Details

analyze10.0ms (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)

sample1.8s (37.2%)

Results

1.7s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify56.0ms (1.1%)

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

prune3.0ms (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)

localize14.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series15.0ms (0.3%)

Counts

3 → 24

Calls

3 calls:

8.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
4.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
3.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

rewrite44.0ms (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:

14.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
12.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

simplify324.0ms (6.5%)

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

prune237.0ms (4.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	0	0
Picked	0	1	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 (-.f64 1 x) (+.f64 1 x)))))
▶	0.0b	(.f64 2 (atan.f64 (sqrt.f64 (.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))))))

Status

Error

Program

✓

0.0b

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

▶

0.0b

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

Compiler

Compiled 2600 to 2123 computations (18.3% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series42.0ms (0.8%)

Counts

4 → 40

Calls

4 calls:

27.0ms	(/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
7.0ms	(cbrt.f64 (-.f64 1 x))
4.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
3.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))

rewrite159.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

167×	`add-sqr-sqrt_binary64`
165×	`*-un-lft-identity_binary64`
155×	`times-frac_binary64`
102×	`cbrt-prod_binary64`
91×	`sqrt-prod_binary64`

Counts

4 → 247

Calls

4 calls:

70.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
16.0ms	(/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
5.0ms	(cbrt.f64 (-.f64 1 x))
2.0ms	(atan.f64 (sqrt.f64 (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x))) (sqrt.f64 (+.f64 1 x))) (/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))))

simplify581.0ms (11.7%)

Algorithm

1×	egg-herbie

Rules

739×	`times-frac_binary64`
388×	`fma-def_binary64`
366×	`fma-neg_binary64`
233×	`cancel-sign-sub-inv_binary64`
209×	`associate-*r/_binary64`

Counts

287 → 298

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	300	8714
1	772	7935
2	2441	7844
3	4563	7763
4	4965	7763
5	4959	7763

prune868.0ms (17.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	382	0	382
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	382	2	384

Error

Counts

384 → 2

Alt Table

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

Status

Error

Program

✓

0.0b

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

✓

0.0b

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

Compiler

Compiled 14467 to 11824 computations (18.3% saved)

regimes614.0ms (12.4%)

Accuracy

Total 0.0b remaining (49.6%)

Threshold costs 0.0b (49.6%)

Counts

71 → 1

Compiler

Compiled 7644 to 6331 computations (17.2% saved)

simplify5.0ms (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

end113.0ms (2.3%)

Compiler: Compiled 77 to 64 computations (16.9% 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

analyze10.0ms (0.2%)

sample1.8s (37.2%)

simplify56.0ms (1.1%)

prune3.0ms (0.1%)

localize14.0ms (0.3%)

series15.0ms (0.3%)

rewrite44.0ms (0.9%)

simplify324.0ms (6.5%)

prune237.0ms (4.8%)

localize25.0ms (0.5%)

series42.0ms (0.8%)

rewrite159.0ms (3.2%)

simplify581.0ms (11.7%)

prune868.0ms (17.5%)

regimes614.0ms (12.4%)

simplify5.0ms (0.1%)

end113.0ms (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