Main:bigenough2 from A

Percentage Accurate: 100.0% → 99.1%

Time: 3.0s

Alternatives: 9

Speedup: 1.0×

• 20.6% 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: 99.1% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. distribute-rgt-in 98.4%

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

   2. fma-def 100.0%

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

   3. *-commutative 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 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. Final simplification 100.0%

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

Alternative 3: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+183}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-56}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+243}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+305}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.36e+183)
   (* z y)
   (if (<= y -1.4e+68)
     (* x y)
     (if (<= y -1.9e-56)
       (* z y)
       (if (<= y 1.4e-9)
         x
         (if (<= y 3.7e+243) (* z y) (if (<= y 9e+305) (* x y) (* z y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.36e+183) {
		tmp = z * y;
	} else if (y <= -1.4e+68) {
		tmp = x * y;
	} else if (y <= -1.9e-56) {
		tmp = z * y;
	} else if (y <= 1.4e-9) {
		tmp = x;
	} else if (y <= 3.7e+243) {
		tmp = z * y;
	} else if (y <= 9e+305) {
		tmp = x * y;
	} else {
		tmp = 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) :: tmp
    if (y <= (-1.36d+183)) then
        tmp = z * y
    else if (y <= (-1.4d+68)) then
        tmp = x * y
    else if (y <= (-1.9d-56)) then
        tmp = z * y
    else if (y <= 1.4d-9) then
        tmp = x
    else if (y <= 3.7d+243) then
        tmp = z * y
    else if (y <= 9d+305) then
        tmp = x * y
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.36e+183) {
		tmp = z * y;
	} else if (y <= -1.4e+68) {
		tmp = x * y;
	} else if (y <= -1.9e-56) {
		tmp = z * y;
	} else if (y <= 1.4e-9) {
		tmp = x;
	} else if (y <= 3.7e+243) {
		tmp = z * y;
	} else if (y <= 9e+305) {
		tmp = x * y;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.36e+183:
		tmp = z * y
	elif y <= -1.4e+68:
		tmp = x * y
	elif y <= -1.9e-56:
		tmp = z * y
	elif y <= 1.4e-9:
		tmp = x
	elif y <= 3.7e+243:
		tmp = z * y
	elif y <= 9e+305:
		tmp = x * y
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.36e+183)
		tmp = Float64(z * y);
	elseif (y <= -1.4e+68)
		tmp = Float64(x * y);
	elseif (y <= -1.9e-56)
		tmp = Float64(z * y);
	elseif (y <= 1.4e-9)
		tmp = x;
	elseif (y <= 3.7e+243)
		tmp = Float64(z * y);
	elseif (y <= 9e+305)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.36e+183)
		tmp = z * y;
	elseif (y <= -1.4e+68)
		tmp = x * y;
	elseif (y <= -1.9e-56)
		tmp = z * y;
	elseif (y <= 1.4e-9)
		tmp = x;
	elseif (y <= 3.7e+243)
		tmp = z * y;
	elseif (y <= 9e+305)
		tmp = x * y;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.36e+183], N[(z * y), $MachinePrecision], If[LessEqual[y, -1.4e+68], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.9e-56], N[(z * y), $MachinePrecision], If[LessEqual[y, 1.4e-9], x, If[LessEqual[y, 3.7e+243], N[(z * y), $MachinePrecision], If[LessEqual[y, 9e+305], N[(x * y), $MachinePrecision], N[(z * y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35999999999999995e183 or -1.4e68 < y < -1.9000000000000001e-56 or 1.39999999999999992e-9 < y < 3.7000000000000002e243 or 9.0000000000000006e305 < y

   1. Initial program 100.0%

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

      1. distribute-rgt-in 97.0%

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

      2. fma-def 100.0%

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

      3. *-commutative 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 64.4%

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

   if -1.35999999999999995e183 < y < -1.4e68 or 3.7000000000000002e243 < y < 9.0000000000000006e305

   1. Initial program 99.9%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around inf 99.9%

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

   3. Taylor expanded in z around 0 74.9%

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

   if -1.9000000000000001e-56 < y < 1.39999999999999992e-9

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around 0 77.7%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+183}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-56}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+243}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+305}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]

Alternative 4: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-57} \lor \neg \left(y \leq 1.85 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.35e-57) (not (<= y 1.85e-10))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.35e-57) || !(y <= 1.85e-10)) {
		tmp = y * (x + 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 <= (-1.35d-57)) .or. (.not. (y <= 1.85d-10))) then
        tmp = y * (x + 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 <= -1.35e-57) || !(y <= 1.85e-10)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.35e-57) or not (y <= 1.85e-10):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.35e-57) || !(y <= 1.85e-10))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.35e-57) || ~((y <= 1.85e-10)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.35e-57], N[Not[LessEqual[y, 1.85e-10]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e-57 or 1.85000000000000007e-10 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around inf 95.9%

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

   if -1.3500000000000001e-57 < y < 1.85000000000000007e-10

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around 0 77.7%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-57} \lor \neg \left(y \leq 1.85 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-53} \lor \neg \left(y \leq 1.7 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e-53) (not (<= y 1.7e-10))) (* y (+ x z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e-53) || !(y <= 1.7e-10)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	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 <= (-4.2d-53)) .or. (.not. (y <= 1.7d-10))) then
        tmp = y * (x + z)
    else
        tmp = x * (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e-53) || !(y <= 1.7e-10)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e-53) or not (y <= 1.7e-10):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e-53) || !(y <= 1.7e-10))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x * Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.2e-53) || ~((y <= 1.7e-10)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e-53], N[Not[LessEqual[y, 1.7e-10]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.19999999999999955e-53 or 1.70000000000000007e-10 < y

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around inf 95.9%

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

   if -4.19999999999999955e-53 < y < 1.70000000000000007e-10

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in x around inf 78.2%

      \[\leadsto \color{blue}{\left(1 + y\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-53} \lor \neg \left(y \leq 1.7 \cdot 10^{-10}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]

Alternative 6: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -195 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -195.0) (not (<= y 1.0))) (* y (+ x z)) (+ x (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -195.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (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) :: tmp
    if ((y <= (-195.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x + z)
    else
        tmp = x + (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -195.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -195.0) or not (y <= 1.0):
		tmp = y * (x + z)
	else:
		tmp = x + (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -195.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x + Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -195.0) || ~((y <= 1.0)))
		tmp = y * (x + z);
	else
		tmp = x + (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -195.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -195 or 1 < y

   1. Initial program 99.9%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around inf 99.3%

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

   if -195 < y < 1

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in z around inf 99.2%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -195 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot y\\ \end{array} \]

Alternative 7: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -195:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -195.0) (* x y) (if (<= y 1.0) x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -195.0) {
		tmp = x * y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-195.0d0)) then
        tmp = x * y
    else if (y <= 1.0d0) then
        tmp = x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -195.0) {
		tmp = x * y;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -195.0:
		tmp = x * y
	elif y <= 1.0:
		tmp = x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -195.0)
		tmp = Float64(x * y);
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -195.0)
		tmp = x * y;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -195.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.0], x, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -195 or 1 < y

   1. Initial program 99.9%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around inf 99.3%

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

   3. Taylor expanded in z around 0 49.2%

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

   if -195 < y < 1

   1. Initial program 100.0%

      \[x + y \cdot \left(z + x\right) \]

   2. Taylor expanded in y around 0 73.2%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -195:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 8: 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. Final simplification 100.0%

   \[\leadsto x + y \cdot \left(x + z\right) \]

Alternative 9: 35.9% 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. Taylor expanded in y around 0 40.5%

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

3. Final simplification 40.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023221 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))