Details

analyze166.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 43 to 28 computations (34.9% saved)

sample1.8s (17.9%)

Results

1.0s	6702×	body	128	valid
379.0ms	697×	body	1024	valid
221.0ms	518×	body	512	valid
82.0ms	287×	body	256	valid
42.0ms	52×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

847×	`times-frac_binary64`
817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
537×	`div-sub_binary64`
535×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	110	37
3	435	37
4	1672	37
5	2494	37
6	3358	37
7	5392	37

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

17.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.8b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)
	22.6b	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

Status

Error

Program

▶

17.8b

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

22.6b

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

Compiler

Compiled 180 to 106 computations (41.1% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	12.4b	(fma.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)
✓	14.8b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series853.0ms (8.4%)

Counts

3 → 108

Calls

3 calls:

531.0ms

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

302.0ms

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

20.0ms

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

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
7×	`add-cube-cbrt_binary64`

Counts

3 → 67

Calls

3 calls:

7.0ms

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

6.0ms

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

0.0ms

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

simplify204.0ms (2%)

Algorithm

1×	egg-herbie

Rules

561×	`+-commutative_binary64`
490×	`fma-def_binary64`
487×	`associate-+r+_binary64`
392×	`*-commutative_binary64`
294×	`associate-*r/_binary64`

Counts

175 → 205

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1400	19973
1	5450	19973

prune563.0ms (5.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	201	4	205
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	203	4	207

Error

Counts

207 → 4

Alt Table

Status	Error	Program
	51.9b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	17.8b	(/.f64 (+.f64 (.f64 (+.f64 alpha beta) (/.f64 (-.f64 beta alpha) (.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
▶	12.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

Compiler

Compiled 24695 to 15944 computations (35.4% saved)

localize28.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓	12.4b	(fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1)

series919.0ms (9.1%)

Counts

3 → 108

Calls

3 calls:

511.0ms

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

309.0ms

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

98.0ms

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

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
66×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
31×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`

Counts

3 → 129

Calls

3 calls:

15.0ms

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

8.0ms

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

0.0ms

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

simplify230.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

552×	`fma-def_binary64`
538×	`associate-+r+_binary64`
365×	`associate-*r/_binary64`
173×	`associate-/l*_binary64`
154×	`associate-/r*_binary64`

Counts

237 → 293

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1615	24106
1	5207	24106

prune670.0ms (6.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	292	1	293
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	293	4	297

Error

Counts

297 → 4

Alt Table

Status	Error	Program
▶	12.4b	(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	51.9b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
✓	12.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

Compiler

Compiled 30981 to 19670 computations (36.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))
✓	3.3b	(*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta))))
✓	4.1b	(+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1)

series1.6s (15.8%)

Counts

3 → 108

Calls

3 calls:

761.0ms

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

500.0ms

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

341.0ms

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

rewrite104.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

299×	`times-frac_binary64`
256×	`*-un-lft-identity_binary64`
193×	`add-sqr-sqrt_binary64`
128×	`add-cube-cbrt_binary64`
82×	`associate-r_binary64`

Counts

3 → 250

Calls

3 calls:

25.0ms

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

16.0ms

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

11.0ms

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

simplify374.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-def_binary64`
555×	`associate-+r+_binary64`
405×	`associate-*r/_binary64`
204×	`associate-/r*_binary64`
200×	`associate-/l*_binary64`

Counts

358 → 402

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1802	35564
1	5760	35564

prune1.0s (10.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	491	0	491
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	491	4	495

Error

Counts

495 → 4

Alt Table

Status	Error	Program
✓	12.4b	(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
▶	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	51.9b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
✓	12.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

Compiler

Compiled 49258 to 30434 computations (38.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	0.2b	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

series39.0ms (0.4%)

Counts

2 → 72

Calls

2 calls:

21.0ms	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
18.0ms	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
52×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
16×	`associate-/l*_binary64`

Counts

2 → 101

Calls

2 calls:

4.0ms	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
2.0ms	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

simplify126.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

729×	`associate-+l+_binary64`
538×	`associate-/r/_binary64`
521×	`fma-def_binary64`
427×	`*-commutative_binary64`
295×	`associate-/l/_binary64`

Counts

173 → 204

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	195	4203
1	404	3697
2	959	3623
3	2432	3454
4	3741	3454
5	5162	3454

prune129.0ms (1.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	204	0	204
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	204	4	208

Error

Counts

208 → 4

Alt Table

Status	Error	Program
✓	12.4b	(/.f64 (+.f64 (*.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
✓	49.7b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	51.9b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (.f64 4 (/.f64 i alpha)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i i) (.f64 alpha alpha)) (fma.f64 12 (/.f64 (.f64 i beta) (.f64 alpha alpha)) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (*.f64 alpha alpha))))))))) 2)
✓	12.4b	(/.f64 (fma.f64 (+.f64 alpha beta) (*.f64 (/.f64 1 (fma.f64 2 i (+.f64 alpha beta))) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))) 1) 2)

Compiler

Compiled 4847 to 3546 computations (26.8% saved)

regimes968.0ms (9.6%)

Accuracy

Total 1.3b remaining (91.2%)

Threshold costs 0b (0%)

Counts

101 → 2

Compiler

Compiled 17503 to 12219 computations (30.2% saved)

bsearch4.0ms (0%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	96
1	43	96
2	47	96
3	49	96
4	50	96
5	49	96

end119.0ms (1.2%)

Compiler: Compiled 279 to 164 computations (41.2% saved)

Details

analyze166.0ms (1.6%)

sample1.8s (17.9%)

simplify43.0ms (0.4%)

prune5.0ms (0%)

localize14.0ms (0.1%)

series853.0ms (8.4%)

rewrite17.0ms (0.2%)

simplify204.0ms (2%)

prune563.0ms (5.6%)

localize28.0ms (0.3%)

series919.0ms (9.1%)

rewrite37.0ms (0.4%)

simplify230.0ms (2.3%)

prune670.0ms (6.6%)

localize13.0ms (0.1%)

series1.6s (15.8%)

rewrite104.0ms (1%)

simplify374.0ms (3.7%)

prune1.0s (10.3%)

localize8.0ms (0.1%)

series39.0ms (0.4%)

rewrite15.0ms (0.2%)

simplify126.0ms (1.2%)

prune129.0ms (1.3%)

regimes968.0ms (9.6%)

bsearch4.0ms (0%)

simplify9.0ms (0.1%)

end119.0ms (1.2%)

Profiling