Details

analyze56.0ms (0.2%)

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)

sample111.0ms (0.3%)

Algorithm

1×

intervals

Symmetry

(sort alpha beta)

Results

31.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 126 to 65 computations (48.4% saved)

simplify39.0ms (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

prune7.0ms (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)

localize14.0ms (0%)

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)))
✓	37.3b	(/.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))
✓	45.2b	(/.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))))

series3.7s (10.5%)

Counts

4 → 144

Calls

4 calls:

3.1s	(/.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))
538.0ms	(/.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))))
59.0ms	(.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
16.0ms	(*.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite53.0ms (0.1%)

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:

11.0ms	(/.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))
9.0ms	(/.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))))
9.0ms	(.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)))

simplify458.0ms (1.3%)

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

prune1.2s (3.3%)

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

10.8b

Counts

297 → 9

Alt Table

Status	Error	Program
	58.8b	(/.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))
	40.9b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.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))
	53.0b	(/.f64 (.f64 (sqrt.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))))) (sqrt.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))
	57.0b	(/.f64 (-.f64 (fma.f64 i alpha (.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (/.f64 (.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	55.0b	(/.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)))
▶	19.0b	1/16
	53.1b	(.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (/.f64 (cbrt.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)))
	41.9b	(/.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))
	40.9b	(/.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))

Compiler

Compiled 63749 to 36735 computations (42.4% saved)

localize0.0ms (0%)

prune32.0ms (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

10.8b

Counts

9 → 9

Alt Table

Status	Error	Program
	58.8b	(/.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))
	40.9b	(/.f64 (.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (/.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))
	53.0b	(/.f64 (.f64 (sqrt.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))))) (sqrt.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))
	57.0b	(/.f64 (-.f64 (fma.f64 i alpha (.f64 i i)) (fma.f64 2 (/.f64 (pow.f64 i 3) beta) (fma.f64 3 (/.f64 (.f64 (.f64 i i) alpha) beta) (/.f64 (.f64 i (*.f64 alpha alpha)) beta)))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	55.0b	(/.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)))
✓	19.0b	1/16
	53.1b	(.f64 (.f64 (cbrt.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))))) (cbrt.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)))))) (/.f64 (cbrt.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)))
	41.9b	(/.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))
▶	40.9b	(/.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))

Compiler

Compiled 916 to 402 computations (56.1% saved)

localize20.0ms (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)))
✓	4.5b	(/.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))))
✓	37.3b	(/.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))
✓	41.4b	(/.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)))

series3.4s (9.5%)

Counts

3 → 108

Calls

3 calls:

2.8s

(/.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))

284.0ms

(/.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)))

262.0ms

(/.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))))

rewrite58.0ms (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:

11.0ms

(/.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))

9.0ms

(/.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))))

4.0ms

(/.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)))

simplify524.0ms (1.5%)

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 → 318

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3034	56371
1	5017	56371

prune1.4s (4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	365	6	371
Fresh	5	2	7
Picked	1	0	1
Done	0	1	1
Total	371	9	380

Error

10.8b

Counts

380 → 9

Alt Table

Status	Error	Program
	42.1b	(/.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 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))))))
	41.2b	(.f64 (/.f64 (/.f64 i (/.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 (+.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))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (cbrt.f64 (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))))
	41.1b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (.f64 (.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))) (.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (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))
	58.8b	(/.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))
	41.1b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (pow.f64 (+.f64 beta (.f64 2 i)) 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))
✓	19.0b	1/16
▶	40.9b	(.f64 (/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))))
	41.9b	(/.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))
	41.1b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (cbrt.f64 (.f64 (.f64 (/.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))) (/.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)))) (/.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))

Compiler

Compiled 75120 to 41748 computations (44.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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)))
✓	0.1b	(.f64 (/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))))
✓	35.2b	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
✓	39.9b	(sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

series10.0s (28.3%)

Counts

4 → 112

Calls

4 calls:

6.9s	(/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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)))
2.9s	(.f64 (/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))))
204.0ms	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))
80.0ms	(sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

rewrite4.4s (12.5%)

Algorithm

1×	rewrite-expression-head

Rules

4626×	`times-frac_binary64`
2518×	`*-un-lft-identity_binary64`
2346×	`add-sqr-sqrt_binary64`
1858×	`add-cube-cbrt_binary64`
1509×	`sqrt-prod_binary64`

Counts

4 → 1803

Calls

4 calls:

2.8s	(.f64 (/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))))
21.0ms	(/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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)))
1.0ms	(sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
1.0ms	(sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))

simplify2.3s (6.6%)

Algorithm

1×	egg-herbie

Counts

1915 → 1205

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5323	290663

prune3.5s (10%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1281	4	1285
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	1286	8	1294

Error

10.8b

Counts

1294 → 8

Alt Table

Status	Error	Program
	40.9b	(.f64 (/.f64 (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta))) 1) (.f64 (/.f64 (/.f64 i (/.f64 1 (sqrt.f64 (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))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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)))))
	40.9b	(/.f64 (.f64 (/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))) (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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)))
	58.8b	(/.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))
✓	19.0b	1/16
	42.8b	(.f64 (.f64 (/.f64 (/.f64 i (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))) (/.f64 (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta))) (sqrt.f64 (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 1 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))))) (sqrt.f64 (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))))
	41.9b	(/.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))
	42.1b	(/.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 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))))))
	40.9b	(.f64 (/.f64 (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (/.f64 i (/.f64 1 (sqrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))))))) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (sqrt.f64 (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))))

Compiler

Compiled 196260 to 87693 computations (55.3% saved)

regimes1.9s (5.4%)

Accuracy

Total 3.1b remaining (23.1%)

Threshold costs 0b (0%)

Counts

217 → 2

Compiler

Compiled 60684 to 27421 computations (54.8% saved)

bsearch40.0ms (0.1%)

Steps

Iters	Range		Point
4	8.567079605378714e+110	1.7056480118816137e+111	8.753749276189037e+110

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	62
1	32	62
2	32	62

end8.0ms (0%)

Compiler: Compiled 138 to 81 computations (41.3% saved)

sample2.0s (5.8%)

Algorithm

1×

intervals

Results

957.0ms	8000×	body	128	valid
206.0ms	8000×	pre	128	true

Compiler

Compiled 588 to 286 computations (51.4% saved)

Details

analyze56.0ms (0.2%)

sample111.0ms (0.3%)

simplify39.0ms (0.1%)

prune7.0ms (0%)

localize14.0ms (0%)

series3.7s (10.5%)

rewrite53.0ms (0.1%)

simplify458.0ms (1.3%)

prune1.2s (3.3%)

localize0.0ms (0%)

prune32.0ms (0.1%)

localize20.0ms (0.1%)

series3.4s (9.5%)

rewrite58.0ms (0.2%)

simplify524.0ms (1.5%)

prune1.4s (4%)

localize20.0ms (0.1%)

series10.0s (28.3%)

rewrite4.4s (12.5%)

simplify2.3s (6.6%)

prune3.5s (10%)

regimes1.9s (5.4%)

bsearch40.0ms (0.1%)

simplify3.0ms (0%)

end8.0ms (0%)

sample2.0s (5.8%)

Profiling