Details

analyze379.0ms (6.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample3.3s (58%)

Results

1.4s	2066×	body	1024	valid
768.0ms	4417×	body	128	valid
531.0ms	1020×	body	512	valid
220.0ms	219×	body	2048	valid
174.0ms	534×	body	256	valid
71.0ms	421×	body	128	invalid
11.0ms	17×	body	1024	invalid
3.0ms	7×	body	512	invalid
3.0ms	8×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
577×	`div-sub_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`fma-neg_binary64`
467×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	57	45
2	153	37
3	394	37
4	1347	37
5	4048	37
6	4614	37
7	5259	37

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

30.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	30.1b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	44.3b	(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

Status

Error

Program

▶

30.1b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

44.3b

(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 1 eps) x)
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
✓	2.7b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series58.0ms (1%)

Counts

4 → 92

Calls

4 calls:

41.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
6.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
6.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(*.f64 (+.f64 1 eps) x)

rewrite95.0ms (1.7%)

Algorithm

2×	batch-egg-rewrite

Rules

128× egg-rr

Counts

4 → 128

Calls

2 calls:

90.0ms

((-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x))) (*.f64 (+.f64 1 eps) x))

1.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	71
1	407	62
2	4376	62
3	5336	62
0	0	0
1	0	0

simplify81.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

542×	`associate--l+_binary64`
347×	`associate--r+_binary64`
297×	`cancel-sign-sub-inv_binary64`
257×	`fma-def_binary64`
188×	`distribute-rgt-out_binary64`

Counts

220 → 182

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	168	2012
1	532	1964
2	2062	1869
3	4873	1869
4	4981	1869

prune193.0ms (3.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	180	4	184

Error

0.0b

Counts

184 → 4

Alt Table

Status	Error	Program
	47.1b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3)) 2)
	47.1b	(/.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3) 1/3) 2)
▶	0.7b	(/.f64 (*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x))) 2)
	0.7b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)

Compiler

Compiled 7863 to 5915 computations (24.8% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series13.0ms (0.2%)

Counts

2 → 16

Calls

2 calls:

7.0ms	(*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x)))
6.0ms	(/.f64 2 (exp.f64 x))

rewrite50.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

66× egg-rr

Counts

2 → 66

Calls

2 calls:

49.0ms	((/.f64 2 (exp.f64 x)) (*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	169	18
2	2006	18
3	5106	18
0	0	0
1	0	0

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

358×	`distribute-rgt-neg-in_binary64`
351×	`fma-def_binary64`
300×	`distribute-lft-neg-in_binary64`
260×	`associate-l_binary64`
259×	`cancel-sign-sub-inv_binary64`

Counts

82 → 82

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	32	202
1	93	187
2	234	182
3	632	176
4	2141	158
5	4474	158
6	4948	158

prune70.0ms (1.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	82	4	86

Error

0.0b

Counts

86 → 4

Alt Table

Status	Error	Program
	47.1b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3)) 2)
▶	0.7b	(/.f64 (.f64 (+.f64 x 1) (.f64 2 (exp.f64 (neg.f64 x)))) 2)
	47.1b	(/.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3) 1/3) 2)
✓	0.7b	(/.f64 (*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x))) 2)

Compiler

Compiled 1293 to 953 computations (26.3% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (+.f64 x 1) (.f64 2 (exp.f64 (neg.f64 x))))

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(*.f64 (+.f64 x 1) (*.f64 2 (exp.f64 (neg.f64 x))))

rewrite50.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

25× egg-rr

Counts

1 → 25

Calls

2 calls:

50.0ms	((.f64 (+.f64 x 1) (.f64 2 (exp.f64 (neg.f64 x)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	185	12
2	1869	12
3	5007	12
0	0	0
1	0	0

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-neg_binary64`
534×	`times-frac_binary64`
389×	`*-commutative_binary64`
266×	`associate-l_binary64`
243×	`associate-r_binary64`

