Details

analyze18.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample1.8s (47.6%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify124.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1572×	`fma-neg_binary64`
1419×	`fma-def_binary64`
565×	`sub-neg_binary64`
397×	`div-sub_binary64`
395×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	31	19
2	50	19
3	71	19
4	84	19
5	103	19
6	137	19
7	208	19
8	304	19
9	493	19
10	931	19
11	1441	19
12	2503	19
13	3175	19
14	3604	19
15	4118	19
16	4302	19
17	4751	19

prune6.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.3b	(fma.f64 x 27061/100000 230753/100000)
✓	13.6b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series16.0ms (0.4%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
4.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
3.0ms	(fma.f64 x 27061/100000 230753/100000)
3.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 59

Calls

4 calls:

4.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
1.0ms	(fma.f64 x 27061/100000 230753/100000)
1.0ms	(fma.f64 x 4481/100000 99229/100000)
1.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)

simplify135.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-def_binary64`
477×	`associate-l_binary64`
447×	`fma-neg_binary64`
424×	`distribute-rgt-in_binary64`
411×	`distribute-lft-in_binary64`

Counts

107 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1537
1	235	1385
2	582	1380
3	1485	1370
4	4572	1370
5	4900	1370

prune186.0ms (5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	99	2	101

Error

Counts

101 → 2

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)
✓	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Status

Error

Program

▶

0.3b

(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)

✓

0.0b

(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Compiler

Compiled 1968 to 1482 computations (24.7% saved)

localize26.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
✓	0.2b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
	0.3b	(fma.f64 x 27061/100000 230753/100000)
✓	13.5b	(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series43.0ms (1.1%)

Counts

3 → 36

Calls

3 calls:

18.0ms

(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

15.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

10.0ms

(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

rewrite73.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`

Counts

3 → 141

Calls

3 calls:

32.0ms

(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

6.0ms

(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

2.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

simplify308.0ms (8.3%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-def_binary64`
340×	`fma-neg_binary64`
339×	`times-frac_binary64`
249×	`cancel-sign-sub-inv_binary64`
226×	`distribute-rgt-in_binary64`

Counts

177 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	6185
1	738	5177
2	2413	5161
3	4875	5150
4	4965	5150

prune705.0ms (19%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	286	2	288

Error

Counts

288 → 2

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)
✓	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Status

Error

Program

✓

0.3b

(-.f64 (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)

✓

0.0b

(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Compiler

Compiled 10590 to 8458 computations (20.1% saved)

regimes138.0ms (3.7%)

Accuracy

Total 0.0b remaining (33.2%)

Threshold costs 0.0b (33.2%)

Counts

33 → 1

Compiler

Compiled 1124 to 850 computations (24.4% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	17	22
2	21	22
3	23	22
4	24	22
5	23	22

end128.0ms (3.5%)

Compiler: Compiled 76 to 58 computations (23.7% saved)

Details

analyze18.0ms (0.5%)

sample1.8s (47.6%)

simplify124.0ms (3.3%)

prune6.0ms (0.2%)

localize20.0ms (0.5%)

series16.0ms (0.4%)

rewrite13.0ms (0.4%)

simplify135.0ms (3.6%)

prune186.0ms (5%)

localize26.0ms (0.7%)

series43.0ms (1.1%)

rewrite73.0ms (2%)

simplify308.0ms (8.3%)

prune705.0ms (19%)

regimes138.0ms (3.7%)

simplify5.0ms (0.1%)

end128.0ms (3.5%)

Profiling