Details

analyze325.0ms (5.4%)

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)

sample3.5s (58.2%)

Results

1.5s	2111×	body	1024	valid
824.0ms	4375×	body	128	valid
511.0ms	1013×	body	512	valid
248.0ms	232×	body	2048	valid
164.0ms	525×	body	256	valid
95.0ms	451×	body	128	invalid
21.0ms	32×	body	1024	invalid
8.0ms	17×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify65.0ms (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

31.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	43.3b	(*.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)))))
▶	31.5b	(/.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)

Status

Error

Program

43.3b

(*.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)))))

▶

31.5b

(/.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)

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
✓	0.2b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
✓	0.2b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
✓	1.7b	(-.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)))))

series80.0ms (1.3%)

Counts

4 → 96

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)))))
16.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
15.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
8.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

rewrite67.0ms (1.1%)

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)))))
14.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
9.0ms	(.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)))

simplify239.0ms (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

prune413.0ms (6.9%)

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

Counts

346 → 3

Alt Table

Status	Error	Program
	17.1b	(/.f64 2 2)
	48.5b	(/.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)
▶	0.4b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 17725 to 13137 computations (25.9% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`frac-times_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`

Counts

1 → 30

Calls

1 calls:

9.0ms

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

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-neg_binary64`
438×	`associate-*l/_binary64`
360×	`associate-/l*_binary64`
273×	`fma-def_binary64`
266×	`distribute-rgt-in_binary64`

Counts

42 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	88	671
1	244	543
2	771	537
3	2084	533
4	4357	533
5	4922	533

prune46.0ms (0.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Error

Counts

64 → 2

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (exp.f64 (-.f64 (log.f64 (fma.f64 2 x 2)) x)) 2)
	48.5b	(/.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)

Status

Error

Program

▶

0.4b

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

48.5b

(/.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)

Compiler

Compiled 1151 to 802 computations (30.3% saved)

localize7.0ms (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))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

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

rewrite11.0ms (0.2%)

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:

7.0ms	(-.f64 (log.f64 (fma.f64 2 x 2)) x)
1.0ms	(log.f64 (fma.f64 2 x 2))

simplify118.0ms (2%)

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

prune62.0ms (1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	95	2	97

Error

Counts

97 → 2

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (exp.f64 (-.f64 (log.f64 (fma.f64 2 x 2)) x)) 2)
▶	48.5b	(/.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)

Status

Error

Program

✓

0.4b

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

▶

48.5b

(/.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)

Compiler

Compiled 1867 to 1386 computations (25.8% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (*.f64 x (-.f64 1 eps)))
✓	0.2b	(/.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))))
✓	3.9b	(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)))
✓	11.6b	(fma.f64 x (-.f64 1 eps) (fma.f64 x eps x))

series122.0ms (2%)

Counts

4 → 96

Calls

4 calls:

71.0ms	(/.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))))
35.0ms	(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)))
8.0ms	(exp.f64 (*.f64 x (-.f64 1 eps)))
6.0ms	(fma.f64 x (-.f64 1 eps) (fma.f64 x eps x))

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`exp-sum_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`

Counts

4 → 91

Calls

4 calls:

3.0ms	(exp.f64 (*.f64 x (-.f64 1 eps)))
3.0ms	(/.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))))
0.0ms	(fma.f64 x (-.f64 1 eps) (fma.f64 x eps x))
0.0ms	(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)))

simplify140.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

756×	`times-frac_binary64`
246×	`fma-def_binary64`
243×	`unswap-sqr_binary64`
238×	`associate-r_binary64`
198×	`associate-l_binary64`

Counts

187 → 191

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	346	6542
1	814	6100
2	2956	5948
3	4979	5948

prune185.0ms (3.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	191	0	191
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	191	2	193

Error

Counts

193 → 2

Alt Table

Status	Error	Program
✓	0.4b	(/.f64 (exp.f64 (-.f64 (log.f64 (fma.f64 2 x 2)) x)) 2)
✓	48.5b	(/.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)

Status

Error

Program

✓

0.4b

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

✓

48.5b

(/.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)

Compiler

Compiled 9883 to 5697 computations (42.4% saved)

regimes407.0ms (6.8%)

Accuracy

Total 0.5b remaining (71.1%)

Threshold costs 0.5b (71.1%)

Counts

84 → 1

Compiler

Compiled 10997 to 8615 computations (21.7% saved)

simplify3.0ms (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

end63.0ms (1.1%)

Compiler: Compiled 74 to 55 computations (25.7% saved)

Details

analyze325.0ms (5.4%)

sample3.5s (58.2%)

simplify65.0ms (1.1%)

prune5.0ms (0.1%)

localize17.0ms (0.3%)

series80.0ms (1.3%)

rewrite67.0ms (1.1%)

simplify239.0ms (4%)

prune413.0ms (6.9%)

localize6.0ms (0.1%)

series3.0ms (0.1%)

rewrite10.0ms (0.2%)

simplify60.0ms (1%)

prune46.0ms (0.8%)

localize7.0ms (0.1%)

series5.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify118.0ms (2%)

prune62.0ms (1%)

localize21.0ms (0.3%)

series122.0ms (2%)

rewrite14.0ms (0.2%)

simplify140.0ms (2.3%)

prune185.0ms (3.1%)

regimes407.0ms (6.8%)

simplify3.0ms (0%)

end63.0ms (1.1%)

Profiling