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

Percentage Accurate: 92.9% → 99.9%

Time: 5.3s

Alternatives: 4

Speedup: 1.1×

• 24.8% 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, 0.8× 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 92.3%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

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

   5. /-lowering-/.f64 99.9

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

4. Applied egg-rr 99.9%

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

Alternative 2: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot y}{z}\\ t_1 := y \cdot \frac{y}{z}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 100000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* y y) z)) (t_1 (* y (/ y z))))
   (if (<= t_0 -1e+78) t_1 (if (<= t_0 100000000.0) x t_1))))

C

double code(double x, double y, double z) {
	double t_0 = (y * y) / z;
	double t_1 = y * (y / z);
	double tmp;
	if (t_0 <= -1e+78) {
		tmp = t_1;
	} else if (t_0 <= 100000000.0) {
		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 * (y / z)
    if (t_0 <= (-1d+78)) then
        tmp = t_1
    else if (t_0 <= 100000000.0d0) 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 * (y / z);
	double tmp;
	if (t_0 <= -1e+78) {
		tmp = t_1;
	} else if (t_0 <= 100000000.0) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * y) / z
	t_1 = y * (y / z)
	tmp = 0
	if t_0 <= -1e+78:
		tmp = t_1
	elif t_0 <= 100000000.0:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * y) / z)
	t_1 = Float64(y * Float64(y / z))
	tmp = 0.0
	if (t_0 <= -1e+78)
		tmp = t_1;
	elseif (t_0 <= 100000000.0)
		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 * (y / z);
	tmp = 0.0;
	if (t_0 <= -1e+78)
		tmp = t_1;
	elseif (t_0 <= 100000000.0)
		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[(y * N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e+78], t$95$1, If[LessEqual[t$95$0, 100000000.0], x, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y y) z) < -1.00000000000000001e78 or 1e8 < (/.f64 (*.f64 y y) z)

   1. Initial program 86.8%

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

   3. Taylor expanded in x around 0

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

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

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

      2. unpow2 N/A

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

      3. *-lowering-*.f64 82.4

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

   5. Simplified 82.4%

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

      1. associate-*l/ N/A

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

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

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

      3. /-lowering-/.f64 92.3

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

   7. Applied egg-rr 92.3%

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

   if -1.00000000000000001e78 < (/.f64 (*.f64 y y) z) < 1e8

   1. Initial program 97.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 91.5%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot y}{z} \leq -1 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y \cdot y}{z} \leq 100000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{z}, y, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 92.3%

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

   1. +-commutative N/A

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

   2. associate-*l/ N/A

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

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

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, y, x\right)} \]

   4. /-lowering-/.f64 99.9

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{z}}, y, x\right) \]

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{z}, y, x\right)} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 20.0× 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 92.3%

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

3. Taylor expanded in x around inf

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

5. Simplified 52.5%

   \[\leadsto \color{blue}{x} \]
6. 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 2024205 
(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)))