Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

Alternatives: 7

Speedup: 1.0×

• 20.8% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + y \cdot \left(z + x\right) \]
2. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{y \cdot \left(z + x\right) + x} \]

   2. fma-def 100.0%

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

   3. +-commutative 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, x + z, x\right) \]
6. Add Preprocessing

Alternative 2: 61.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+128}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-121}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-128}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+81} \lor \neg \left(y \leq 3.2 \cdot 10^{+126}\right) \land y \leq 1.2 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.8e+128)
   (* y x)
   (if (<= y -3.3e-7)
     (* y z)
     (if (<= y -5e-103)
       x
       (if (<= y -3.1e-121)
         (* y z)
         (if (<= y 2.3e-145)
           x
           (if (<= y 4.3e-128)
             (* y z)
             (if (<= y 1.8e-20)
               x
               (if (or (<= y 3.4e+81)
                       (and (not (<= y 3.2e+126)) (<= y 1.2e+156)))
                 (* y z)
                 (* y x))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+128) {
		tmp = y * x;
	} else if (y <= -3.3e-7) {
		tmp = y * z;
	} else if (y <= -5e-103) {
		tmp = x;
	} else if (y <= -3.1e-121) {
		tmp = y * z;
	} else if (y <= 2.3e-145) {
		tmp = x;
	} else if (y <= 4.3e-128) {
		tmp = y * z;
	} else if (y <= 1.8e-20) {
		tmp = x;
	} else if ((y <= 3.4e+81) || (!(y <= 3.2e+126) && (y <= 1.2e+156))) {
		tmp = y * z;
	} else {
		tmp = y * 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 <= (-2.8d+128)) then
        tmp = y * x
    else if (y <= (-3.3d-7)) then
        tmp = y * z
    else if (y <= (-5d-103)) then
        tmp = x
    else if (y <= (-3.1d-121)) then
        tmp = y * z
    else if (y <= 2.3d-145) then
        tmp = x
    else if (y <= 4.3d-128) then
        tmp = y * z
    else if (y <= 1.8d-20) then
        tmp = x
    else if ((y <= 3.4d+81) .or. (.not. (y <= 3.2d+126)) .and. (y <= 1.2d+156)) then
        tmp = y * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.8e+128) {
		tmp = y * x;
	} else if (y <= -3.3e-7) {
		tmp = y * z;
	} else if (y <= -5e-103) {
		tmp = x;
	} else if (y <= -3.1e-121) {
		tmp = y * z;
	} else if (y <= 2.3e-145) {
		tmp = x;
	} else if (y <= 4.3e-128) {
		tmp = y * z;
	} else if (y <= 1.8e-20) {
		tmp = x;
	} else if ((y <= 3.4e+81) || (!(y <= 3.2e+126) && (y <= 1.2e+156))) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.8e+128:
		tmp = y * x
	elif y <= -3.3e-7:
		tmp = y * z
	elif y <= -5e-103:
		tmp = x
	elif y <= -3.1e-121:
		tmp = y * z
	elif y <= 2.3e-145:
		tmp = x
	elif y <= 4.3e-128:
		tmp = y * z
	elif y <= 1.8e-20:
		tmp = x
	elif (y <= 3.4e+81) or (not (y <= 3.2e+126) and (y <= 1.2e+156)):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.8e+128)
		tmp = Float64(y * x);
	elseif (y <= -3.3e-7)
		tmp = Float64(y * z);
	elseif (y <= -5e-103)
		tmp = x;
	elseif (y <= -3.1e-121)
		tmp = Float64(y * z);
	elseif (y <= 2.3e-145)
		tmp = x;
	elseif (y <= 4.3e-128)
		tmp = Float64(y * z);
	elseif (y <= 1.8e-20)
		tmp = x;
	elseif ((y <= 3.4e+81) || (!(y <= 3.2e+126) && (y <= 1.2e+156)))
		tmp = Float64(y * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.8e+128)
		tmp = y * x;
	elseif (y <= -3.3e-7)
		tmp = y * z;
	elseif (y <= -5e-103)
		tmp = x;
	elseif (y <= -3.1e-121)
		tmp = y * z;
	elseif (y <= 2.3e-145)
		tmp = x;
	elseif (y <= 4.3e-128)
		tmp = y * z;
	elseif (y <= 1.8e-20)
		tmp = x;
	elseif ((y <= 3.4e+81) || (~((y <= 3.2e+126)) && (y <= 1.2e+156)))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.8e+128], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.3e-7], N[(y * z), $MachinePrecision], If[LessEqual[y, -5e-103], x, If[LessEqual[y, -3.1e-121], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.3e-145], x, If[LessEqual[y, 4.3e-128], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.8e-20], x, If[Or[LessEqual[y, 3.4e+81], And[N[Not[LessEqual[y, 3.2e+126]], $MachinePrecision], LessEqual[y, 1.2e+156]]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999983e128 or 3.40000000000000003e81 < y < 3.1999999999999998e126 or 1.2000000000000001e156 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in y around inf 67.7%

