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

Percentage Accurate: 92.9% → 99.9%

Time: 4.5s

Alternatives: 4

Speedup: 1.0×

• 25.0% 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: 92.9% 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 91.2%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot y}{z}\right)}\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{y}{z}}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

   4. /-lowering-/.f64 99.9%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

3. Simplified 99.9%

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

Alternative 2: 87.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* y y) z)))
   (if (<= t_0 -1e-24) (* y (/ y z)) (if (<= t_0 5e-35) x (/ y (/ z y))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * y) / z;
	double tmp;
	if (t_0 <= -1e-24) {
		tmp = y * (y / z);
	} else if (t_0 <= 5e-35) {
		tmp = x;
	} else {
		tmp = y / (z / y);
	}
	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) :: tmp
    t_0 = (y * y) / z
    if (t_0 <= (-1d-24)) then
        tmp = y * (y / z)
    else if (t_0 <= 5d-35) then
        tmp = x
    else
        tmp = y / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * y) / z;
	double tmp;
	if (t_0 <= -1e-24) {
		tmp = y * (y / z);
	} else if (t_0 <= 5e-35) {
		tmp = x;
	} else {
		tmp = y / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * y) / z
	tmp = 0
	if t_0 <= -1e-24:
		tmp = y * (y / z)
	elif t_0 <= 5e-35:
		tmp = x
	else:
		tmp = y / (z / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * y) / z)
	tmp = 0.0
	if (t_0 <= -1e-24)
		tmp = Float64(y * Float64(y / z));
	elseif (t_0 <= 5e-35)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * y) / z;
	tmp = 0.0;
	if (t_0 <= -1e-24)
		tmp = y * (y / z);
	elseif (t_0 <= 5e-35)
		tmp = x;
	else
		tmp = y / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * y), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-24], N[(y * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-35], x, N[(y / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y y) z) < -9.99999999999999924e-25

   1. Initial program 81.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot y}{z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{y}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{y}^{2}}{z}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({y}^{2}\right), \color{blue}{z}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot y\right), z\right) \]

      3. *-lowering-*.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), z\right) \]

   7. Simplified 74.8%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 90.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), y\right) \]

   9. Applied egg-rr 90.7%

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

   if -9.99999999999999924e-25 < (/.f64 (*.f64 y y) z) < 4.99999999999999964e-35

   1. Initial program 96.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot y}{z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{y}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 88.0%

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

   if 4.99999999999999964e-35 < (/.f64 (*.f64 y y) z)

   1. Initial program 94.7%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot y}{z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{y}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{y}^{2}}{z}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({y}^{2}\right), \color{blue}{z}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot y\right), z\right) \]

      3. *-lowering-*.f64 89.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), z\right) \]

   7. Simplified 89.4%

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

      1. associate-*l/ N/A

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

      2. associate-/r/ N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

      4. /-lowering-/.f64 94.6%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 94.6%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot y}{z} \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y \cdot y}{z} \leq 5 \cdot 10^{-35}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 8.5e-12) x (* y (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8.5e-12) {
		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 <= 8.5d-12) 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 <= 8.5e-12) {
		tmp = x;
	} else {
		tmp = y * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8.5e-12:
		tmp = x
	else:
		tmp = y * (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8.5e-12)
		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 <= 8.5e-12)
		tmp = x;
	else
		tmp = y * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8.5e-12], x, N[(y * N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.4999999999999997e-12

   1. Initial program 92.4%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot y}{z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{y}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 55.2%

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

   if 8.4999999999999997e-12 < y

   1. Initial program 88.0%

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

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot y}{z}\right)}\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{y}{z}}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

      4. /-lowering-/.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{{y}^{2}}{z}} \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left({y}^{2}\right), \color{blue}{z}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot y\right), z\right) \]

      3. *-lowering-*.f64 74.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, y\right), z\right) \]

   7. Simplified 74.0%

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

      1. associate-*l/ N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{y}{z}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 85.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), y\right) \]

   9. Applied egg-rr 85.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% 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 91.2%

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

   1. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{y \cdot y}{z}\right)}\right) \]

   2. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \color{blue}{\frac{y}{z}}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{y}{z}\right)}\right)\right) \]

   4. /-lowering-/.f64 99.9%

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(y, \color{blue}{z}\right)\right)\right) \]

3. Simplified 99.9%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 44.3%

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

Developer Target 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]

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z)
  :name "Crypto.Random.Test:calculate from crypto-random-0.0.9"
  :precision binary64

  :alt
  (! :herbie-platform default (+ x (* y (/ y z))))

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