Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2

Average Error: 0.0 → 0.0

Time: 2.6s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (y + y)
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (y + y)
end function

Java

public static double code(double x, double y) {
	return (x + y) / (y + y);
}

↓

public static double code(double x, double y) {
	return (x + y) / (y + y);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	0.0
Target	0.0
Herbie	0.0

\[0.5 \cdot \frac{x}{y} + 0.5 \]

Derivation

1. Initial program 0.0

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

2. Final simplification 0.0

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

Alternatives

Alternative 1
Error	18.6
Cost	848

\[\begin{array}{l} t_0 := 0.5 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -1920:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-5}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+92}:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	18.5
Cost	848

\[\begin{array}{l} t_0 := 0.5 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -3850000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-7}:\\ \;\;\;\;0.5\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+86}:\\ \;\;\;\;0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot x}{y}\\ \end{array} \]

Alternative 3
Error	0.0
Cost	448

\[0.5 + 0.5 \cdot \frac{x}{y} \]

Alternative 4
Error	26.9
Cost	64

\[0.5 \]

Reproduce

herbie shell --seed 2023096 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :herbie-target
  (+ (* 0.5 (/ x y)) 0.5)

  (/ (+ x y) (+ y y)))