Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.1s (51.5%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

preprocess35.0ms (1.7%)

Algorithm

2×	egg-herbie

Rules

396×	`fma-neg_binary64`
375×	`fma-def_binary64`
260×	`div-sub_binary64`
121×	`times-frac_binary64`
111×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	58	17
5	82	17
6	117	17
7	189	17
8	356	17
9	577	17
10	789	17
11	1134	17
12	1524	17
13	1940	17
14	2181	17
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 10 computations (16.7% saved)

simplify26.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

396×	`fma-neg_binary64`
375×	`fma-def_binary64`
260×	`div-sub_binary64`
121×	`times-frac_binary64`
111×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	58	17
5	82	17
6	117	17
7	189	17
8	356	17
9	577	17
10	789	17
11	1134	17
12	1524	17
13	1940	17
14	2181	17

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

Compiler

Compiled 47 to 39 computations (17% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
✓	0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
✓	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

series11.0ms (0.6%)

Counts

3 → 24

Calls

9 calls:

5.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))	x	-inf
2.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))	x	inf
1.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))	x	0
1.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))	x	inf
1.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))	x	-inf

rewrite81.0ms (3.9%)

Algorithm

1×	batch-egg-rewrite

Rules

913×	`log1p-expm1-u_binary64`
913×	`expm1-log1p-u_binary64`
311×	`prod-diff_binary64`
161×	`egg-rr`
85×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	177	36
2	2408	36

Stop Event

1×	node limit

Counts

3 → 161

simplify30.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
444×	`cancel-sign-sub-inv_binary64`
314×	`fma-neg_binary64`
262×	`associate-/l/_binary64`
194×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	494
1	189	468
2	609	456
3	2374	394

Stop Event

1×	node limit

Counts

185 → 187

prune171.0ms (8.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	185	2	187
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	186	2	188

Error

Counts

188 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (atan.f64 (exp.f64 (.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
▶	0.0b	(*.f64 2 (atan.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))))

Compiler

Compiled 6033 to 4056 computations (32.8% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))
✓	0.0b	(/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))
✓	0.0b	(atan.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))))
✓	0.0b	(/.f64 (+.f64 1 x) (-.f64 1 x))

series12.0ms (0.6%)

Counts

4 → 48

Calls

12 calls:

2.0ms	(/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))	x	inf
2.0ms	(/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))	x	-inf
2.0ms	(sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))	x	-inf
2.0ms	(sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x)))	x	inf
1.0ms	(/.f64 (+.f64 1 x) (-.f64 1 x))	x	0

rewrite58.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

460×	`log-prod_binary64`
186×	`prod-diff_binary64`
174×	`fma-def_binary64`
168×	`expm1-udef_binary64`
167×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	54
1	201	48
2	2695	48

Stop Event

1×	node limit

Counts

4 → 130

simplify40.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

472×	`cancel-sign-sub-inv_binary64`
328×	`sub-neg_binary64`
307×	`associate-+l+_binary64`
298×	`fma-neg_binary64`
287×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	1015
1	259	958
2	870	947
3	3555	946

Stop Event

1×	node limit

Counts

178 → 168

prune126.0ms (6.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	168	0	168
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	168	2	170

Error

Counts

170 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (atan.f64 (exp.f64 (.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
✓	0.0b	(*.f64 2 (atan.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))))

Compiler

Compiled 3246 to 2750 computations (15.3% saved)

localize8.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
✓	0.0b	(atan.f64 (exp.f64 (*.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

series5.0ms (0.2%)

Counts

2 → 16

Calls

6 calls:

1.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))	x	0
1.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))	x	-inf
1.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))	x	inf
1.0ms	(atan.f64 (exp.f64 (*.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))	x	0
1.0ms	(atan.f64 (exp.f64 (*.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))	x	inf

rewrite43.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`expm1-log1p-u_binary64`
791×	`log1p-expm1-u_binary64`
391×	`prod-diff_binary64`
103×	`add-sqr-sqrt_binary64`
96×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	207	23
2	2706	23

Stop Event

1×	node limit

Counts

2 → 67

simplify32.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

622×	`fma-neg_binary64`
452×	`sub-neg_binary64`
326×	`cancel-sign-sub-inv_binary64`
194×	`associate-+l-_binary64`
189×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	254
1	161	248
2	473	240
3	1609	238
4	4252	238

Stop Event

1×	node limit

Counts

83 → 92

prune58.0ms (2.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	92	2	94

Error

Counts

94 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (atan.f64 (exp.f64 (.f64 1/2 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
✓	0.0b	(*.f64 2 (atan.f64 (/.f64 1 (sqrt.f64 (/.f64 (+.f64 1 x) (-.f64 1 x))))))

Compiler

Compiled 1742 to 1111 computations (36.2% saved)

regimes136.0ms (6.6%)

Accuracy

Total 0.0b remaining (67.6%)

Threshold costs 0.0b (67.6%)

Counts

32 → 1

Compiler

Compiled 2530 to 2155 computations (14.8% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	17	20
2	21	20
3	23	20
4	24	20

Stop Event

1×

saturated

end102.0ms (4.9%)

Stop Event

1×

done

Compiler

Compiled 55 to 47 computations (14.5% saved)

Details

analyze5.0ms (0.3%)

sample1.1s (51.5%)

preprocess35.0ms (1.7%)

simplify26.0ms (1.3%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

series11.0ms (0.6%)

rewrite81.0ms (3.9%)

simplify30.0ms (1.4%)

prune171.0ms (8.3%)

localize8.0ms (0.4%)

series12.0ms (0.6%)

rewrite58.0ms (2.8%)

simplify40.0ms (1.9%)

prune126.0ms (6.1%)

localize8.0ms (0.4%)

series5.0ms (0.2%)

rewrite43.0ms (2.1%)

simplify32.0ms (1.6%)

prune58.0ms (2.8%)

regimes136.0ms (6.6%)

simplify2.0ms (0.1%)

end102.0ms (4.9%)

Profiling