Details

analyze10.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

Compiler

Compiled 17 to 14 computations (17.6% saved)

sample1.5s (51.3%)

Results

469.0ms	4655×	body	128	valid
454.0ms	1328×	body	1024	valid
411.0ms	1541×	body	512	valid
122.0ms	732×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 50 to 41 computations (18% saved)

simplify17.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

127×	`fma-neg_binary64`
82×	`fma-def_binary64`
42×	`cancel-sign-sub-inv_binary64`
41×	`sub-neg_binary64`
28×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	22	22
2	38	22
3	64	22
4	122	22
5	237	22
6	388	22
7	509	22
8	615	22
9	635	22

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (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

9.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	9.8b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

Compiler

Compiled 63 to 51 computations (19% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
2.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.0ms	(/.f64 1 (-.f64 x 1))

rewrite74.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

236×	`expm1-udef_binary64`
236×	`log1p-udef_binary64`
136×	`add-sqr-sqrt_binary64`
134×	`log1p-expm1-u_binary64`
134×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
1	273	42
2	4302	42

Stop Event

1×	node limit

Counts

3 → 127

Calls

3 calls:

72.0ms	(/.f64 1 (-.f64 x 1))
72.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
72.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify32.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

587×	`fma-neg_binary64`
416×	`cancel-sign-sub-inv_binary64`
250×	`associate-l_binary64`
242×	`fma-def_binary64`
184×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	581
1	219	559
2	647	553
3	2026	550

Stop Event

1×	node limit

Counts

163 → 168

prune149.0ms (5.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	166	2	168
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	2	169

Error

0.1b

Counts

169 → 2

Alt Table

Status	Error	Program
	33.9b	(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9))))
▶	23.4b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))

Status

Error

Program

33.9b

(+.f64 (/.f64 2 (pow.f64 x 5)) (+.f64 (+.f64 (/.f64 2 (pow.f64 x 3)) (/.f64 2 (pow.f64 x 7))) (/.f64 2 (pow.f64 x 9))))

▶

23.4b

(/.f64 (+.f64 (*.f64 x (+.f64 1 x)) (*.f64 (+.f64 x -1) (-.f64 x (*.f64 (+.f64 1 x) 2)))) (*.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))

Compiler

Compiled 4096 to 3239 computations (20.9% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))
✓	0.0b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))
✓	0.1b	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
✓	14.5b	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

series9.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))
2.0ms	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
2.0ms	(.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))
1.0ms	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

rewrite86.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

285×	`log1p-udef_binary64`
160×	`add-sqr-sqrt_binary64`
155×	`log1p-expm1-u_binary64`
155×	`expm1-log1p-u_binary64`
153×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	90
1	325	90
2	4873	90

Stop Event

1×	node limit

Counts

4 → 148

Calls

4 calls:

81.0ms	(.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))
81.0ms	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))
81.0ms	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
81.0ms	(+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (*.f64 (+.f64 1 x) 2))))

simplify36.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

497×	`fma-neg_binary64`
354×	`cancel-sign-sub-inv_binary64`
262×	`sub-neg_binary64`
220×	`associate-l_binary64`
196×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	50	404
1	152	382
2	432	376
3	1404	376
4	4384	376

Stop Event

1×	node limit

Counts

196 → 174

prune151.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	172	2	174
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	173	3	176

Error

0.1b

Counts

176 → 3

Alt Table

Status	Error	Program
▶	0.1b	(/.f64 2 (.f64 (+.f64 x -1) (.f64 x (+.f64 1 x))))
✓	23.4b	(/.f64 (+.f64 (.f64 x (+.f64 1 x)) (.f64 (+.f64 x -1) (-.f64 x (.f64 (+.f64 1 x) 2)))) (.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))
	33.9b	(+.f64 (/.f64 2 (pow.f64 x 3)) (+.f64 (/.f64 2 (pow.f64 x 5)) (/.f64 2 (pow.f64 x 7))))

Compiler

Compiled 5996 to 3895 computations (35% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.1b	(.f64 (+.f64 x -1) (.f64 x (+.f64 1 x)))
✓	0.1b	(/.f64 2 (.f64 (+.f64 x -1) (.f64 x (+.f64 1 x))))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 2 (*.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))

rewrite55.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

489×	`log-prod_binary64`
282×	`fma-def_binary64`
248×	`prod-diff_binary64`
184×	`expm1-udef_binary64`
184×	`log1p-udef_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	222	16
2	2874	11

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

54.0ms

(/.f64 2 (*.f64 (+.f64 x -1) (*.f64 x (+.f64 1 x))))

