Details

analyze221.0ms (2.5%)

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
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 42 to 27 computations (35.7% saved)

sample49.0ms (0.5%)

Algorithm

1×

intervals

Results

17.0ms	206×	body	128	valid
6.0ms	22×	body	1024	valid
6.0ms	256×	pre	128	true
3.0ms	13×	body	512	valid
2.0ms	13×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 77 to 50 computations (35.1% saved)

simplify54.0ms (0.6%)

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 → 1

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

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

20.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	20.1b	(/.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)
	24.1b	(/.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

▶

20.1b

(/.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)

24.1b

(/.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 151 to 91 computations (39.7% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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)

18.0b

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

rewrite275.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

12.2b

Rules

20×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
16×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cbrt-cube_binary64`

Counts

3 → 136

Calls

3 calls:

19.0ms

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

17.0ms

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

11.0ms

(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)

Compiler

Compiled 4839 to 2397 computations (50.5% saved)

series819.0ms (9.2%)

Error

0.0b

Counts

3 → 81

Calls

3 calls:

413.0ms

(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)

256.0ms

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

66.0ms

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

Compiler

Compiled 13664 to 10143 computations (25.8% saved)

simplify188.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

928×	`fma-def_binary64`
575×	`associate-/l*_binary64`
267×	`+-commutative_binary64`
209×	`associate-+r+_binary64`
197×	`*-commutative_binary64`

Counts

217 → 116

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	781	10932
1	2727	10181
2	5577	10181

prune111.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	114	4	118

Error

0.0b

Counts

118 → 4

Alt Table

Status	Error	Program
	51.5b	(/.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 beta (.f64 alpha alpha)) i) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 6 (fma.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)) (.f64 12 (/.f64 i (*.f64 alpha alpha))))))))) 2)
	49.6b	(/.f64 (/.f64 (fma.f64 2 beta (fma.f64 i 4 2)) alpha) 2)
✓	20.1b	(/.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)
▶	20.1b	(/.f64 (+.f64 1 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2)))) 2)

Compiler

Compiled 4885 to 2694 computations (44.9% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2)))
2.0b	(+.f64 1 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2))))

rewrite158.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-cube-cbrt_binary64`
12×	`div-sub_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`

Counts

2 → 100

Calls

2 calls:

18.0ms	(/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2)))
15.0ms	(+.f64 1 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2))))

Compiler

Compiled 2233 to 1419 computations (36.5% saved)

series121.0ms (1.4%)

Error

0.0b

Counts

2 → 44

Calls

2 calls:

55.0ms	(+.f64 1 (/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2))))
38.0ms	(/.f64 (-.f64 beta alpha) (+.f64 beta (+.f64 alpha 2)))

Compiler

Compiled 2970 to 2362 computations (20.5% saved)

simplify139.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

349×	`cancel-sign-sub-inv_binary64`
296×	`sub-neg_binary64`
277×	`fma-neg_binary64`
177×	`fma-def_binary64`
170×	`+-commutative_binary64`

Counts

144 → 104

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	278	4025
1	858	3927
2	3228	3819
3	4872	3819
4	4971	3819

prune115.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	104	4	108

Error

0.0b

Counts

108 → 4

Alt Table

Status	Error	Program
▶	20.1b	(/.f64 (exp.f64 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))) 2)
	51.5b	(/.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 beta (.f64 alpha alpha)) i) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 6 (fma.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)) (.f64 12 (/.f64 i (*.f64 alpha alpha))))))))) 2)
	49.6b	(/.f64 (/.f64 (fma.f64 2 beta (fma.f64 i 4 2)) alpha) 2)
✓	20.1b	(/.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)

Compiler

Compiled 2472 to 1548 computations (37.4% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))
0.1b	(exp.f64 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
2.0b	(log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))

rewrite579.0ms (6.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`add-cube-cbrt_binary64`
13×	`pow1_binary64`
13×	`add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`expm1-log1p-u_binary64`

Counts

3 → 113

Calls

3 calls:

258.0ms	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))
10.0ms	(log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
9.0ms	(exp.f64 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))

Compiler

Compiled 2115 to 1330 computations (37.1% saved)

series413.0ms (4.7%)

Error

0.0b

Counts

3 → 60

Calls

3 calls:

