Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 7

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: 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 2: 60.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+253}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+16}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e+253)
   (* y z)
   (if (<= y -1.02e+16)
     (* y x)
     (if (<= y -3.5e-24)
       (* y z)
       (if (<= y -2.65e-49)
         x
         (if (<= y -5.5e-97)
           (* y z)
           (if (<= y 1e-51) x (if (<= y 5.9e+138) (* y z) (* y x)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e+253) {
		tmp = y * z;
	} else if (y <= -1.02e+16) {
		tmp = y * x;
	} else if (y <= -3.5e-24) {
		tmp = y * z;
	} else if (y <= -2.65e-49) {
		tmp = x;
	} else if (y <= -5.5e-97) {
		tmp = y * z;
	} else if (y <= 1e-51) {
		tmp = x;
	} else if (y <= 5.9e+138) {
		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 <= (-4d+253)) then
        tmp = y * z
    else if (y <= (-1.02d+16)) then
        tmp = y * x
    else if (y <= (-3.5d-24)) then
        tmp = y * z
    else if (y <= (-2.65d-49)) then
        tmp = x
    else if (y <= (-5.5d-97)) then
        tmp = y * z
    else if (y <= 1d-51) then
        tmp = x
    else if (y <= 5.9d+138) 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 <= -4e+253) {
		tmp = y * z;
	} else if (y <= -1.02e+16) {
		tmp = y * x;
	} else if (y <= -3.5e-24) {
		tmp = y * z;
	} else if (y <= -2.65e-49) {
		tmp = x;
	} else if (y <= -5.5e-97) {
		tmp = y * z;
	} else if (y <= 1e-51) {
		tmp = x;
	} else if (y <= 5.9e+138) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4e+253:
		tmp = y * z
	elif y <= -1.02e+16:
		tmp = y * x
	elif y <= -3.5e-24:
		tmp = y * z
	elif y <= -2.65e-49:
		tmp = x
	elif y <= -5.5e-97:
		tmp = y * z
	elif y <= 1e-51:
		tmp = x
	elif y <= 5.9e+138:
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4e+253)
		tmp = Float64(y * z);
	elseif (y <= -1.02e+16)
		tmp = Float64(y * x);
	elseif (y <= -3.5e-24)
		tmp = Float64(y * z);
	elseif (y <= -2.65e-49)
		tmp = x;
	elseif (y <= -5.5e-97)
		tmp = Float64(y * z);
	elseif (y <= 1e-51)
		tmp = x;
	elseif (y <= 5.9e+138)
		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 <= -4e+253)
		tmp = y * z;
	elseif (y <= -1.02e+16)
		tmp = y * x;
	elseif (y <= -3.5e-24)
		tmp = y * z;
	elseif (y <= -2.65e-49)
		tmp = x;
	elseif (y <= -5.5e-97)
		tmp = y * z;
	elseif (y <= 1e-51)
		tmp = x;
	elseif (y <= 5.9e+138)
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4e+253], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.02e+16], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.5e-24], N[(y * z), $MachinePrecision], If[LessEqual[y, -2.65e-49], x, If[LessEqual[y, -5.5e-97], N[(y * z), $MachinePrecision], If[LessEqual[y, 1e-51], x, If[LessEqual[y, 5.9e+138], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999997e253 or -1.02e16 < y < -3.4999999999999996e-24 or -2.6500000000000001e-49 < y < -5.49999999999999948e-97 or 1e-51 < y < 5.8999999999999999e138

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.3%

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

   if -3.9999999999999997e253 < y < -1.02e16 or 5.8999999999999999e138 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 61.5%

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

      1. *-commutative 61.5%

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

   7. Simplified 61.5%

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

   if -3.4999999999999996e-24 < y < -2.6500000000000001e-49 or -5.49999999999999948e-97 < y < 1e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.6%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+253}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+16}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-24}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 10^{-51}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.9 \cdot 10^{+138}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 83.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -1.12 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -1.12e-24)
     t_0
     (if (<= y -3.9e-44)
       x
       (if (<= y -4.3e-97) (* y z) (if (<= y 5.2e-52) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -1.12e-24) {
		tmp = t_0;
	} else if (y <= -3.9e-44) {
		tmp = x;
	} else if (y <= -4.3e-97) {
		tmp = y * z;
	} else if (y <= 5.2e-52) {
		tmp = x;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y * (x + z)
    if (y <= (-1.12d-24)) then
        tmp = t_0
    else if (y <= (-3.9d-44)) then
        tmp = x
    else if (y <= (-4.3d-97)) then
        tmp = y * z
    else if (y <= 5.2d-52) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -1.12e-24) {
		tmp = t_0;
	} else if (y <= -3.9e-44) {
		tmp = x;
	} else if (y <= -4.3e-97) {
		tmp = y * z;
	} else if (y <= 5.2e-52) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -1.12e-24:
		tmp = t_0
	elif y <= -3.9e-44:
		tmp = x
	elif y <= -4.3e-97:
		tmp = y * z
	elif y <= 5.2e-52:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -1.12e-24)
		tmp = t_0;
	elseif (y <= -3.9e-44)
		tmp = x;
	elseif (y <= -4.3e-97)
		tmp = Float64(y * z);
	elseif (y <= 5.2e-52)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x + z);
	tmp = 0.0;
	if (y <= -1.12e-24)
		tmp = t_0;
	elseif (y <= -3.9e-44)
		tmp = x;
	elseif (y <= -4.3e-97)
		tmp = y * z;
	elseif (y <= 5.2e-52)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.12e-24], t$95$0, If[LessEqual[y, -3.9e-44], x, If[LessEqual[y, -4.3e-97], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.2e-52], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999995e-24 or 5.1999999999999997e-52 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.8%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 96.8%