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

591×	`fma-def_binary64`
448×	`fma-neg_binary64`
277×	`cancel-sign-sub-inv_binary64`
228×	`distribute-rgt-neg-in_binary64`
210×	`sub-neg_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	223
1	127	217
2	375	211
3	1222	211
4	3953	211

Stop Event

1×	node limit

Counts

38 → 40

prune83.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	71	4	75
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	73	5	78

Error

0.0b

Counts

78 → 5

Alt Table

Status	Error	Program
	0.9b	(.f64 (cbrt.f64 (/.f64 2 (.f64 x (fma.f64 x x -1)))) (pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1)))) 2))
✓	0.1b	(/.f64 2 (.f64 (+.f64 x -1) (.f64 x (+.f64 1 x))))
	31.0b	(cbrt.f64 (pow.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1))) 3))
▶	0.1b	(*.f64 (/.f64 2 (-.f64 x 1)) (/.f64 1 (fma.f64 x x x)))
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 1180 to 829 computations (29.7% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 2 (-.f64 x 1))
✓	0.1b	(*.f64 (/.f64 2 (-.f64 x 1)) (/.f64 1 (fma.f64 x x x)))
✓	0.8b	(/.f64 1 (fma.f64 x x x))

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(*.f64 (/.f64 2 (-.f64 x 1)) (/.f64 1 (fma.f64 x x x)))
2.0ms	(/.f64 1 (fma.f64 x x x))
2.0ms	(/.f64 2 (-.f64 x 1))

rewrite50.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

453×	`log-prod_binary64`
181×	`prod-diff_binary64`
167×	`log-div_binary64`
166×	`expm1-udef_binary64`
166×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	205	29
2	2745	29

Stop Event

1×	node limit

Counts

3 → 109

Calls

3 calls:

48.0ms	(/.f64 2 (-.f64 x 1))
48.0ms	(*.f64 (/.f64 2 (-.f64 x 1)) (/.f64 1 (fma.f64 x x x)))
48.0ms	(/.f64 1 (fma.f64 x x x))

simplify34.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

691×	`fma-neg_binary64`
507×	`cancel-sign-sub-inv_binary64`
341×	`fma-def_binary64`
208×	`distribute-lft-out_binary64`
160×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	611
1	231	592
2	687	582
3	2229	577

Stop Event

1×	node limit

Counts

145 → 152

prune133.0ms (4.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	149	3	152
Fresh	1	2	3
Picked	1	0	1
Done	1	0	1
Total	152	5	157

Error

Counts

157 → 5

Alt Table

Status	Error	Program
	0.1b	(/.f64 (/.f64 2 (fma.f64 x x x)) (+.f64 x -1))
	0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
	0.9b	(.f64 (cbrt.f64 (/.f64 2 (.f64 x (fma.f64 x x -1)))) (pow.f64 (cbrt.f64 (/.f64 2 (*.f64 x (fma.f64 x x -1)))) 2))
	0.1b	(/.f64 (/.f64 2 (+.f64 x -1)) (fma.f64 x x x))
	49.8b	(*.f64 (pow.f64 (sqrt.f64 (/.f64 2 (+.f64 x -1))) 2) (/.f64 1 (fma.f64 x x x)))

Compiler

Compiled 2472 to 1631 computations (34% saved)

regimes326.0ms (11.2%)

Accuracy

Total 0.1b remaining (88.6%)

Threshold costs 0.1b (88.6%)

Counts

142 → 1

Compiler

Compiled 4950 to 3906 computations (21.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	9	14

Stop Event

1×

saturated

end77.0ms (2.7%)

Compiler: Compiled 90 to 62 computations (31.1% saved)

Details

analyze10.0ms (0.3%)

sample1.5s (51.3%)

simplify17.0ms (0.6%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series7.0ms (0.3%)

rewrite74.0ms (2.6%)

simplify32.0ms (1.1%)

prune149.0ms (5.1%)

localize14.0ms (0.5%)

series9.0ms (0.3%)

rewrite86.0ms (3%)

simplify36.0ms (1.3%)

prune151.0ms (5.2%)

localize6.0ms (0.2%)

series3.0ms (0.1%)

rewrite55.0ms (1.9%)

simplify33.0ms (1.2%)

prune83.0ms (2.8%)

localize6.0ms (0.2%)

series8.0ms (0.3%)

rewrite50.0ms (1.7%)

simplify34.0ms (1.2%)

prune133.0ms (4.6%)

regimes326.0ms (11.2%)

simplify2.0ms (0.1%)

end77.0ms (2.7%)

Profiling