Details

analyze69.0ms (0.8%)

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
50%	50%	0.1%	3
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	8
92.5%	6.2%	1.3%	9
92.5%	6.2%	1.3%	10
94.9%	3.1%	2%	11
94.9%	3.1%	2%	12
96.1%	1.6%	2.3%	13
96.1%	1.6%	2.3%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample3.3s (38.9%)

Results

1.3s	6082×	body	128	valid
1.1s	1198×	body	1024	valid
324.0ms	572×	body	512	valid
261.0ms	899×	body	128	invalid
139.0ms	117×	body	2048	valid
105.0ms	287×	body	256	valid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify77.0ms (0.9%)

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

17.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	17.0b	(/.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)
	27.2b	(*.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

▶

17.0b

(/.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)

27.2b

(*.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)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
✓	0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
✓	0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
✓	1.5b	(-.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)))))

series87.0ms (1%)

Counts

4 → 96

Calls

4 calls:

45.0ms	(-.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)))))
17.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
17.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
8.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

rewrite80.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`exp-neg_binary64`
81×	`frac-sub_binary64`
80×	`frac-times_binary64`
61×	`exp-diff_binary64`
61×	`neg-sub0_binary64`

Counts

4 → 187

Calls

4 calls:

15.0ms	(-.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)))))
13.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
10.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
2.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

simplify288.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-neg_binary64`
564×	`fma-def_binary64`
532×	`associate-r_binary64`
517×	`associate-l_binary64`
241×	`distribute-rgt-in_binary64`

Counts

283 → 344

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	580	12761
1	1570	11954
2	4781	11954
3	5192	11954

prune564.0ms (6.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	341	3	344
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	343	3	346

Error

0.0b

Counts

346 → 3

Alt Table

Status	Error	Program
	24.6b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)
▶	17.3b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))))) 2)
	26.4b	(/.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) 2) (*.f64 x x)) 2)

Compiler

Compiled 17739 to 13143 computations (25.9% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps))))
✓	0.0b	(/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))
✓	0.5b	(log1p.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))))
✓	1.5b	(+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x))))

series1.6s (18.5%)

Counts

4 → 96

Calls

4 calls:

1.3s	(log1p.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))))
121.0ms	(+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x))))
49.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps))))
40.0ms	(/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))

rewrite319.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

457×	`*-un-lft-identity_binary64`
318×	`times-frac_binary64`
291×	`exp-sum_binary64`
239×	`add-sqr-sqrt_binary64`
239×	`add-cube-cbrt_binary64`

Counts

4 → 416

Calls

4 calls:

149.0ms	(+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x))))
28.0ms	(/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps))))
17.0ms	(/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))
1.0ms	(log1p.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))))

simplify271.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

427×	`fma-def_binary64`
340×	`associate-r_binary64`
284×	`times-frac_binary64`
279×	`associate-/r*_binary64`
266×	`associate-l_binary64`

Counts

512 → 464

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	643	14674
1	1671	14069
2	5259	14069

prune676.0ms (8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	463	1	464
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	464	3	467

Error

0.0b

Counts

467 → 3

Alt Table

Status	Error	Program
	24.6b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)
✓	17.3b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))))) 2)
▶	23.1b	(/.f64 (expm1.f64 (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x x)) 1/3 (log.f64 3)) (.f64 (*.f64 x x) 1/3))) 2)

Compiler

Compiled 23541 to 14418 computations (38.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (.f64 (.f64 eps eps) (*.f64 x x)) 1/3 (log.f64 3))
✓	0.2b	(.f64 (.f64 x x) 1/3)
✓	7.1b	(-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x x)) 1/3 (log.f64 3)) (.f64 (*.f64 x x) 1/3))
✓	14.2b	(.f64 (.f64 eps eps) (*.f64 x x))

series97.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

41.0ms	(-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x x)) 1/3 (log.f64 3)) (.f64 (*.f64 x x) 1/3))
37.0ms	(fma.f64 (.f64 (.f64 eps eps) (*.f64 x x)) 1/3 (log.f64 3))
15.0ms	(.f64 (.f64 eps eps) (*.f64 x x))
4.0ms	(.f64 (.f64 x x) 1/3)

rewrite36.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
21×	`add-cbrt-cube_binary64`
21×	`add-exp-log_binary64`
17×	`pow-prod-down_binary64`
11×	`cbrt-unprod_binary64`

