Details

analyze2.7s (5.6%)

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
0%	14%	86%	7
0%	14%	86%	8
0%	14%	86%	9
0%	14%	86%	10
0%	14%	86%	11
0%	14%	86%	12
0.1%	14%	86%	13
0.2%	13.8%	86%	14

Compiler

Compiled 67 to 35 computations (47.8% saved)

sample1.9s (4%)

Symmetry

(sort alpha beta)

Results

1.9s

8256×

body

128

valid

Compiler

Compiled 123 to 62 computations (49.6% saved)

simplify40.0ms (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

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

51.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	51.3b	(/.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))

Status

Error

Program

▶

51.3b

(/.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))

Compiler

Compiled 203 to 89 computations (56.2% saved)

localize16.0ms (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)))
✓	32.5b	(/.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))
✓	44.2b	(/.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))))

series2.9s (6.1%)

Counts

4 → 144

Calls

4 calls:

2.6s	(/.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))
262.0ms	(/.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))))
47.0ms	(.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)))

rewrite56.0ms (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:

10.0ms	(/.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))))
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)))

simplify481.0ms (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 (3.4%)

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

9.7b

Counts

297 → 7

Alt Table

Status	Error	Program
	51.6b	(/.f64 (/.f64 (.f64 i (.f64 (+.f64 (pow.f64 i 2) (.f64 beta i)) (+.f64 beta i))) (pow.f64 (+.f64 beta (.f64 2 i)) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	58.7b	(/.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))
	37.1b	(.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))))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	37.1b	(/.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))
▶	19.6b	1/16
	51.4b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (sqrt.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 63395 to 36615 computations (42.2% saved)

localize0.0ms (0%)

prune10.0ms (0%)

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

9.7b

Counts

7 → 7

Alt Table

Status	Error	Program
	51.6b	(/.f64 (/.f64 (.f64 i (.f64 (+.f64 (pow.f64 i 2) (.f64 beta i)) (+.f64 beta i))) (pow.f64 (+.f64 beta (.f64 2 i)) 2)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	58.7b	(/.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))
	37.1b	(.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))))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
▶	37.1b	(/.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))
✓	19.6b	1/16
	51.4b	(/.f64 (/.f64 (.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (*.f64 (sqrt.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 562 to 282 computations (49.8% saved)

localize17.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.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))))
✓	5.6b	(/.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)))))
✓	32.4b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	32.5b	(/.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))

series3.3s (6.9%)

Counts

4 → 144

Calls

4 calls:

2.7s	(/.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))
299.0ms	(/.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)))))
262.0ms	(/.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))))
62.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite195.0ms (0.4%)

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:

19.0ms	(/.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))
14.0ms	(/.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)))))
4.0ms	(/.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)))

simplify803.0ms (1.7%)

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

prune1.7s (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	629	5	634
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	633	8	641

Error

9.7b

Counts

641 → 8

Alt Table

Status	Error	Program
	37.5b	(/.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (cbrt.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))))))))
	38.2b	(/.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 (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))))))
	58.7b	(/.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))
✓	19.6b	1/16
▶	37.3b	(.f64 (/.f64 (/.f64 i (/.f64 1 (/.f64 1 (sqrt.f64 (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 (+.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)) (sqrt.f64 (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))))
	37.5b	(/.f64 (/.f64 i (/.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (/.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)))) 1))) (/.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 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))))))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	57.5b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (-.f64 (+.f64 i alpha) (+.f64 (/.f64 (pow.f64 alpha 2) beta) (+.f64 (/.f64 (pow.f64 i 2) beta) (.f64 2 (/.f64 (*.f64 i alpha) beta))))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 99712 to 51503 computations (48.3% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	12.8b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))
✓	20.0b	(/.f64 (/.f64 (+.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)) (sqrt.f64 (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)))
✓	20.1b	(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))
✓	35.3b	(sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

series18.7s (39.2%)

Counts

4 → 72

Calls

4 calls:

17.0s	(/.f64 (/.f64 (+.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)) (sqrt.f64 (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)))
1.4s	(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))
289.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))
80.0ms	(sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

rewrite2.5s (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

9001×	`times-frac_binary64`
5976×	`*-un-lft-identity_binary64`
3492×	`add-sqr-sqrt_binary64`
3491×	`add-cube-cbrt_binary64`
2079×	`sqrt-prod_binary64`

Counts

4 → 2711

Calls

4 calls:

89.0ms	(/.f64 (/.f64 (+.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)) (sqrt.f64 (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)))
6.0ms	(/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))
3.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))
1.0ms	(sqrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

simplify2.8s (5.9%)

Algorithm

1×	egg-herbie

Counts

2783 → 1384

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6248	428720

prune3.4s (7.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1430	0	1430
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1430	8	1438

Error

9.7b

Counts

1438 → 8

Alt Table

Status	Error	Program
	37.5b	(/.f64 (.f64 (cbrt.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)))))) (cbrt.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))))))) (/.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1) (cbrt.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))))))))
	38.2b	(/.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 (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))))))
	58.7b	(/.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))
✓	19.6b	1/16
✓	37.3b	(.f64 (/.f64 (/.f64 i (/.f64 1 (/.f64 1 (sqrt.f64 (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 (+.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)) (sqrt.f64 (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))))
	37.5b	(/.f64 (/.f64 i (/.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (/.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)))) 1))) (/.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 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta)))))))
	51.0b	(/.f64 (*.f64 i (+.f64 i alpha)) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	57.5b	(/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (/.f64 (fma.f64 i 2 (+.f64 alpha beta)) (-.f64 (+.f64 i alpha) (+.f64 (/.f64 (pow.f64 alpha 2) beta) (+.f64 (/.f64 (pow.f64 i 2) beta) (.f64 2 (/.f64 (*.f64 i alpha) beta))))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

Compiler

Compiled 222926 to 110028 computations (50.6% saved)

regimes4.2s (8.9%)

Accuracy

Total 1.8b remaining (14%)

Threshold costs 0b (0%)

Counts

403 → 3

Compiler

Compiled 123112 to 59217 computations (51.9% saved)

bsearch101.0ms (0.2%)

Steps

Iters	Range		Point
6	1.7496409088718536e+141	9.509168816083116e+141	8.475228041884615e+141
7	9.518643268634403e+36	6.714917966540901e+38	5.975232987600116e+38

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	111
1	39	111
2	38	111

end208.0ms (0.4%)

Remove: (sort alpha beta)
Compiler: Compiled 783 to 369 computations (52.9% saved)

Details

analyze2.7s (5.6%)

sample1.9s (4%)

simplify40.0ms (0.1%)

prune4.0ms (0%)

localize16.0ms (0%)

series2.9s (6.1%)

rewrite56.0ms (0.1%)

simplify481.0ms (1%)

prune1.6s (3.4%)

localize0.0ms (0%)

prune10.0ms (0%)

localize17.0ms (0%)

series3.3s (6.9%)

rewrite195.0ms (0.4%)

simplify803.0ms (1.7%)

prune1.7s (3.5%)

localize23.0ms (0%)

series18.7s (39.2%)

rewrite2.5s (5.2%)

simplify2.8s (5.9%)

prune3.4s (7.2%)

regimes4.2s (8.9%)

bsearch101.0ms (0.2%)

simplify3.0ms (0%)

end208.0ms (0.4%)

Profiling