Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

Alternatives: 5

Speedup: 1.0×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + y \cdot \left(z + x\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(z + x\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \left(x + z\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(x + z\right) \]
4. Add Preprocessing

Alternative 2: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-7} \lor \neg \left(z \leq 2.05 \cdot 10^{+92}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.3e-7) (not (<= z 2.05e+92))) (* y z) (+ x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e-7) || !(z <= 2.05e+92)) {
		tmp = y * z;
	} else {
		tmp = x + (x * 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) :: tmp
    if ((z <= (-4.3d-7)) .or. (.not. (z <= 2.05d+92))) then
        tmp = y * z
    else
        tmp = x + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e-7) || !(z <= 2.05e+92)) {
		tmp = y * z;
	} else {
		tmp = x + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.3e-7) or not (z <= 2.05e+92):
		tmp = y * z
	else:
		tmp = x + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.3e-7) || !(z <= 2.05e+92))
		tmp = Float64(y * z);
	else
		tmp = Float64(x + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.3e-7) || ~((z <= 2.05e+92)))
		tmp = y * z;
	else
		tmp = x + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.3e-7], N[Not[LessEqual[z, 2.05e+92]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000001e-7 or 2.05000000000000012e92 < z

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.5%

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

   4. Taylor expanded in x around 0 75.1%

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

   if -4.3000000000000001e-7 < z < 2.05000000000000012e92

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 83.7%

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

      1. *-commutative 83.7%

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

   5. Simplified 83.7%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-7} \lor \neg \left(z \leq 2.05 \cdot 10^{+92}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-79} \lor \neg \left(z \leq 3.7 \cdot 10^{-35}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.65e-79) (not (<= z 3.7e-35))) (+ x (* y z)) (+ x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-79) || !(z <= 3.7e-35)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (x * 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) :: tmp
    if ((z <= (-2.65d-79)) .or. (.not. (z <= 3.7d-35))) then
        tmp = x + (y * z)
    else
        tmp = x + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-79) || !(z <= 3.7e-35)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.65e-79) or not (z <= 3.7e-35):
		tmp = x + (y * z)
	else:
		tmp = x + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.65e-79) || !(z <= 3.7e-35))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.65e-79) || ~((z <= 3.7e-35)))
		tmp = x + (y * z);
	else
		tmp = x + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.65e-79], N[Not[LessEqual[z, 3.7e-35]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6499999999999999e-79 or 3.6999999999999999e-35 < z

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.0%

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

   if -2.6499999999999999e-79 < z < 3.6999999999999999e-35

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.8%

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

      1. *-commutative 92.8%

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

   5. Simplified 92.8%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-79} \lor \neg \left(z \leq 3.7 \cdot 10^{-35}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{-49} \lor \neg \left(y \leq 1.6 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.7e-49) (not (<= y 1.6e-53))) (* y z) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.7e-49) || !(y <= 1.6e-53)) {
		tmp = y * z;
	} else {
		tmp = 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 <= (-6.7d-49)) .or. (.not. (y <= 1.6d-53))) then
        tmp = y * z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.7e-49) || !(y <= 1.6e-53)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.7e-49) or not (y <= 1.6e-53):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.7e-49) || !(y <= 1.6e-53))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.7e-49) || ~((y <= 1.6e-53)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.7e-49], N[Not[LessEqual[y, 1.6e-53]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.7e-49 or 1.6e-53 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 59.4%

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

   4. Taylor expanded in x around 0 52.8%

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

   if -6.7e-49 < y < 1.6e-53

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 100.0%

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

   4. Taylor expanded in x around inf 77.4%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{-49} \lor \neg \left(y \leq 1.6 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 36.8% 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 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Add Preprocessing

3. Taylor expanded in z around inf 76.8%

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

4. Taylor expanded in x around inf 38.4%

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

5. Final simplification 38.4%

   \[\leadsto x \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))