Crypto.Random.Test:calculate from crypto-random-0.0.9

Percentage Accurate: 93.1% → 99.9%

Time: 4.9s

Alternatives: 4

Speedup: 1.0×

• 24.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot y}{z} \end{array} \]

FPCore

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

C

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

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 * y) / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot y}{z} \end{array} \]

FPCore

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

C

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

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 * y) / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{z}{y}} \end{array} \]

FPCore

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

C

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

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 / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

   \[x + \frac{y \cdot y}{z} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 4.5e-27) x (* y (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.5e-27) {
		tmp = x;
	} else {
		tmp = y * (y / z);
	}
	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
    real(8) :: tmp
    if (y <= 4.5d-27) then
        tmp = x
    else
        tmp = y * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.5e-27) {
		tmp = x;
	} else {
		tmp = y * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.5e-27:
		tmp = x
	else:
		tmp = y * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.5e-27)
		tmp = x;
	else
		tmp = Float64(y * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.5e-27)
		tmp = x;
	else
		tmp = y * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.5e-27], x, N[(y * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.5000000000000002e-27

   1. Initial program 94.9%

      \[x + \frac{y \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 61.4%

      \[\leadsto \color{blue}{x} \]

   if 4.5000000000000002e-27 < y

   1. Initial program 87.3%

      \[x + \frac{y \cdot y}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{y}{z} \cdot y} \]
   4. Step-by-step derivation

      1. associate-*l/ 87.3%

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

      2. clear-num 87.3%

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

      3. div-inv 87.3%

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

      4. pow2 87.3%

         \[\leadsto x + \frac{1}{z \cdot \frac{1}{\color{blue}{{y}^{2}}}} \]

      5. pow-flip 88.6%

         \[\leadsto x + \frac{1}{z \cdot \color{blue}{{y}^{\left(-2\right)}}} \]

      6. metadata-eval 88.6%

         \[\leadsto x + \frac{1}{z \cdot {y}^{\color{blue}{-2}}} \]

   5. Applied egg-rr 88.6%

      \[\leadsto x + \color{blue}{\frac{1}{z \cdot {y}^{-2}}} \]

   6. Taylor expanded in z around 0 87.3%

      \[\leadsto x + \frac{1}{\color{blue}{\frac{z}{{y}^{2}}}} \]
   7. Step-by-step derivation

      1. unpow2 87.3%

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

   8. Simplified 87.3%

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

   10. Applied egg-rr 98.7%

       \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{y}{z} \cdot y + x}\right)}^{3}} \]

   11. Taylor expanded in x around 0 71.3%

       \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \frac{{y}^{2}}{z}} \]
   12. Step-by-step derivation

       1. pow-base-1 71.3%

          \[\leadsto \color{blue}{1} \cdot \frac{{y}^{2}}{z} \]

       2. unpow2 71.3%

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

       3. associate-*r/ 78.7%

          \[\leadsto 1 \cdot \color{blue}{\left(y \cdot \frac{y}{z}\right)} \]

       4. *-lft-identity 78.7%

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

   13. Simplified 78.7%

       \[\leadsto \color{blue}{y \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{y}{z} \end{array} \]

FPCore

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

C

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

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 * (y / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

   \[x + \frac{y \cdot y}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 4: 51.5% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 92.7%

   \[x + \frac{y \cdot y}{z} \]
2. Step-by-step derivation

   1. associate-*l/ 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around inf 49.6%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 49.6%

   \[\leadsto x \]

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{y}{z} \end{array} \]

FPCore

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

C

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

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 * (y / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

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

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