Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2

Average Error: 14.5 → 2.5

Time: 15.0s

Precision: binary64

Cost: 2248

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

↓

\[\begin{array}{l} t_0 := \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ t_1 := \frac{\frac{\frac{y}{z}}{\frac{z + 1}{x}}}{z}\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+295}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0))))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) (* (* z z) (+ z 1.0))))
        (t_1 (/ (/ (/ y z) (/ (+ z 1.0) x)) z)))
   (if (<= t_0 5e+144) t_1 (if (<= t_0 5e+295) t_0 t_1))))

C

double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

↓

double code(double x, double y, double z) {
	double t_0 = (x * y) / ((z * z) * (z + 1.0));
	double t_1 = ((y / z) / ((z + 1.0) / x)) / z;
	double tmp;
	if (t_0 <= 5e+144) {
		tmp = t_1;
	} else if (t_0 <= 5e+295) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * y) / ((z * z) * (z + 1.0d0))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (x * y) / ((z * z) * (z + 1.0d0))
    t_1 = ((y / z) / ((z + 1.0d0) / x)) / z
    if (t_0 <= 5d+144) then
        tmp = t_1
    else if (t_0 <= 5d+295) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

↓

public static double code(double x, double y, double z) {
	double t_0 = (x * y) / ((z * z) * (z + 1.0));
	double t_1 = ((y / z) / ((z + 1.0) / x)) / z;
	double tmp;
	if (t_0 <= 5e+144) {
		tmp = t_1;
	} else if (t_0 <= 5e+295) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	return (x * y) / ((z * z) * (z + 1.0))

↓

def code(x, y, z):
	t_0 = (x * y) / ((z * z) * (z + 1.0))
	t_1 = ((y / z) / ((z + 1.0) / x)) / z
	tmp = 0
	if t_0 <= 5e+144:
		tmp = t_1
	elif t_0 <= 5e+295:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	return Float64(Float64(x * y) / Float64(Float64(z * z) * Float64(z + 1.0)))
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(x * y) / Float64(Float64(z * z) * Float64(z + 1.0)))
	t_1 = Float64(Float64(Float64(y / z) / Float64(Float64(z + 1.0) / x)) / z)
	tmp = 0.0
	if (t_0 <= 5e+144)
		tmp = t_1;
	elseif (t_0 <= 5e+295)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) / ((z * z) * (z + 1.0));
end

↓

function tmp_2 = code(x, y, z)
	t_0 = (x * y) / ((z * z) * (z + 1.0));
	t_1 = ((y / z) / ((z + 1.0) / x)) / z;
	tmp = 0.0;
	if (t_0 <= 5e+144)
		tmp = t_1;
	elseif (t_0 <= 5e+295)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] / N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(y / z), $MachinePrecision] / N[(N[(z + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+144], t$95$1, If[LessEqual[t$95$0, 5e+295], t$95$0, t$95$1]]]]

Target

Original	14.5
Target	4.1
Herbie	2.5

\[\begin{array}{l} \mathbf{if}\;z < 249.6182814532307:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1))) < 4.9999999999999999e144 or 4.99999999999999991e295 < (/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1)))

   1. Initial program 15.0

      \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

   2. Applied egg-rr 10.7

      \[\leadsto \color{blue}{\frac{y}{z \cdot z} \cdot \frac{x}{z + 1}} \]

   3. Applied egg-rr 2.5

      \[\leadsto \color{blue}{\frac{\frac{y}{z} \cdot \frac{x}{z + 1}}{z}} \]

   4. Applied egg-rr 2.6

      \[\leadsto \frac{\color{blue}{\frac{\frac{y}{z}}{\frac{z + 1}{x}}}}{z} \]

   if 4.9999999999999999e144 < (/.f64 (*.f64 x y) (*.f64 (*.f64 z z) (+.f64 z 1))) < 4.99999999999999991e295

   1. Initial program 1.2

      \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \leq 5 \cdot 10^{+144}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{\frac{z + 1}{x}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \leq 5 \cdot 10^{+295}:\\ \;\;\;\;\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{\frac{z + 1}{x}}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Error	5.9
Cost	840

\[\begin{array}{l} t_0 := \frac{\frac{x}{z}}{\frac{z \cdot z}{y}}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	3.6
Cost	840

\[\begin{array}{l} t_0 := \frac{\frac{y}{z} \cdot \frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	3.4
Cost	840

\[\begin{array}{l} t_0 := \frac{\frac{y}{z} \cdot \frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\frac{x}{z} - x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	3.4
Cost	840

\[\begin{array}{l} t_0 := \frac{\frac{y}{z} \cdot \frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\frac{y}{z} - y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	17.2
Cost	712

\[\begin{array}{l} t_0 := x \cdot \frac{y}{z \cdot z}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10^{-101}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	16.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq 2.4024866218640344 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{y}{z}}}\\ \mathbf{elif}\;y \leq 10^{+66}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 7
Error	2.7
Cost	704

\[\frac{\frac{\frac{y}{z}}{\frac{z + 1}{x}}}{z} \]

Alternative 8
Error	42.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 3.1768043714456734 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 9
Error	42.4
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 1.7091222887697795 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]

Alternative 10
Error	42.1
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 1.7091222887697795 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]

Alternative 11
Error	21.4
Cost	448

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

Alternative 12
Error	48.4
Cost	320

\[\frac{x \cdot y}{z} \]

Alternative 13
Error	45.7
Cost	320

\[x \cdot \frac{y}{z} \]

Reproduce

herbie shell --seed 2022316 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

  (/ (* x y) (* (* z z) (+ z 1.0))))