Metrics for Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

analyze11.0ms (0.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
75%	74.9%	25%	0.1%	0%	0%	0%	5
75%	74.9%	25%	0.1%	0%	0%	0%	6
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	7
87.5%	87.4%	12.5%	0.1%	0%	0%	0%	8
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	9
93.8%	93.7%	6.2%	0.1%	0%	0%	0%	10
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	11
96.9%	96.8%	3.1%	0.1%	0%	0%	0%	12

Compiler

Compiled 10 to 6 computations (40% saved)

sample882.0ms (57.3%)

Results

756.0ms	7257×	body	256	valid
114.0ms	999×	body	256	infinite

Bogosity

preprocess146.0ms (9.5%)

Algorithm

1×	egg-herbie

Rules

2102×	`div-sub`
2076×	`fma-def`
1234×	`fma-neg`
946×	`sub-neg`
756×	`times-frac`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	18	103
1	34	95
2	74	95
3	180	95
4	410	95
5	1023	87
6	2971	79
7	5222	79
8	6246	79
9	6855	79
10	7349	79
11	7665	79

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 x y) (+.f64 y y))
(/.f64 (+.f64 (neg.f64 x) y) (+.f64 y y))
(/.f64 (+.f64 x (neg.f64 y)) (+.f64 (neg.f64 y) (neg.f64 y)))
(/.f64 (+.f64 y x) (+.f64 x x))

Outputs
(/.f64 (+.f64 x y) (+.f64 y y))
(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))
(fma.f64 x (/.f64 1/2 y) 1/2)
(/.f64 (+.f64 x y) (+.f64 y y))
(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))
(fma.f64 x (/.f64 1/2 y) 1/2)
(/.f64 (+.f64 (neg.f64 x) y) (+.f64 y y))
(/.f64 (+.f64 y (neg.f64 x)) (+.f64 y y))
(/.f64 (-.f64 y x) (+.f64 y y))
(-.f64 1/2 (/.f64 x (+.f64 y y)))
(+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))
(fma.f64 -1/2 (/.f64 x y) 1/2)
(fma.f64 x (/.f64 -1/2 y) 1/2)
(/.f64 (+.f64 x (neg.f64 y)) (+.f64 (neg.f64 y) (neg.f64 y)))
(/.f64 (+.f64 y (neg.f64 x)) (+.f64 y y))
(/.f64 (-.f64 y x) (+.f64 y y))
(-.f64 1/2 (/.f64 x (+.f64 y y)))
(+.f64 1/2 (*.f64 -1/2 (/.f64 x y)))
(fma.f64 -1/2 (/.f64 x y) 1/2)
(fma.f64 x (/.f64 -1/2 y) 1/2)
(/.f64 (+.f64 y x) (+.f64 x x))
(/.f64 (+.f64 x y) (+.f64 x x))
(-.f64 (/.f64 (/.f64 y x) 2) -1/2)
(+.f64 1/2 (/.f64 (/.f64 y x) 2))

Compiler

Compiled 9 to 5 computations (44.4% saved)

eval1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

prune1.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))
▶	100.0%	(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize29.0ms (1.9%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f64 -1/2 (/.f64 x y))

Compiler

Compiled 22 to 12 computations (45.5% saved)

series10.0ms (0.6%)

Counts

1 → 0

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	y	@	0	(*.f64 -1/2 (/.f64 x y))
2.0ms	x	@	inf	(*.f64 -1/2 (/.f64 x y))
2.0ms	x	@	0	(*.f64 -1/2 (/.f64 x y))
1.0ms	x	@	-inf	(*.f64 -1/2 (/.f64 x y))
1.0ms	y	@	inf	(*.f64 -1/2 (/.f64 x y))

rewrite65.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1500×	`pow1`
1386×	`add-exp-log`
1386×	`log1p-expm1-u`
1386×	`expm1-log1p-u`
1356×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	147	13
2	1849	13

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(*.f64 -1/2 (/.f64 x y))

Outputs
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 x y))) 1)
(/.f64 -1/2 (/.f64 y x))
(/.f64 1 (/.f64 y (*.f64 -1/2 x)))
(/.f64 (*.f64 -1/2 x) y)
(/.f64 (neg.f64 (*.f64 -1/2 x)) (neg.f64 y))
(/.f64 (*.f64 -1/2 (neg.f64 x)) (neg.f64 y))
(/.f64 (*.f64 (neg.f64 x) -1/2) (neg.f64 y))
(/.f64 (/.f64 (*.f64 -1/2 x) 1) y)
(/.f64 (/.f64 (*.f64 -1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(/.f64 (/.f64 (*.f64 -1/2 x) (sqrt.f64 y)) (sqrt.f64 y))
(pow.f64 (*.f64 -1/2 (/.f64 x y)) 1)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 x y))) 3)
(pow.f64 (pow.f64 (*.f64 -1/2 (/.f64 x y)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 x y))) 2)
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(log.f64 (pow.f64 (exp.f64 (/.f64 x y)) -1/2))
(cbrt.f64 (pow.f64 (*.f64 -1/2 (/.f64 x y)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (/.f64 x y))))
(exp.f64 (log.f64 (*.f64 -1/2 (/.f64 x y))))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (/.f64 x y))))

simplify61.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

1400×	`log-prod`
916×	`associate-r`
904×	`distribute-lft-neg-out`
882×	`fma-def`
824×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	500
1	145	380
2	513	260
3	3929	260

