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)

sample1.2s (32.6%)

Results

1.2s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify38.0ms (1%)

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%)

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 (0.2%)

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 (0.3%)

Counts

3 → 24

Calls

3 calls:

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

rewrite190.0ms (5%)

Algorithm

3×	egg-rewrite

Rules

125×	`egg`
31×	`egg`
18×	`egg`

Counts

3 → 174

Calls

3 calls:

72.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
58.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
55.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	135	10
2	1867	10
3	5287	10
0	7	12
1	155	12
2	2083	12
3	5764	12
0	8	14
1	174	14
2	2291	14
3	6247	14

simplify61.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

692×	`fma-def_binary64`
653×	`fma-neg_binary64`
443×	`cancel-sign-sub-inv_binary64`
264×	`associate-/l/_binary64`
194×	`sub-neg_binary64`

Counts

198 → 200

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	494
1	188	468
2	590	456
3	1925	394
4	4421	390
5	4962	390

prune218.0ms (5.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	199	2	201

Error

Counts

201 → 2

Alt Table

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

Compiler

Compiled 6365 to 4750 computations (25.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

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

rewrite192.0ms (5.1%)

Algorithm

3×	egg-rewrite

Rules

129×	`egg`
30×	`egg`
16×	`egg`

Counts

3 → 175

Calls

3 calls:

75.0ms	(expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
56.0ms	(sqrt.f64 (expm1.f64 (log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
56.0ms	(log1p.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	154	10
2	2059	10
3	6118	10
0	9	12
1	173	12
2	2257	12
3	5011	12
0	7	12
1	153	12
2	2046	12
3	6073	12

simplify158.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

728×	`cancel-sign-sub-inv_binary64`
726×	`fma-neg_binary64`
405×	`sub-neg_binary64`
217×	`associate-+l+_binary64`
202×	`associate--l+_binary64`

Counts

211 → 220

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	716
1	270	676
2	867	664
3	2848	662
4	4797	662
5	5015	662

prune333.0ms (8.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	359	0	359
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	359	2	361

Error

Counts

361 → 2

Alt Table

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

Compiler

Compiled 12409 to 9251 computations (25.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series11.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

6.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)))
3.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
2.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)

rewrite235.0ms (6.2%)

Algorithm

3×	egg-rewrite

Rules

131×	`egg`
40×	`egg`
34×	`egg`

Counts

3 → 205

Calls

3 calls:

109.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3))
63.0ms	(pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)
57.0ms	(sqrt.f64 (cbrt.f64 (pow.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)) 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	184	10
2	2340	10
3	4921	10
4	5151	10
0	8	13
1	182	13
2	2300	13
3	6251	13
0	10	12
1	203	12
2	2519	12
3	4995	12

simplify105.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-neg_binary64`
602×	`cancel-sign-sub-inv_binary64`
274×	`associate-/l/_binary64`
267×	`sub-neg_binary64`
190×	`unswap-sqr_binary64`

Counts

241 → 241

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	80	639
1	251	609
2	768	593
3	2365	532
4	4537	527
5	4980	527
6	4999	527
7	4914	527

prune357.0ms (9.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	380	0	380
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	380	2	382

Error

Counts

382 → 2

Alt Table

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

Compiler

Compiled 12737 to 9663 computations (24.1% saved)

regimes533.0ms (14.1%)

Accuracy

Total 0.0b remaining (24.3%)

Threshold costs 0.0b (24.3%)

Counts

78 → 1

Compiler

Compiled 6788 to 5734 computations (15.5% 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

end54.0ms (1.4%)

Compiler: Compiled 57 to 49 computations (14% 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%)

sample1.2s (32.6%)

simplify38.0ms (1%)

prune2.0ms (0%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite190.0ms (5%)

simplify61.0ms (1.6%)

prune218.0ms (5.8%)

localize11.0ms (0.3%)

series11.0ms (0.3%)

rewrite192.0ms (5.1%)

simplify158.0ms (4.2%)

prune333.0ms (8.8%)

localize9.0ms (0.2%)

series11.0ms (0.3%)

rewrite235.0ms (6.2%)

simplify105.0ms (2.8%)

prune357.0ms (9.5%)

regimes533.0ms (14.1%)

simplify2.0ms (0.1%)

end54.0ms (1.4%)

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