Details

analyze120.0ms (1.5%)

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
7%	21.1%	71.9%	3
17.5%	10.5%	71.9%	4
21.1%	7%	71.9%	5
22.8%	5.3%	71.9%	6
23.2%	4.8%	71.9%	7
23.7%	4.4%	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)

sample1.9s (24.3%)

Infinites

0% of outputs are infinite.

Results

1.1s	6719×	body	128	valid
474.0ms	673×	body	1024	valid
169.0ms	505×	body	512	valid
76.0ms	311×	body	256	valid
26.0ms	48×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify43.0ms (0.5%)

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 (0.1%)

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

21.4b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	21.5b	(/.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)
	24.8b	(/.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

▶

21.5b

(/.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)

24.8b

(/.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)

localize36.0ms (0.5%)

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))))
✓	12.5b	(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)
✓	20.2b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series863.0ms (11%)

Counts

3 → 108

Calls

3 calls:

541.0ms

(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)

301.0ms

(/.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))))

rewrite20.0ms (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:

11.0ms

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

4.0ms

(*.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)

simplify235.0ms (3%)

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

prune468.0ms (5.9%)

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

0.1b

Counts

207 → 4

Alt Table

Status	Error	Program
▶	12.5b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
	48.4b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
	52.3b	(/.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)
	49.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 24675 to 15938 computations (35.4% saved)

localize13.0ms (0.2%)

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))))
✓	0.0b	(/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
✓	0.2b	(/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))
✓	12.5b	(fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)

series995.0ms (12.7%)

Counts

4 → 144

Calls

4 calls:

553.0ms	(fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)
300.0ms	(/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))
73.0ms	(/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
68.0ms	(/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

rewrite170.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

979×	`times-frac_binary64`
704×	`*-un-lft-identity_binary64`
532×	`add-sqr-sqrt_binary64`
394×	`add-cube-cbrt_binary64`
113×	`associate-/r*_binary64`

Counts

4 → 544

Calls

4 calls:

20.0ms	(/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))))
9.0ms	(/.f64 (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 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1)

simplify484.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
384×	`associate-*r/_binary64`
211×	`associate-/l*_binary64`
194×	`associate-/r/_binary64`
160×	`associate-/r*_binary64`

Counts

688 → 713

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2054	49670
1	4984	49670

prune1.0s (13.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	712	1	713
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	713	4	717

Error

0.1b

Counts

717 → 4

Alt Table

Status	Error	Program
✓	12.5b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
▶	13.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha))))) 1) 2)
	52.3b	(/.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)
	49.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 54764 to 32226 computations (41.2% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha))))
✓	0.0b	(fma.f64 4 i (*.f64 3 alpha))
✓	0.1b	(/.f64 1 (+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha)))))

series70.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

58.0ms	(/.f64 1 (+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha)))))
7.0ms	(+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha))))
4.0ms	(fma.f64 4 i (*.f64 3 alpha))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
15×	`distribute-lft-out_binary64`
15×	`times-frac_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 73

Calls

3 calls:

7.0ms	(/.f64 1 (+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha)))))
4.0ms	(+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha))))
0.0ms	(fma.f64 4 i (*.f64 3 alpha))

simplify104.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

358×	`cancel-sign-sub-inv_binary64`
351×	`associate-+r+_binary64`
338×	`fma-def_binary64`
256×	`sub-neg_binary64`
247×	`+-commutative_binary64`

Counts

169 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	4827
1	1107	4643
2	4204	4641
3	5190	4641

prune160.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	148	4	152

Error

0.1b

Counts

152 → 4

Alt Table

Status	Error	Program
✓	12.5b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
✓	13.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha))))) 1) 2)
	52.3b	(/.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)
▶	49.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)

Compiler

Compiled 5720 to 4036 computations (29.4% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

series16.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

16.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

3.0ms

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

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Rules

726×	`distribute-rgt-in_binary64`
711×	`distribute-lft-in_binary64`
389×	`fma-def_binary64`
352×	`associate-/r/_binary64`
323×	`div-sub_binary64`

Counts

65 → 61

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	75	1277
1	132	1117
2	332	1081
3	934	1079
4	4676	1025
5	4834	1025
6	5397	1025

prune44.0ms (0.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	59	6	65

Error

0.1b

Counts

65 → 6

Alt Table

Status	Error	Program
✓	12.5b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (/.f64 (fma.f64 2 i (+.f64 alpha beta)) (/.f64 (-.f64 beta alpha) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))) 1) 2)
✓	13.2b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 1 (+.f64 beta (+.f64 2 (fma.f64 4 i (*.f64 3 alpha))))) 1) 2)
	52.3b	(/.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)
	50.6b	(/.f64 (exp.f64 (-.f64 (log.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4)))) (log.f64 alpha))) 2)
✓	49.1b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	49.4b	(/.f64 (/.f64 (/.f64 (fma.f64 2 beta (fma.f64 4 i 2)) (sqrt.f64 alpha)) (sqrt.f64 alpha)) 2)

Compiler

Compiled 1384 to 991 computations (28.4% saved)

regimes803.0ms (10.2%)

Accuracy

Total 1.1b remaining (89.8%)

Threshold costs 0b (0%)

Counts

88 → 2

Compiler

Compiled 15118 to 10837 computations (28.3% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-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	31	99
1	43	99
2	47	99
3	49	99
4	50	99
5	49	99

end132.0ms (1.7%)

Compiler: Compiled 313 to 197 computations (37.1% saved)

Details

analyze120.0ms (1.5%)

sample1.9s (24.3%)

simplify43.0ms (0.5%)

prune5.0ms (0.1%)

localize36.0ms (0.5%)

series863.0ms (11%)

rewrite20.0ms (0.2%)

simplify235.0ms (3%)

prune468.0ms (5.9%)

localize13.0ms (0.2%)

series995.0ms (12.7%)

rewrite170.0ms (2.2%)

simplify484.0ms (6.2%)

prune1.0s (13.3%)

localize13.0ms (0.2%)

series70.0ms (0.9%)

rewrite15.0ms (0.2%)

simplify104.0ms (1.3%)

prune160.0ms (2%)

localize7.0ms (0.1%)

series16.0ms (0.2%)

rewrite4.0ms (0.1%)

simplify79.0ms (1%)

prune44.0ms (0.6%)

regimes803.0ms (10.2%)

bsearch3.0ms (0%)

simplify4.0ms (0.1%)

end132.0ms (1.7%)

Profiling