Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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. Final simplification 100.0%

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

Alternative 2: 61.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+229}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+207}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+57}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.2e+229)
   (* y x)
   (if (<= y -1.05e+207)
     (* y z)
     (if (<= y -6.2e+166)
       (* y x)
       (if (<= y -5.6e+57)
         (* y z)
         (if (<= y -4.5e+18)
           (* y x)
           (if (<= y -1.55e-47)
             (* y z)
             (if (<= y 3.2e-84)
               x
               (if (<= y 2.4e-40)
                 (* y z)
                 (if (<= y 2.65e-14) x (* y z)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.2e+229) {
		tmp = y * x;
	} else if (y <= -1.05e+207) {
		tmp = y * z;
	} else if (y <= -6.2e+166) {
		tmp = y * x;
	} else if (y <= -5.6e+57) {
		tmp = y * z;
	} else if (y <= -4.5e+18) {
		tmp = y * x;
	} else if (y <= -1.55e-47) {
		tmp = y * z;
	} else if (y <= 3.2e-84) {
		tmp = x;
	} else if (y <= 2.4e-40) {
		tmp = y * z;
	} else if (y <= 2.65e-14) {
		tmp = 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 (y <= (-7.2d+229)) then
        tmp = y * x
    else if (y <= (-1.05d+207)) then
        tmp = y * z
    else if (y <= (-6.2d+166)) then
        tmp = y * x
    else if (y <= (-5.6d+57)) then
        tmp = y * z
    else if (y <= (-4.5d+18)) then
        tmp = y * x
    else if (y <= (-1.55d-47)) then
        tmp = y * z
    else if (y <= 3.2d-84) then
        tmp = x
    else if (y <= 2.4d-40) then
        tmp = y * z
    else if (y <= 2.65d-14) then
        tmp = 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 (y <= -7.2e+229) {
		tmp = y * x;
	} else if (y <= -1.05e+207) {
		tmp = y * z;
	} else if (y <= -6.2e+166) {
		tmp = y * x;
	} else if (y <= -5.6e+57) {
		tmp = y * z;
	} else if (y <= -4.5e+18) {
		tmp = y * x;
	} else if (y <= -1.55e-47) {
		tmp = y * z;
	} else if (y <= 3.2e-84) {
		tmp = x;
	} else if (y <= 2.4e-40) {
		tmp = y * z;
	} else if (y <= 2.65e-14) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.2e+229:
		tmp = y * x
	elif y <= -1.05e+207:
		tmp = y * z
	elif y <= -6.2e+166:
		tmp = y * x
	elif y <= -5.6e+57:
		tmp = y * z
	elif y <= -4.5e+18:
		tmp = y * x
	elif y <= -1.55e-47:
		tmp = y * z
	elif y <= 3.2e-84:
		tmp = x
	elif y <= 2.4e-40:
		tmp = y * z
	elif y <= 2.65e-14:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.2e+229)
		tmp = Float64(y * x);
	elseif (y <= -1.05e+207)
		tmp = Float64(y * z);
	elseif (y <= -6.2e+166)
		tmp = Float64(y * x);
	elseif (y <= -5.6e+57)
		tmp = Float64(y * z);
	elseif (y <= -4.5e+18)
		tmp = Float64(y * x);
	elseif (y <= -1.55e-47)
		tmp = Float64(y * z);
	elseif (y <= 3.2e-84)
		tmp = x;
	elseif (y <= 2.4e-40)
		tmp = Float64(y * z);
	elseif (y <= 2.65e-14)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.2e+229)
		tmp = y * x;
	elseif (y <= -1.05e+207)
		tmp = y * z;
	elseif (y <= -6.2e+166)
		tmp = y * x;
	elseif (y <= -5.6e+57)
		tmp = y * z;
	elseif (y <= -4.5e+18)
		tmp = y * x;
	elseif (y <= -1.55e-47)
		tmp = y * z;
	elseif (y <= 3.2e-84)
		tmp = x;
	elseif (y <= 2.4e-40)
		tmp = y * z;
	elseif (y <= 2.65e-14)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.2e+229], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.05e+207], N[(y * z), $MachinePrecision], If[LessEqual[y, -6.2e+166], N[(y * x), $MachinePrecision], If[LessEqual[y, -5.6e+57], N[(y * z), $MachinePrecision], If[LessEqual[y, -4.5e+18], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.55e-47], N[(y * z), $MachinePrecision], If[LessEqual[y, 3.2e-84], x, If[LessEqual[y, 2.4e-40], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.65e-14], x, N[(y * z), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.19999999999999973e229 or -1.05e207 < y < -6.19999999999999966e166 or -5.59999999999999999e57 < y < -4.5e18

