Details

analyze10.0ms (0.4%)

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)

sample1.1s (40.3%)

Results

963.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify107.0ms (4%)

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

prune3.0ms (0.1%)

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)

localize8.0ms (0.3%)

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)
✓	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	14.3b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series9.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

4.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
2.0ms	(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)

rewrite5.0ms (0.2%)

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:

2.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
0.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
0.0ms	(fma.f64 x 27061/100000 230753/100000)
0.0ms	(fma.f64 x 4481/100000 99229/100000)

simplify83.0ms (3%)

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

prune106.0ms (3.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Error

Counts

101 → 2

Alt Table

Status	Error	Program
	25.5b	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)
▶	0.0b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) x)

Status

Error

Program

25.5b

(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)

▶

0.0b

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

Compiler

Compiled 1963 to 1477 computations (24.8% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	0.2b	(/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	14.2b	(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series16.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

7.0ms

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

6.0ms

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

3.0ms

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

rewrite47.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
156×	`*-un-lft-identity_binary64`
156×	`add-cube-cbrt_binary64`
147×	`sqrt-prod_binary64`

Counts

3 → 233

Calls

3 calls:

10.0ms

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

3.0ms

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

1.0ms

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

simplify344.0ms (12.7%)

Algorithm

1×	egg-herbie

Rules

547×	`associate-/l/_binary64`
509×	`fma-neg_binary64`
445×	`fma-def_binary64`
366×	`times-frac_binary64`
262×	`sub-neg_binary64`

Counts

269 → 321

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	357	12762
1	881	11663
2	2280	10965
3	4398	10742
4	4879	10742
5	4935	10742

prune491.0ms (18.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	375	0	375
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	375	2	377

Error

Counts

377 → 2

Alt Table

Status	Error	Program
▶	25.5b	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)
✓	0.0b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) x)

Status

Error

Program

▶

25.5b

(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)

✓

0.0b

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

Compiler

Compiled 14731 to 11646 computations (20.9% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)
✓	0.4b	(fma.f64 x -20191289437/10000000000 230753/100000)

series4.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)
2.0ms	(fma.f64 x -20191289437/10000000000 230753/100000)

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 41

Calls

2 calls:

3.0ms	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)
0.0ms	(fma.f64 x -20191289437/10000000000 230753/100000)

simplify67.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

889×	`fma-neg_binary64`
354×	`associate-l_binary64`
305×	`times-frac_binary64`
293×	`associate-r_binary64`
244×	`fma-def_binary64`

Counts

65 → 61

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	587
1	142	534
2	452	462
3	2014	426
4	4060	426
5	5218	426

prune37.0ms (1.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	61	0	61
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	61	2	63

Error

Counts

63 → 2

Alt Table

Status	Error	Program
✓	25.5b	(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)
✓	0.0b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) x)

Status

Error

Program

✓

25.5b

(-.f64 (fma.f64 x -20191289437/10000000000 230753/100000) x)

✓

0.0b

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

Compiler

Compiled 843 to 543 computations (35.6% saved)

regimes194.0ms (7.1%)

Accuracy

Total -0.0b remaining (-188.3%)

Threshold costs -0.0b (-188.3%)

Counts

94 → 1

Compiler

Compiled 3470 to 2662 computations (23.3% saved)

simplify4.0ms (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	14	23
1	18	23
2	22	23
3	24	23
4	25	23
5	24	23

end66.0ms (2.4%)

Compiler: Compiled 66 to 50 computations (24.2% saved)

Details

analyze10.0ms (0.4%)

sample1.1s (40.3%)

simplify107.0ms (4%)

prune3.0ms (0.1%)

localize8.0ms (0.3%)

series9.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify83.0ms (3%)

prune106.0ms (3.9%)

localize11.0ms (0.4%)

series16.0ms (0.6%)

rewrite47.0ms (1.7%)

simplify344.0ms (12.7%)

prune491.0ms (18.1%)

localize4.0ms (0.1%)

series4.0ms (0.1%)

rewrite7.0ms (0.3%)

simplify67.0ms (2.5%)

prune37.0ms (1.4%)

regimes194.0ms (7.1%)

simplify4.0ms (0.1%)

end66.0ms (2.4%)

Profiling