Details

analyze63.0ms (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)

sample1.6s (7.3%)

Symmetry

(sort alpha beta)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 190 to 97 computations (48.9% saved)

simplify126.0ms (0.6%)

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

55.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	55.3b	(/.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

▶

55.3b

(/.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)

localize17.0ms (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)))
✓	39.7b	(/.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))
✓	46.9b	(/.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))))

series3.0s (13.2%)

Counts

4 → 144

Calls

4 calls:

2.5s	(/.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))
412.0ms	(/.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))))
45.0ms	(.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 (0.2%)

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:

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))))
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)))

simplify413.0ms (1.8%)

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 (7.1%)

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

9.5b

Counts

297 → 7

Alt Table

Status	Error	Program
	42.8b	(.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))))
	44.7b	(/.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))
	42.8b	(/.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))
	55.3b	(/.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))
	60.0b	(/.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))
▶	17.3b	1/16
	43.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.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))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))

Compiler

Compiled 63443 to 36643 computations (42.2% saved)

localize0.0ms (0%)

prune12.0ms (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

9.5b

Counts

7 → 7

Alt Table

Status	Error	Program
	42.8b	(.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))))
	44.7b	(/.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))
▶	42.8b	(/.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))
	55.3b	(/.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))
	60.0b	(/.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))
✓	17.3b	1/16
	43.1b	(.f64 (/.f64 (/.f64 (.f64 i (+.f64 i (+.f64 alpha beta))) (fma.f64 i 2 (+.f64 alpha beta))) (.f64 (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)) (cbrt.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))) (cbrt.f64 (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))))

Compiler

Compiled 610 to 310 computations (49.2% 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)) (/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta))))
✓	5.2b	(/.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)))))
✓	38.6b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	39.7b	(/.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 (14.4%)

Counts

4 → 144

Calls

4 calls:

2.6s	(/.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))
286.0ms	(/.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))))
273.0ms	(/.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)))))
66.0ms	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))

rewrite238.0ms (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:

22.0ms	(/.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))
16.0ms	(/.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)))

simplify913.0ms (4%)

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

prune2.0s (8.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	630	4	634
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	634	7	641

Error

9.5b

Counts

641 → 7

Alt Table

Status	Error	Program
	42.9b	(.f64 (/.f64 (/.f64 i (/.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) 1)) 1) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (sqrt.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)))
	43.2b	(.f64 (/.f64 (/.f64 i (/.f64 (.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.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)))) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))) 1) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (/.f64 (cbrt.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (.f64 alpha beta))) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1)))
	60.0b	(/.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))
▶	42.7b	(/.f64 (.f64 (/.f64 i 1) (/.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)) (fma.f64 i 2 (+.f64 alpha beta)))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	42.8b	(.f64 1 (/.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)))
✓	17.3b	1/16
	44.7b	(/.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 99470 to 51415 computations (48.3% saved)

localize21.0ms (0.1%)

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))))
✓	0.0b	(/.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)) (fma.f64 i 2 (+.f64 alpha beta)))))
	38.6b	(/.f64 (fma.f64 i (+.f64 i (+.f64 alpha beta)) (*.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)))
✓	39.7b	(/.f64 (.f64 (/.f64 i 1) (/.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)) (fma.f64 i 2 (+.f64 alpha beta)))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))

series3.5s (15.4%)

Counts

2 → 72

Calls

2 calls:

3.2s

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

246.0ms

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

rewrite172.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

619×	`times-frac_binary64`
484×	`*-un-lft-identity_binary64`
259×	`add-sqr-sqrt_binary64`
259×	`add-cube-cbrt_binary64`
135×	`distribute-lft-out_binary64`

Counts

2 → 334

Calls

2 calls:

32.0ms

(/.f64 (*.f64 (/.f64 i 1) (/.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)) (fma.f64 i 2 (+.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 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)))))

simplify560.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

700×	`fma-def_binary64`
557×	`associate-/l*_binary64`
349×	`times-frac_binary64`
310×	`associate-/r/_binary64`
56×	`sqr-pow_binary64`

Counts

406 → 478

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2867	64595
1	5755	64595

prune2.0s (8.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	666	2	668
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	669	6	675

Error

9.4b

Counts

675 → 6

Alt Table

Status	Error	Program
	43.0b	(/.f64 (.f64 (/.f64 i 1) (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 i (+.f64 alpha beta))) (cbrt.f64 (+.f64 i (+.f64 alpha beta)))) (.f64 (.f64 (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) (cbrt.f64 (fma.f64 i 2 (+.f64 alpha beta)))) (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))))) (/.f64 (cbrt.f64 (+.f64 i (+.f64 alpha beta))) (/.f64 (cbrt.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)))))))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
✓	17.3b	1/16
	58.9b	(/.f64 (.f64 (/.f64 i 1) (/.f64 (.f64 beta alpha) (+.f64 beta alpha))) (fma.f64 (fma.f64 i 2 (+.f64 alpha beta)) (fma.f64 i 2 (+.f64 alpha beta)) -1))
	42.9b	(.f64 (/.f64 (/.f64 i (/.f64 (sqrt.f64 (fma.f64 i 2 (+.f64 alpha beta))) 1)) 1) (/.f64 (/.f64 (+.f64 i (+.f64 alpha beta)) (/.f64 (sqrt.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)))
	42.8b	(.f64 1 (/.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)))
	44.7b	(/.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 100729 to 51457 computations (48.9% saved)

regimes2.9s (12.9%)

Accuracy

Total 2.4b remaining (18.4%)

Threshold costs 0b (0%)

Counts

325 → 2

Compiler

Compiled 85680 to 39901 computations (53.4% saved)

bsearch54.0ms (0.2%)

Steps

Iters	Range		Point
5	6.124328244585836e+139	1.3253130301630863e+140	7.852118722167694e+139

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (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	24	74
1	31	74
2	30	74

end144.0ms (0.6%)

Remove: (sort alpha beta)
Compiler: Compiled 484 to 236 computations (51.2% saved)

Details

analyze63.0ms (0.3%)

sample1.6s (7.3%)

simplify126.0ms (0.6%)

prune4.0ms (0%)

localize17.0ms (0.1%)

series3.0s (13.2%)

rewrite56.0ms (0.2%)

simplify413.0ms (1.8%)

prune1.6s (7.1%)

localize0.0ms (0%)

prune12.0ms (0.1%)

localize16.0ms (0.1%)

series3.3s (14.4%)

rewrite238.0ms (1%)

simplify913.0ms (4%)

prune2.0s (8.8%)

localize21.0ms (0.1%)

series3.5s (15.4%)

rewrite172.0ms (0.8%)

simplify560.0ms (2.5%)

prune2.0s (8.6%)

regimes2.9s (12.9%)

bsearch54.0ms (0.2%)

simplify3.0ms (0%)

end144.0ms (0.6%)

Profiling