Statistics.Sample:$skurtosis from math-functions-0.1.5.2

Average Accuracy: 91.7% → 99.8%

Time: 2.6s

Precision: binary64

Cost: 6912

Math

\[\frac{x}{y \cdot y} - 3 \]

↓

\[{\left(\frac{y}{\frac{x}{y}}\right)}^{-1} - 3 \]

FPCore

(FPCore (x y) :precision binary64 (- (/ x (* y y)) 3.0))

↓

(FPCore (x y) :precision binary64 (- (pow (/ y (/ x y)) -1.0) 3.0))

C

double code(double x, double y) {
	return (x / (y * y)) - 3.0;
}

↓

double code(double x, double y) {
	return pow((y / (x / y)), -1.0) - 3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / (y * y)) - 3.0d0
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((y / (x / y)) ** (-1.0d0)) - 3.0d0
end function

Java

public static double code(double x, double y) {
	return (x / (y * y)) - 3.0;
}

↓

public static double code(double x, double y) {
	return Math.pow((y / (x / y)), -1.0) - 3.0;
}

Python

def code(x, y):
	return (x / (y * y)) - 3.0

↓

def code(x, y):
	return math.pow((y / (x / y)), -1.0) - 3.0

Julia

function code(x, y)
	return Float64(Float64(x / Float64(y * y)) - 3.0)
end

↓

function code(x, y)
	return Float64((Float64(y / Float64(x / y)) ^ -1.0) - 3.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x / (y * y)) - 3.0;
end

↓

function tmp = code(x, y)
	tmp = ((y / (x / y)) ^ -1.0) - 3.0;
end

Wolfram

code[x_, y_] := N[(N[(x / N[(y * y), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]

↓

code[x_, y_] := N[(N[Power[N[(y / N[(x / y), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision] - 3.0), $MachinePrecision]

Target

Original	91.7%
Target	99.9%
Herbie	99.8%

\[\frac{\frac{x}{y}}{y} - 3 \]

Derivation

1. Initial program 91.7%

   \[\frac{x}{y \cdot y} - 3 \]

2. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{{\left(\frac{y}{\frac{x}{y}}\right)}^{-1}} - 3 \]
   Proof

   [Start] 91.7	\[ \frac{x}{y \cdot y} - 3 \]
   clear-num [=>] 91.7	\[ \color{blue}{\frac{1}{\frac{y \cdot y}{x}}} - 3 \]
   inv-pow [=>] 91.7	\[ \color{blue}{{\left(\frac{y \cdot y}{x}\right)}^{-1}} - 3 \]
   associate-/l* [=>] 99.8	\[ {\color{blue}{\left(\frac{y}{\frac{x}{y}}\right)}}^{-1} - 3 \]

3. Final simplification 99.8%

   \[\leadsto {\left(\frac{y}{\frac{x}{y}}\right)}^{-1} - 3 \]

Alternatives

Alternative 1
Accuracy	91.7%
Cost	448

\[\frac{x}{y \cdot y} - 3 \]

Alternative 2
Accuracy	99.9%
Cost	448

\[\frac{\frac{x}{y}}{y} - 3 \]

Reproduce

herbie shell --seed 2023147 
(FPCore (x y)
  :name "Statistics.Sample:$skurtosis from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (/ (/ x y) y) 3.0)

  (- (/ x (* y y)) 3.0))