Counts

4 → 83

Calls

4 calls:

13.0ms	(.f64 (.f64 eps eps) (*.f64 x x))
10.0ms	(.f64 (.f64 x x) 1/3)
5.0ms	(-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x x)) 1/3 (log.f64 3)) (.f64 (*.f64 x x) 1/3))
1.0ms	(fma.f64 (.f64 (.f64 eps eps) (*.f64 x x)) 1/3 (log.f64 3))

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

574×	`associate-+l+_binary64`
449×	`unswap-sqr_binary64`
341×	`fma-def_binary64`
318×	`*-commutative_binary64`
207×	`cancel-sign-sub-inv_binary64`

Counts

167 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	2659
1	267	2272
2	936	2184
3	2515	2154
4	5296	2154

prune108.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	118	3	121

Error

0.0b

Counts

121 → 3

Alt Table

Status	Error	Program
▶	24.6b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)
✓	17.3b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))))) 2)
✓	23.1b	(/.f64 (expm1.f64 (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x x)) 1/3 (log.f64 3)) (.f64 (*.f64 x x) 1/3))) 2)

Compiler

Compiled 3203 to 1789 computations (44.1% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (exp.f64 (neg.f64 x)))
✓	0.3b	(+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x))))

series8.0ms (0.1%)

Counts

2 → 21

Calls

2 calls:

5.0ms	(+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x))))
3.0ms	(*.f64 x (exp.f64 (neg.f64 x)))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`associate-*r/_binary64`
14×	`exp-neg_binary64`
9×	`frac-add_binary64`
7×	`exp-diff_binary64`
7×	`neg-sub0_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(*.f64 x (exp.f64 (neg.f64 x)))
8.0ms	(+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x))))

simplify94.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

966×	`fma-neg_binary64`
499×	`fma-def_binary64`
392×	`cancel-sign-sub-inv_binary64`
318×	`unswap-sqr_binary64`
240×	`*-commutative_binary64`

Counts

68 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	995
1	272	795
2	948	726
3	2833	719
4	4432	719
5	4928	719

prune91.0ms (1.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	88	3	91

Error

0.0b

Counts

91 → 3

Alt Table

Status	Error	Program
✓	24.6b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)
✓	17.3b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (*.f64 x (-.f64 1 eps)))) (/.f64 (+.f64 (/.f64 -1 eps) 1) (exp.f64 (fma.f64 x eps x)))))) 2)
✓	23.1b	(/.f64 (expm1.f64 (-.f64 (fma.f64 (.f64 (.f64 eps eps) (.f64 x x)) 1/3 (log.f64 3)) (.f64 (*.f64 x x) 1/3))) 2)

Compiler

Compiled 1753 to 988 computations (43.6% saved)

regimes448.0ms (5.3%)

Accuracy

Total 0.5b remaining (72.1%)

Threshold costs 0.5b (72.1%)

Counts

97 → 1

Compiler

Compiled 8319 to 6485 computations (22% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	20	23
2	25	23
3	28	23
4	29	23
5	29	23

end78.0ms (0.9%)

Compiler: Compiled 103 to 72 computations (30.1% saved)

Details

analyze69.0ms (0.8%)

sample3.3s (38.9%)

simplify77.0ms (0.9%)

prune5.0ms (0.1%)

localize18.0ms (0.2%)

series87.0ms (1%)

rewrite80.0ms (1%)

simplify288.0ms (3.4%)

prune564.0ms (6.7%)

localize27.0ms (0.3%)

series1.6s (18.5%)

rewrite319.0ms (3.8%)

simplify271.0ms (3.2%)

prune676.0ms (8%)

localize17.0ms (0.2%)

series97.0ms (1.2%)

rewrite36.0ms (0.4%)

simplify92.0ms (1.1%)

prune108.0ms (1.3%)

localize8.0ms (0.1%)

series8.0ms (0.1%)

rewrite20.0ms (0.2%)

simplify94.0ms (1.1%)

prune91.0ms (1.1%)

regimes448.0ms (5.3%)

simplify3.0ms (0%)

end78.0ms (0.9%)

Profiling