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

   4. Simplified 96.8%

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

   if -1.11999999999999995e-24 < y < -3.9000000000000002e-44 or -4.3e-97 < y < 5.1999999999999997e-52

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.6%

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

   if -3.9000000000000002e-44 < y < -4.3e-97

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-97}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]

Alternative 4: 83.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-98}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -1.4e-23)
     t_0
     (if (<= y -3.25e-49)
       (+ x (* y x))
       (if (<= y -8e-98) (* y z) (if (<= y 1.5e-51) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -1.4e-23) {
		tmp = t_0;
	} else if (y <= -3.25e-49) {
		tmp = x + (y * x);
	} else if (y <= -8e-98) {
		tmp = y * z;
	} else if (y <= 1.5e-51) {
		tmp = x;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y * (x + z)
    if (y <= (-1.4d-23)) then
        tmp = t_0
    else if (y <= (-3.25d-49)) then
        tmp = x + (y * x)
    else if (y <= (-8d-98)) then
        tmp = y * z
    else if (y <= 1.5d-51) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -1.4e-23) {
		tmp = t_0;
	} else if (y <= -3.25e-49) {
		tmp = x + (y * x);
	} else if (y <= -8e-98) {
		tmp = y * z;
	} else if (y <= 1.5e-51) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -1.4e-23:
		tmp = t_0
	elif y <= -3.25e-49:
		tmp = x + (y * x)
	elif y <= -8e-98:
		tmp = y * z
	elif y <= 1.5e-51:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -1.4e-23)
		tmp = t_0;
	elseif (y <= -3.25e-49)
		tmp = Float64(x + Float64(y * x));
	elseif (y <= -8e-98)
		tmp = Float64(y * z);
	elseif (y <= 1.5e-51)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x + z);
	tmp = 0.0;
	if (y <= -1.4e-23)
		tmp = t_0;
	elseif (y <= -3.25e-49)
		tmp = x + (y * x);
	elseif (y <= -8e-98)
		tmp = y * z;
	elseif (y <= 1.5e-51)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e-23], t$95$0, If[LessEqual[y, -3.25e-49], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e-98], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.5e-51], x, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3999999999999999e-23 or 1.50000000000000001e-51 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.8%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 96.8%

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

   4. Simplified 96.8%

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

   if -1.3999999999999999e-23 < y < -3.24999999999999984e-49

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 75.4%

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

      1. *-commutative 2.2%

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

   4. Simplified 75.4%

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

   if -3.24999999999999984e-49 < y < -7.99999999999999951e-98

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 87.1%

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

   if -7.99999999999999951e-98 < y < 1.50000000000000001e-51

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 75.6%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-23}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq -3.25 \cdot 10^{-49}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-98}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]

Alternative 5: 59.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-8} \lor \neg \left(y \leq 1400000000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.4e-8) (not (<= y 1400000000000.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.4e-8) || !(y <= 1400000000000.0)) {
		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 <= (-8.4d-8)) .or. (.not. (y <= 1400000000000.0d0))) 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 <= -8.4e-8) || !(y <= 1400000000000.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.4e-8) or not (y <= 1400000000000.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.4e-8) || !(y <= 1400000000000.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.4e-8) || ~((y <= 1400000000000.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.4e-8], N[Not[LessEqual[y, 1400000000000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.39999999999999978e-8 or 1.4e12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.5%

      \[\leadsto \color{blue}{y \cdot \left(x + z\right)} \]
   3. Step-by-step derivation

      1. +-commutative 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in z around 0 51.9%

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

      1. *-commutative 51.9%

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

   7. Simplified 51.9%

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

   if -8.39999999999999978e-8 < y < 1.4e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 66.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-8} \lor \neg \left(y \leq 1400000000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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. Final simplification 100.0%

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

Alternative 7: 36.0% 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 35.1%

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

3. Final simplification 35.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023332 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))