Details

analyze6.0ms (0.2%)

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 (45.9%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify36.0ms (1.5%)

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)

localize7.0ms (0.3%)

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))

series10.0ms (0.4%)

Counts

3 → 24

Calls

3 calls:

5.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
3.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite23.0ms (0.9%)

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:

7.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
6.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify135.0ms (5.5%)

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

prune118.0ms (4.7%)

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 (.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x))))))
▶	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))

Compiler

Compiled 2594 to 2119 computations (18.3% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
✓	0.0b	(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

series10.0ms (0.4%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
3.0ms	(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
2.0ms	(atan.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
3×	`sqrt-prod_binary64`

Counts

3 → 35

Calls

3 calls:

1.0ms	(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
0.0ms	(atan.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify91.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

714×	`fma-def_binary64`
643×	`fma-neg_binary64`
443×	`cancel-sign-sub-inv_binary64`
271×	`associate-/l/_binary64`
197×	`sub-neg_binary64`

Counts

71 → 84

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	100	1234
1	233	1149
2	666	1135
3	2110	1073
4	4666	1069
5	4989	1069
6	4932	1069

prune116.0ms (4.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	1	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 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x))))))
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))

Compiler

Compiled 2939 to 2461 computations (16.3% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series25.0ms (1%)

Counts

4 → 32

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x))
7.0ms	(sqrt.f64 (-.f64 1 x))
5.0ms	(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x))))
2.0ms	(*.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x)))

rewrite142.0ms (5.7%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`*-un-lft-identity_binary64`
95×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
72×	`sqrt-prod_binary64`
45×	`add-cube-cbrt_binary64`

Counts

4 → 182

Calls

4 calls:

105.0ms	(*.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x)))
10.0ms	(sqrt.f64 (*.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x))))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x))
4.0ms	(sqrt.f64 (-.f64 1 x))

simplify156.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

534×	`fma-neg_binary64`
481×	`times-frac_binary64`
459×	`associate-/l*_binary64`
316×	`associate-/r*_binary64`
314×	`fma-def_binary64`

Counts

214 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	4082
1	568	3942
2	1721	3869
3	4379	3847
4	4985	3847
5	5197	3847

prune250.0ms (10.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	277	2	279

Error

Counts

279 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (atan.f64 (sqrt.f64 (.f64 (sqrt.f64 (-.f64 1 x)) (/.f64 (sqrt.f64 (-.f64 1 x)) (+.f64 1 x))))))
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))

Compiler

Compiled 6878 to 5627 computations (18.2% saved)

regimes137.0ms (5.5%)

Accuracy

Total 0.0b remaining (21.2%)

Threshold costs 0.0b (21.2%)

Counts

36 → 1

Compiler

Compiled 2720 to 2302 computations (15.4% 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	12	21
1	18	21
2	22	21
3	24	21
4	25	21
5	24	21

end52.0ms (2.1%)

Compiler: Compiled 60 to 51 computations (15% 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 (0.2%)

sample1.1s (45.9%)

simplify36.0ms (1.5%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

series10.0ms (0.4%)

rewrite23.0ms (0.9%)

simplify135.0ms (5.5%)

prune118.0ms (4.7%)

localize12.0ms (0.5%)

series10.0ms (0.4%)

rewrite3.0ms (0.1%)

simplify91.0ms (3.7%)

prune116.0ms (4.7%)

localize9.0ms (0.4%)

series25.0ms (1%)

rewrite142.0ms (5.7%)

simplify156.0ms (6.3%)

prune250.0ms (10.1%)

regimes137.0ms (5.5%)

simplify2.0ms (0.1%)

end52.0ms (2.1%)

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