Details

analyze61.0ms (0.3%)

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)

sample1.9s (8.8%)

Symmetry

(sort alpha beta)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify43.0ms (0.2%)

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

53.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	53.0b	(/.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

▶

53.0b

(/.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)))
✓	37.2b	(/.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))
✓	45.1b	(/.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))))

series3.3s (14.8%)

Counts

4 → 144

Calls

4 calls:

2.9s	(/.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))
272.0ms	(/.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))))
50.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
17.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

61×	`add-cbrt-cube_binary64`
61×	`add-exp-log_binary64`
22×	`cbrt-unprod_binary64`
22×	`prod-exp_binary64`
21×	`add-sqr-sqrt_binary64`

Counts

4 → 132

Calls

4 calls:

12.0ms	(/.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))
10.0ms	(/.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))))
8.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
3.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify473.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-def_binary64`
507×	`associate-/l*_binary64`
344×	`times-frac_binary64`
54×	`sqr-pow_binary64`
54×	`sub-neg_binary64`

Counts

276 → 296

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2566	48816
1	5158	48816

prune1.6s (7.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	287	9	296
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	288	9	297

Error

8.4b

Counts

297 → 9

Alt Table

Status	Error	Program
	58.7b	(/.f64 (-.f64 (+.f64 (/.f64 (.f64 i (pow.f64 alpha 3)) (.f64 beta beta)) (fma.f64 5 (/.f64 (pow.f64 i 4) (.f64 beta beta)) (fma.f64 10 (/.f64 (.f64 (pow.f64 i 3) alpha) (.f64 beta beta)) (fma.f64 i alpha (+.f64 (.f64 i i) (.f64 6 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (.f64 beta beta)))))))) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (fma.f64 30 (/.f64 (.f64 (pow.f64 i 4) alpha) (pow.f64 beta 3)) (+.f64 (/.f64 (.f64 i (.f64 alpha alpha)) beta) (fma.f64 12 (/.f64 (pow.f64 i 5) (pow.f64 beta 3)) (+.f64 (/.f64 (.f64 i (pow.f64 alpha 4)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 3)) (.f64 26 (/.f64 (.f64 (pow.f64 i 3) (.f64 alpha alpha)) (pow.f64 beta 3))))))))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	40.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
	40.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.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))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
	53.9b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
	40.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (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))
▶	17.6b	1/16
	47.3b	(/.f64 (-.f64 (fma.f64 1/4 (.f64 i alpha) (fma.f64 1/8 (.f64 beta alpha) (.f64 1/4 (+.f64 (.f64 i i) (.f64 beta i))))) (.f64 1/16 (+.f64 (.f64 alpha alpha) (.f64 beta beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	59.7b	(/.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))
	43.1b	(/.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))

Compiler

Compiled 63771 to 36835 computations (42.2% saved)

localize0.0ms (0%)

prune18.0ms (0.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	8	8
Picked	1	1
Done	0	0
Total	9	9

Error

8.4b

Counts

9 → 9

Alt Table

Status	Error	Program
	58.7b	(/.f64 (-.f64 (+.f64 (/.f64 (.f64 i (pow.f64 alpha 3)) (.f64 beta beta)) (fma.f64 5 (/.f64 (pow.f64 i 4) (.f64 beta beta)) (fma.f64 10 (/.f64 (.f64 (pow.f64 i 3) alpha) (.f64 beta beta)) (fma.f64 i alpha (+.f64 (.f64 i i) (.f64 6 (/.f64 (.f64 (.f64 i i) (.f64 alpha alpha)) (.f64 beta beta)))))))) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (fma.f64 30 (/.f64 (.f64 (pow.f64 i 4) alpha) (pow.f64 beta 3)) (+.f64 (/.f64 (.f64 i (.f64 alpha alpha)) beta) (fma.f64 12 (/.f64 (pow.f64 i 5) (pow.f64 beta 3)) (+.f64 (/.f64 (.f64 i (pow.f64 alpha 4)) (pow.f64 beta 3)) (fma.f64 9 (/.f64 (.f64 (.f64 i i) (pow.f64 alpha 3)) (pow.f64 beta 3)) (.f64 26 (/.f64 (.f64 (pow.f64 i 3) (.f64 alpha alpha)) (pow.f64 beta 3))))))))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	40.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
	40.2b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.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))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
	53.9b	(/.f64 (.f64 i (.f64 (+.f64 (.f64 i i) (.f64 beta i)) (+.f64 beta i))) (.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 2) (-.f64 (+.f64 (.f64 beta beta) (.f64 4 (+.f64 (.f64 i i) (.f64 beta i)))) 1)))
	40.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (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))
✓	17.6b	1/16
	47.3b	(/.f64 (-.f64 (fma.f64 1/4 (.f64 i alpha) (fma.f64 1/8 (.f64 beta alpha) (.f64 1/4 (+.f64 (.f64 i i) (.f64 beta i))))) (.f64 1/16 (+.f64 (.f64 alpha alpha) (.f64 beta beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	59.7b	(/.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))
	43.1b	(/.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))

