Details

analyze3.0ms (0%)

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)

sample262.0ms (2.9%)

Algorithm

1×

intervals

Results

8.0ms	189×	body	128	valid
6.0ms	37×	body	1024	valid
5.0ms	256×	pre	128	true
2.0ms	18×	body	512	valid
1.0ms	10×	body	256	valid
0.0ms	2×	body	2048	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify184.0ms (2%)

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%)

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

16.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.4b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series55.0ms (0.6%)

Counts

2 → 48

Calls

2 calls:

35.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
19.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite14.0ms (0.2%)

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)

simplify87.0ms (1%)

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 (1.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	4	143

Error

0.0b

Counts

143 → 4

Alt Table

Status	Error	Program
▶	16.4b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	44.2b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	45.9b	(-.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)))))
	45.1b	(/.f64 (+.f64 beta 1) alpha)

Compiler

Compiled 4307 to 2645 computations (38.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.1b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	1.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	1.4b	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

series200.0ms (2.2%)

Counts

2 → 48

Calls

2 calls:

150.0ms	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
49.0ms	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite4.0ms (0%)

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:

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

simplify95.0ms (1%)

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 → 117

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	556	6288
1	1886	6047
2	5229	6047

prune315.0ms (3.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	256	3	259
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	257	6	263

Error

0.0b

Counts

263 → 6

Alt Table

Status	Error	Program
✓	16.4b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	47.7b	(exp.f64 (log.f64 (-.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)))))))
	45.9b	(-.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)))))
	45.1b	(/.f64 (+.f64 beta 1) alpha)
	44.3b	(exp.f64 (neg.f64 (/.f64 (+.f64 alpha 1) beta)))
▶	16.4b	(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 12487 to 8595 computations (31.2% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.1b	(pow.f64 (E.f64) (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	1.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
	1.4b	(log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))

series177.0ms (2%)

Counts

1 → 24

Calls

1 calls:

177.0ms

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

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow-unpow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`pow1_binary64`

Counts

1 → 24

Calls

1 calls:

2.0ms

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

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Rules

298×	`times-frac_binary64`
294×	`sub-neg_binary64`
271×	`associate-/r*_binary64`
239×	`associate-/l*_binary64`
232×	`fma-def_binary64`

Counts

48 → 75

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	294	3718
1	1016	3263
2	4394	3176
3	5048	3176

prune347.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	278	1	279
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	279	6	285

Error

0.0b

Counts

285 → 6

Alt Table

Status	Error	Program
✓	16.4b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	47.7b	(exp.f64 (log.f64 (-.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)))))))
	45.9b	(-.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)))))
	45.1b	(/.f64 (+.f64 beta 1) alpha)
▶	16.8b	(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
	44.3b	(exp.f64 (neg.f64 (/.f64 (+.f64 alpha 1) beta)))

Compiler

Compiled 15378 to 10560 computations (31.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))
✓	0.4b	(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
	1.2b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	1.9b	(log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

series4.7s (51.8%)

Counts

3 → 48

Calls

3 calls:

2.6s

(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))

1.1s

(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))

1.0s

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

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`add-sqr-sqrt_binary64`
60×	`log-prod_binary64`
54×	`unpow-prod-up_binary64`
30×	`sqrt-prod_binary64`
25×	`unswap-sqr_binary64`

Counts

3 → 145

Calls

3 calls:

11.0ms

(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))

5.0ms

(pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))

1.0ms

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

simplify253.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

641×	`fma-def_binary64`
561×	`times-frac_binary64`
464×	`associate-/r*_binary64`
402×	`associate-/l*_binary64`
190×	`*-commutative_binary64`

Counts

193 → 254

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	620	13080
1	2039	11959
2	5526	11959

prune681.0ms (7.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	465	1	466
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	466	6	472

Error

0.0b

Counts

472 → 6

Alt Table

Status	Error	Program
	16.9b	(*.f64 (pow.f64 (E.f64) (log.f64 (sqrt.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (pow.f64 (E.f64) (log.f64 (sqrt.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 beta (+.f64 2 alpha))) -1/2 1/2)))))))
	45.1b	(/.f64 (+.f64 beta 1) alpha)
✓	16.4b	(exp.f64 (log.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	47.7b	(exp.f64 (log.f64 (-.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)))))))
	45.9b	(-.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)))))
	44.3b	(exp.f64 (neg.f64 (/.f64 (+.f64 alpha 1) beta)))

Compiler

Compiled 32553 to 22039 computations (32.3% saved)

regimes294.0ms (3.2%)

Accuracy

Total 0.1b remaining (55.5%)

Threshold costs 0.1b (55.5%)

Counts

46 → 2

Compiler

Compiled 4262 to 3253 computations (23.7% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

13×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`*-commutative_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	43	80
2	57	80
3	72	80
4	79	80
5	81	80
6	79	80

end1.0ms (0%)

Compiler: Compiled 56 to 32 computations (42.9% saved)

sample1.1s (12.1%)

Algorithm

1×

intervals

Results

263.0ms	5988×	body	128	valid
178.0ms	1030×	body	1024	valid
156.0ms	8000×	pre	128	true
66.0ms	544×	body	512	valid
29.0ms	329×	body	256	valid
23.0ms	109×	body	2048	valid

Compiler

Compiled 211 to 133 computations (37% saved)

Details

analyze3.0ms (0%)

sample262.0ms (2.9%)

simplify184.0ms (2%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series55.0ms (0.6%)

rewrite14.0ms (0.2%)

simplify87.0ms (1%)

prune107.0ms (1.2%)

localize9.0ms (0.1%)

series200.0ms (2.2%)

rewrite4.0ms (0%)

simplify95.0ms (1%)

prune315.0ms (3.5%)

localize20.0ms (0.2%)

series177.0ms (2%)

rewrite3.0ms (0%)

simplify92.0ms (1%)

prune347.0ms (3.8%)

localize14.0ms (0.2%)

series4.7s (51.8%)

rewrite40.0ms (0.4%)

simplify253.0ms (2.8%)

prune681.0ms (7.5%)

regimes294.0ms (3.2%)

bsearch1.0ms (0%)

simplify4.0ms (0%)

end1.0ms (0%)

sample1.1s (12.1%)

Profiling