Details

analyze6.0ms (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 (50%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify38.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize8.0ms (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))

series10.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
2.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite80.0ms (3.5%)

Algorithm

2×	batch-egg-rewrite

Rules

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

Counts

3 → 164

Calls

3 calls:

75.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
75.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
75.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	36
1	174	36
2	2291	36
3	6247	36
0	0	0
1	0	0

simplify56.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
653×	`fma-neg_binary64`
443×	`cancel-sign-sub-inv_binary64`
264×	`associate-/l/_binary64`
194×	`sub-neg_binary64`

Counts

188 → 190

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	494
1	188	468
2	590	456
3	1925	394
4	4421	390
5	4962	390

prune185.0ms (8.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	2	191

Error

Counts

191 → 2

Alt Table

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

Compiler

Compiled 6174 to 4603 computations (25.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(sqrt.f64 (*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x))))
2.0ms	(/.f64 1 (+.f64 1 x))
2.0ms	(*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))
2.0ms	(atan.f64 (sqrt.f64 (*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))))

rewrite64.0ms (2.8%)

Algorithm

2×	batch-egg-rewrite

Rules

921×	`log1p-expm1-u_binary64`
921×	`expm1-log1p-u_binary64`
177×	`prod-diff_binary64`
113×	`egg-rr`
94×	`add-sqr-sqrt_binary64`

Counts

4 → 113

Calls

4 calls:

62.0ms	(sqrt.f64 (*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x))))
62.0ms	(atan.f64 (sqrt.f64 (*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))))
62.0ms	(*.f64 (-.f64 1 x) (/.f64 1 (+.f64 1 x)))
62.0ms	(/.f64 1 (+.f64 1 x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	43
1	195	43
2	2375	43
3	6008	43
0	0	0
1	0	0

simplify60.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

796×	`fma-def_binary64`
731×	`fma-neg_binary64`
668×	`times-frac_binary64`
500×	`cancel-sign-sub-inv_binary64`
270×	`associate-/l/_binary64`

Counts

161 → 150

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	77	833
1	231	803
2	698	791
3	2159	727
4	4477	723
5	5654	723

prune200.0ms (8.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	150	2	152

Error

Counts

152 → 2

Alt Table

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

Compiler

Compiled 2508 to 2074 computations (17.3% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series17.0ms (0.7%)

Counts

3 → 16

Calls

3 calls:

11.0ms	(sqrt.f64 (*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))))
4.0ms	(*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))
2.0ms	(atan.f64 (sqrt.f64 (*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))))

rewrite52.0ms (2.3%)

Algorithm

2×	batch-egg-rewrite

Rules

786×	`expm1-log1p-u_binary64`
785×	`log1p-expm1-u_binary64`
132×	`prod-diff_binary64`
95×	`add-sqr-sqrt_binary64`
88×	`add-log-exp_binary64`

Counts

3 → 72

Calls

3 calls:

51.0ms	(sqrt.f64 (*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x)))))
51.0ms	(atan.f64 (sqrt.f64 (*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))))
51.0ms	(*.f64 (-.f64 1 x) (exp.f64 (neg.f64 (log1p.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	198	36
2	2054	36
3	5018	36
0	0	0
1	0	0

simplify71.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

678×	`fma-def_binary64`
488×	`cancel-sign-sub-inv_binary64`
475×	`div-sub_binary64`
418×	`fma-neg_binary64`
383×	`sub-neg_binary64`

Counts

88 → 95

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	184
1	162	172
2	443	164
3	1152	154
4	3907	152
5	4440	152
6	5129	152

prune63.0ms (2.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

97 → 2

Alt Table

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

Compiler

Compiled 1495 to 1233 computations (17.5% saved)

regimes139.0ms (6.1%)

Accuracy

Total 0.0b remaining (4.4%)

Threshold costs 0.0b (4.4%)

Counts

33 → 1

Compiler

Compiled 2848 to 2378 computations (16.5% 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	20
1	21	20
2	26	20
3	29	20
4	30	20
5	29	20

end51.0ms (2.3%)

Compiler: Compiled 53 to 45 computations (15.1% saved)

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17

Details

analyze6.0ms (0.3%)

sample1.1s (50%)

simplify38.0ms (1.7%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series10.0ms (0.4%)

rewrite80.0ms (3.5%)

simplify56.0ms (2.5%)

prune185.0ms (8.2%)

localize8.0ms (0.3%)

series10.0ms (0.4%)

rewrite64.0ms (2.8%)

simplify60.0ms (2.7%)

prune200.0ms (8.8%)

localize9.0ms (0.4%)

series17.0ms (0.7%)

rewrite52.0ms (2.3%)

simplify71.0ms (3.1%)

prune63.0ms (2.8%)

regimes139.0ms (6.1%)

simplify3.0ms (0.1%)

end51.0ms (2.3%)

Profiling

Iter	Nodes	Cost
0	10	17
1	19	17
2	25	17
3	35	17
4	57	17
5	73	17
6	102	17
7	158	17
8	240	17
9	299	17
10	391	17
11	536	17
12	777	17
13	826	17
14	799	17
15	722	17