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

Average Error: 5.1 → 0.1

Time: 18.0s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

code[x_, y_] := N[(N[(N[(x / y), $MachinePrecision] / y), $MachinePrecision] - 3.0), $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. Applied egg-rr 5.5

   \[\leadsto \color{blue}{\left(x + x\right) \cdot \left(\frac{1}{y} \cdot \frac{0.5}{y}\right)} - 3 \]

3. Simplified 5.5

   \[\leadsto \color{blue}{x \cdot \left(\frac{0.5}{y} \cdot \frac{2}{y}\right)} - 3 \]
   Proof

   [Start] 5.5	\[ \left(x + x\right) \cdot \left(\frac{1}{y} \cdot \frac{0.5}{y}\right) - 3 \]
   rational.json-simplify-53 [=>] 0.2	\[ \color{blue}{\left(\frac{1}{y} + \frac{1}{y}\right) \cdot \left(\frac{0.5}{y} \cdot x\right)} - 3 \]
   rational.json-simplify-2 [=>] 0.2	\[ \left(\frac{1}{y} + \frac{1}{y}\right) \cdot \color{blue}{\left(x \cdot \frac{0.5}{y}\right)} - 3 \]

4. Applied egg-rr 0.1

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

5. Final simplification 0.1

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

Alternatives

Alternative 1
Error	5.1
Cost	448

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

Alternative 2
Error	21.5
Cost	64

\[-3 \]

Reproduce

herbie shell --seed 2023064 
(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))