Metrics for Data.Random.Distribution.Normal:normalF from random-fu-0.2.6.2

analyze1.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample905.0ms (72.5%)

Results

668.0ms	6259×	body	256	valid
197.0ms	1997×	body	256	infinite

Bogosity

preprocess86.0ms (6.9%)

Algorithm

1×	egg-herbie

Rules

1462×	`fma-def`
812×	`sqr-pow`
812×	`div-sub`
768×	`associate-/r*`
704×	`fma-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	89
1	53	89
2	131	89
3	349	89
4	793	89
5	1960	89
6	5103	89

Stop Event

1×	node limit

Calls

Call 1

Inputs
(exp.f64 (.f64 (.f64 x y) y))
(exp.f64 (.f64 (.f64 x y) y))
(exp.f64 (.f64 (.f64 (neg.f64 x) y) y))
(exp.f64 (.f64 (.f64 x (neg.f64 y)) (neg.f64 y)))
(exp.f64 (.f64 (.f64 y x) x))

Outputs
(exp.f64 (.f64 (.f64 x y) y))
(pow.f64 (exp.f64 (*.f64 x y)) y)
(pow.f64 (pow.f64 (exp.f64 y) x) y)
(exp.f64 (.f64 (.f64 x y) y))
(pow.f64 (exp.f64 (*.f64 x y)) y)
(pow.f64 (pow.f64 (exp.f64 y) x) y)
(exp.f64 (.f64 (.f64 (neg.f64 x) y) y))
(pow.f64 (exp.f64 (*.f64 x (neg.f64 y))) y)
(pow.f64 (pow.f64 (exp.f64 (neg.f64 y)) x) y)
(pow.f64 (pow.f64 (exp.f64 y) x) (neg.f64 y))
(pow.f64 (exp.f64 (*.f64 x y)) (neg.f64 y))
(exp.f64 (.f64 (.f64 x (neg.f64 y)) (neg.f64 y)))
(pow.f64 (exp.f64 (*.f64 x y)) y)
(pow.f64 (pow.f64 (exp.f64 y) x) y)
(exp.f64 (.f64 (.f64 y x) x))
(exp.f64 (.f64 y (.f64 x x)))
(pow.f64 (pow.f64 (exp.f64 y) x) x)
(pow.f64 (exp.f64 (*.f64 x y)) x)

Symmetry

(abs y)

Compiler

Compiled 8 to 5 computations (37.5% saved)

eval1.0ms (0.1%)

Compiler: Compiled 14 to 8 computations (42.9% saved)

prune2.0ms (0.2%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(exp.f64 (.f64 (.f64 x y) y))
▶	100.0%	(exp.f64 (.f64 (.f64 x y) y))

Compiler

Compiled 16 to 10 computations (37.5% saved)

localize47.0ms (3.8%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	99.8%	(.f64 (.f64 x y) y)

Compiler

Compiled 19 to 6 computations (68.4% saved)

series5.0ms (0.4%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(.f64 (.f64 x y) y)
1.0ms	y	@	inf	(.f64 (.f64 x y) y)
1.0ms	x	@	inf	(.f64 (.f64 x y) y)
1.0ms	y	@	0	(.f64 (.f64 x y) y)
0.0ms	x	@	-inf	(.f64 (.f64 x y) y)

rewrite69.0ms (5.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1136×	`pow1`
1036×	`add-exp-log`
1036×	`log1p-expm1-u`
1036×	`expm1-log1p-u`
1012×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	119	13
2	1436	13

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(.f64 (.f64 x y) y)

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

simplify79.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

2142×	`log-prod`
1110×	`distribute-rgt-in`
1088×	`distribute-lft-in`
792×	`associate-r`
670×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	455
1	84	455
2	312	455
3	2134	455
4	7074	455

Stop Event

1×	node limit

Counts

35 → 14

Calls

Call 1

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

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

eval5.0ms (0.4%)

Compiler: Compiled 114 to 55 computations (51.8% saved)

prune5.0ms (0.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	14	0	14
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	14	1	15

Accuracy

100.0%

Counts

15 → 1

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(exp.f64 (.f64 (.f64 x y) y))

Compiler

Compiled 16 to 10 computations (37.5% saved)

simplify10.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	17
1	10	17

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(exp.f64 (.f64 (.f64 x y) y))

Outputs
(exp.f64 (.f64 (.f64 x y) y))
(exp.f64 (.f64 y (.f64 x y)))

Compiler

Compiled 8 to 5 computations (37.5% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess33.0ms (2.7%)

Remove: (abs y)
Compiler: Compiled 48 to 30 computations (37.5% saved)

analyze1.0ms (0%)

sample905.0ms (72.5%)

preprocess86.0ms (6.9%)

eval1.0ms (0.1%)

prune2.0ms (0.2%)

localize47.0ms (3.8%)

series5.0ms (0.4%)

rewrite69.0ms (5.5%)

simplify79.0ms (6.4%)

eval5.0ms (0.4%)

prune5.0ms (0.4%)

simplify10.0ms (0.8%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess33.0ms (2.7%)

Profiling