Stop Event

1×	node limit

Counts

20 → 23

Calls

Call 1

Inputs
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 x y))) 1)
(/.f64 -1/2 (/.f64 y x))
(/.f64 1 (/.f64 y (*.f64 -1/2 x)))
(/.f64 (*.f64 -1/2 x) y)
(/.f64 (neg.f64 (*.f64 -1/2 x)) (neg.f64 y))
(/.f64 (*.f64 -1/2 (neg.f64 x)) (neg.f64 y))
(/.f64 (*.f64 (neg.f64 x) -1/2) (neg.f64 y))
(/.f64 (/.f64 (*.f64 -1/2 x) 1) y)
(/.f64 (/.f64 (*.f64 -1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(/.f64 (/.f64 (*.f64 -1/2 x) (sqrt.f64 y)) (sqrt.f64 y))
(pow.f64 (*.f64 -1/2 (/.f64 x y)) 1)
(pow.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 x y))) 3)
(pow.f64 (pow.f64 (*.f64 -1/2 (/.f64 x y)) 3) 1/3)
(pow.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 x y))) 2)
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(log.f64 (pow.f64 (exp.f64 (/.f64 x y)) -1/2))
(cbrt.f64 (pow.f64 (*.f64 -1/2 (/.f64 x y)) 3))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (/.f64 x y))))
(exp.f64 (log.f64 (*.f64 -1/2 (/.f64 x y))))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (/.f64 x y))))

Outputs
(-.f64 (+.f64 1 (*.f64 -1/2 (/.f64 x y))) 1)
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 -1/2 (/.f64 y x))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 1 (/.f64 y (*.f64 -1/2 x)))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 (*.f64 -1/2 x) y)
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 (neg.f64 (*.f64 -1/2 x)) (neg.f64 y))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 (*.f64 -1/2 (neg.f64 x)) (neg.f64 y))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 (*.f64 (neg.f64 x) -1/2) (neg.f64 y))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 (/.f64 (*.f64 -1/2 x) 1) y)
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 (/.f64 (*.f64 -1/2 x) (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(/.f64 (/.f64 (*.f64 -1/2 x) (sqrt.f64 y)) (sqrt.f64 y))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(pow.f64 (*.f64 -1/2 (/.f64 x y)) 1)
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(pow.f64 (cbrt.f64 (*.f64 -1/2 (/.f64 x y))) 3)
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(pow.f64 (pow.f64 (*.f64 -1/2 (/.f64 x y)) 3) 1/3)
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(pow.f64 (sqrt.f64 (*.f64 -1/2 (/.f64 x y))) 2)
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(sqrt.f64 (*.f64 (pow.f64 (/.f64 x y) 2) 1/4))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(log.f64 (pow.f64 (exp.f64 (/.f64 x y)) -1/2))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(cbrt.f64 (pow.f64 (*.f64 -1/2 (/.f64 x y)) 3))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(expm1.f64 (log1p.f64 (*.f64 -1/2 (/.f64 x y))))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(exp.f64 (log.f64 (*.f64 -1/2 (/.f64 x y))))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))
(log1p.f64 (expm1.f64 (*.f64 -1/2 (/.f64 x y))))
(+.f64 1 (-.f64 (*.f64 -1/2 (/.f64 x y)) 1))
(+.f64 (*.f64 x (/.f64 -1/2 y)) 0)
(*.f64 -1/2 (/.f64 x y))

eval5.0ms (0.3%)

Compiler: Compiled 219 to 154 computations (29.7% saved)

prune4.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	1	24

Accuracy

100.0%

Counts

24 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))

Compiler

Compiled 25 to 17 computations (32% saved)

regimes9.0ms (0.6%)

Accuracy

Total -0.0b remaining (-∞%)

Threshold costs -0b (-∞%)

Counts

2 → 1

Calls

Call 1

Inputs
(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))
(/.f64 (+.f64 x y) (+.f64 y y))

Outputs
(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))

Calls

3 calls:

3.0ms	(/.f64 (+.f64 x y) (+.f64 y y))
3.0ms	y
3.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(/.f64 (+.f64 x y) (+.f64 y y))`

Compiler

Compiled 31 to 19 computations (38.7% saved)

simplify7.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

10×	`sub-neg`
10×	`+-commutative`
10×	`*-commutative`
8×	`neg-mul-1`
8×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	16	19
2	28	19
3	36	19
4	42	19
5	45	19
6	46	19

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))

Outputs
(-.f64 1/2 (*.f64 -1/2 (/.f64 x y)))

Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness277.0ms (18%)

Rules

2102×	`div-sub`
2076×	`fma-def`
1234×	`fma-neg`
946×	`sub-neg`
756×	`times-frac`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	18	103
1	34	95
2	74	95
3	180	95
4	410	95
5	1023	87
6	2971	79
7	5222	79
8	6246	79
9	6855	79
10	7349	79
11	7665	79

Stop Event

1×	node limit

Compiler

Compiled 162 to 67 computations (58.6% saved)

end0.0ms (0%)

preprocess32.0ms (2.1%)

Compiler: Compiled 54 to 38 computations (29.6% saved)

analyze11.0ms (0.7%)

sample882.0ms (57.3%)

preprocess146.0ms (9.5%)

eval1.0ms (0%)

prune1.0ms (0.1%)

localize29.0ms (1.9%)

series10.0ms (0.6%)

rewrite65.0ms (4.2%)

simplify61.0ms (3.9%)

eval5.0ms (0.3%)

prune4.0ms (0.2%)

regimes9.0ms (0.6%)

simplify7.0ms (0.5%)

soundness277.0ms (18%)

end0.0ms (0%)

preprocess32.0ms (2.1%)

Profiling