Details

analyze334.0ms (6.8%)

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
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)

sample3.4s (69%)

Results

1.5s	2072×	body	1024	valid
763.0ms	4431×	body	128	valid
537.0ms	1016×	body	512	valid
243.0ms	240×	body	2048	valid
183.0ms	497×	body	256	valid
77.0ms	456×	body	128	invalid
11.0ms	16×	body	1024	invalid
6.0ms	13×	body	512	invalid
3.0ms	8×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify67.0ms (1.3%)

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

30.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	30.3b	(/.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)
	43.1b	(*.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

▶

30.3b

(/.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)

43.1b

(*.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 (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	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))))
✓	0.0b	(*.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)))))

series73.0ms (1.5%)

Counts

4 → 92

Calls

4 calls:

40.0ms	(-.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)))))
15.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
14.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
4.0ms	(*.f64 (+.f64 1 eps) x)

rewrite70.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 191

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)))))
12.0ms	(.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))))
4.0ms	(*.f64 (+.f64 1 eps) x)

simplify246.0ms (5%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-neg_binary64`
538×	`associate-l_binary64`
535×	`associate-r_binary64`
518×	`fma-def_binary64`
273×	`distribute-rgt-in_binary64`

Counts

283 → 340

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	575	12489
1	1523	11687
2	4721	11687
3	5065	11687

prune380.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	339	3	342

Error

Counts

342 → 3

Alt Table

Status	Error	Program
	20.5b	(/.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) 2) (*.f64 x x)) 2)
✓	30.3b	(/.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)
▶	0.9b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 17418 to 12994 computations (25.4% saved)

localize7.0ms (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:

7.0ms

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

simplify62.0ms (1.3%)

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

prune41.0ms (0.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

64 → 2

Alt Table

Status	Error	Program
▶	0.9b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
✓	30.3b	(/.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

▶

0.9b

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

✓

30.3b

(/.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 1104 to 775 computations (29.8% saved)

localize5.0ms (0.1%)

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

2 → 2

Alt Table

Status	Error	Program
✓	0.9b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
✓	30.3b	(/.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

✓

0.9b

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

✓

30.3b

(/.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 42 to 34 computations (19% saved)

regimes147.0ms (3%)

Accuracy

Total 0.9b remaining (97%)

Threshold costs 0.9b (97%)

Counts

33 → 1

Compiler

Compiled 3424 to 2640 computations (22.9% saved)

simplify3.0ms (0.1%)

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

end58.0ms (1.2%)

Compiler: Compiled 76 to 56 computations (26.3% saved)

Details

analyze334.0ms (6.8%)

sample3.4s (69%)

simplify67.0ms (1.3%)

prune5.0ms (0.1%)

localize18.0ms (0.4%)

series73.0ms (1.5%)

rewrite70.0ms (1.4%)

simplify246.0ms (5%)

prune380.0ms (7.7%)

localize7.0ms (0.1%)

series3.0ms (0.1%)

rewrite10.0ms (0.2%)

simplify62.0ms (1.3%)

prune41.0ms (0.8%)

localize5.0ms (0.1%)

prune2.0ms (0%)

regimes147.0ms (3%)

simplify3.0ms (0.1%)

end58.0ms (1.2%)

Profiling