Details

analyze243.0ms (7.7%)

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)

sample39.0ms (1.2%)

Algorithm

1×

intervals

Results

27.0ms

256×

body

128

valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify43.0ms (1.4%)

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

prune3.0ms (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)

localize14.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

series22.0ms (0.7%)

Counts

3 → 24

Calls

3 calls:

13.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
4.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite43.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`

Counts

3 → 106

Calls

3 calls:

15.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
13.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify237.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

697×	`fma-neg_binary64`
247×	`associate-/r*_binary64`
244×	`sub-neg_binary64`
227×	`fma-def_binary64`
215×	`associate-l_binary64`

Counts

130 → 130

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	182	2612
1	410	2466
2	1096	2454
3	3353	2449
4	4751	2449
5	4985	2449
6	4920	2449

prune211.0ms (6.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	2	131

Error

Counts

131 → 2

Alt Table

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

Compiler

Compiled 2578 to 2103 computations (18.4% saved)

localize18.0ms (0.6%)

Local error

Found 3 expressions with local error:

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

series21.0ms (0.7%)

Counts

3 → 28

Calls

3 calls:

10.0ms	(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
7.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
4.0ms	(atan.f64 (sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
16×	`sqrt-prod_binary64`

Counts

3 → 76

Calls

3 calls:

10.0ms	(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
8.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
1.0ms	(atan.f64 (sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

simplify168.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
468×	`fma-def_binary64`
441×	`associate-l_binary64`
376×	`associate-r_binary64`
192×	`associate-/r*_binary64`

Counts

104 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	231	2273
1	472	1681
2	1367	1623
3	4459	1623
4	5064	1623

prune151.0ms (4.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	129	2	131

Error

Counts

131 → 2

Alt Table

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

Compiler

Compiled 2802 to 1414 computations (49.5% saved)

localize29.0ms (0.9%)

Local error

Found 2 expressions with local error:

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

series9.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(-.f64 (fma.f64 (*.f64 x x) 1/2 1) x)
4.0ms	(atan.f64 (-.f64 (fma.f64 (*.f64 x x) 1/2 1) x))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 40

Calls

2 calls:

8.0ms	(-.f64 (fma.f64 (*.f64 x x) 1/2 1) x)
1.0ms	(atan.f64 (-.f64 (fma.f64 (*.f64 x x) 1/2 1) x))

simplify114.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-+l+_binary64`
290×	`associate-l_binary64`
289×	`fma-def_binary64`
254×	`exp-prod_binary64`
246×	`fma-neg_binary64`

Counts

64 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	84	913
1	139	844
2	423	810
3	1847	799
4	4327	799
5	4888	799

prune125.0ms (4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	68	2	70

Error

Counts

70 → 2

Alt Table

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

Compiler

Compiled 1373 to 835 computations (39.2% saved)

regimes135.0ms (4.3%)

Accuracy

Total 0.0b remaining (41.1%)

Threshold costs 0.0b (41.1%)

Counts

12 → 1

Compiler

Compiled 852 to 725 computations (14.9% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

3×	`+-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	11	19
1	18	19
2	23	19
3	26	19
4	27	19
5	27	19

end1.0ms (0%)

Compiler: Compiled 12 to 10 computations (16.7% saved)

sample1.5s (47%)

Algorithm

1×

intervals

Results

1.1s

8000×

body

128

valid

Compiler

Compiled 50 to 41 computations (18% 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

analyze243.0ms (7.7%)

sample39.0ms (1.2%)

simplify43.0ms (1.4%)

prune3.0ms (0.1%)

localize14.0ms (0.4%)

series22.0ms (0.7%)

rewrite43.0ms (1.4%)

simplify237.0ms (7.5%)

prune211.0ms (6.7%)

localize18.0ms (0.6%)

series21.0ms (0.7%)

rewrite29.0ms (0.9%)

simplify168.0ms (5.3%)

prune151.0ms (4.8%)

localize29.0ms (0.9%)

series9.0ms (0.3%)

rewrite13.0ms (0.4%)

simplify114.0ms (3.6%)

prune125.0ms (4%)

regimes135.0ms (4.3%)

simplify5.0ms (0.2%)

end1.0ms (0%)

sample1.5s (47%)

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