Details

analyze54.0ms (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)

sample1.5s (7.9%)

Symmetry

(sort alpha beta)

Results

1.5s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify40.0ms (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

52.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	52.8b	(/.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

▶

52.8b

(/.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)

localize15.0ms (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)))
✓	36.9b	(/.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))
✓	44.9b	(/.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))))

series3.5s (17.9%)

Counts

4 → 144

Calls

4 calls:

3.2s	(/.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))
230.0ms	(/.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))))
46.0ms	(.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 (0.3%)

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:

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))
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))))
7.0ms	(.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)))

simplify418.0ms (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

prune1.2s (6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	289	7	296
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	290	7	297

Error

10.0b

Counts

297 → 7

Alt Table

Status	Error	Program
	63.8b	(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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))
▶	16.9b	1/16
	57.8b	(/.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))
	39.4b	(/.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)))))
	39.4b	(.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))))
	41.8b	(/.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 63337 to 36585 computations (42.2% saved)

localize0.0ms (0%)

prune10.0ms (0.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	6	6
Picked	1	1
Done	0	0
Total	7	7

Error

10.0b

Counts

7 → 7

Alt Table

Status	Error	Program
	63.8b	(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
▶	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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))
✓	16.9b	1/16
	57.8b	(/.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))
	39.4b	(/.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)))))
	39.4b	(.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))))
	41.8b	(/.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 504 to 252 computations (50% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (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))))
✓	3.1b	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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)))))
✓	34.5b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	36.9b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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))

series3.0s (15.2%)

Counts

4 → 144

Calls

4 calls:

2.4s	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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))
243.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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)))))
236.0ms	(/.f64 (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))))
58.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite186.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

847×	`times-frac_binary64`
318×	`*-un-lft-identity_binary64`
318×	`add-sqr-sqrt_binary64`
318×	`add-cube-cbrt_binary64`
63×	`associate-/r*_binary64`

Counts

4 → 443

Calls

4 calls:

18.0ms	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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))
13.0ms	(/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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)))))
6.0ms	(/.f64 (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))))
2.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

simplify1.0s (5.2%)

Algorithm

1×	egg-herbie

Rules

867×	`fma-def_binary64`
371×	`times-frac_binary64`
13×	`cube-mult_binary64`
13×	`unpow2_binary64`
13×	`unpow3_binary64`

Counts

587 → 634

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3686	86910
1	5292	86910

prune1.8s (9.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	633	1	634
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	633	8	641

Error

10.0b

Counts

641 → 8

Alt Table

Status	Error	Program
	63.8b	(/.f64 (*.f64 i (+.f64 beta i)) (pow.f64 alpha 2))
✓	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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))
✓	16.9b	1/16
	57.8b	(/.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))
▶	39.4b	(/.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)))))
	39.4b	(.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))))
	45.7b	(/.f64 (/.f64 i (/.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (/.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 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta)))))))
	41.8b	(/.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 99374 to 51385 computations (48.3% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.0b	(/.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)))))
✓	30.6b	(/.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))))
✓	33.8b	(/.f64 (*.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))
	34.5b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

series2.8s (14.3%)

Counts

3 → 108

Calls

3 calls:

2.3s

(/.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)))))

439.0ms

(/.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))))

38.0ms

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

rewrite208.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

1049×	`times-frac_binary64`
417×	`*-un-lft-identity_binary64`
417×	`add-sqr-sqrt_binary64`
417×	`add-cube-cbrt_binary64`
84×	`div-inv_binary64`

Counts

3 → 488

Calls

3 calls:

17.0ms

(/.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))))

simplify819.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

596 → 632

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3679	99118
1	5245	99118

prune1.7s (9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	701	2	703
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	704	7	711

Error

9.9b

Counts

711 → 7

Alt Table

Status	Error	Program
	45.7b	(/.f64 (/.f64 i (/.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)))) (/.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 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 1 (fma.f64 i 2 (+.f64 alpha beta)))))))
	44.5b	(/.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))))
✓	39.4b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (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))
✓	16.9b	1/16
	57.8b	(/.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))
	39.4b	(/.f64 1 (/.f64 (/.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)))) (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))))
	41.8b	(/.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 108651 to 53796 computations (50.5% saved)

regimes969.0ms (5%)

Accuracy

Total 2.9b remaining (22.3%)

Threshold costs 0b (0%)

Counts

109 → 2

Compiler

Compiled 28832 to 15341 computations (46.8% saved)

bsearch34.0ms (0.2%)

Steps

Iters	Range		Point
7	8.143927723013591e+120	1.9215748691433878e+122	2.6414897057870313e+121

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	74
1	26	74
2	26	74

end147.0ms (0.8%)

Remove: (sort alpha beta)
Compiler: Compiled 485 to 240 computations (50.5% saved)

Details

analyze54.0ms (0.3%)

sample1.5s (7.9%)

simplify40.0ms (0.2%)

prune4.0ms (0%)

localize15.0ms (0.1%)

series3.5s (17.9%)

rewrite53.0ms (0.3%)

simplify418.0ms (2.1%)

prune1.2s (6%)

localize0.0ms (0%)

prune10.0ms (0.1%)

localize19.0ms (0.1%)

series3.0s (15.2%)

rewrite186.0ms (1%)

simplify1.0s (5.2%)

prune1.8s (9.1%)

localize20.0ms (0.1%)

series2.8s (14.3%)

rewrite208.0ms (1.1%)

simplify819.0ms (4.2%)

prune1.7s (9%)

regimes969.0ms (5%)

bsearch34.0ms (0.2%)

simplify3.0ms (0%)

end147.0ms (0.8%)

Profiling