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

Percentage Accurate: 93.2% → 99.9%

Time: 4.2s

Alternatives: 4

Speedup: 1.0×

• 24.6% 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: 93.2% 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

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

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 89.2%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot \frac{y}{z}} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3.5e+43) x (/ z (/ z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.5e+43) {
		tmp = x;
	} else {
		tmp = z / (z / x);
	}
	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 <= 3.5d+43) then
        tmp = x
    else
        tmp = z / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.5e+43) {
		tmp = x;
	} else {
		tmp = z / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3.5e+43:
		tmp = x
	else:
		tmp = z / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3.5e+43)
		tmp = x;
	else
		tmp = Float64(z / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.5e+43)
		tmp = x;
	else
		tmp = z / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3.5e+43], x, N[(z / N[(z / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.5000000000000001e43

   1. Initial program 90.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + y \cdot \frac{y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.1%

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

   if 3.5000000000000001e43 < y

   1. Initial program 83.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + y \cdot \frac{y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 71.9%

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

   6. Taylor expanded in x around inf 10.8%

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

      1. *-commutative 10.8%

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

   8. Simplified 10.8%

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

      1. associate-/l* 33.6%

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

      2. *-commutative 33.6%

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

   10. Applied egg-rr 33.6%

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

       1. *-commutative 33.6%

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

       2. clear-num 33.5%

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

       3. un-div-inv 33.6%

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

   12. Applied egg-rr 33.6%

       \[\leadsto \color{blue}{\frac{z}{\frac{z}{x}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 3e+43) x (* z (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 3e+43) {
		tmp = x;
	} else {
		tmp = z * (x / 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 <= 3d+43) then
        tmp = x
    else
        tmp = z * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3e+43) {
		tmp = x;
	} else {
		tmp = z * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 3e+43:
		tmp = x
	else:
		tmp = z * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 3e+43)
		tmp = x;
	else
		tmp = Float64(z * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3e+43)
		tmp = x;
	else
		tmp = z * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 3e+43], x, N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.00000000000000017e43

   1. Initial program 90.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + y \cdot \frac{y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.1%

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

   if 3.00000000000000017e43 < y

   1. Initial program 83.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + y \cdot \frac{y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 71.9%

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

   6. Taylor expanded in x around inf 10.8%

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

      1. *-commutative 10.8%

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

   8. Simplified 10.8%

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

      1. associate-/l* 33.6%

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

      2. *-commutative 33.6%

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

   10. Applied egg-rr 33.6%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{+43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% 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 89.2%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot \frac{y}{z}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 48.9%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

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 2024103 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

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

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