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)

sample1.5s (44.1%)

Results

764.0ms	6177×	body	128	valid
381.0ms	1011×	body	1024	valid
181.0ms	651×	body	512	valid
62.0ms	324×	body	256	valid
50.0ms	93×	body	2048	valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

preprocess39.0ms (1.2%)

Algorithm

2×	egg-herbie

Rules

954×	`fma-neg_binary64`
549×	`div-sub_binary64`
376×	`times-frac_binary64`
249×	`cancel-sign-sub-inv_binary64`
246×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	38
1	39	38
2	64	38
3	109	38
4	201	38
5	404	34
6	859	34
7	2060	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 15 to 11 computations (26.7% saved)

simplify28.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

434×	`cancel-sign-sub-inv_binary64`
372×	`div-sub_binary64`
343×	`sub-neg_binary64`
331×	`fma-neg_binary64`
292×	`fma-def_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	40	19
3	67	19
4	118	19
5	238	17
6	445	17
7	753	17
8	1572	17
9	3643	17

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

16.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	16.8b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)

Compiler

Compiled 57 to 41 computations (28.1% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
✓	1.9b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series36.0ms (1.1%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	alpha	-inf
5.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	alpha	inf
4.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	beta	-inf
3.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))	beta	inf
3.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)	alpha	0

rewrite66.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

585×	`fma-def_binary64`
369×	`fma-neg_binary64`
219×	`log1p-udef_binary64`
218×	`expm1-udef_binary64`
127×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	243	29
2	3699	29

Stop Event

1×	node limit

Counts

2 → 127

simplify54.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

877×	`fma-def_binary64`
595×	`times-frac_binary64`
359×	`cancel-sign-sub-inv_binary64`
303×	`sub-neg_binary64`
160×	`+-commutative_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	172	2372
1	564	2336
2	2232	2166

Stop Event

1×	node limit

Counts

175 → 188

prune170.0ms (5.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	185	3	188
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	185	4	189

Error

0.0b

Counts

189 → 4

Alt Table

Status	Error	Program
✓	16.8b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
	47.7b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 3)))))))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 alpha 2))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 16 (/.f64 1 (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 36 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (pow.f64 alpha 2))) (.f64 2 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 2))))))))))) 2)
▶	44.4b	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)
	46.8b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)

Compiler

Compiled 5684 to 3883 computations (31.7% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)

series8.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

1.0ms	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)	beta	-inf
1.0ms	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)	beta	inf
1.0ms	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)	beta	0
1.0ms	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)	alpha	0
1.0ms	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)	alpha	-inf

rewrite39.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

776×	`log1p-expm1-u_binary64`
776×	`expm1-log1p-u_binary64`
142×	`log1p-udef_binary64`
79×	`add-sqr-sqrt_binary64`
74×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	156	11
2	2064	11

Stop Event

1×	node limit

Counts

1 → 29

simplify29.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1132×	`distribute-rgt-in_binary64`
688×	`fma-def_binary64`
512×	`distribute-lft-in_binary64`
351×	`associate-/l*_binary64`
278×	`associate-*l/_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	15	222
1	25	222
2	39	222
3	59	222
4	102	159
5	254	159
6	841	159
7	2320	159
8	4620	159

Stop Event

1×	node limit

Counts

53 → 35

prune27.0ms (0.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	35	4	39

Error

0.0b

Counts

39 → 4

Alt Table

Status	Error	Program
✓	16.8b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
	47.7b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 3)))))))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 alpha 2))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 16 (/.f64 1 (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 36 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (pow.f64 alpha 2))) (.f64 2 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 2))))))))))) 2)
✓	44.4b	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)
▶	46.8b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)

Compiler

Compiled 687 to 544 computations (20.8% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.5%)

Counts

2 → 39

Calls

12 calls:

2.0ms	(+.f64 (/.f64 1 beta) (/.f64 alpha beta))	beta	inf
2.0ms	(fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2)	alpha	inf
2.0ms	(fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2)	alpha	-inf
2.0ms	(fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2)	alpha	0
1.0ms	(+.f64 (/.f64 1 beta) (/.f64 alpha beta))	alpha	inf

rewrite49.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

959×	`prod-diff_binary64`
183×	`log1p-udef_binary64`
105×	`add-sqr-sqrt_binary64`
101×	`log1p-expm1-u_binary64`
101×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	218	24
2	2918	24

Stop Event

1×	node limit

Counts

2 → 77

simplify51.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def_binary64`
679×	`fma-neg_binary64`
215×	`cancel-sign-sub-inv_binary64`
97×	`sub-neg_binary64`
78×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	419
1	50	381
2	110	381
3	206	325
4	433	325
5	962	325
6	1883	325
7	2688	325
8	3133	325
9	3272	325
10	3273	325