Counts

37 → 38

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	177
1	78	145
2	177	133
3	486	117
4	1668	117
5	3851	117
6	4745	117
7	4992	117
8	4892	117

prune28.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	38	4	42

Error

0.0b

Counts

42 → 4

Alt Table

Status	Error	Program
▶	47.1b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3)) 2)
✓	0.7b	(/.f64 (.f64 (+.f64 x 1) (.f64 2 (exp.f64 (neg.f64 x)))) 2)
	47.1b	(/.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3) 1/3) 2)
✓	0.7b	(/.f64 (*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x))) 2)

Compiler

Compiled 633 to 476 computations (24.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (*.f64 x (+.f64 1 eps)))
✓	1.6b	(exp.f64 (+.f64 (*.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps))))
✓	8.6b	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3))
✓	16.8b	(-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))

series69.0ms (1.2%)

Counts

4 → 96

Calls

4 calls:

27.0ms	(cbrt.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3))
23.0ms	(-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps)))))
10.0ms	(exp.f64 (*.f64 x (+.f64 1 eps)))
9.0ms	(exp.f64 (+.f64 (*.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps))))

rewrite178.0ms (3.1%)

Algorithm

2×	batch-egg-rewrite

Rules

156× egg-rr

Counts

4 → 156

Calls

2 calls:

166.0ms

((-.f64 (exp.f64 (+.f64 (*.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (*.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3)) (exp.f64 (+.f64 (*.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (exp.f64 (*.f64 x (+.f64 1 eps))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	94
1	408	94
2	4679	94
3	5891	94
0	0	0
1	0	0

simplify136.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

725×	`associate--l+_binary64`
380×	`cancel-sign-sub-inv_binary64`
274×	`fma-def_binary64`
210×	`associate-+r+_binary64`
199×	`sub-neg_binary64`

Counts

252 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	3127
1	616	2982
2	2332	2839
3	5192	2839

prune311.0ms (5.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	157	4	161

Error

0.0b

Counts

161 → 4

Alt Table

Status	Error	Program
✓	47.1b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3)) 2)
✓	0.7b	(/.f64 (.f64 (+.f64 x 1) (.f64 2 (exp.f64 (neg.f64 x)))) 2)
	47.1b	(/.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 (+.f64 (.f64 (-.f64 1 eps) x) (log1p.f64 (/.f64 1 eps)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (*.f64 x (+.f64 1 eps))))) 3) 1/3) 2)
✓	0.7b	(/.f64 (*.f64 (+.f64 x 1) (/.f64 2 (exp.f64 x))) 2)

Compiler

Compiled 7135 to 5274 computations (26.1% saved)

regimes326.0ms (5.7%)

Accuracy

Total 0.6b remaining (88%)

Threshold costs 0.6b (88%)

Counts

56 → 1

Compiler

Compiled 6188 to 4904 computations (20.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	18	17
2	20	17
3	21	17
4	20	17

end78.0ms (1.4%)

Compiler: Compiled 114 to 94 computations (17.5% saved)

Details

analyze379.0ms (6.7%)

sample3.3s (58%)

simplify67.0ms (1.2%)

prune5.0ms (0.1%)

localize16.0ms (0.3%)

series58.0ms (1%)

rewrite95.0ms (1.7%)

simplify81.0ms (1.4%)

prune193.0ms (3.4%)

localize6.0ms (0.1%)

series13.0ms (0.2%)

rewrite50.0ms (0.9%)

simplify61.0ms (1.1%)

prune70.0ms (1.2%)

localize6.0ms (0.1%)

series4.0ms (0.1%)

rewrite50.0ms (0.9%)

simplify90.0ms (1.6%)

prune28.0ms (0.5%)

localize17.0ms (0.3%)

series69.0ms (1.2%)

rewrite178.0ms (3.1%)

simplify136.0ms (2.4%)

prune311.0ms (5.5%)

regimes326.0ms (5.7%)

simplify2.0ms (0%)

end78.0ms (1.4%)

Profiling