f64 beta i)) (+.f64 beta (.f64 2 i))) (.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))))
	40.6b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
	40.6b	(.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) (fma.f64 4 (.f64 i i) (.f64 4 (*.f64 beta i)))) 1))))
▶	21.9b	(.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))
✓	22.2b	1/16
	55.5b	(/.f64 (.f64 (+.f64 i alpha) i) (.f64 beta beta))
	25.9b	(-.f64 (+.f64 1/16 (.f64 1/64 (/.f64 1 (.f64 i i)))) (fma.f64 1/32 (/.f64 (.f64 beta beta) (.f64 i i)) (.f64 1/32 (/.f64 (.f64 alpha alpha) (*.f64 i i)))))
	47.1b	(.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 (+.f64 i alpha) beta)))
	40.7b	(.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))) 3) (.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))))

Compiler

Compiled 82251 to 51646 computations (37.2% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 i (+.f64 alpha (fma.f64 i 2 beta)))
✓	0.0b	(/.f64 1 (+.f64 alpha (fma.f64 i 2 beta)))
	0.1b	(*.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha 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))

series155.0ms (1.4%)

Counts

3 → 108

Calls

27 calls:

23.0ms	(.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
23.0ms	(.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
12.0ms	(.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
11.0ms	(.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
8.0ms	(.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	inf

rewrite36.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

188×	`add-sqr-sqrt_binary64`
182×	`*-un-lft-identity_binary64`
182×	`pow1_binary64`
177×	`add-cbrt-cube_binary64`
177×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	55
1	369	48

Stop Event

1×	node limit

Counts

3 → 82

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

668×	`times-frac_binary64`
662×	`fma-def_binary64`
588×	`associate-/l*_binary64`
206×	`+-commutative_binary64`
191×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	654	7661
1	2246	7489

Stop Event

1×	node limit

Counts

190 → 216

prune365.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	287	3	290
Fresh	1	6	7
Picked	1	0	1
Done	1	0	1
Total	290	9	299

Error

7.1b

Counts

299 → 9

Alt Table

Status	Error	Program
	40.5b	(.f64 (/.f64 (.f64 i (+.f64 beta i)) (+.f64 beta (.f64 2 i))) (.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))))
	40.6b	(.f64 (.f64 (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 i (+.f64 alpha beta))) (pow.f64 (sqrt.f64 (/.f64 (/.f64 (fma.f64 i (+.f64 (+.f64 i alpha) beta) (*.f64 alpha beta)) (+.f64 alpha (fma.f64 i 2 beta))) (+.f64 (pow.f64 (+.f64 alpha (fma.f64 i 2 beta)) 2) -1))) 2))
	23.1b	(.f64 (.f64 (-.f64 1/2 (.f64 1/4 (+.f64 (/.f64 alpha i) (/.f64 beta i)))) (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
	55.5b	(/.f64 (.f64 (+.f64 i alpha) i) (.f64 beta beta))
	23.0b	(-.f64 1/16 (fma.f64 1/32 (.f64 (/.f64 beta (.f64 i i)) alpha) (.f64 1/64 (+.f64 (.f64 (/.f64 beta i) (/.f64 beta i)) (*.f64 (/.f64 alpha i) (/.f64 alpha i))))))
	47.1b	(.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 (+.f64 i alpha) beta)))
	40.6b	(.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) (fma.f64 4 (.f64 i i) (.f64 4 (*.f64 beta i)))) 1))))
	22.2b	(.f64 (.f64 1/2 i) (*.f64 (/.f64 1 (+.f64 alpha (fma.f64 i 2 beta))) 1/4))
	40.7b	(.f64 (pow.f64 (cbrt.f64 (.f64 (+.f64 (+.f64 i alpha) beta) (/.f64 i (+.f64 alpha (fma.f64 i 2 beta))))) 3) (.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))))

Compiler

Compiled 15336 to 9091 computations (40.7% saved)

regimes1.2s (11.3%)

Accuracy

Total 8.7b remaining (63.6%)

Threshold costs 0b (0%)

Counts

159 → 2

Compiler

Compiled 30652 to 19009 computations (38% saved)

bsearch34.0ms (0.3%)

Algorithm

1×	binary-search

Calls

1 calls:

24.0ms

beta

Steps

Iters	Point		Range
2.6961695257071656e+174	∈ [	2.6634037250163645e+174	,	5.019001367555495e+175	]

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	81
1	38	81

Stop Event

1×

saturated

end313.0ms (2.9%)

Stop Event

1×

fuel

Compiler

Compiled 555 to 330 computations (40.5% saved)

Details

analyze54.0ms (0.5%)

sample1.5s (13.7%)

preprocess31.0ms (0.3%)

simplify19.0ms (0.2%)

prune5.0ms (0%)

localize15.0ms (0.1%)

series1.4s (13.2%)

rewrite53.0ms (0.5%)

simplify368.0ms (3.4%)

prune1.5s (13.8%)

localize0.0ms (0%)

prune19.0ms (0.2%)

localize24.0ms (0.2%)

series1.7s (16%)

rewrite40.0ms (0.4%)

simplify392.0ms (3.6%)

prune1.4s (13.2%)

localize11.0ms (0.1%)

series155.0ms (1.4%)

rewrite36.0ms (0.3%)

simplify101.0ms (0.9%)

prune365.0ms (3.4%)

regimes1.2s (11.3%)

bsearch34.0ms (0.3%)

simplify3.0ms (0%)

end313.0ms (2.9%)

Profiling