Details

analyze292.0ms (6%)

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)

sample64.0ms (1.3%)

Algorithm

1×

intervals

Results

17.0ms	193×	body	128	valid
14.0ms	39×	body	1024	valid
8.0ms	256×	pre	128	true
4.0ms	16×	body	512	valid
1.0ms	3×	body	2048	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 39 to 29 computations (25.6% saved)

simplify239.0ms (4.9%)

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

prune6.0ms (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

15.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.9b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	1.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series141.0ms (2.9%)

Counts

2 → 48

Calls

2 calls:

90.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
51.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite30.0ms (0.6%)

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:

19.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
1.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

simplify178.0ms (3.7%)

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

prune237.0ms (4.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	137	5	142
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	5	143

Error

0.1b

Counts

143 → 5

Alt Table

Status	Error	Program
	45.7b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	46.6b	(-.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)))))
▶	15.9b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	15.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	15.9b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 4357 to 2683 computations (38.4% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))
✓	0.3b	(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))
✓	1.1b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

series207.0ms (4.3%)

Counts

3 → 72

Calls

3 calls:

90.0ms

(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))

70.0ms

(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

46.0ms

(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log1p-expm1-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

3 → 32

Calls

3 calls:

1.0ms

(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)

1.0ms

(expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))

1.0ms

(log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))))

simplify160.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

309×	`times-frac_binary64`
309×	`fma-def_binary64`
276×	`associate-+l+_binary64`
250×	`associate-/r*_binary64`
233×	`associate-/l*_binary64`

Counts

104 → 142

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	432	4807
1	1373	4631
2	5006	4631

prune445.0ms (9.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	238	5	243

Error

0.1b

Counts

243 → 5

Alt Table

Status	Error	Program
	45.7b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	46.6b	(-.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)))))
✓	15.9b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	15.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
▶	15.9b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

Compiler

Compiled 8337 to 5527 computations (33.7% saved)

localize26.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
✓	0.0b	(log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
✓	0.0b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	1.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series201.0ms (4.1%)

Counts

2 → 48

Calls

2 calls:

137.0ms	(log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
64.0ms	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

1.0ms	(log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
0.0ms	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

simplify76.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

464×	`times-frac_binary64`
383×	`associate-/r*_binary64`
362×	`fma-def_binary64`
307×	`associate-/l*_binary64`
201×	`associate-r_binary64`

Counts

70 → 94

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	407	4584
1	1378	4415
2	5011	4415

prune244.0ms (5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	234	2	236
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	235	6	241

Error

0.0b

Counts

241 → 6

Alt Table

Status	Error	Program
	46.2b	(expm1.f64 (-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 5/2 (.f64 alpha alpha)) (fma.f64 4 (/.f64 beta (.f64 alpha alpha)) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) 3/2)))))
	45.7b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
✓	15.9b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
▶	15.9b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
✓	15.9b	(expm1.f64 (log1p.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))
	48.2b	(expm1.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) 7/3 (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 19/3 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 (/.f64 beta (pow.f64 alpha 3)) 14 (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10)))))) (+.f64 (/.f64 5/2 (.f64 alpha alpha)) (fma.f64 4 (/.f64 beta (.f64 alpha alpha)) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) 3/2)))))

Compiler

Compiled 9948 to 6757 computations (32.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
	1.1b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
✓	1.1b	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

series85.0ms (1.7%)

Counts

2 → 48

Calls

2 calls:

47.0ms	(exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))
37.0ms	(log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

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

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Rules

363×	`sub-neg_binary64`
288×	`times-frac_binary64`
253×	`fma-def_binary64`
251×	`+-commutative_binary64`
247×	`associate-+r+_binary64`

Counts

80 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	370	4045
1	1105	3894
2	4579	3852
3	5169	3852

prune256.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	253	2	255
Fresh	0	3	3
Picked	1	0	1
Done	1	1	2
Total	255	6	261

Error

0.0b

Counts

261 → 6

Alt Table

Status	Error	Program
	46.2b	(expm1.f64 (-.f64 (+.f64 (/.f64 1 alpha) (/.f64 beta alpha)) (+.f64 (/.f64 5/2 (.f64 alpha alpha)) (fma.f64 4 (/.f64 beta (.f64 alpha alpha)) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) 3/2)))))
	45.7b	(-.f64 1 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)))
	16.3b	(.f64 (.f64 (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))))) (cbrt.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
	16.3b	(cbrt.f64 (.f64 (.f64 (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2))) (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))) (log.f64 (exp.f64 (fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)))))
✓	15.9b	(fma.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)))) -1/2 1/2)
	48.2b	(expm1.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) 7/3 (+.f64 (/.f64 1 alpha) (+.f64 (/.f64 19/3 (pow.f64 alpha 3)) (+.f64 (/.f64 beta alpha) (fma.f64 (/.f64 beta (pow.f64 alpha 3)) 14 (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) 10)))))) (+.f64 (/.f64 5/2 (.f64 alpha alpha)) (fma.f64 4 (/.f64 beta (.f64 alpha alpha)) (.f64 (.f64 (/.f64 beta alpha) (/.f64 beta alpha)) 3/2)))))

Compiler

Compiled 9388 to 6255 computations (33.4% saved)

regimes376.0ms (7.7%)

Accuracy

Total 0.0b remaining (55.8%)

Threshold costs 0.0b (55.8%)

Counts

53 → 2

Compiler

Compiled 4734 to 3630 computations (23.3% saved)

bsearch2.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	85
1	48	85
2	62	85
3	77	85
4	84	85
5	86	85
6	84	85

end1.0ms (0%)

Compiler: Compiled 59 to 35 computations (40.7% saved)

sample1.4s (29.4%)

Algorithm

1×

intervals

Results

299.0ms	5983×	body	128	valid
190.0ms	1056×	body	1024	valid
155.0ms	8000×	pre	128	true
81.0ms	582×	body	512	valid
30.0ms	282×	body	256	valid
20.0ms	97×	body	2048	valid

Compiler

Compiled 304 to 197 computations (35.2% saved)

Details

analyze292.0ms (6%)

sample64.0ms (1.3%)

simplify239.0ms (4.9%)

prune6.0ms (0.1%)

localize15.0ms (0.3%)

series141.0ms (2.9%)

rewrite30.0ms (0.6%)

simplify178.0ms (3.7%)

prune237.0ms (4.9%)

localize21.0ms (0.4%)

series207.0ms (4.3%)

rewrite4.0ms (0.1%)

simplify160.0ms (3.3%)

prune445.0ms (9.2%)

localize26.0ms (0.5%)

series201.0ms (4.1%)

rewrite2.0ms (0%)

simplify76.0ms (1.6%)

prune244.0ms (5%)

localize10.0ms (0.2%)

series85.0ms (1.7%)

rewrite4.0ms (0.1%)

simplify97.0ms (2%)

prune256.0ms (5.3%)

regimes376.0ms (7.7%)

bsearch2.0ms (0.1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.4s (29.4%)

Profiling