Details

analyze5.0ms (0.2%)

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%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample970.0ms (43.6%)

Results

866.0ms	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 62 to 47 computations (24.2% saved)

simplify82.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

750×	`div-sub_binary64`
748×	`fma-neg_binary64`
599×	`fma-def_binary64`
502×	`associate-/l*_binary64`
423×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	27
3	201	27
4	526	27
5	991	25
6	1614	25
7	3273	25
8	3653	25
9	4694	25
10	4942	25

prune4.0ms (0.2%)

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 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
▶	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

Compiler

Compiled 113 to 86 computations (23.9% saved)

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

series27.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

16.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
11.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

rewrite18.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`distribute-lft-in_binary64`
16×	`distribute-rgt-in_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`

Counts

2 → 61

Calls

2 calls:

8.0ms	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))
6.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (*.f64 -1/4 (fma.f64 v v -1)))

simplify140.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-def_binary64`
599×	`fma-neg_binary64`
524×	`cancel-sign-sub-inv_binary64`
376×	`distribute-rgt-in_binary64`
248×	`associate-r_binary64`

Counts

85 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	197	2874
1	538	2641
2	2041	2536
3	4657	2530
4	4997	2530
5	4999	2530
6	4982	2530

prune107.0ms (4.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	104	3	107

Error

Counts

107 → 3

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
	0.3b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

Compiler

Compiled 3221 to 2658 computations (17.5% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	0.0b	(-.f64 1 (*.f64 v v))
✓	0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
✓	0.2b	(.f64 3 (.f64 v v))

series30.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

13.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
11.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
3.0ms	(.f64 3 (.f64 v v))
2.0ms	(-.f64 1 (*.f64 v v))

rewrite42.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
26×	`associate-l_binary64`
25×	`add-cube-cbrt_binary64`
23×	`add-cbrt-cube_binary64`

Counts

4 → 148

Calls

4 calls:

11.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
9.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
6.0ms	(.f64 3 (.f64 v v))
2.0ms	(-.f64 1 (*.f64 v v))

simplify136.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

597×	`cancel-sign-sub-inv_binary64`
416×	`times-frac_binary64`
377×	`associate-l_binary64`
361×	`associate-r_binary64`
248×	`*-commutative_binary64`

Counts

196 → 251

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	5214
1	874	4853
2	3123	4767
3	4973	4767

prune250.0ms (11.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	251	3	254

Error

Counts

254 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
▶	0.3b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

Compiler

Compiled 7813 to 5780 computations (26% saved)

localize11.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.1b	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))
✓	0.3b	(*.f64 (pow.f64 v 2) (sqrt.f64 2))

series19.0ms (0.9%)

Counts

3 → 3

Calls

3 calls:

10.0ms	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
5.0ms	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))
4.0ms	(*.f64 (pow.f64 v 2) (sqrt.f64 2))

rewrite20.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
18×	`add-exp-log_binary64`
11×	`associate-l_binary64`
10×	`add-cbrt-cube_binary64`
10×	`prod-exp_binary64`

Counts

3 → 73

Calls

3 calls:

6.0ms	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
6.0ms	(*.f64 (pow.f64 v 2) (sqrt.f64 2))
5.0ms	(.f64 5/8 (.f64 (pow.f64 v 2) (sqrt.f64 2)))

simplify111.0ms (5%)

Algorithm

1×	egg-herbie

Rules

761×	`fma-def_binary64`
403×	`distribute-rgt-neg-in_binary64`
380×	`distribute-lft-neg-in_binary64`
272×	`*-commutative_binary64`
272×	`fma-neg_binary64`

Counts

76 → 109

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1271
1	255	1054
2	818	1031
3	1873	1002
4	4330	1002
5	4893	1002
6	4981	1002
7	4715	1002

prune108.0ms (4.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
✓	0.3b	(-.f64 (.f64 1/4 (sqrt.f64 2)) (.f64 5/8 (*.f64 (pow.f64 v 2) (sqrt.f64 2))))
✓	0.0b	(.f64 (sqrt.f64 2) (.f64 (sqrt.f64 (fma.f64 v (.f64 v -3) 1)) (.f64 -1/4 (fma.f64 v v -1))))

Compiler

Compiled 2125 to 1842 computations (13.3% saved)

regimes55.0ms (2.5%)

Accuracy

Total 0.0b remaining (36.4%)

Threshold costs 0.0b (36.4%)

Counts

22 → 1

Compiler

Compiled 925 to 768 computations (17% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
3×	`distribute-rgt-neg-in_binary64`
3×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	42	29
3	48	29
4	51	29
5	49	29

end65.0ms (2.9%)

Compiler: Compiled 92 to 72 computations (21.7% saved)

Details

analyze5.0ms (0.2%)

sample970.0ms (43.6%)

simplify82.0ms (3.7%)

prune4.0ms (0.2%)

localize10.0ms (0.5%)

series27.0ms (1.2%)

rewrite18.0ms (0.8%)

simplify140.0ms (6.3%)

prune107.0ms (4.8%)

localize10.0ms (0.5%)

series30.0ms (1.4%)

rewrite42.0ms (1.9%)

simplify136.0ms (6.1%)

prune250.0ms (11.3%)

localize11.0ms (0.5%)

series19.0ms (0.9%)

rewrite20.0ms (0.9%)

simplify111.0ms (5%)

prune108.0ms (4.9%)

regimes55.0ms (2.5%)

simplify3.0ms (0.1%)

end65.0ms (2.9%)

Profiling