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)

sample106.0ms (4.2%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify36.0ms (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

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

rewrite20.0ms (0.8%)

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))))

simplify218.0ms (8.6%)

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

prune116.0ms (4.6%)

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

0.0b

Counts

131 → 2

Alt Table

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

Compiler

Compiled 2586 to 2113 computations (18.3% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.9%)

Counts

4 → 32

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 1 x))
7.0ms	(sqrt.f64 (-.f64 1 x))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
2.0ms	(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))

rewrite26.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`sqrt-prod_binary64`
92×	`*-un-lft-identity_binary64`
77×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`

Counts

4 → 149

Calls

4 calls:

9.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
3.0ms	(sqrt.f64 (-.f64 1 x))
3.0ms	(sqrt.f64 (+.f64 1 x))
0.0ms	(atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))

simplify139.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-neg_binary64`
552×	`cancel-sign-sub-inv_binary64`
478×	`times-frac_binary64`
246×	`fma-def_binary64`
225×	`associate-/r*_binary64`

Counts

181 → 183

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	188	3758
1	381	3607
2	946	3502
3	2765	3484
4	4646	3484
5	4985	3484

prune168.0ms (6.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	182	3	185

Error

Counts

185 → 3

Alt Table

Status	Error	Program
	0.6b	(*.f64 2 (atan.f64 (fabs.f64 (/.f64 (fma.f64 x -1/2 1) (sqrt.f64 (+.f64 1 x))))))
▶	0.0b	(*.f64 2 (log1p.f64 (expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
✓	0.0b	(*.f64 2 (atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 4032 to 3379 computations (16.2% saved)

localize10.0ms (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	(expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
✓	0.0b	(log1p.f64 (expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

series7.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

4.0ms	(expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
2.0ms	(log1p.f64 (expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

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

simplify66.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

932×	`unsub-neg_binary64`
460×	`distribute-neg-out_binary64`
355×	`distribute-rgt-in_binary64`
298×	`sub-neg_binary64`
295×	`distribute-lft-in_binary64`

Counts

46 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	805
1	42	743
2	75	734
3	133	734
4	383	734
5	1710	734
6	3228	734
7	4850	734

prune136.0ms (5.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	151	3	154

Error

Counts

154 → 3

Alt Table

Status	Error	Program
▶	0.6b	(*.f64 2 (atan.f64 (fabs.f64 (/.f64 (fma.f64 x -1/2 1) (sqrt.f64 (+.f64 1 x))))))
✓	0.0b	(*.f64 2 (log1p.f64 (expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
✓	0.0b	(*.f64 2 (atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 3240 to 2709 computations (16.4% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series16.0ms (0.6%)

Counts

2 → 16

Calls

2 calls:

14.0ms	(/.f64 (fma.f64 x -1/2 1) (sqrt.f64 (+.f64 1 x)))
2.0ms	(atan.f64 (fabs.f64 (/.f64 (fma.f64 x -1/2 1) (sqrt.f64 (+.f64 1 x)))))

rewrite8.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
18×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64`
16×	`sqrt-prod_binary64`

Counts

2 → 56

Calls

2 calls:

5.0ms	(/.f64 (fma.f64 x -1/2 1) (sqrt.f64 (+.f64 1 x)))
0.0ms	(atan.f64 (fabs.f64 (/.f64 (fma.f64 x -1/2 1) (sqrt.f64 (+.f64 1 x)))))

simplify112.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

740×	`fma-neg_binary64`
562×	`cancel-sign-sub-inv_binary64`
266×	`associate-l_binary64`
260×	`fma-def_binary64`
237×	`times-frac_binary64`

Counts

72 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1586
1	183	1489
2	410	1489
3	858	1483
4	2568	1483
5	4024	1483
6	4983	1483
7	4911	1483

prune88.0ms (3.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	94	3	97

Error

Counts

97 → 3

Alt Table

Status	Error	Program
✓	0.6b	(*.f64 2 (atan.f64 (fabs.f64 (/.f64 (fma.f64 x -1/2 1) (sqrt.f64 (+.f64 1 x))))))
✓	0.0b	(*.f64 2 (log1p.f64 (expm1.f64 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
✓	0.0b	(*.f64 2 (atan.f64 (fabs.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))

Compiler

Compiled 1988 to 1679 computations (15.5% saved)

regimes344.0ms (13.5%)

Accuracy

Total 0.0b remaining (54.5%)

Threshold costs 0.0b (54.5%)

Counts

51 → 1

Compiler

Compiled 4376 to 3738 computations (14.6% saved)

simplify3.0ms (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	27
1	18	27
2	22	27
3	24	27
4	25	27
5	24	27

end1.0ms (0%)

Compiler: Compiled 18 to 15 computations (16.7% saved)

sample861.0ms (33.8%)

Algorithm

1×

intervals

Results

559.0ms

8000×

body

128

valid

Compiler

Compiled 74 to 63 computations (14.9% 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%)

sample106.0ms (4.2%)

simplify36.0ms (1.4%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

series10.0ms (0.4%)

rewrite20.0ms (0.8%)

simplify218.0ms (8.6%)

prune116.0ms (4.6%)

localize8.0ms (0.3%)

series23.0ms (0.9%)

rewrite26.0ms (1%)

simplify139.0ms (5.5%)

prune168.0ms (6.6%)

localize10.0ms (0.4%)

series7.0ms (0.3%)

rewrite1.0ms (0.1%)

simplify66.0ms (2.6%)

prune136.0ms (5.3%)

localize8.0ms (0.3%)

series16.0ms (0.6%)

rewrite8.0ms (0.3%)

simplify112.0ms (4.4%)

prune88.0ms (3.5%)

regimes344.0ms (13.5%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample861.0ms (33.8%)

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