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

Average Error: 5.1 → 0.1

Time: 52.8s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (-3.0d0) + ((x / y) / y)
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 -3.0 + ((x / y) / y);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	5.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 5.1

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

2. Simplified 0.1

   \[\leadsto \color{blue}{-3 + \frac{\frac{x}{y}}{y}} \]
   Proof

Reproduce

herbie shell --seed 2023033 
(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))