Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample300.0ms (6.8%)

Algorithm

1×

intervals

Results

9.0ms	196×	body	128	valid
6.0ms	256×	pre	128	true
5.0ms	28×	body	1024	valid
2.0ms	18×	body	512	valid
1.0ms	12×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify209.0ms (4.7%)

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

15.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.5b	(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 (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	2.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series51.0ms (1.1%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
18.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite14.0ms (0.3%)

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:

9.0ms	(/.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)

simplify106.0ms (2.4%)

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

prune135.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	136	6	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	137	6	143

Error

0.1b

Counts

143 → 6

Alt Table

Status	Error	Program
	46.2b	(/.f64 (+.f64 beta 1) alpha)
	15.5b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	46.5b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
	15.6b	(fma.f64 (/.f64 (/.f64 (-.f64 alpha beta) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) (sqrt.f64 (+.f64 (+.f64 beta alpha) 2))) -1/2 1/2)
	47.6b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))
▶	15.5b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

Compiler

Compiled 4463 to 2751 computations (38.4% saved)

localize9.0ms (0.2%)

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)))
✓	2.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

series71.0ms (1.6%)

Counts

3 → 72

Calls

3 calls:

36.0ms

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

19.0ms

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

16.0ms

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

rewrite47.0ms (1.1%)

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:

11.0ms

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

10.0ms

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

1.0ms

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

simplify183.0ms (4.1%)

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

prune289.0ms (6.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	309	3	312
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	312	6	318

Error

0.1b

Counts

318 → 6

Alt Table

Status	Error	Program
	46.5b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
	15.5b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 alpha (+.f64 2 beta))))) -1/2 1/2)
	46.2b	(/.f64 (+.f64 beta 1) alpha)
▶	15.5b	(exp.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)))
	15.7b	(fma.f64 (/.f64 1 (*.f64 (+.f64 (+.f64 beta alpha) 2) (/.f64 1 (-.f64 alpha beta)))) -1/2 1/2)
	47.6b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 9441 to 5746 computations (39.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta)))
✓	0.2b	(exp.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)))
✓	0.8b	(log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))
	2.9b	(fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)

series178.0ms (4%)

Counts

2 → 48

Calls

2 calls:

138.0ms	(log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))
39.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2)))
1.0ms	(log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))

simplify101.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

594×	`times-frac_binary64`
585×	`associate-/r*_binary64`
539×	`fma-def_binary64`
383×	`associate-/l*_binary64`
182×	`+-commutative_binary64`

Counts

79 → 119

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	557	6408
1	1886	6146
2	5233	6146

prune416.0ms (9.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	335	1	336
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	336	6	342

Error

0.1b

Counts

342 → 6

Alt Table

Status	Error	Program
	46.5b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
▶	15.5b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 alpha (+.f64 2 beta))))) -1/2 1/2)
	46.2b	(/.f64 (+.f64 beta 1) alpha)
	15.7b	(fma.f64 (/.f64 1 (*.f64 (+.f64 (+.f64 beta alpha) 2) (/.f64 1 (-.f64 alpha beta)))) -1/2 1/2)
	16.2b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))))
	47.6b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 15328 to 10445 computations (31.9% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 alpha (+.f64 2 beta)))
✓	2.9b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 alpha (+.f64 2 beta))))) -1/2 1/2)
✓	3.8b	(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 alpha (+.f64 2 beta)))))

series88.0ms (2%)

Counts

3 → 72

Calls

3 calls:

44.0ms

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

23.0ms

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

21.0ms

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

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`*-un-lft-identity_binary64`
50×	`times-frac_binary64`
49×	`add-sqr-sqrt_binary64`
33×	`distribute-lft-out_binary64`
32×	`log-pow_binary64`

Counts

3 → 110

Calls

3 calls:

14.0ms

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

9.0ms

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

0.0ms

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

simplify137.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

964×	`times-frac_binary64`
218×	`+-commutative_binary64`
209×	`fma-def_binary64`
196×	`fma-neg_binary64`
193×	`associate-+r+_binary64`

Counts

182 → 194

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	367	5558
1	1008	5375
2	3573	5311
3	4999	5311

prune203.0ms (4.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	194	6	200

Error

0.1b

Counts

200 → 6

Alt Table

Status	Error	Program
	46.5b	(fma.f64 (*.f64 (+.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (/.f64 (-.f64 (sqrt.f64 alpha) (sqrt.f64 beta)) (+.f64 beta (+.f64 2 alpha)))) -1/2 1/2)
✓	15.5b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 alpha (+.f64 2 beta))))) -1/2 1/2)
	46.2b	(/.f64 (+.f64 beta 1) alpha)
	15.7b	(fma.f64 (/.f64 1 (*.f64 (+.f64 (+.f64 beta alpha) 2) (/.f64 1 (-.f64 alpha beta)))) -1/2 1/2)
	16.2b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))))) (cbrt.f64 (log.f64 (fma.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 beta alpha) 2) (-.f64 alpha beta))) -1/2 1/2))))
	47.6b	(-.f64 (+.f64 (pow.f64 (/.f64 beta alpha) 3) (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 4 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 8 (/.f64 beta (pow.f64 alpha 3)) (.f64 5 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)))))))) (+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha)))))

Compiler

Compiled 5855 to 3732 computations (36.3% saved)

regimes633.0ms (14.3%)

Accuracy

Total 0.0b remaining (26.5%)

Threshold costs 0.0b (26.5%)

Counts

88 → 2

Compiler

Compiled 7814 to 5830 computations (25.4% saved)

bsearch6.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`*-commutative_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	85
1	42	85
2	58	85
3	75	85
4	84	85
5	87	85
6	85	85

end1.0ms (0%)

Compiler: Compiled 60 to 33 computations (45% saved)

sample1.2s (26.1%)

Algorithm

1×

intervals

Results

269.0ms	5928×	body	128	valid
174.0ms	1044×	body	1024	valid
168.0ms	8000×	pre	128	true
79.0ms	601×	body	512	valid
28.0ms	333×	body	256	valid
19.0ms	94×	body	2048	valid

Compiler

Compiled 259 to 168 computations (35.1% saved)

Details

analyze2.0ms (0.1%)

sample300.0ms (6.8%)

simplify209.0ms (4.7%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series51.0ms (1.1%)

rewrite14.0ms (0.3%)

simplify106.0ms (2.4%)

prune135.0ms (3.1%)

localize9.0ms (0.2%)

series71.0ms (1.6%)

rewrite47.0ms (1.1%)

simplify183.0ms (4.1%)

prune289.0ms (6.6%)

localize11.0ms (0.2%)

series178.0ms (4%)

rewrite4.0ms (0.1%)

simplify101.0ms (2.3%)

prune416.0ms (9.4%)

localize10.0ms (0.2%)

series88.0ms (2%)

rewrite44.0ms (1%)

simplify137.0ms (3.1%)

prune203.0ms (4.6%)

regimes633.0ms (14.3%)

bsearch6.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.2s (26.1%)

Profiling