Details

analyze2.0ms (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)

sample1.8s (35.4%)

Results

787.0ms	6220×	body	128	valid
443.0ms	1055×	body	1024	valid
159.0ms	578×	body	512	valid
59.0ms	304×	body	256	valid
43.0ms	99×	body	2048	valid

Compiler

Compiled 59 to 43 computations (27.1% saved)

simplify206.0ms (4.1%)

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

15.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	15.1b	(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))
✓	0.7b	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

series40.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

26.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)
14.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))

rewrite67.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

472×	`fma-def_binary64`
257×	`fma-neg_binary64`
236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
132×	`add-sqr-sqrt_binary64`

Counts

2 → 76

Calls

2 calls:

65.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2))
65.0ms	(fma.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 beta alpha) 2)) -1/2 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	30
1	261	30
2	3563	30
3	4908	30

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

935×	`times-frac_binary64`
498×	`cancel-sign-sub-inv_binary64`
367×	`sub-neg_binary64`
205×	`+-commutative_binary64`
189×	`associate-+r+_binary64`

Counts

124 → 130

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	221	2358
1	749	2323
2	2913	2279
3	5252	2279

prune146.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	126	4	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	4	131

Error

0.0b

Counts

131 → 4

Alt Table

Status	Error	Program
	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
	47.3b	(-.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)))))
▶	15.1b	(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
	49.6b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))

Compiler

Compiled 4133 to 2638 computations (36.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta))
✓	0.1b	(pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1)
✓	0.7b	(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)

series94.0ms (1.9%)

Counts

3 → 72

Calls

3 calls:

48.0ms

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

32.0ms

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

12.0ms

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

rewrite71.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

647×	`prod-diff_binary64`
144×	`add-sqr-sqrt_binary64`
140×	`log1p-expm1-u_binary64`
140×	`expm1-log1p-u_binary64`
136×	`add-log-exp_binary64`

Counts

3 → 108

Calls

3 calls:

69.0ms

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

69.0ms

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

69.0ms

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	295	43
2	3673	43
3	4892	43

simplify138.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-def_binary64`
430×	`associate-+l+_binary64`
329×	`times-frac_binary64`
287×	`associate-/r*_binary64`
193×	`associate-/l*_binary64`

Counts

180 → 191

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	422	4212
1	1483	4134
2	5280	4134

prune193.0ms (3.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	191	4	195

Error

0.0b

Counts

195 → 4

Alt Table

Status	Error	Program
▶	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
	47.3b	(-.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)))))
✓	15.1b	(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
	49.6b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))

Compiler

Compiled 7172 to 4779 computations (33.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))
✓	0.0b	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))
✓	0.7b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
✓	6.4b	(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))))

series81.0ms (1.6%)

Counts

4 → 96

Calls

4 calls:

27.0ms	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
25.0ms	(exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))
14.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))
14.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))))

rewrite223.0ms (4.5%)

Algorithm

1×	batch-egg-rewrite

Rules

863×	`prod-diff_binary64`
537×	`egg-rr`
137×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`

Counts

4 → 537

Calls

4 calls:

196.0ms	(exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))
196.0ms	(/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))
196.0ms	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
196.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	58
1	274	58
2	3639	58
3	5349	58

simplify103.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

309×	`times-frac_binary64`
306×	`fma-def_binary64`
294×	`associate-+r+_binary64`
252×	`associate-+l+_binary64`
250×	`associate-/r*_binary64`

Counts

633 → 387

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	391	5127
1	1291	5061
2	5260	5061

prune465.0ms (9.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	387	0	387
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	387	4	391

Error

0.0b

Counts

391 → 4

Alt Table

Status	Error	Program
✓	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
▶	47.3b	(-.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)))))
✓	15.1b	(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
	49.6b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))

Compiler

Compiled 21001 to 12740 computations (39.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	2.9b	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
✓	3.0b	(-.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)))))
✓	4.2b	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
✓	8.0b	(/.f64 beta (*.f64 alpha alpha))

series117.0ms (2.3%)

Counts

4 → 96

Calls

4 calls:

