Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 8

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. +-commutative N/A

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

   2. *-commutative N/A

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

   3. fma-define N/A

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

   4. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(z + x\right), \color{blue}{y}, x\right) \]

   5. +-commutative N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(x + z\right), y, x\right) \]

   6. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{+.f64}\left(x, z\right), y, x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x + z, y, x\right)} \]
5. Add Preprocessing

Alternative 2: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+224}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e-7)
   (* z y)
   (if (<= y 1.45e-143) x (if (<= y 3.3e+224) (* z y) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e-7) {
		tmp = z * y;
	} else if (y <= 1.45e-143) {
		tmp = x;
	} else if (y <= 3.3e+224) {
		tmp = z * y;
	} 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 <= (-1.8d-7)) then
        tmp = z * y
    else if (y <= 1.45d-143) then
        tmp = x
    else if (y <= 3.3d+224) then
        tmp = z * y
    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 <= -1.8e-7) {
		tmp = z * y;
	} else if (y <= 1.45e-143) {
		tmp = x;
	} else if (y <= 3.3e+224) {
		tmp = z * y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.8e-7:
		tmp = z * y
	elif y <= 1.45e-143:
		tmp = x
	elif y <= 3.3e+224:
		tmp = z * y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e-7)
		tmp = Float64(z * y);
	elseif (y <= 1.45e-143)
		tmp = x;
	elseif (y <= 3.3e+224)
		tmp = Float64(z * y);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.8e-7)
		tmp = z * y;
	elseif (y <= 1.45e-143)
		tmp = x;
	elseif (y <= 3.3e+224)
		tmp = z * y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e-7], N[(z * y), $MachinePrecision], If[LessEqual[y, 1.45e-143], x, If[LessEqual[y, 3.3e+224], N[(z * y), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999997e-7 or 1.45e-143 < y < 3.29999999999999996e224

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 58.0%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 58.0%

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

   if -1.79999999999999997e-7 < y < 1.45e-143

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 76.1%

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

   if 3.29999999999999996e224 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 66.4%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   5. Simplified 66.4%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 66.4%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   8. Simplified 66.4%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-7}:\\ \;\;\;\;z \cdot y\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-143}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+224}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.00021:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -1.0) t_0 (if (<= y 0.00021) (+ x (* z y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.00021) {
		tmp = x + (z * y);
	} 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 <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 0.00021d0) then
        tmp = x + (z * y)
    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 <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.00021) {
		tmp = x + (z * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 0.00021:
		tmp = x + (z * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.00021)
		tmp = Float64(x + Float64(z * y));
	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 <= -1.0)
		tmp = t_0;
	elseif (y <= 0.00021)
		tmp = x + (z * y);
	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, -1.0], t$95$0, If[LessEqual[y, 0.00021], N[(x + N[(z * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.1000000000000001e-4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(z + \color{blue}{x}\right)\right) \]

      3. +-lowering-+.f64 97.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \color{blue}{x}\right)\right) \]

   5. Simplified 97.9%

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

   if -1 < y < 2.1000000000000001e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot z\right)}\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 98.1%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 98.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 0.00021:\\ \;\;\;\;x + z \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -0.0074:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -0.0074) t_0 (if (<= y 1.26e-143) (* x (+ y 1.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -0.0074) {
		tmp = t_0;
	} else if (y <= 1.26e-143) {
		tmp = x * (y + 1.0);
	} 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 <= (-0.0074d0)) then
        tmp = t_0
    else if (y <= 1.26d-143) then
        tmp = x * (y + 1.0d0)
    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 <= -0.0074) {
		tmp = t_0;
	} else if (y <= 1.26e-143) {
		tmp = x * (y + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -0.0074:
		tmp = t_0
	elif y <= 1.26e-143:
		tmp = x * (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -0.0074)
		tmp = t_0;
	elseif (y <= 1.26e-143)
		tmp = Float64(x * Float64(y + 1.0));
	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 <= -0.0074)
		tmp = t_0;
	elseif (y <= 1.26e-143)
		tmp = x * (y + 1.0);
	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, -0.0074], t$95$0, If[LessEqual[y, 1.26e-143], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0074000000000000003 or 1.2600000000000001e-143 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(x + z\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(z + \color{blue}{x}\right)\right) \]

      3. +-lowering-+.f64 89.2%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(z, \color{blue}{x}\right)\right) \]

   5. Simplified 89.2%

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

   if -0.0074000000000000003 < y < 1.2600000000000001e-143

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 76.6%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   5. Simplified 76.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0074:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(y + 1\right)\\ \mathbf{if}\;x \leq -6 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+50}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ y 1.0))))
   (if (<= x -6e+35) t_0 (if (<= x 1.75e+50) (* z y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x * (y + 1.0);
	double tmp;
	if (x <= -6e+35) {
		tmp = t_0;
	} else if (x <= 1.75e+50) {
		tmp = z * y;
	} 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 = x * (y + 1.0d0)
    if (x <= (-6d+35)) then
        tmp = t_0
    else if (x <= 1.75d+50) then
        tmp = z * y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (y + 1.0);
	double tmp;
	if (x <= -6e+35) {
		tmp = t_0;
	} else if (x <= 1.75e+50) {
		tmp = z * y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (y + 1.0)
	tmp = 0
	if x <= -6e+35:
		tmp = t_0
	elif x <= 1.75e+50:
		tmp = z * y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(y + 1.0))
	tmp = 0.0
	if (x <= -6e+35)
		tmp = t_0;
	elseif (x <= 1.75e+50)
		tmp = Float64(z * y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (y + 1.0);
	tmp = 0.0;
	if (x <= -6e+35)
		tmp = t_0;
	elseif (x <= 1.75e+50)
		tmp = z * y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e+35], t$95$0, If[LessEqual[x, 1.75e+50], N[(z * y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999981e35 or 1.75000000000000003e50 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 88.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   5. Simplified 88.0%

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

   if -5.99999999999999981e35 < x < 1.75000000000000003e50

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 68.3%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{z}\right) \]

   5. Simplified 68.3%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+35}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+50}:\\ \;\;\;\;z \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 0.00021:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.0) (* x y) (if (<= y 0.00021) x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 0.00021) {
		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 <= (-1.0d0)) then
        tmp = x * y
    else if (y <= 0.00021d0) 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 <= -1.0) {
		tmp = x * y;
	} else if (y <= 0.00021) {
		tmp = x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.0:
		tmp = x * y
	elif y <= 0.00021:
		tmp = x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * y);
	elseif (y <= 0.00021)
		tmp = x;
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x * y;
	elseif (y <= 0.00021)
		tmp = x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 0.00021], x, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.1000000000000001e-4 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(1 + y\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(y + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 46.3%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{1}\right)\right) \]

   5. Simplified 46.3%

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

   6. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 44.3%

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]

   8. Simplified 44.3%

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

   if -1 < y < 2.1000000000000001e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 65.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 0.00021:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 8: 36.2% 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

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 32.6%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024149 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))