Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 7

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-define 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: 61.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+35}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+173} \lor \neg \left(y \leq 5.8 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.5e+129)
   (* y z)
   (if (<= y -6.3e+35)
     (* y x)
     (if (<= y -2.8e-11)
       (* y z)
       (if (<= y 1.18e-32)
         x
         (if (or (<= y 4.2e+173) (not (<= y 5.8e+242))) (* y z) (* y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.5e+129) {
		tmp = y * z;
	} else if (y <= -6.3e+35) {
		tmp = y * x;
	} else if (y <= -2.8e-11) {
		tmp = y * z;
	} else if (y <= 1.18e-32) {
		tmp = x;
	} else if ((y <= 4.2e+173) || !(y <= 5.8e+242)) {
		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 <= (-7.5d+129)) then
        tmp = y * z
    else if (y <= (-6.3d+35)) then
        tmp = y * x
    else if (y <= (-2.8d-11)) then
        tmp = y * z
    else if (y <= 1.18d-32) then
        tmp = x
    else if ((y <= 4.2d+173) .or. (.not. (y <= 5.8d+242))) 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 <= -7.5e+129) {
		tmp = y * z;
	} else if (y <= -6.3e+35) {
		tmp = y * x;
	} else if (y <= -2.8e-11) {
		tmp = y * z;
	} else if (y <= 1.18e-32) {
		tmp = x;
	} else if ((y <= 4.2e+173) || !(y <= 5.8e+242)) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.5e+129:
		tmp = y * z
	elif y <= -6.3e+35:
		tmp = y * x
	elif y <= -2.8e-11:
		tmp = y * z
	elif y <= 1.18e-32:
		tmp = x
	elif (y <= 4.2e+173) or not (y <= 5.8e+242):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.5e+129)
		tmp = Float64(y * z);
	elseif (y <= -6.3e+35)
		tmp = Float64(y * x);
	elseif (y <= -2.8e-11)
		tmp = Float64(y * z);
	elseif (y <= 1.18e-32)
		tmp = x;
	elseif ((y <= 4.2e+173) || !(y <= 5.8e+242))
		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 <= -7.5e+129)
		tmp = y * z;
	elseif (y <= -6.3e+35)
		tmp = y * x;
	elseif (y <= -2.8e-11)
		tmp = y * z;
	elseif (y <= 1.18e-32)
		tmp = x;
	elseif ((y <= 4.2e+173) || ~((y <= 5.8e+242)))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.5e+129], N[(y * z), $MachinePrecision], If[LessEqual[y, -6.3e+35], N[(y * x), $MachinePrecision], If[LessEqual[y, -2.8e-11], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.18e-32], x, If[Or[LessEqual[y, 4.2e+173], N[Not[LessEqual[y, 5.8e+242]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999998e129 or -6.29999999999999969e35 < y < -2.8e-11 or 1.17999999999999997e-32 < y < 4.2e173 or 5.79999999999999994e242 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 67.9%

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

   if -7.4999999999999998e129 < y < -6.29999999999999969e35 or 4.2e173 < y < 5.79999999999999994e242

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 79.1%

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

      1. *-commutative 79.1%

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

   8. Simplified 79.1%

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

   if -2.8e-11 < y < 1.17999999999999997e-32

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+129}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -6.3 \cdot 10^{+35}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-11}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+173} \lor \neg \left(y \leq 5.8 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-90} \lor \neg \left(x \leq -2.55 \cdot 10^{-138} \lor \neg \left(x \leq -3.8 \cdot 10^{-173}\right) \land x \leq 3000\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5e-90)
         (not
          (or (<= x -2.55e-138) (and (not (<= x -3.8e-173)) (<= x 3000.0)))))
   (* x (+ y 1.0))
   (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5e-90) || !((x <= -2.55e-138) || (!(x <= -3.8e-173) && (x <= 3000.0)))) {
		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 <= (-5d-90)) .or. (.not. (x <= (-2.55d-138)) .or. (.not. (x <= (-3.8d-173))) .and. (x <= 3000.0d0))) 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 <= -5e-90) || !((x <= -2.55e-138) || (!(x <= -3.8e-173) && (x <= 3000.0)))) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5e-90) or not ((x <= -2.55e-138) or (not (x <= -3.8e-173) and (x <= 3000.0))):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5e-90) || !((x <= -2.55e-138) || (!(x <= -3.8e-173) && (x <= 3000.0))))
		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 <= -5e-90) || ~(((x <= -2.55e-138) || (~((x <= -3.8e-173)) && (x <= 3000.0)))))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5e-90], N[Not[Or[LessEqual[x, -2.55e-138], And[N[Not[LessEqual[x, -3.8e-173]], $MachinePrecision], LessEqual[x, 3000.0]]]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000019e-90 or -2.5500000000000001e-138 < x < -3.8000000000000003e-173 or 3e3 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   if -5.00000000000000019e-90 < x < -2.5500000000000001e-138 or -3.8000000000000003e-173 < x < 3e3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-90} \lor \neg \left(x \leq -2.55 \cdot 10^{-138} \lor \neg \left(x \leq -3.8 \cdot 10^{-173}\right) \land x \leq 3000\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-10} \lor \neg \left(y \leq 2.2 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.12e-10) (not (<= y 2.2e-36))) (* y (+ x z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.12e-10) || !(y <= 2.2e-36)) {
		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 <= (-1.12d-10)) .or. (.not. (y <= 2.2d-36))) 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 <= -1.12e-10) || !(y <= 2.2e-36)) {
		tmp = y * (x + z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.12e-10) or not (y <= 2.2e-36):
		tmp = y * (x + z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.12e-10) || !(y <= 2.2e-36))
		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 <= -1.12e-10) || ~((y <= 2.2e-36)))
		tmp = y * (x + z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.12e-10], N[Not[LessEqual[y, 2.2e-36]], $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 < -1.12e-10 or 2.1999999999999999e-36 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 97.1%

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

      1. +-commutative 97.1%

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

   5. Simplified 97.1%

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

   if -1.12e-10 < y < 2.1999999999999999e-36

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.9%

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

      1. +-commutative 80.9%

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

   5. Simplified 80.9%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-10} \lor \neg \left(y \leq 2.2 \cdot 10^{-36}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-10} \lor \neg \left(y \leq 105000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.1e-10) (not (<= y 105000000.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.1e-10) || !(y <= 105000000.0)) {
		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 <= (-4.1d-10)) .or. (.not. (y <= 105000000.0d0))) 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 <= -4.1e-10) || !(y <= 105000000.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.1e-10) or not (y <= 105000000.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.1e-10) || !(y <= 105000000.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -4.1e-10) || ~((y <= 105000000.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.1e-10], N[Not[LessEqual[y, 105000000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999998e-10 or 1.05e8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 48.6%

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

      1. *-commutative 48.6%

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

   8. Simplified 48.6%

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

   if -4.0999999999999998e-10 < y < 1.05e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.5%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-10} \lor \neg \left(y \leq 105000000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 36.8% 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 41.0%

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

4. Final simplification 41.0%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024082 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))