Details

analyze389.0ms (6.3%)

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)

sample4.1s (65.5%)

Results

1.5s	2051×	body	1024	valid
876.0ms	235×	body	2048	valid
769.0ms	4411×	body	128	valid
491.0ms	1051×	body	512	valid
200.0ms	508×	body	256	valid
90.0ms	440×	body	128	invalid
17.0ms	21×	body	1024	invalid
5.0ms	10×	body	512	invalid
3.0ms	3×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify69.0ms (1.1%)

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

26.6b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	26.7b	(/.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)
	43.6b	(*.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

▶

26.7b

(/.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)

43.6b

(*.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 (0.3%)

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)))
✓	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)))))

series65.0ms (1%)

Counts

4 → 92

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)))))
8.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
7.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
4.0ms	(*.f64 (+.f64 1 eps) x)

rewrite52.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
74×	`exp-neg_binary64`
72×	`frac-times_binary64`
56×	`exp-diff_binary64`
56×	`neg-sub0_binary64`

Counts

4 → 158

Calls

4 calls:

14.0ms	(-.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)))))
4.0ms	(*.f64 (+.f64 1 eps) x)
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
2.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

simplify218.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

523×	`fma-neg_binary64`
506×	`associate-r_binary64`
495×	`associate-l_binary64`
435×	`fma-def_binary64`
245×	`distribute-rgt-in_binary64`

Counts

250 → 285

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	517	10874
1	1352	9874
2	4807	9874
3	5140	9874

prune383.0ms (6.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	281	4	285
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	283	4	287

Error

0.0b

Counts

287 → 4

Alt Table

Status	Error	Program
▶	0.5b	(/.f64 (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x)))) 2)
	41.4b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
	26.7b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	15.1b	(/.f64 2 2)

Compiler

Compiled 15027 to 11330 computations (24.6% saved)

localize17.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

4.0ms	(+.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)))

rewrite17.0ms (0.3%)

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:

7.0ms	(+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (*.f64 2 (exp.f64 (neg.f64 x))))
7.0ms	(*.f64 x (exp.f64 (neg.f64 x)))

simplify78.0ms (1.2%)

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

prune81.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Error

Counts

92 → 4

Alt Table

Status	Error	Program
	41.4b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
	0.5b	(/.f64 (exp.f64 (-.f64 (log.f64 (fma.f64 2 x 2)) x)) 2)
▶	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
	26.7b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 1870 to 1078 computations (42.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 2 x 2) (exp.f64 x))

series6.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

6.0ms

(/.f64 (fma.f64 2 x 2) (exp.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

3.0ms

(/.f64 (fma.f64 2 x 2) (exp.f64 x))

simplify81.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

963×	`fma-neg_binary64`
303×	`associate-l_binary64`
273×	`fma-def_binary64`
268×	`associate-r_binary64`
253×	`div-sub_binary64`

Counts

41 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	693
1	152	641
2	358	641
3	854	635
4	2825	635
5	4582	635
6	5087	635

prune37.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	44	4	48

Error

Counts

48 → 4

Alt Table

Status	Error	Program
	41.4b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
▶	0.5b	(/.f64 (exp.f64 (-.f64 (log.f64 (fma.f64 2 x 2)) x)) 2)
✓	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
	26.7b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 851 to 594 computations (30.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log.f64 (fma.f64 2 x 2)) x)
✓	0.0b	(log.f64 (fma.f64 2 x 2))

series7.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(-.f64 (log.f64 (fma.f64 2 x 2)) x)
3.0ms	(log.f64 (fma.f64 2 x 2))

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`prod-diff_binary64`
8×	`pow1_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(-.f64 (log.f64 (fma.f64 2 x 2)) x)
1.0ms	(log.f64 (fma.f64 2 x 2))

simplify117.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

915×	`fma-neg_binary64`
536×	`fma-def_binary64`
451×	`sub-neg_binary64`
377×	`associate-l_binary64`
316×	`associate-r_binary64`

Counts

76 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	1076
1	309	984
2	951	970
3	3693	965
4	4856	961
5	4974	961
6	4984	961
7	4876	961

prune82.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	95	4	99

Error

Counts

99 → 4

Alt Table

Status	Error	Program
	41.4b	(/.f64 (/.f64 (fma.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 x eps x)) (.f64 (exp.f64 (.f64 x (-.f64 1 eps))) (+.f64 (/.f64 -1 eps) 1))) (exp.f64 (fma.f64 x (-.f64 1 eps) (fma.f64 x eps x)))) 2)
✓	0.5b	(/.f64 (exp.f64 (-.f64 (log.f64 (fma.f64 2 x 2)) x)) 2)
✓	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
	26.7b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 -1) (.f64 (-.f64 1 eps) x))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)

Compiler

Compiled 1872 to 1396 computations (25.4% saved)

regimes287.0ms (4.6%)

Accuracy

Total 0.8b remaining (98%)

Threshold costs 0.8b (98%)

Counts

56 → 1

Compiler

Compiled 7264 to 5696 computations (21.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	10	15
2	15	15
3	17	15
4	18	15
5	18	15

end100.0ms (1.6%)

Compiler: Compiled 117 to 90 computations (23.1% saved)

Details

analyze389.0ms (6.3%)

sample4.1s (65.5%)

simplify69.0ms (1.1%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

series65.0ms (1%)

rewrite52.0ms (0.8%)

simplify218.0ms (3.5%)

prune383.0ms (6.2%)

localize17.0ms (0.3%)

series8.0ms (0.1%)

rewrite17.0ms (0.3%)

simplify78.0ms (1.2%)

prune81.0ms (1.3%)

localize6.0ms (0.1%)

series6.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify81.0ms (1.3%)

prune37.0ms (0.6%)

localize8.0ms (0.1%)

series7.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify117.0ms (1.9%)

prune82.0ms (1.3%)

regimes287.0ms (4.6%)

simplify2.0ms (0%)

end100.0ms (1.6%)

Profiling