Details

analyze224.0ms (0.6%)

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 66 to 34 computations (48.5% saved)

sample97.0ms (0.2%)

Algorithm

1×

intervals

Results

54.0ms	256×	body	128	valid
12.0ms	256×	pre	128	true

Compiler

Compiled 125 to 64 computations (48.8% saved)

simplify59.0ms (0.1%)

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

prune8.0ms (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)

localize31.0ms (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)))
✓	40.4b	(/.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))
✓	45.0b	(/.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))))

rewrite97.0ms (0.2%)

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:

31.0ms	(/.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))
19.0ms	(/.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))))
19.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
4.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

series5.9s (14.8%)

Counts

4 → 144

Calls

4 calls:

5.3s	(/.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))
497.0ms	(/.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))))
106.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
48.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify1.0s (2.6%)

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 → 457

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2566	48816
1	5158	48816

prune2.9s (7.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	448	9	457
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	449	9	458

Error

8.1b

Counts

458 → 9

Alt Table

Status	Error	Program
	42.2b	(/.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)))))
	60.3b	(/.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))
	58.9b	(-.f64 (+.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)) (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 alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (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))))))
	42.2b	(/.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))
	58.2b	(-.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))))))
	42.3b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (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)))
	55.3b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	53.5b	(/.f64 1 (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.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))))))
▶	14.7b	1/16

Compiler

Compiled 63595 to 36755 computations (42.2% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify18.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune36.0ms (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

8.1b

Counts

9 → 9

Alt Table

Status	Error	Program
	42.2b	(/.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)))))
	60.3b	(/.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))
	58.9b	(-.f64 (+.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)) (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 alpha) (.f64 beta beta)) (/.f64 (.f64 i alpha) (pow.f64 beta 4))))))))) (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))))))
▶	42.2b	(/.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))
	58.2b	(-.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))))))
	42.3b	(.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (/.f64 (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)))
	55.3b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	53.5b	(/.f64 1 (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.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))))))
✓	14.7b	1/16

Compiler

Compiled 856 to 448 computations (47.7% saved)

localize34.0ms (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)))
✓	3.3b	(/.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))))
✓	40.4b	(/.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))
✓	42.4b	(/.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)))

rewrite93.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`times-frac_binary64`
58×	`add-cbrt-cube_binary64`
58×	`add-exp-log_binary64`
34×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`

Counts

3 → 143

Calls

3 calls:

24.0ms

(/.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))

21.0ms

(/.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))))

8.0ms

(/.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)))

series6.2s (15.5%)

Counts

3 → 108

Calls

3 calls:

5.2s

(/.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))

495.0ms

(/.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)))

493.0ms

(/.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))))

simplify1.4s (3.5%)

Algorithm

1×	egg-herbie

Rules

833×	`fma-def_binary64`
371×	`times-frac_binary64`
75×	`sub-neg_binary64`
65×	`sqr-pow_binary64`
60×	`associate-/l/_binary64`

Counts

251 → 399

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3034	56371
1	5017	56371

prune3.1s (7.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	505	4	509
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	510	8	518

Error

8.1b

Counts

518 → 8

Alt Table

Status	Error	Program
	42.2b	(/.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)))))
	60.3b	(/.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 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.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)))))
	58.2b	(-.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))))))
	42.2b	(.f64 (/.f64 i (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))) (/.f64 (/.f64 (+.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)))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
▶	42.2b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))
	44.9b	(/.f64 (.f64 1/4 (.f64 i i)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	14.7b	1/16

Compiler

Compiled 74665 to 41598 computations (44.3% saved)

localize38.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.3b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))))))
	38.2b	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	38.2b	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	40.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))

rewrite104.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-cbrt-cube_binary64`
97×	`add-exp-log_binary64`
47×	`cbrt-undiv_binary64`
47×	`div-exp_binary64`
29×	`times-frac_binary64`

Counts

3 → 125

Calls

3 calls:

33.0ms

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

28.0ms

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

2.0ms

(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

series5.8s (14.6%)

Counts

3 → 92

Calls

3 calls:

5.4s

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

251.0ms

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

179.0ms

(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

simplify547.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
520×	`associate-/l*_binary64`
352×	`times-frac_binary64`
72×	`sub-neg_binary64`
57×	`sqr-pow_binary64`

Counts

217 → 361

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2690	51810
1	5361	51810

prune2.4s (6.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	417	1	418
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	419	7	426

Error

8.1b

Counts

426 → 7

Alt Table

Status	Error	Program
	42.2b	(/.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)))))
	60.3b	(/.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))
	42.2b	(.f64 (sqrt.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))) (sqrt.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta)))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))))
	43.1b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (/.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)))))
	42.2b	(.f64 (/.f64 i (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))) (/.f64 (/.f64 (+.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)))) (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))
	44.9b	(/.f64 (.f64 1/4 (.f64 i i)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	14.7b	1/16

Compiler

Compiled 74430 to 40040 computations (46.2% saved)

regimes6.6s (16.5%)

Accuracy

Total 2.6b remaining (20.8%)

Threshold costs 0b (0%)

Compiler

Compiled 83688 to 44897 computations (46.4% saved)

bsearch49.0ms (0.1%)

Steps

Iters	Range		Point
5	8.581677762338824e+146	2.554300194427697e+147	1.1436716707325213e+147

Compiler

Compiled 4 to 3 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	94
1	27	94
2	27	94

end10.0ms (0%)

Remove: (sort alpha beta)
Compiler: Compiled 204 to 84 computations (58.8% saved)

sample3.1s (7.7%)

Algorithm

1×

intervals

Results

2.4s	8000×	body	128	valid
205.0ms	8000×	pre	128	true

Compiler

Compiled 498 to 222 computations (55.4% saved)

Details

analyze224.0ms (0.6%)

sample97.0ms (0.2%)

simplify59.0ms (0.1%)

prune8.0ms (0%)

localize31.0ms (0.1%)

rewrite97.0ms (0.2%)

series5.9s (14.8%)

simplify1.0s (2.6%)

prune2.9s (7.3%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify18.0ms (0%)

prune36.0ms (0.1%)

localize34.0ms (0.1%)

rewrite93.0ms (0.2%)

series6.2s (15.5%)

simplify1.4s (3.5%)

prune3.1s (7.8%)

localize38.0ms (0.1%)

rewrite104.0ms (0.3%)

series5.8s (14.6%)

simplify547.0ms (1.4%)

prune2.4s (6.1%)

regimes6.6s (16.5%)

bsearch49.0ms (0.1%)

simplify4.0ms (0%)

end10.0ms (0%)

sample3.1s (7.7%)

Profiling