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.5%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   3. Step-by-step derivation

      1. +-commutative 79.5%

         \[\leadsto x \cdot \color{blue}{\left(y + 1\right)} \]

   4. Simplified 79.5%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]

   5. Taylor expanded in y around inf 79.5%

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

   if -7.19999999999999973e229 < y < -1.05e207 or -6.19999999999999966e166 < y < -5.59999999999999999e57 or -4.5e18 < y < -1.5499999999999999e-47 or 3.1999999999999999e-84 < y < 2.39999999999999991e-40 or 2.6500000000000001e-14 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 78.8%

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

   3. Taylor expanded in x around 0 73.7%

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

   if -1.5499999999999999e-47 < y < 3.1999999999999999e-84 or 2.39999999999999991e-40 < y < 2.6500000000000001e-14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+229}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+207}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+166}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+57}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-47}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-40}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-70} \lor \neg \left(x \leq 1.22 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.1e-70) (not (<= x 1.22e+15))) (* x (+ y 1.0)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.1e-70) || !(x <= 1.22e+15)) {
		tmp = x * (y + 1.0);
	} 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 <= (-2.1d-70)) .or. (.not. (x <= 1.22d+15))) then
        tmp = x * (y + 1.0d0)
    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 <= -2.1e-70) || !(x <= 1.22e+15)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.1e-70) or not (x <= 1.22e+15):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.1e-70) || !(x <= 1.22e+15))
		tmp = Float64(x * Float64(y + 1.0));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.1e-70) || ~((x <= 1.22e+15)))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.1e-70], N[Not[LessEqual[x, 1.22e+15]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1000000000000001e-70 or 1.22e15 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 83.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   3. Step-by-step derivation

      1. +-commutative 83.2%

         \[\leadsto x \cdot \color{blue}{\left(y + 1\right)} \]

   4. Simplified 83.2%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]

   if -2.1000000000000001e-70 < x < 1.22e15

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 92.9%

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

   3. Taylor expanded in x around 0 74.6%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-70} \lor \neg \left(x \leq 1.22 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-131} \lor \neg \left(z \leq 3.45 \cdot 10^{-43}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.15e-131) (not (<= z 3.45e-43)))
   (+ x (* y z))
   (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.15e-131) || !(z <= 3.45e-43)) {
		tmp = x + (y * 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 ((z <= (-1.15d-131)) .or. (.not. (z <= 3.45d-43))) then
        tmp = x + (y * 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 ((z <= -1.15e-131) || !(z <= 3.45e-43)) {
		tmp = x + (y * z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.15e-131) or not (z <= 3.45e-43):
		tmp = x + (y * z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.15e-131) || !(z <= 3.45e-43))
		tmp = Float64(x + Float64(y * 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 ((z <= -1.15e-131) || ~((z <= 3.45e-43)))
		tmp = x + (y * z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.15e-131], N[Not[LessEqual[z, 3.45e-43]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000011e-131 or 3.44999999999999982e-43 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 91.4%

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

   if -1.15000000000000011e-131 < z < 3.44999999999999982e-43

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 87.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   3. Step-by-step derivation

      1. +-commutative 87.8%

         \[\leadsto x \cdot \color{blue}{\left(y + 1\right)} \]

   4. Simplified 87.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{-131} \lor \neg \left(z \leq 3.45 \cdot 10^{-43}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]

Alternative 5: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -22:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -22.0) (* y x) (if (<= y 14000.0) x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -22.0) {
		tmp = y * x;
	} else if (y <= 14000.0) {
		tmp = x;
	} 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 <= (-22.0d0)) then
        tmp = y * x
    else if (y <= 14000.0d0) then
        tmp = x
    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 <= -22.0) {
		tmp = y * x;
	} else if (y <= 14000.0) {
		tmp = x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -22.0:
		tmp = y * x
	elif y <= 14000.0:
		tmp = x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -22.0)
		tmp = Float64(y * x);
	elseif (y <= 14000.0)
		tmp = x;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -22.0)
		tmp = y * x;
	elseif (y <= 14000.0)
		tmp = x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -22.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 14000.0], x, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -22 or 14000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 47.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   3. Step-by-step derivation

      1. +-commutative 47.4%

         \[\leadsto x \cdot \color{blue}{\left(y + 1\right)} \]

   4. Simplified 47.4%

      \[\leadsto \color{blue}{x \cdot \left(y + 1\right)} \]

   5. Taylor expanded in y around inf 46.6%

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

   if -22 < y < 14000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 63.1%

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

4. Final simplification 54.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -22:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 14000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

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: 36.6% 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 33.2%

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

3. Final simplification 33.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))