Details

analyze169.0ms (1.7%)

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)

sample2.2s (21.5%)

Results

1.2s	6704×	body	128	valid
601.0ms	690×	body	1024	valid
213.0ms	510×	body	512	valid
97.0ms	303×	body	256	valid
33.0ms	49×	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 (0.1%)

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

20.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	24.9b	(/.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)
▶	20.9b	(/.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)

Status

Error

Program

24.9b

(/.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)

▶

20.9b

(/.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 180 to 106 computations (41.1% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
✓	0.0b	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	11.8b	(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)
✓	19.8b	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))

series1.3s (12.7%)

Counts

4 → 144

Calls

4 calls:

949.0ms	(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)
296.0ms	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
25.0ms	(*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
10.0ms	(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`add-cbrt-cube_binary64`
11×	`add-exp-log_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 85

Calls

4 calls:

13.0ms	(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
8.0ms	(/.f64 (-.f64 beta alpha) (*.f64 (fma.f64 2 i (+.f64 alpha beta)) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))))
5.0ms	(*.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)

simplify243.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

563×	`+-commutative_binary64`
490×	`fma-def_binary64`
488×	`associate-+r+_binary64`
393×	`*-commutative_binary64`
294×	`associate-*r/_binary64`

Counts

229 → 235

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1410	20564
1	5474	20564

prune594.0ms (5.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	230	5	235
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	232	5	237

Error

0.1b

Counts

237 → 5

Alt Table

Status	Error	Program
▶	11.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)
	21.3b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 beta (.f64 (+.f64 beta (.f64 2 i)) (+.f64 beta (+.f64 2 (*.f64 2 i))))) 1) 2)
	53.1b	(/.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)
	49.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
	48.1b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)

Compiler

Compiled 25654 to 16440 computations (35.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))
✓	0.0b	(/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta)))
✓	0.1b	(/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta))))
✓	11.8b	(fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1)

series879.0ms (8.7%)

Counts

3 → 108

Calls

3 calls:

494.0ms

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

336.0ms

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

48.0ms

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

rewrite41.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

166×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
78×	`add-cube-cbrt_binary64`
24×	`associate-/l*_binary64`

Counts

3 → 169

Calls

3 calls:

10.0ms

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

6.0ms

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

1.0ms

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

simplify293.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

490×	`fma-def_binary64`
477×	`associate-+r+_binary64`
326×	`associate-*r/_binary64`
177×	`associate-/l*_binary64`
171×	`associate-/r*_binary64`

Counts

277 → 297

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1591	25853
1	5046	25853

prune657.0ms (6.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	326	1	327
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	327	5	332

Error

0.1b

Counts

332 → 5

Alt Table

Status	Error	Program
	53.1b	(/.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)
	49.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	13.0b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 beta (+.f64 2 (*.f64 2 i)))) 1) 2)
	48.1b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
✓	11.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)

Compiler

Compiled 31187 to 19211 computations (38.4% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series1.5s (14.5%)

Counts

2 → 72

Calls

2 calls:

813.0ms

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

645.0ms

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

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

151×	`times-frac_binary64`
137×	`*-un-lft-identity_binary64`
97×	`add-sqr-sqrt_binary64`
67×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`

Counts

2 → 129

Calls

2 calls:

11.0ms

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

0.0ms

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

simplify277.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

513×	`associate-+r+_binary64`
475×	`fma-def_binary64`
300×	`associate-*r/_binary64`
252×	`associate-/r*_binary64`
192×	`associate-/l*_binary64`

Counts

201 → 220

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1593	26070
1	5097	26070

prune684.0ms (6.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	303	0	303
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	303	5	308

Error

0.1b

Counts

308 → 5

Alt Table

Status	Error	Program
	53.1b	(/.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)
	49.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	13.0b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 beta (+.f64 2 (*.f64 2 i)))) 1) 2)
▶	48.1b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
✓	11.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)

Compiler

Compiled 32805 to 21279 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series90.0ms (0.9%)

Counts

3 → 96

Calls

3 calls:

45.0ms	(-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta))))
36.0ms	(fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))
9.0ms	(fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
5×	`add-log-exp_binary64`

Counts

3 → 51

Calls

3 calls:

3.0ms	(-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta))))
1.0ms	(fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta))
0.0ms	(fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))

simplify115.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

572×	`fma-neg_binary64`
470×	`cancel-sign-sub-inv_binary64`
403×	`distribute-rgt-in_binary64`
397×	`distribute-lft-in_binary64`
358×	`associate-l_binary64`

Counts

147 → 90

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	108	2992
1	191	2714
2	641	2506
3	3185	2492
4	4594	2472
5	4873	2472

prune68.0ms (0.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	90	5	95

Error

0.1b

Counts

95 → 5

Alt Table

Status	Error	Program
	53.1b	(/.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)
	49.9b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	13.0b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 beta (+.f64 2 (*.f64 2 i)))) 1) 2)
✓	48.1b	(/.f64 (-.f64 2 (fma.f64 4 (/.f64 i beta) (fma.f64 2 (/.f64 alpha beta) (/.f64 2 beta)))) 2)
✓	11.9b	(/.f64 (fma.f64 (+.f64 alpha beta) (/.f64 (/.f64 (-.f64 beta alpha) (fma.f64 2 i (+.f64 alpha beta))) (+.f64 2 (fma.f64 2 i (+.f64 alpha beta)))) 1) 2)

Compiler

Compiled 2865 to 1745 computations (39.1% saved)

regimes718.0ms (7.1%)

Accuracy

Total 1.2b remaining (92.3%)

Threshold costs 0b (0%)

Counts

76 → 2

Compiler

Compiled 13601 to 9457 computations (30.5% saved)

bsearch3.0ms (0%)

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

simplify4.0ms (0%)

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	30	96
1	42	96
2	46	96
3	48	96
4	49	96
5	48	96

end161.0ms (1.6%)

Compiler: Compiled 297 to 179 computations (39.7% saved)

Details

analyze169.0ms (1.7%)

sample2.2s (21.5%)

simplify43.0ms (0.4%)

prune5.0ms (0.1%)

localize13.0ms (0.1%)

series1.3s (12.7%)

rewrite31.0ms (0.3%)

simplify243.0ms (2.4%)

prune594.0ms (5.9%)

localize13.0ms (0.1%)

series879.0ms (8.7%)

rewrite41.0ms (0.4%)

simplify293.0ms (2.9%)

prune657.0ms (6.5%)

localize14.0ms (0.1%)

series1.5s (14.5%)

rewrite36.0ms (0.4%)

simplify277.0ms (2.8%)

prune684.0ms (6.8%)

localize11.0ms (0.1%)

series90.0ms (0.9%)

rewrite7.0ms (0.1%)

simplify115.0ms (1.1%)

prune68.0ms (0.7%)

regimes718.0ms (7.1%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end161.0ms (1.6%)

Profiling