Compiler

Compiled 938 to 502 computations (46.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	4.9b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
✓	30.9b	(/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
✓	35.1b	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
✓	35.8b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

series3.5s (15.9%)

Counts

4 → 144

Calls

4 calls:

2.8s	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
540.0ms	(/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
70.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
54.0ms	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite221.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

1058×	`times-frac_binary64`
426×	`*-un-lft-identity_binary64`
426×	`add-sqr-sqrt_binary64`
426×	`add-cube-cbrt_binary64`
85×	`div-inv_binary64`

Counts

4 → 517

Calls

4 calls:

19.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
6.0ms	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
5.0ms	(/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
2.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify881.0ms (4%)

Algorithm

1×	egg-herbie

Rules

854×	`fma-def_binary64`
368×	`times-frac_binary64`
13×	`cube-mult_binary64`
13×	`unpow2_binary64`
13×	`unpow3_binary64`

Counts

661 → 700

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3820	103095
1	5417	103095

prune1.7s (7.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	696	4	700
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	700	9	709

Error

8.4b

Counts

709 → 9

Alt Table

Status	Error	Program
▶	40.1b	(.f64 (/.f64 1 (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))))
	40.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (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))
	59.7b	(/.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))
	40.7b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))))
	40.3b	(.f64 (/.f64 (/.f64 i 1) (/.f64 1 (/.f64 1 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))))
✓	40.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
✓	17.6b	1/16
	47.3b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 4 beta (fma.f64 8 i (.f64 4 alpha))))
	43.1b	(/.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))

Compiler

Compiled 109018 to 53969 computations (50.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))))
✓	0.1b	(.f64 (/.f64 1 (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))))
	35.1b	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
✓	40.6b	(/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

series3.7s (16.7%)

Counts

3 → 108

Calls

3 calls:

3.1s

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

334.0ms

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

265.0ms

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

rewrite97.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

197×	`times-frac_binary64`
135×	`add-sqr-sqrt_binary64`
134×	`add-exp-log_binary64`
106×	`*-un-lft-identity_binary64`
102×	`add-cube-cbrt_binary64`

Counts

3 → 240

Calls

3 calls:

28.0ms

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

4.0ms

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

2.0ms

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

simplify734.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-def_binary64`
370×	`times-frac_binary64`
69×	`sub-neg_binary64`
65×	`sqr-pow_binary64`
13×	`unpow2_binary64`

Counts

348 → 444

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	3122	65491
1	4977	63055
2	5033	63055

prune1.6s (7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	506	3	509
Fresh	3	3	6
Picked	1	0	1
Done	0	2	2
Total	510	8	518

Error

6.1b

Counts

518 → 8

Alt Table

Status	Error	Program
	59.7b	(/.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))
	40.7b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (.f64 (/.f64 (.f64 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta))) (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))))
	53.8b	(.f64 (/.f64 (+.f64 i alpha) beta) (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))))
	40.1b	(.f64 (/.f64 1 (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (*.f64 (/.f64 i 1) (/.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))) (fma.f64 i 2 (+.f64 alpha beta))))
✓	17.6b	1/16
	40.3b	(.f64 (.f64 (/.f64 1 (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (/.f64 i (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))
✓	40.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))))
	43.1b	(/.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))

Compiler

Compiled 89896 to 48585 computations (46% saved)

regimes1.9s (8.7%)

Accuracy

Total 3.8b remaining (29.7%)

Threshold costs 0b (0%)

Counts

199 → 2

Compiler

Compiled 53524 to 28005 computations (47.7% saved)

bsearch58.0ms (0.3%)

Steps

Iters	Range		Point
7	3.8755206345416724e+117	1.5614586996851896e+119	8.978405601751764e+118

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	77
1	32	77
2	31	77

end174.0ms (0.8%)

Remove: (sort alpha beta)
Compiler: Compiled 583 to 279 computations (52.1% saved)

Details

analyze61.0ms (0.3%)

sample1.9s (8.8%)

simplify43.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0.1%)

series3.3s (14.8%)

rewrite56.0ms (0.3%)

simplify473.0ms (2.1%)

prune1.6s (7.4%)

localize0.0ms (0%)

prune18.0ms (0.1%)

localize16.0ms (0.1%)

series3.5s (15.9%)

rewrite221.0ms (1%)

simplify881.0ms (4%)

prune1.7s (7.7%)

localize16.0ms (0.1%)

series3.7s (16.7%)

rewrite97.0ms (0.4%)

simplify734.0ms (3.3%)

prune1.6s (7%)

regimes1.9s (8.7%)

bsearch58.0ms (0.3%)

simplify2.0ms (0%)

end174.0ms (0.8%)

Profiling