Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 8

Speedup: 1.0×

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: 61.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+170}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+23} \lor \neg \left(y \leq 6.7 \cdot 10^{+64}\right) \land \left(y \leq 10^{+123} \lor \neg \left(y \leq 7.4 \cdot 10^{+210}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+170)
   (* y z)
   (if (<= y -3.35e-9)
     (* y x)
     (if (<= y 1.5e-73)
       x
       (if (or (<= y 1.1e+23)
               (and (not (<= y 6.7e+64))
                    (or (<= y 1e+123) (not (<= y 7.4e+210)))))
         (* y z)
         (* y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+170) {
		tmp = y * z;
	} else if (y <= -3.35e-9) {
		tmp = y * x;
	} else if (y <= 1.5e-73) {
		tmp = x;
	} else if ((y <= 1.1e+23) || (!(y <= 6.7e+64) && ((y <= 1e+123) || !(y <= 7.4e+210)))) {
		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 <= (-1.5d+170)) then
        tmp = y * z
    else if (y <= (-3.35d-9)) then
        tmp = y * x
    else if (y <= 1.5d-73) then
        tmp = x
    else if ((y <= 1.1d+23) .or. (.not. (y <= 6.7d+64)) .and. (y <= 1d+123) .or. (.not. (y <= 7.4d+210))) 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 <= -1.5e+170) {
		tmp = y * z;
	} else if (y <= -3.35e-9) {
		tmp = y * x;
	} else if (y <= 1.5e-73) {
		tmp = x;
	} else if ((y <= 1.1e+23) || (!(y <= 6.7e+64) && ((y <= 1e+123) || !(y <= 7.4e+210)))) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+170:
		tmp = y * z
	elif y <= -3.35e-9:
		tmp = y * x
	elif y <= 1.5e-73:
		tmp = x
	elif (y <= 1.1e+23) or (not (y <= 6.7e+64) and ((y <= 1e+123) or not (y <= 7.4e+210))):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+170)
		tmp = Float64(y * z);
	elseif (y <= -3.35e-9)
		tmp = Float64(y * x);
	elseif (y <= 1.5e-73)
		tmp = x;
	elseif ((y <= 1.1e+23) || (!(y <= 6.7e+64) && ((y <= 1e+123) || !(y <= 7.4e+210))))
		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 <= -1.5e+170)
		tmp = y * z;
	elseif (y <= -3.35e-9)
		tmp = y * x;
	elseif (y <= 1.5e-73)
		tmp = x;
	elseif ((y <= 1.1e+23) || (~((y <= 6.7e+64)) && ((y <= 1e+123) || ~((y <= 7.4e+210)))))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+170], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.35e-9], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.5e-73], x, If[Or[LessEqual[y, 1.1e+23], And[N[Not[LessEqual[y, 6.7e+64]], $MachinePrecision], Or[LessEqual[y, 1e+123], N[Not[LessEqual[y, 7.4e+210]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999998e170 or 1.5e-73 < y < 1.10000000000000004e23 or 6.69999999999999946e64 < y < 9.99999999999999978e122 or 7.39999999999999996e210 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 68.5%

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

   if -1.49999999999999998e170 < y < -3.34999999999999981e-9 or 1.10000000000000004e23 < y < 6.69999999999999946e64 or 9.99999999999999978e122 < y < 7.39999999999999996e210

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.4%

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

   3. Taylor expanded in z around 0 65.3%

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

   if -3.34999999999999981e-9 < y < 1.5e-73

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+170}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+23} \lor \neg \left(y \leq 6.7 \cdot 10^{+64}\right) \land \left(y \leq 10^{+123} \lor \neg \left(y \leq 7.4 \cdot 10^{+210}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 84.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-12} \lor \neg \left(y \leq 1.3 \cdot 10^{-74}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.3e-12) (not (<= y 1.3e-74))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.3e-12) || !(y <= 1.3e-74)) {
		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 <= (-2.3d-12)) .or. (.not. (y <= 1.3d-74))) 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 <= -2.3e-12) || !(y <= 1.3e-74)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.3e-12) or not (y <= 1.3e-74):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.3e-12) || !(y <= 1.3e-74))
		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 <= -2.3e-12) || ~((y <= 1.3e-74)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.3e-12], N[Not[LessEqual[y, 1.3e-74]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.29999999999999989e-12 or 1.3e-74 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 96.4%

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

   if -2.29999999999999989e-12 < y < 1.3e-74

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-12} \lor \neg \left(y \leq 1.3 \cdot 10^{-74}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-12} \lor \neg \left(y \leq 6.2 \cdot 10^{-74}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e-12) (not (<= y 6.2e-74))) (* y (+ x z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e-12) || !(y <= 6.2e-74)) {
		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 <= (-2.7d-12)) .or. (.not. (y <= 6.2d-74))) 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 <= -2.7e-12) || !(y <= 6.2e-74)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e-12) or not (y <= 6.2e-74):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e-12) || !(y <= 6.2e-74))
		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 <= -2.7e-12) || ~((y <= 6.2e-74)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e-12], N[Not[LessEqual[y, 6.2e-74]], $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 < -2.6999999999999998e-12 or 6.2000000000000003e-74 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 96.4%

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

   if -2.6999999999999998e-12 < y < 6.2000000000000003e-74

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.5%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-12} \lor \neg \left(y \leq 6.2 \cdot 10^{-74}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]

Alternative 5: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -25500000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -25500000000.0) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -25500000000.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (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 <= (-25500000000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * (x + z)
    else
        tmp = x + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -25500000000.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -25500000000.0) or not (y <= 1.0):
		tmp = y * (x + z)
	else:
		tmp = x + (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -25500000000.0) || !(y <= 1.0))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = Float64(x + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -25500000000.0) || ~((y <= 1.0)))
		tmp = y * (x + z);
	else
		tmp = x + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -25500000000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.55e10 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.9%

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

   if -2.55e10 < y < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. fma-def 100.0%

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

      5. *-commutative 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in x around 0 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -25500000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]

Alternative 6: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.35e-9) (* y x) (if (<= y 1.0) x (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.35e-9) {
		tmp = y * x;
	} else if (y <= 1.0) {
		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 <= (-3.35d-9)) then
        tmp = y * x
    else if (y <= 1.0d0) 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 <= -3.35e-9) {
		tmp = y * x;
	} else if (y <= 1.0) {
		tmp = x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.35e-9:
		tmp = y * x
	elif y <= 1.0:
		tmp = x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.35e-9)
		tmp = Float64(y * x);
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.35e-9)
		tmp = y * x;
	elseif (y <= 1.0)
		tmp = x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.35e-9], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.0], x, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.34999999999999981e-9 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.9%

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

   3. Taylor expanded in z around 0 49.5%

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

   if -3.34999999999999981e-9 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 7: 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 8: 37.0% 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 38.6%

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

3. Final simplification 38.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023252 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))