Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
56.2%	0%	43.8%	1

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.3s (26.5%)

Infinites

0% of outputs are infinite.

Results

502.0ms	6114×	body	128	valid
279.0ms	1110×	body	1024	valid
120.0ms	629×	body	512	valid
41.0ms	307×	body	256	valid
30.0ms	96×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify205.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

890×	`sub-neg_binary64`
434×	`cancel-sign-sub-inv_binary64`
422×	`associate-/l*_binary64`
388×	`distribute-rgt-neg-in_binary64`
379×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	39	19
3	64	19
4	108	19
5	215	17
6	353	17
7	603	17
8	1141	17
9	2484	17
10	3195	17
11	3981	17
12	4235	17
13	4399	17
14	4503	17
15	4531	17
16	4533	17
17	4768	17
18	4708	17
19	4930	17
20	4826	17

prune3.0ms (0.1%)

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

19.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.3b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series65.0ms (1.4%)

Counts

2 → 48

Calls

2 calls:

34.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
31.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
18×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
0.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify86.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

960×	`times-frac_binary64`
218×	`+-commutative_binary64`
206×	`fma-def_binary64`
194×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

112 → 142

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	3790
1	962	3664
2	3486	3620
3	4984	3620

prune107.0ms (2.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	2	143

Error

0.0b

Counts

143 → 2

Alt Table

Status	Error	Program
▶	19.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
	42.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Status

Error

Program

▶

19.9b

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

42.4b

(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 4271 to 2619 computations (38.7% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))
✓	0.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta)))
✓	1.3b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

series73.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

35.0ms

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

19.0ms

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

18.0ms

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

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

273×	`*-un-lft-identity_binary64`
218×	`times-frac_binary64`
143×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
78×	`distribute-lft-out_binary64`

Counts

3 → 213

Calls

3 calls:

12.0ms

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

9.0ms

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

0.0ms

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

simplify182.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

351×	`associate-+r+_binary64`
322×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`associate-+l+_binary64`
239×	`fma-neg_binary64`

Counts

285 → 312

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	429	8554
1	1278	7974
2	4784	7972
3	4975	7972

prune235.0ms (5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	312	2	314

Error

0.0b

Counts

314 → 2

Alt Table

Status	Error	Program
✓	19.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
▶	42.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Status

Error

Program

✓

19.9b

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

▶

42.4b

(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (*.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 9237 to 5600 computations (39.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.6b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	2.8b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	3.3b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	8.5b	(/.f64 beta (*.f64 alpha alpha))

series132.0ms (2.8%)

Counts

4 → 96

Calls

4 calls:

38.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
35.0ms	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
31.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
27.0ms	(/.f64 beta (*.f64 alpha alpha))

rewrite68.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`*-un-lft-identity_binary64`
48×	`prod-diff_binary64`
46×	`distribute-lft-out_binary64`
41×	`times-frac_binary64`
38×	`add-sqr-sqrt_binary64`

Counts

4 → 150

Calls

4 calls:

25.0ms	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
6.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
3.0ms	(/.f64 beta (*.f64 alpha alpha))
0.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))

simplify245.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

685×	`times-frac_binary64`
502×	`fma-neg_binary64`
299×	`cancel-sign-sub-inv_binary64`
192×	`distribute-rgt-neg-in_binary64`
161×	`distribute-rgt-in_binary64`

Counts

246 → 203

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	227	10949
1	623	9056
2	2377	7436
3	4711	7436
4	4930	7436

prune172.0ms (3.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	202	3	205

Error

0.0b

Counts

205 → 3

Alt Table

Status	Error	Program
✓	19.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
✓	42.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
▶	42.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))) (cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 3 (.f64 beta (/.f64 beta (*.f64 alpha alpha))))))

Compiler

Compiled 11549 to 4207 computations (63.6% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	3.5b	(-.f64 (/.f64 -2 (.f64 alpha alpha)) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 3 (.f64 beta (/.f64 beta (.f64 alpha alpha)))))
✓	4.0b	(.f64 beta (/.f64 beta (.f64 alpha alpha)))
✓	7.4b	(cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))
	8.5b	(/.f64 beta (*.f64 alpha alpha))

series317.0ms (6.7%)

Counts

3 → 72

Calls

3 calls:

252.0ms

(cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))

34.0ms

(-.f64 (/.f64 -2 (*.f64 alpha alpha)) (fma.f64 (/.f64 beta (*.f64 alpha alpha)) 3 (*.f64 beta (/.f64 beta (*.f64 alpha alpha)))))

31.0ms

(*.f64 beta (/.f64 beta (*.f64 alpha alpha)))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
24×	`times-frac_binary64`
21×	`prod-diff_binary64`

Counts

3 → 103

Calls

3 calls:

11.0ms

(cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))

8.0ms

(-.f64 (/.f64 -2 (*.f64 alpha alpha)) (fma.f64 (/.f64 beta (*.f64 alpha alpha)) 3 (*.f64 beta (/.f64 beta (*.f64 alpha alpha)))))

6.0ms

(*.f64 beta (/.f64 beta (*.f64 alpha alpha)))

simplify146.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

476×	`fma-neg_binary64`
272×	`distribute-rgt-in_binary64`
241×	`distribute-lft-in_binary64`
239×	`exp-prod_binary64`
213×	`cancel-sign-sub-inv_binary64`

Counts

175 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	285	5095
1	639	3722
2	2057	3160
3	4580	3040
4	4995	3040

prune302.0ms (6.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	353	0	353
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	353	3	356

Error

0.0b

Counts

356 → 3

Alt Table

Status	Error	Program
✓	19.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)
✓	42.4b	(-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
✓	42.7b	(fma.f64 (.f64 (cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)))) (cbrt.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha))) (-.f64 (/.f64 -2 (.f64 alpha alpha)) (fma.f64 (/.f64 beta (.f64 alpha alpha)) 3 (.f64 beta (/.f64 beta (*.f64 alpha alpha))))))

Compiler

Compiled 21064 to 9589 computations (54.5% saved)

regimes895.0ms (18.8%)

Accuracy

Total 0.9b remaining (92.8%)

Threshold costs 0.9b (92.8%)

Counts

87 → 2

Compiler

Compiled 14840 to 8466 computations (43% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
7×	`sub-neg_binary64`
4×	`*-commutative_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	65
1	39	65
2	51	65
3	59	65
4	64	65
5	65	65
6	64	65

end79.0ms (1.7%)

Compiler: Compiled 188 to 112 computations (40.4% saved)

Details

analyze1.0ms (0%)

sample1.3s (26.5%)

simplify205.0ms (4.3%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series65.0ms (1.4%)

rewrite39.0ms (0.8%)

simplify86.0ms (1.8%)

prune107.0ms (2.3%)

localize13.0ms (0.3%)

series73.0ms (1.5%)

rewrite45.0ms (0.9%)

simplify182.0ms (3.8%)

prune235.0ms (5%)

localize15.0ms (0.3%)

series132.0ms (2.8%)

rewrite68.0ms (1.4%)

simplify245.0ms (5.2%)

prune172.0ms (3.6%)

localize18.0ms (0.4%)

series317.0ms (6.7%)

rewrite35.0ms (0.7%)

simplify146.0ms (3.1%)

prune302.0ms (6.4%)

regimes895.0ms (18.8%)

bsearch5.0ms (0.1%)

simplify4.0ms (0.1%)

end79.0ms (1.7%)

Profiling