Details

analyze12.0ms (0.4%)

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)

sample129.0ms (4.1%)

Algorithm

1×

intervals

Results

53.0ms

256×

body

128

valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify62.0ms (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 (0.2%)

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:

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

rewrite22.0ms (0.7%)

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:

8.0ms	(/.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))))

simplify183.0ms (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

prune106.0ms (3.3%)

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

Status

Error

Program

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)))))))

▶

0.0b

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

Compiler

Compiled 2616 to 2137 computations (18.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series12.0ms (0.4%)

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)))
3.0ms	(expm1.f64 (log1p.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×	`expm1-log1p-u_binary64`

Counts

3 → 37

Calls

3 calls:

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

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

728×	`cancel-sign-sub-inv_binary64`
723×	`fma-neg_binary64`
411×	`sub-neg_binary64`
218×	`associate-+l+_binary64`
202×	`associate--l+_binary64`

Counts

73 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	124	1273
1	313	1178
2	947	1164
3	3044	1162
4	4942	1162
5	5152	1162

prune133.0ms (4.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	166	2	168

Error

Counts

168 → 2

Alt Table

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

Status

Error

Program

▶

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)))))))

✓

0.0b

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

Compiler

Compiled 3266 to 2724 computations (16.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series43.0ms (1.4%)

Counts

4 → 40

Calls

4 calls:

24.0ms	(/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
10.0ms	(*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x)))
6.0ms	(cbrt.f64 (-.f64 1 x))
3.0ms	(.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))))

rewrite95.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

195×	`add-sqr-sqrt_binary64`
191×	`*-un-lft-identity_binary64`
155×	`times-frac_binary64`
134×	`cbrt-prod_binary64`
91×	`sqrt-prod_binary64`

Counts

4 → 299

Calls

4 calls:

36.0ms	(.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))))
10.0ms	(*.f64 (cbrt.f64 (-.f64 1 x)) (cbrt.f64 (-.f64 1 x)))
8.0ms	(/.f64 (cbrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
2.0ms	(cbrt.f64 (-.f64 1 x))

simplify295.0ms (9.3%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
410×	`fma-neg_binary64`
303×	`cancel-sign-sub-inv_binary64`
218×	`associate-l_binary64`
202×	`associate-r_binary64`

Counts

339 → 393

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	352	9629
1	891	8820
2	2926	8346
3	4515	8164
4	4980	8164
5	4981	8164

prune807.0ms (25.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	479	0	479
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	479	2	481

Error

Counts

481 → 2

Alt Table

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

Status

Error

Program

✓

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)))))))

✓

0.0b

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

Compiler

Compiled 18111 to 14835 computations (18.1% saved)

regimes278.0ms (8.8%)

Accuracy

Total 0.0b remaining (39.3%)

Threshold costs 0.0b (39.3%)

Counts

46 → 1

Compiler

Compiled 4644 to 3946 computations (15% 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

end1.0ms (0%)

Compiler: Compiled 14 to 12 computations (14.3% saved)

sample864.0ms (27.3%)

Algorithm

1×

intervals

Results

605.0ms

8000×

body

128

valid

Compiler

Compiled 71 to 60 computations (15.5% 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

analyze12.0ms (0.4%)

sample129.0ms (4.1%)

simplify62.0ms (2%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

series10.0ms (0.3%)

rewrite22.0ms (0.7%)

simplify183.0ms (5.8%)

prune106.0ms (3.3%)

localize13.0ms (0.4%)

series12.0ms (0.4%)

rewrite3.0ms (0.1%)

simplify75.0ms (2.4%)

prune133.0ms (4.2%)

localize13.0ms (0.4%)

series43.0ms (1.4%)

rewrite95.0ms (3%)

simplify295.0ms (9.3%)

prune807.0ms (25.5%)

regimes278.0ms (8.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample864.0ms (27.3%)

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