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

   if -2.79999999999999983e128 < y < -3.3000000000000002e-7 or -4.99999999999999966e-103 < y < -3.0999999999999998e-121 or 2.30000000000000007e-145 < y < 4.29999999999999994e-128 or 1.79999999999999987e-20 < y < 3.40000000000000003e81 or 3.1999999999999998e126 < y < 1.2000000000000001e156

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 77.6%

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

   4. Taylor expanded in x around 0 75.5%

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

   if -3.3000000000000002e-7 < y < -4.99999999999999966e-103 or -3.0999999999999998e-121 < y < 2.30000000000000007e-145 or 4.29999999999999994e-128 < y < 1.79999999999999987e-20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.1%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+128}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-7}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-121}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-128}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+81} \lor \neg \left(y \leq 3.2 \cdot 10^{+126}\right) \land y \leq 1.2 \cdot 10^{+156}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-63} \lor \neg \left(x \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;x + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.2e-63) (not (<= x 8e-70))) (+ x (* y x)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e-63) || !(x <= 8e-70)) {
		tmp = x + (y * x);
	} else {
		tmp = 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 ((x <= (-7.2d-63)) .or. (.not. (x <= 8d-70))) then
        tmp = x + (y * x)
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.2e-63) || !(x <= 8e-70)) {
		tmp = x + (y * x);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.2e-63) or not (x <= 8e-70):
		tmp = x + (y * x)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.2e-63) || !(x <= 8e-70))
		tmp = Float64(x + Float64(y * x));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.2e-63) || ~((x <= 8e-70)))
		tmp = x + (y * x);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.2e-63], N[Not[LessEqual[x, 8e-70]], $MachinePrecision]], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.20000000000000016e-63 or 7.99999999999999997e-70 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.1%

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

      1. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   if -7.20000000000000016e-63 < x < 7.99999999999999997e-70

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 90.7%

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

   4. Taylor expanded in x around 0 77.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-63} \lor \neg \left(x \leq 8 \cdot 10^{-70}\right):\\ \;\;\;\;x + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-45} \lor \neg \left(z \leq 1.2 \cdot 10^{-37}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.6e-45) (not (<= z 1.2e-37))) (+ x (* y z)) (+ x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e-45) || !(z <= 1.2e-37)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (y * 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 ((z <= (-2.6d-45)) .or. (.not. (z <= 1.2d-37))) then
        tmp = x + (y * z)
    else
        tmp = x + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e-45) || !(z <= 1.2e-37)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.6e-45) or not (z <= 1.2e-37):
		tmp = x + (y * z)
	else:
		tmp = x + (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.6e-45) || !(z <= 1.2e-37))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.6e-45) || ~((z <= 1.2e-37)))
		tmp = x + (y * z);
	else
		tmp = x + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.6e-45], N[Not[LessEqual[z, 1.2e-37]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.59999999999999987e-45 or 1.19999999999999995e-37 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 87.5%

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

   if -2.59999999999999987e-45 < z < 1.19999999999999995e-37

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 92.0%

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

      1. *-commutative 92.0%

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

   5. Simplified 92.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-45} \lor \neg \left(z \leq 1.2 \cdot 10^{-37}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 5\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 5.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 5.0)) {
		tmp = y * x;
	} 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 <= (-1.0d0)) .or. (.not. (y <= 5.0d0))) then
        tmp = y * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 5.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 5.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 5.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 5.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 5.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 56.1%

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

      1. *-commutative 56.1%

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

   5. Simplified 56.1%

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

   6. Taylor expanded in y around inf 55.3%

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

   if -1 < y < 5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.4%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 5\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 7: 37.1% 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 100.0%

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

3. Taylor expanded in y around 0 36.1%

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

4. Final simplification 36.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024017 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))