Details

analyze10.0ms (0.6%)

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)

sample1.1s (67.6%)

Results

1.0s

8256×

body

128

valid

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify36.0ms (2.2%)

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 (0.5%)

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))

series12.0ms (0.7%)

Counts

3 → 24

Calls

3 calls:

7.0ms	(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))))

rewrite21.0ms (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:

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))))

simplify133.0ms (8.2%)

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

prune90.0ms (5.6%)

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

0.0b

Counts

131 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
▶	0.4b	(*.f64 2 (atan.f64 (-.f64 1 x)))

Compiler

Compiled 2556 to 2087 computations (18.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series1.0ms (0.1%)

Counts

1 → 0

Calls

1 calls:

1.0ms

(atan.f64 (-.f64 1 x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 9

Calls

1 calls:

1.0ms

(atan.f64 (-.f64 1 x))

simplify127.0ms (7.8%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

9 → 10

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	96
1	19	83
2	25	83
3	36	83
4	48	83
5	67	83
6	95	83
7	157	83
8	335	83
9	640	83
10	644	83
11	774	83
12	928	83
13	1096	83
14	1325	83
15	1626	83
16	1974	83
17	2449	83
18	3067	83
19	3263	83
20	3437	83
21	3551	83
22	3598	83
23	3650	83
24	4528	83
25	4817	83

prune6.0ms (0.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	10	2	12

Error

0.0b

Counts

12 → 2

Alt Table

Status	Error	Program
✓	0.0b	(*.f64 2 (atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
✓	0.4b	(*.f64 2 (atan.f64 (-.f64 1 x)))

Compiler

Compiled 126 to 108 computations (14.3% saved)

regimes30.0ms (1.8%)

Accuracy

Total 0.0b remaining (25%)

Threshold costs 0.0b (25%)

Counts

5 → 1

Compiler

Compiled 302 to 259 computations (14.2% saved)

simplify2.0ms (0.2%)

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	10	17
1	16	17
2	20	17
3	22	17
4	23	17
5	22	17

end44.0ms (2.7%)

Compiler: Compiled 43 to 36 computations (16.3% 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 (0.6%)

sample1.1s (67.6%)

simplify36.0ms (2.2%)

prune2.0ms (0.1%)

localize7.0ms (0.5%)

series12.0ms (0.7%)

rewrite21.0ms (1.3%)

simplify133.0ms (8.2%)

prune90.0ms (5.6%)

localize4.0ms (0.2%)

series1.0ms (0.1%)

rewrite1.0ms (0%)

simplify127.0ms (7.8%)

prune6.0ms (0.4%)

regimes30.0ms (1.8%)

simplify2.0ms (0.2%)

end44.0ms (2.7%)

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