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

Average Error: 4.8 → 0.1

Time: 5.6s

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	4.8
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 4.8

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

2. Applied egg-rr 4.9

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

3. Taylor expanded in y around 0 4.8

   \[\leadsto \color{blue}{\frac{x}{{y}^{2}}} - 3 \]

4. Simplified 0.1

   \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} - 3 \]
   Proof
   (/.f64 (/.f64 x y) y): 0 points increase in error, 0 points decrease in error
   (Rewrite<= associate-/r*_binary64 (/.f64 x (*.f64 y y))): 46 points increase in error, 48 points decrease in error
   (/.f64 x (Rewrite<= unpow2_binary64 (pow.f64 y 2))): 0 points increase in error, 1 points decrease in error

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2022301 
(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))