Details

analyze370.0ms (8.2%)

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)

sample80.0ms (1.8%)

Algorithm

1×

intervals

Results

29.0ms	59×	body	1024	valid
15.0ms	33×	body	512	valid
14.0ms	142×	body	128	valid
6.0ms	8×	body	2048	valid
3.0ms	14×	body	256	valid
1.0ms	7×	body	128	overflowed
1.0ms	5×	body	128	invalid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 65 to 53 computations (18.5% saved)

simplify67.0ms (1.5%)

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

28.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	40.9b	(*.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)))))
▶	28.0b	(/.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)

Status

Error

Program

40.9b

(*.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)))))

▶

28.0b

(/.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)

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series64.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

44.0ms	(-.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)))))
9.0ms	(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)

rewrite53.0ms (1.2%)

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 → 160

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)))))
8.0ms	(*.f64 (-.f64 1 eps) x)
2.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
2.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

simplify211.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-neg_binary64`
504×	`associate-r_binary64`
494×	`associate-l_binary64`
429×	`fma-def_binary64`
221×	`distribute-rgt-in_binary64`

Counts

244 → 286

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	521	10912
1	1357	9904
2	4761	9904
3	5094	9904

prune370.0ms (8.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	283	3	286
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	285	3	288

Error

Counts

288 → 3

Alt Table

Status	Error	Program
	21.6b	(/.f64 (-.f64 (fma.f64 (.f64 eps eps) (.f64 x x) 2) (*.f64 x x)) 2)
	47.5b	(/.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)
▶	0.5b	(/.f64 (.f64 (exp.f64 (neg.f64 x)) (+.f64 (.f64 2 x) 2)) 2)

Compiler

Compiled 15028 to 11364 computations (24.4% saved)

localize7.0ms (0.2%)

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))

rewrite9.0ms (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:

8.0ms

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

simplify60.0ms (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

prune40.0ms (0.9%)

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
▶	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
	47.5b	(/.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

▶

0.5b

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

47.5b

(/.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 1149 to 800 computations (30.4% saved)

localize5.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Error

Counts

2 → 2

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
▶	47.5b	(/.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

✓

0.5b

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

▶

47.5b

(/.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 87 to 59 computations (32.2% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (fma.f64 x eps x))
✓	0.0b	(*.f64 x (-.f64 1 eps))
✓	3.4b	(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)))
✓	12.8b	(fma.f64 x (-.f64 1 eps) (fma.f64 x eps x))

series49.0ms (1.1%)

Counts

4 → 80

Calls

4 calls:

31.0ms	(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)))
7.0ms	(fma.f64 x (-.f64 1 eps) (fma.f64 x eps x))
6.0ms	(exp.f64 (fma.f64 x eps x))
5.0ms	(*.f64 x (-.f64 1 eps))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
21×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

4 → 85

Calls

4 calls:

6.0ms	(*.f64 x (-.f64 1 eps))
1.0ms	(exp.f64 (fma.f64 x eps x))
1.0ms	(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)))

simplify121.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

605×	`times-frac_binary64`
433×	`+-commutative_binary64`
319×	`fma-neg_binary64`
243×	`associate-r_binary64`
215×	`associate-l_binary64`

Counts

165 → 149

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	259	2837
1	586	2652
2	2101	2415
3	3939	2415
4	4939	2395
5	4981	2395

prune127.0ms (2.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	149	2	151

Error

Counts

151 → 2

Alt Table

Status	Error	Program
✓	0.5b	(/.f64 (/.f64 (fma.f64 2 x 2) (exp.f64 x)) 2)
✓	47.5b	(/.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

✓

0.5b

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

✓

47.5b

(/.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 6800 to 3932 computations (42.2% saved)

regimes374.0ms (8.3%)

Accuracy

Total 0.8b remaining (96.6%)

Threshold costs 0.8b (96.6%)

Counts

82 → 1

Compiler

Compiled 10869 to 8403 computations (22.7% saved)

simplify4.0ms (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

end1.0ms (0%)

Compiler: Compiled 17 to 11 computations (35.3% saved)

sample2.4s (54%)

Algorithm

1×

intervals

Results

1.0s	1962×	body	1024	valid
460.0ms	4362×	body	128	valid
327.0ms	1014×	body	512	valid
160.0ms	195×	body	2048	valid
93.0ms	467×	body	256	valid
23.0ms	214×	body	128	invalid
21.0ms	213×	body	128	overflowed
9.0ms	18×	body	1024	invalid
2.0ms	7×	body	512	invalid
1.0ms	5×	body	256	invalid

Compiler

Compiled 100 to 73 computations (27% saved)

Details

analyze370.0ms (8.2%)

sample80.0ms (1.8%)

simplify67.0ms (1.5%)

prune5.0ms (0.1%)

localize17.0ms (0.4%)

series64.0ms (1.4%)

rewrite53.0ms (1.2%)

simplify211.0ms (4.7%)

prune370.0ms (8.2%)

localize7.0ms (0.2%)

series3.0ms (0.1%)

rewrite9.0ms (0.2%)

simplify60.0ms (1.3%)

prune40.0ms (0.9%)

localize5.0ms (0.1%)

prune2.0ms (0.1%)

localize19.0ms (0.4%)

series49.0ms (1.1%)

rewrite12.0ms (0.3%)

simplify121.0ms (2.7%)

prune127.0ms (2.8%)

regimes374.0ms (8.3%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.4s (54%)

Profiling