141.0ms	(exp.f64 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))
115.0ms	(log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
38.0ms	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 7757 to 6269 computations (19.2% saved)

simplify124.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

620×	`times-frac_binary64`
607×	`associate-/r*_binary64`
488×	`fma-def_binary64`
419×	`associate-/l*_binary64`
158×	`+-commutative_binary64`

Counts

173 → 79

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	6762
1	1897	6034
2	5482	6034

prune77.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	79	4	83

Error

0.0b

Counts

83 → 4

Alt Table

Status	Error	Program
	51.5b	(/.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 beta (.f64 alpha alpha)) i) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 6 (fma.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)) (.f64 12 (/.f64 i (*.f64 alpha alpha))))))))) 2)
	49.6b	(/.f64 (/.f64 (fma.f64 2 beta (fma.f64 i 4 2)) alpha) 2)
✓	20.1b	(/.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)
▶	20.1b	(/.f64 (sqrt.f64 (exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))))) 2)

Compiler

Compiled 3300 to 2246 computations (31.9% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))))
0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))
0.1b	(exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))))
2.0b	(log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))

rewrite217.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-log-exp_binary64`
13×	`pow1_binary64`

Counts

4 → 152

Calls

4 calls:

50.0ms	(sqrt.f64 (exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))))
19.0ms	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))
12.0ms	(exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))))
11.0ms	(log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))

Compiler

Compiled 3033 to 2053 computations (32.3% saved)

series622.0ms (7%)

Error

0.0b

Counts

4 → 79

Calls

4 calls:

177.0ms	(exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))))
159.0ms	(sqrt.f64 (exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))))))
118.0ms	(log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))
42.0ms	(/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta)))

Compiler

Compiled 13643 to 11124 computations (18.5% saved)

simplify202.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

781×	`times-frac_binary64`
767×	`fma-def_binary64`
245×	`+-commutative_binary64`
209×	`*-commutative_binary64`
185×	`associate-+r+_binary64`

Counts

231 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	790	11152
1	2751	10689
2	4967	10689

prune150.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	117	4	121

Error

0.0b

Counts

121 → 4

Alt Table

Status	Error	Program
	51.5b	(/.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 beta (.f64 alpha alpha)) i) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 6 (fma.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha)) (.f64 12 (/.f64 i (*.f64 alpha alpha))))))))) 2)
	49.6b	(/.f64 (/.f64 (fma.f64 2 beta (fma.f64 i 4 2)) alpha) 2)
	20.1b	(/.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)
	20.1b	(/.f64 (sqrt.f64 (exp.f64 (*.f64 2 (log1p.f64 (/.f64 (-.f64 beta alpha) (+.f64 alpha (+.f64 2 beta))))))) 2)

Compiler

Compiled 6439 to 4487 computations (30.3% saved)

regimes2.6s (29.5%)

Accuracy

Total 1.1b remaining (74.6%)

Threshold costs 0b (0%)

Compiler

Compiled 48035 to 34043 computations (29.1% saved)

bsearch12.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`+-commutative_binary64`
3×	`*-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	29	94
1	39	94
2	43	94
3	45	94
4	46	94
5	45	94

end1.0ms (0%)

Compiler: Compiled 68 to 39 computations (42.6% saved)

sample1.5s (17.4%)

Algorithm

1×

intervals

Results

505.0ms	6470×	body	128	valid
206.0ms	697×	body	1024	valid
201.0ms	8000×	pre	128	true
111.0ms	498×	body	512	valid
45.0ms	294×	body	256	valid
18.0ms	41×	body	2048	valid

Compiler

Compiled 242 to 148 computations (38.8% saved)

Details

analyze221.0ms (2.5%)

sample49.0ms (0.5%)

simplify54.0ms (0.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite275.0ms (3.1%)

series819.0ms (9.2%)

simplify188.0ms (2.1%)

prune111.0ms (1.3%)

localize8.0ms (0.1%)

rewrite158.0ms (1.8%)

series121.0ms (1.4%)

simplify139.0ms (1.6%)

prune115.0ms (1.3%)

localize12.0ms (0.1%)

rewrite579.0ms (6.5%)

series413.0ms (4.7%)

simplify124.0ms (1.4%)

prune77.0ms (0.9%)

localize29.0ms (0.3%)

rewrite217.0ms (2.4%)

series622.0ms (7%)

simplify202.0ms (2.3%)

prune150.0ms (1.7%)

regimes2.6s (29.5%)

bsearch12.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.5s (17.4%)

Profiling