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

Percentage Accurate: 93.1% → 99.9%

Time: 9.1s

Alternatives: 5

Speedup: 1.0×

• 25.6% 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: 93.1% 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return (y / (z / y)) + 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 = (y / (z / y)) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.1%

   \[x + \frac{y \cdot y}{z} \]
2. Add Preprocessing

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 2: 86.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ t_1 := \frac{y}{z} \cdot y\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* y y) z)) (t_1 (* (/ y z) y)))
   (if (<= t_0 -5e+127) t_1 (if (<= t_0 2e-56) x t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (y * y) / z;
	double t_1 = (y / z) * y;
	double tmp;
	if (t_0 <= -5e+127) {
		tmp = t_1;
	} else if (t_0 <= 2e-56) {
		tmp = x;
	} 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
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (y * y) / z
    t_1 = (y / z) * y
    if (t_0 <= (-5d+127)) then
        tmp = t_1
    else if (t_0 <= 2d-56) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * y) / z;
	double t_1 = (y / z) * y;
	double tmp;
	if (t_0 <= -5e+127) {
		tmp = t_1;
	} else if (t_0 <= 2e-56) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * y) / z
	t_1 = (y / z) * y
	tmp = 0
	if t_0 <= -5e+127:
		tmp = t_1
	elif t_0 <= 2e-56:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * y) / z)
	t_1 = Float64(Float64(y / z) * y)
	tmp = 0.0
	if (t_0 <= -5e+127)
		tmp = t_1;
	elseif (t_0 <= 2e-56)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * y) / z;
	t_1 = (y / z) * y;
	tmp = 0.0;
	if (t_0 <= -5e+127)
		tmp = t_1;
	elseif (t_0 <= 2e-56)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+127], t$95$1, If[LessEqual[t$95$0, 2e-56], x, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y y) z) < -5.0000000000000004e127 or 2.0000000000000001e-56 < (/.f64 (*.f64 y y) z)

   1. Initial program 88.1%

      \[x + \frac{y \cdot y}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]

   if -5.0000000000000004e127 < (/.f64 (*.f64 y y) z) < 2.0000000000000001e-56

   1. Initial program 98.0%

      \[x + \frac{y \cdot y}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9.6 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 9.6e+46) x (* (/ x z) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 9.6e+46) {
		tmp = x;
	} else {
		tmp = (x / z) * 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 <= 9.6d+46) then
        tmp = x
    else
        tmp = (x / z) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 9.6e+46) {
		tmp = x;
	} else {
		tmp = (x / z) * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 9.6e+46:
		tmp = x
	else:
		tmp = (x / z) * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 9.6e+46)
		tmp = x;
	else
		tmp = Float64(Float64(x / z) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 9.6e+46)
		tmp = x;
	else
		tmp = (x / z) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 9.6e+46], x, N[(N[(x / z), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 9.60000000000000034e46

   1. Initial program 95.3%

      \[x + \frac{y \cdot y}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 9.60000000000000034e46 < y

   1. Initial program 85.8%

      \[x + \frac{y \cdot y}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   6. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   8. Simplified 0

      \[\leadsto expr\]

   10. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

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(Float64(y / z) * y))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.1%

   \[x + \frac{y \cdot y}{z} \]
2. Add Preprocessing

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 5: 50.6% 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 93.1%

   \[x + \frac{y \cdot y}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
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 2024110 
(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)))