Details

analyze5.0ms (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)

sample864.0ms (44%)

Infinites

0% of outputs are infinite.

Results

776.0ms

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify35.0ms (1.8%)

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 (0.4%)

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))

series10.0ms (0.5%)

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))))

rewrite25.0ms (1.3%)

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:

12.0ms	(/.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))))

simplify131.0ms (6.7%)

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

prune99.0ms (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 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))))
▶	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))

Compiler

Compiled 2582 to 2109 computations (18.3% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(atan.f64 (sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
✓	0.0b	(sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
	0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
✓	0.9b	(expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

series12.0ms (0.6%)

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)))
2.0ms	(atan.f64 (sqrt.f64 (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 → 35

Calls

3 calls:

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

simplify72.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

405×	`fma-neg_binary64`
253×	`sub-neg_binary64`
250×	`associate-/l/_binary64`
198×	`unswap-sqr_binary64`
192×	`times-frac_binary64`

Counts

71 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1379
1	267	1266
2	784	1252
3	2528	1172
4	4822	1172
5	5039	1172

prune109.0ms (5.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	147	2	149

Error

Counts

149 → 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 (sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))

Compiler

Compiled 2928 to 2456 computations (16.1% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series15.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

6.0ms	(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
3.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
3.0ms	(exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
2.0ms	(atan.f64 (sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

rewrite19.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
27×	`prod-diff_binary64`
26×	`exp-sum_binary64`

Counts

4 → 109

Calls

4 calls:

4.0ms	(sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))))
4.0ms	(-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x))
4.0ms	(exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))
0.0ms	(atan.f64 (sqrt.f64 (exp.f64 (-.f64 (log1p.f64 (neg.f64 x)) (log1p.f64 x)))))

simplify100.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

637×	`fma-def_binary64`
629×	`fma-neg_binary64`
475×	`associate-l_binary64`
310×	`cancel-sign-sub-inv_binary64`
219×	`associate-/r*_binary64`

Counts

149 → 181

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	266	2886
1	579	2205
2	1688	2139
3	4587	2137
4	4874	2137

prune147.0ms (7.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	181	2	183

Error

Counts

183 → 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 (sqrt.f64 (log1p.f64 (expm1.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))))

Compiler

Compiled 3882 to 1878 computations (51.6% saved)

regimes201.0ms (10.2%)

Accuracy

Total 0.0b remaining (28.2%)

Threshold costs 0.0b (28.2%)

Counts

24 → 1

Compiler

Compiled 1678 to 1448 computations (13.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64`
1×	`unsub-neg_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	20	18
2	22	18
3	23	18
4	22	18

end88.0ms (4.5%)

Compiler: Compiled 50 to 42 computations (16% 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

analyze5.0ms (0.2%)

sample864.0ms (44%)

simplify35.0ms (1.8%)

prune2.0ms (0.1%)

localize8.0ms (0.4%)

series10.0ms (0.5%)

rewrite25.0ms (1.3%)

simplify131.0ms (6.7%)

prune99.0ms (5%)

localize10.0ms (0.5%)

series12.0ms (0.6%)

rewrite3.0ms (0.1%)

simplify72.0ms (3.7%)

prune109.0ms (5.6%)

localize8.0ms (0.4%)

series15.0ms (0.8%)

rewrite19.0ms (1%)

simplify100.0ms (5.1%)

prune147.0ms (7.5%)

regimes201.0ms (10.2%)

simplify2.0ms (0.1%)

end88.0ms (4.5%)

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