Stop Event

1×

saturated

Counts

116 → 89

prune60.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	89	4	93

Error

0.0b

Counts

93 → 4

Alt Table

Status	Error	Program
✓	16.8b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
▶	47.7b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 3)))))))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 alpha 2))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 16 (/.f64 1 (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 36 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (pow.f64 alpha 2))) (.f64 2 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 2))))))))))) 2)
✓	44.4b	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)
✓	46.8b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)

Compiler

Compiled 1804 to 1238 computations (31.4% saved)

localize79.0ms (2.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	19.6b	(/.f64 (pow.f64 beta 2) (pow.f64 alpha 2))
✓	21.4b	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))
✓	22.2b	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))
✓	23.0b	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))

series129.0ms (3.9%)

Counts

4 → 0

Calls

24 calls:

11.0ms	(/.f64 (pow.f64 beta 2) (pow.f64 alpha 2))	alpha	inf
10.0ms	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))	beta	inf
8.0ms	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))	beta	inf
8.0ms	(/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))	beta	inf
7.0ms	(/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))	beta	-inf

rewrite62.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

246×	`log1p-udef_binary64`
200×	`prod-diff_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
151×	`egg-rr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	40
1	362	34
2	4318	34

Stop Event

1×	node limit

Counts

4 → 151

simplify10.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

151 → 151

prune387.0ms (11.8%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	151	4	155

Error

0.0b

Counts

155 → 4

Alt Table

Status	Error	Program
✓	16.8b	(/.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1) 2)
✓	47.7b	(/.f64 (-.f64 (+.f64 (.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 1 alpha)) (+.f64 (.f64 8 (/.f64 1 (pow.f64 alpha 3))) (+.f64 (.f64 2 (/.f64 beta alpha)) (+.f64 (.f64 16 (/.f64 beta (pow.f64 alpha 3))) (.f64 10 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 3)))))))) (+.f64 (.f64 4 (/.f64 1 (pow.f64 alpha 2))) (+.f64 (.f64 14 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 4))) (+.f64 (.f64 16 (/.f64 1 (pow.f64 alpha 4))) (+.f64 (.f64 2 (/.f64 (pow.f64 beta 4) (pow.f64 alpha 4))) (+.f64 (.f64 36 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 4))) (+.f64 (.f64 40 (/.f64 beta (pow.f64 alpha 4))) (+.f64 (.f64 6 (/.f64 beta (pow.f64 alpha 2))) (.f64 2 (/.f64 (pow.f64 beta 2) (pow.f64 alpha 2))))))))))) 2)
✓	44.4b	(/.f64 (/.f64 (fma.f64 2 beta 2) alpha) 2)
✓	46.8b	(/.f64 (fma.f64 -2 (+.f64 (/.f64 1 beta) (/.f64 alpha beta)) 2) 2)

Compiler

Compiled 18949 to 14881 computations (21.5% saved)

regimes339.0ms (10.3%)

Accuracy

Total -0.0b remaining (-8.5%)

Threshold costs -0.0b (-8.5%)

Counts

40 → 2

Compiler

Compiled 6114 to 4710 computations (23% saved)

bsearch2.0ms (0.1%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

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

Steps

Iters	Point		Range
-0.9999988829058588	∈ [	-0.9999988829058588	,	-0.9998559781029119	]

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	83
1	37	83
2	44	83
3	48	83
4	50	83

Stop Event

1×

saturated

end134.0ms (4.1%)

Stop Event

1×

done

Compiler

Compiled 280 to 197 computations (29.6% saved)

Details

analyze2.0ms (0.1%)

sample1.5s (44.1%)

preprocess39.0ms (1.2%)

simplify28.0ms (0.8%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series36.0ms (1.1%)

rewrite66.0ms (2%)

simplify54.0ms (1.6%)

prune170.0ms (5.2%)

localize5.0ms (0.1%)

series8.0ms (0.2%)

rewrite39.0ms (1.2%)

simplify29.0ms (0.9%)

prune27.0ms (0.8%)

localize7.0ms (0.2%)

series15.0ms (0.5%)

rewrite49.0ms (1.5%)

simplify51.0ms (1.6%)

prune60.0ms (1.8%)

localize79.0ms (2.4%)

series129.0ms (3.9%)

rewrite62.0ms (1.9%)

simplify10.0ms (0.3%)

prune387.0ms (11.8%)

regimes339.0ms (10.3%)

bsearch2.0ms (0.1%)

simplify3.0ms (0.1%)

end134.0ms (4.1%)

Profiling