Details

analyze101.0ms (3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
50%	50%	0.1%	6
56.2%	37.5%	6.3%	7
68.7%	25%	6.3%	8
71.8%	18.7%	9.5%	9
78%	12.5%	9.5%	10
79.6%	9.4%	11%	11
82.7%	6.2%	11%	12
83.5%	4.7%	11.8%	13
85.1%	3.1%	11.8%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample957.0ms (28.7%)

Results

846.0ms	8256×	body	128	valid
6.0ms	66×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify45.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-neg_binary64`
586×	`fma-def_binary64`
222×	`cancel-sign-sub-inv_binary64`
115×	`sub-neg_binary64`
82×	`associate--r+_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	27	14
2	58	12
3	109	12
4	229	11
5	450	11
6	661	11
7	940	11
8	1194	11
9	1320	11
10	1347	11
11	1268	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
	0.0b	(-.f64 (fma.f64 y (+.f64 x -1/2) 918938533204673/1000000000000000) x)

Compiler

Compiled 67 to 49 computations (26.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
✓	0.0b	(*.f64 x (-.f64 y 1))

series15.0ms (0.5%)

Counts

3 → 72

Calls

3 calls:

6.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
5.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
4.0ms	(*.f64 x (-.f64 y 1))

rewrite36.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`prod-diff_binary64`
54×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64`
52×	`associate--l+_binary64`
48×	`add-cube-cbrt_binary64`

Counts

3 → 142

Calls

3 calls:

10.0ms	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
6.0ms	(-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2))
6.0ms	(*.f64 x (-.f64 y 1))

simplify119.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

498×	`associate-l_binary64`
467×	`cancel-sign-sub-inv_binary64`
407×	`associate-r_binary64`
355×	`fma-def_binary64`
343×	`distribute-rgt-in_binary64`

Counts

214 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	2104
1	343	1880
2	919	1854
3	3620	1854
4	4913	1854
5	4896	1854

prune185.0ms (5.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	235	2	237
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	236	3	239

Error

Counts

239 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
▶	0.0b	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x))) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x))) 918938533204673/1000000000000000)

Compiler

Compiled 5025 to 3718 computations (26% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x))
✓	0.0b	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))

series10.0ms (0.3%)

Counts

2 → 48

Calls

2 calls:

5.0ms	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
5.0ms	(-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`prod-diff_binary64`
17×	`add-cube-cbrt_binary64`
13×	`associate-+r+_binary64`

Counts

2 → 60

Calls

2 calls:

6.0ms	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
3.0ms	(-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x))

simplify99.0ms (3%)

Algorithm

1×	egg-herbie

Rules

950×	`fma-neg_binary64`
447×	`distribute-rgt-in_binary64`
443×	`fma-def_binary64`
437×	`associate-l_binary64`
427×	`distribute-lft-in_binary64`

Counts

108 → 102

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	1300
1	256	1213
2	795	1144
3	3604	1142
4	4317	1142
5	4816	1142

prune84.0ms (2.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	102	3	105

Error

Counts

105 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
✓	0.0b	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
▶	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x))) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x))) 918938533204673/1000000000000000)

Compiler

Compiled 2249 to 1431 computations (36.4% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 x 1/2))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x))) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x)))
✓	0.5b	(.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x)))
✓	0.6b	(cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x))

series156.0ms (4.7%)

Counts

4 → 96

Calls

4 calls:

110.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x)))
35.0ms	(cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x))
6.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x))) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x)))
5.0ms	(*.f64 y (-.f64 x 1/2))

rewrite64.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`cbrt-div_binary64`
45×	`add-sqr-sqrt_binary64`
35×	`flip--_binary64`
35×	`flip3--_binary64`
33×	`*-un-lft-identity_binary64`

Counts

4 → 179

Calls

4 calls:

19.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x))) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x)))
12.0ms	(.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x)))
5.0ms	(*.f64 y (-.f64 x 1/2))
5.0ms	(cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x))

simplify284.0ms (8.5%)

Algorithm

1×	egg-herbie

Rules

724×	`times-frac_binary64`
597×	`fma-def_binary64`
285×	`*-commutative_binary64`
128×	`+-commutative_binary64`
125×	`sub-neg_binary64`

Counts

275 → 326

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	795	12199
1	2413	11205
2	4927	11005
3	5000	11005
4	4934	11005

prune708.0ms (21.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	572	0	572
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	572	3	575

Error

Counts

575 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (-.f64 (.f64 x (-.f64 y 1)) (.f64 y 1/2)) 918938533204673/1000000000000000)
✓	0.0b	(+.f64 (*.f64 y x) (-.f64 918938533204673/1000000000000000 (fma.f64 y 1/2 x)))
✓	1.0b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x)) (cbrt.f64 (-.f64 (.f64 y (-.f64 x 1/2)) x))) (cbrt.f64 (-.f64 (*.f64 y (-.f64 x 1/2)) x))) 918938533204673/1000000000000000)

Compiler

Compiled 31811 to 22946 computations (27.9% saved)

regimes367.0ms (11%)

Accuracy

Total -0.0b remaining (-125%)

Threshold costs -0.0b (-125%)

Counts

85 → 1

Compiler

Compiled 5872 to 4402 computations (25% saved)

simplify2.0ms (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	8	12
1	10	12
2	15	12
3	17	12
4	18	12
5	18	12

end57.0ms (1.7%)

Compiler: Compiled 77 to 53 computations (31.2% saved)

Details

analyze101.0ms (3%)

sample957.0ms (28.7%)

simplify45.0ms (1.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series15.0ms (0.5%)

rewrite36.0ms (1.1%)

simplify119.0ms (3.6%)

prune185.0ms (5.6%)

localize6.0ms (0.2%)

series10.0ms (0.3%)

rewrite12.0ms (0.4%)

simplify99.0ms (3%)

prune84.0ms (2.5%)

localize15.0ms (0.4%)

series156.0ms (4.7%)

rewrite64.0ms (1.9%)

simplify284.0ms (8.5%)

prune708.0ms (21.2%)

regimes367.0ms (11%)

simplify2.0ms (0.1%)

end57.0ms (1.7%)

Profiling