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

Average Error: 7.99% → 0.18%

Time: 4.3s

Precision: binary64

Cost: 576

Math

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

↓

\[\frac{\frac{1}{y}}{\frac{y}{x}} + -3 \]

FPCore

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

↓

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

C

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

↓

double code(double x, double y) {
	return ((1.0 / y) / (y / x)) + -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 = ((1.0d0 / y) / (y / x)) + (-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 ((1.0 / y) / (y / x)) + -3.0;
}

Python

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

↓

def code(x, y):
	return ((1.0 / y) / (y / x)) + -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(1.0 / y) / Float64(y / x)) + -3.0)
end

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	7.99%
Target	0.14%
Herbie	0.18%

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

Derivation

1. Initial program 7.99

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

2. Applied egg-rr 0.19

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

3. Applied egg-rr 0.18

   \[\leadsto \color{blue}{\frac{\frac{1}{y}}{\frac{y}{x}}} - 3 \]

4. Final simplification 0.18

   \[\leadsto \frac{\frac{1}{y}}{\frac{y}{x}} + -3 \]

Alternatives

Alternative 1
Error	0.18%
Cost	576

\[\frac{1}{y \cdot \frac{y}{x}} + -3 \]

Alternative 2
Error	7.99%
Cost	448

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

Alternative 3
Error	0.14%
Cost	448

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

Reproduce

herbie shell --seed 2023090 
(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))