Details

analyze77.0ms (3.1%)

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
46.9%	3.1%	50%	8
46.9%	3.1%	50%	9
47.2%	2.7%	50%	10
47.2%	2.7%	50%	11
47.3%	2.7%	50%	12
47.4%	2.6%	50%	13
47.4%	2.5%	50%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample1.2s (47.3%)

Results

1.1s

8256×

body

128

valid

Compiler

Compiled 25 to 21 computations (16% 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	(/.f64 (-.f64 1 x) (+.f64 1 x))
✓	0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series13.0ms (0.5%)

Counts

3 → 24

Calls

3 calls:

6.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
5.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
2.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite22.0ms (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))))

simplify145.0ms (5.8%)

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

prune114.0ms (4.5%)

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 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
	0.0b	(.f64 2 (atan.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))

Status

Error

Program

▶

0.0b

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

0.0b

(*.f64 2 (atan.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))

Compiler

Compiled 2601 to 2122 computations (18.4% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
✓	0.0b	(sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
✓	0.0b	(log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
✓	1.0b	(expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series13.0ms (0.5%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
4.0ms	(expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
3.0ms	(log1p.f64 (expm1.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`
4×	`log1p-expm1-u_binary64`

Counts

3 → 37

Calls

3 calls:

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

simplify83.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

746×	`times-frac_binary64`
588×	`fma-neg_binary64`
337×	`sub-neg_binary64`
232×	`cancel-sign-sub-inv_binary64`
225×	`fma-def_binary64`

Counts

73 → 95

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	130	1322
1	327	1211
2	977	1187
3	3098	1177
4	4856	1177
5	5654	1177

prune129.0ms (5.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	160	2	162

Error

Counts

162 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
▶	0.0b	(.f64 2 (atan.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))

Status

Error

Program

✓

0.0b

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

▶

0.0b

(*.f64 2 (atan.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))

Compiler

Compiled 3151 to 2624 computations (16.7% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x)))))
✓	0.0b	(sqrt.f64 (fma.f64 x x (-.f64 1 x)))
✓	0.0b	(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))
✓	0.0b	(fma.f64 x x (-.f64 1 x))

series16.0ms (0.6%)

Counts

4 → 48

Calls

4 calls:

7.0ms	(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))
4.0ms	(atan.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x)))))
2.0ms	(fma.f64 x x (-.f64 1 x))
2.0ms	(sqrt.f64 (fma.f64 x x (-.f64 1 x)))

rewrite115.0ms (4.6%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
43×	`sqrt-prod_binary64`
43×	`*-un-lft-identity_binary64`
33×	`associate-l_binary64`
27×	`times-frac_binary64`

Counts

4 → 98

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))
1.0ms	(sqrt.f64 (fma.f64 x x (-.f64 1 x)))
0.0ms	(atan.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x)))))
0.0ms	(fma.f64 x x (-.f64 1 x))

simplify131.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

746×	`fma-neg_binary64`
414×	`times-frac_binary64`
391×	`associate-l_binary64`
294×	`associate-r_binary64`
266×	`unswap-sqr_binary64`

Counts

146 → 186

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	194	3616
1	415	3433
2	1123	3360
3	3485	3357
4	4822	3357
5	5051	3357

prune182.0ms (7.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

188 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))
✓	0.0b	(.f64 2 (atan.f64 (.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))

Status

Error

Program

✓

0.0b

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

✓

0.0b

(*.f64 2 (atan.f64 (*.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 (pow.f64 x 3)))) (sqrt.f64 (fma.f64 x x (-.f64 1 x))))))

Compiler

Compiled 5490 to 4284 computations (22% saved)

regimes154.0ms (6.1%)

Accuracy

Total 0.0b remaining (17.8%)

Threshold costs 0.0b (17.8%)

Counts

36 → 1

Compiler

Compiled 2951 to 2502 computations (15.2% 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	21
1	18	21
2	22	21
3	24	21
4	25	21
5	24	21

end59.0ms (2.3%)

Compiler: Compiled 64 to 53 computations (17.2% 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

analyze77.0ms (3.1%)

sample1.2s (47.3%)

simplify36.0ms (1.4%)

prune2.0ms (0.1%)

localize7.0ms (0.3%)

series13.0ms (0.5%)

rewrite22.0ms (0.9%)

simplify145.0ms (5.8%)

prune114.0ms (4.5%)

localize11.0ms (0.4%)

series13.0ms (0.5%)

rewrite3.0ms (0.1%)

simplify83.0ms (3.3%)

prune129.0ms (5.1%)

localize12.0ms (0.5%)

series16.0ms (0.6%)

rewrite115.0ms (4.6%)

simplify131.0ms (5.2%)

prune182.0ms (7.3%)

regimes154.0ms (6.1%)

simplify3.0ms (0.1%)

end59.0ms (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