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

analyze0.0ms (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)

sample1.1s (65.8%)

Results

830.0ms	6220×	body	256	valid
218.0ms	2036×	body	256	infinite

Bogosity

preprocess170.0ms (10.6%)

Algorithm

1×	egg-herbie

Rules

682×	`sqr-pow`
419×	`div-sub`
380×	`associate-/r*`
330×	`fma-def`
300×	`associate-*r/`

Problems

256×

No Errors

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	89
1	54	89
2	127	89
3	358	89
4	826	89
5	1959	89
6	4966	89
7	7693	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 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 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 x) y) (neg.f64 y))
(pow.f64 (pow.f64 (exp.f64 y) x) (neg.f64 y))
(pow.f64 (pow.f64 (exp.f64 x) (neg.f64 y)) 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 x) y) y)
(pow.f64 (pow.f64 (exp.f64 y) x) y)
(exp.f64 (.f64 (.f64 y x) x))
(pow.f64 (exp.f64 (*.f64 x y)) x)
(pow.f64 (pow.f64 (exp.f64 x) y) x)
(pow.f64 (exp.f64 y) (*.f64 x x))
(pow.f64 (pow.f64 (exp.f64 y) x) x)

Symmetry

(abs y)

Compiler

Compiled 27 to 11 computations (59.3% saved)

eval1.0ms (0.1%)

Compiler: Compiled 50 to 25 computations (50% saved)

prune2.0ms (0.1%)

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)

localize32.0ms (2%)

Localize:

Found 2 expressions with local error:

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

Compiler

Compiled 19 to 6 computations (68.4% saved)

series3.0ms (0.2%)

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)
0.0ms	x	@	inf	(.f64 (.f64 x y) y)
0.0ms	y	@	0	(.f64 (.f64 x y) y)
0.0ms	x	@	-inf	(.f64 (.f64 x y) y)

rewrite190.0ms (11.8%)

Algorithm

3×	rewrite-once
1×	batch-egg-rewrite

Rules

798×	`unswap-sqr`
395×	`swap-sqr`
333×	`sqr-pow`
313×	`prod-exp`
191×	`rem-sqrt-square`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	6	13
1	10	13
2	13	13
3	21	13
4	39	13
5	85	13
6	268	7
7	1627	1
8	1656	1
9	1725	1
10	2229	1
11	4083	1
12	7198	1

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

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

Outputs
x

Calls

3 calls:

1.0ms	(.f64 (.f64 x y) y)
0.0ms	(.f64 (.f64 x y) y)
0.0ms	(.f64 (.f64 x y) y)

simplify108.0ms (6.7%)

Algorithm

1×	egg-herbie

Rules

795×	`fma-def`
550×	`prod-exp`
379×	`*-commutative`
379×	`unswap-sqr`
297×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	539
1	78	539
2	318	539
3	1301	539
4	3241	539
5	5522	539

Stop Event

1×	node limit

Counts

39 → 16

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))
(exp.f64 (log.f64 (.f64 (.f64 x y) y)))
(log.f64 (exp.f64 (.f64 (.f64 x y) y)))
(.f64 (sqrt.f64 (.f64 (.f64 x y) y)) (sqrt.f64 (.f64 (*.f64 x y) y)))
(log1p.f64 (expm1.f64 (.f64 (.f64 x y) y)))
(expm1.f64 (log1p.f64 (.f64 (.f64 x y) y)))
(.f64 1 (.f64 (*.f64 x y) y))
(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (.f64 (.f64 x y) y)))
(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x y) y) (.f64 (.f64 x y) y)) (.f64 (.f64 x y) y)))
(pow.f64 (.f64 (.f64 x y) y) 1)
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (.f32 (.f32 (binary64->binary32 x) (binary64->binary32 y)) (binary64->binary32 y)))
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (.f32 (.f32 (binary64->binary32 x) (binary64->binary32 y)) (binary64->binary32 y)))

Outputs
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(*.f64 x (pow.f64 y 2))
(.f64 x (.f64 y y))
(exp.f64 (log.f64 (.f64 (.f64 x y) y)))
(.f64 x (.f64 y y))
(log.f64 (exp.f64 (.f64 (.f64 x y) y)))
(.f64 x (.f64 y y))
(.f64 (sqrt.f64 (.f64 (.f64 x y) y)) (sqrt.f64 (.f64 (*.f64 x y) y)))
(.f64 x (.f64 y y))
(log1p.f64 (expm1.f64 (.f64 (.f64 x y) y)))
(.f64 x (.f64 y y))
(expm1.f64 (log1p.f64 (.f64 (.f64 x y) y)))
(.f64 x (.f64 y y))
(.f64 1 (.f64 (*.f64 x y) y))
(.f64 x (.f64 y y))
(.f64 (.f64 (cbrt.f64 (.f64 (.f64 x y) y)) (cbrt.f64 (.f64 (.f64 x y) y))) (cbrt.f64 (.f64 (.f64 x y) y)))
(.f64 x (.f64 y y))
(cbrt.f64 (.f64 (.f64 (.f64 (.f64 x y) y) (.f64 (.f64 x y) y)) (.f64 (.f64 x y) y)))
(.f64 x (.f64 y y))
(pow.f64 (.f64 (.f64 x y) y) 1)
(.f64 x (.f64 y y))
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (binary64->binary32 (.f64 x (.f64 y y))))
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (binary64->binary32 (.f64 x (.f64 y y))))
(binary32->binary64 (.f32 (.f32 (binary64->binary32 x) (binary64->binary32 y)) (binary64->binary32 y)))
(binary32->binary64 (.f32 (binary64->binary32 x) (.f32 (binary64->binary32 y) (binary64->binary32 y))))
(binary32->binary64 (.f32 (binary64->binary32 y) (.f32 (binary64->binary32 x) (binary64->binary32 y))))
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (binary64->binary32 (.f64 x (.f64 y y))))
(binary32->binary64 (binary64->binary32 (.f64 (.f64 x y) y)))
(binary32->binary64 (binary64->binary32 (.f64 x (.f64 y y))))
(binary32->binary64 (.f32 (.f32 (binary64->binary32 x) (binary64->binary32 y)) (binary64->binary32 y)))
(binary32->binary64 (.f32 (binary64->binary32 x) (.f32 (binary64->binary32 y) (binary64->binary32 y))))
(binary32->binary64 (.f32 (binary64->binary32 y) (.f32 (binary64->binary32 x) (binary64->binary32 y))))

eval3.0ms (0.2%)

Compiler: Compiled 162 to 59 computations (63.6% saved)

prune3.0ms (0.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	16	0	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	16	1	17

Accuracy

100.0%

Counts

17 → 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)

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`*-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 (2.1%)

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

analyze0.0ms (0%)

sample1.1s (65.8%)

preprocess170.0ms (10.6%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

localize32.0ms (2%)

series3.0ms (0.2%)

rewrite190.0ms (11.8%)

simplify108.0ms (6.7%)

eval3.0ms (0.2%)

prune3.0ms (0.2%)

simplify6.0ms (0.4%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess33.0ms (2.1%)

Profiling