34.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
31.0ms	(-.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)))))
27.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
25.0ms	(/.f64 beta (*.f64 alpha alpha))

rewrite97.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

320×	`log1p-udef_binary64`
182×	`add-sqr-sqrt_binary64`
180×	`log1p-expm1-u_binary64`
180×	`expm1-log1p-u_binary64`
173×	`add-log-exp_binary64`

Counts

4 → 144

Calls

4 calls:

92.0ms	(fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha)))
92.0ms	(-.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)))))
92.0ms	(+.f64 (/.f64 2 (.f64 alpha alpha)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (*.f64 (/.f64 beta alpha) (/.f64 beta alpha))))
92.0ms	(/.f64 beta (*.f64 alpha alpha))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	88
1	378	83
2	4706	83
3	5124	83

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

685×	`associate-/l/_binary64`
318×	`sub-neg_binary64`
297×	`fma-def_binary64`
276×	`distribute-neg-frac_binary64`
203×	`distribute-rgt-neg-in_binary64`

Counts

240 → 173

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	35	1850
1	94	1820
2	244	1623
3	703	1484
4	2529	1387
5	4971	1387

prune154.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	172	5	177

Error

0.0b

Counts

177 → 5

Alt Table

Status	Error	Program
	47.5b	(fma.f64 (sqrt.f64 (+.f64 (/.f64 beta alpha) (/.f64 1 alpha))) (sqrt.f64 (+.f64 (/.f64 beta alpha) (/.f64 1 alpha))) (neg.f64 (fma.f64 2 (pow.f64 alpha -2) (fma.f64 3 (/.f64 beta (*.f64 alpha alpha)) (pow.f64 (/.f64 beta alpha) 2)))))
✓	15.2b	(fma.f64 (log.f64 (exp.f64 (/.f64 (-.f64 alpha beta) (+.f64 (+.f64 alpha beta) 2)))) -1/2 1/2)
✓	47.3b	(-.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)))))
✓	15.1b	(fma.f64 (pow.f64 (/.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 alpha beta)) -1) -1/2 1/2)
	49.6b	(-.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 7 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4)) (+.f64 (/.f64 8 (pow.f64 alpha 4)) (+.f64 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4)) (fma.f64 18 (/.f64 (.f64 beta beta) (pow.f64 alpha 4)) (fma.f64 20 (/.f64 beta (pow.f64 alpha 4)) (fma.f64 3 (/.f64 beta (.f64 alpha alpha)) (.f64 (/.f64 beta alpha) (/.f64 beta alpha))))))))))

Compiler

Compiled 7047 to 3427 computations (51.4% saved)

regimes703.0ms (14.1%)

Accuracy

Total 0.2b remaining (84%)

Threshold costs 0.2b (84%)

Counts

96 → 2

Compiler

Compiled 11594 to 7950 computations (31.4% saved)

bsearch5.0ms (0.1%)

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
11×	`sub-neg_binary64`
9×	`*-commutative_binary64`
8×	`neg-sub0_binary64`
8×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	79
1	46	79
2	60	79
3	79	79
4	99	79
5	108	79
6	112	79
7	113	79
8	110	79

end136.0ms (2.7%)

Compiler: Compiled 307 to 193 computations (37.1% saved)

Details

analyze2.0ms (0%)

sample1.8s (35.4%)

simplify206.0ms (4.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series40.0ms (0.8%)

rewrite67.0ms (1.3%)

simplify66.0ms (1.3%)

prune146.0ms (2.9%)

localize9.0ms (0.2%)

series94.0ms (1.9%)

rewrite71.0ms (1.4%)

simplify138.0ms (2.8%)

prune193.0ms (3.9%)

localize11.0ms (0.2%)

series81.0ms (1.6%)

rewrite223.0ms (4.5%)

simplify103.0ms (2.1%)

prune465.0ms (9.3%)

localize13.0ms (0.3%)

series117.0ms (2.3%)

rewrite97.0ms (1.9%)

simplify70.0ms (1.4%)

prune154.0ms (3.1%)

regimes703.0ms (14.1%)

bsearch5.0ms (0.1%)

simplify5.0ms (0.1%)

end136.0ms (2.7%)

Profiling