Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 6.4s

Alternatives: 8

Speedup: 1.0×

• 22.0% 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, 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 2: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-58}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e+119)
   (* y z)
   (if (<= y -2.95e+44)
     (* x y)
     (if (<= y -5e-58) (* y z) (if (<= y 5.2e-88) x (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e+119) {
		tmp = y * z;
	} else if (y <= -2.95e+44) {
		tmp = x * y;
	} else if (y <= -5e-58) {
		tmp = y * z;
	} else if (y <= 5.2e-88) {
		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 <= (-4.2d+119)) then
        tmp = y * z
    else if (y <= (-2.95d+44)) then
        tmp = x * y
    else if (y <= (-5d-58)) then
        tmp = y * z
    else if (y <= 5.2d-88) 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 <= -4.2e+119) {
		tmp = y * z;
	} else if (y <= -2.95e+44) {
		tmp = x * y;
	} else if (y <= -5e-58) {
		tmp = y * z;
	} else if (y <= 5.2e-88) {
		tmp = x;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.2e+119:
		tmp = y * z
	elif y <= -2.95e+44:
		tmp = x * y
	elif y <= -5e-58:
		tmp = y * z
	elif y <= 5.2e-88:
		tmp = x
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.2e+119)
		tmp = Float64(y * z);
	elseif (y <= -2.95e+44)
		tmp = Float64(x * y);
	elseif (y <= -5e-58)
		tmp = Float64(y * z);
	elseif (y <= 5.2e-88)
		tmp = x;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.2e+119)
		tmp = y * z;
	elseif (y <= -2.95e+44)
		tmp = x * y;
	elseif (y <= -5e-58)
		tmp = y * z;
	elseif (y <= 5.2e-88)
		tmp = x;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.2e+119], N[(y * z), $MachinePrecision], If[LessEqual[y, -2.95e+44], N[(x * y), $MachinePrecision], If[LessEqual[y, -5e-58], N[(y * z), $MachinePrecision], If[LessEqual[y, 5.2e-88], x, N[(y * z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.19999999999999966e119 or -2.94999999999999982e44 < y < -4.99999999999999977e-58 or 5.20000000000000027e-88 < y

   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 60.1%

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

   5. Simplified 60.1%

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

   if -4.19999999999999966e119 < y < -2.94999999999999982e44

   1. Initial program 99.9%

      \[x + y \cdot \left(z + x\right) \]
   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 74.1%

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

   5. Simplified 74.1%

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

   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 74.1%

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

   8. Simplified 74.1%

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

   if -4.99999999999999977e-58 < y < 5.20000000000000027e-88

   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 76.5%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+119}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{+44}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-58}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-88}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -1.0) t_0 (if (<= y 1.0) (+ x (* y z)) 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 <= 1.0) {
		tmp = x + (y * z);
	} 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 <= 1.0d0) then
        tmp = x + (y * z)
    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 <= 1.0) {
		tmp = x + (y * z);
	} 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 <= 1.0:
		tmp = x + (y * z)
	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 <= 1.0)
		tmp = Float64(x + Float64(y * z));
	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 <= 1.0)
		tmp = x + (y * z);
	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, 1.0], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 99.9%

      \[x + y \cdot \left(z + x\right) \]
   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 98.9%

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

   5. Simplified 98.9%

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

   if -1 < y < 1

   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 97.1%

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

   5. Simplified 97.1%

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

4. Final simplification 98.0%

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

Alternative 4: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -2.6:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-88}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -2.6) t_0 (if (<= y 1.12e-88) (+ x (* x y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -2.6) {
		tmp = t_0;
	} else if (y <= 1.12e-88) {
		tmp = x + (x * 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 <= (-2.6d0)) then
        tmp = t_0
    else if (y <= 1.12d-88) then
        tmp = x + (x * 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 <= -2.6) {
		tmp = t_0;
	} else if (y <= 1.12e-88) {
		tmp = x + (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -2.6:
		tmp = t_0
	elif y <= 1.12e-88:
		tmp = x + (x * 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 <= -2.6)
		tmp = t_0;
	elseif (y <= 1.12e-88)
		tmp = Float64(x + Float64(x * 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 <= -2.6)
		tmp = t_0;
	elseif (y <= 1.12e-88)
		tmp = x + (x * 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, -2.6], t$95$0, If[LessEqual[y, 1.12e-88], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000009 or 1.12e-88 < 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 92.9%

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

   5. Simplified 92.9%

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

   if -2.60000000000000009 < y < 1.12e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. *-lowering-*.f64 73.6%

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

   5. Simplified 73.6%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-88}:\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -2.6:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -2.6) t_0 (if (<= y 2.1e-89) (* 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 <= -2.6) {
		tmp = t_0;
	} else if (y <= 2.1e-89) {
		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 <= (-2.6d0)) then
        tmp = t_0
    else if (y <= 2.1d-89) 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 <= -2.6) {
		tmp = t_0;
	} else if (y <= 2.1e-89) {
		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 <= -2.6:
		tmp = t_0
	elif y <= 2.1e-89:
		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 <= -2.6)
		tmp = t_0;
	elseif (y <= 2.1e-89)
		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 <= -2.6)
		tmp = t_0;
	elseif (y <= 2.1e-89)
		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, -2.6], t$95$0, If[LessEqual[y, 2.1e-89], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000009 or 2.1000000000000001e-89 < 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 92.9%

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

   5. Simplified 92.9%

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

   if -2.60000000000000009 < y < 2.1000000000000001e-89

   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 73.5%

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

   5. Simplified 73.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-6}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e-6) (* y z) (if (<= z 7.5e+96) (* x (+ y 1.0)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e-6) {
		tmp = y * z;
	} else if (z <= 7.5e+96) {
		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 (z <= (-8.5d-6)) then
        tmp = y * z
    else if (z <= 7.5d+96) 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 (z <= -8.5e-6) {
		tmp = y * z;
	} else if (z <= 7.5e+96) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e-6:
		tmp = y * z
	elif z <= 7.5e+96:
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e-6)
		tmp = Float64(y * z);
	elseif (z <= 7.5e+96)
		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 (z <= -8.5e-6)
		tmp = y * z;
	elseif (z <= 7.5e+96)
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e-6], N[(y * z), $MachinePrecision], If[LessEqual[z, 7.5e+96], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999999e-6 or 7.4999999999999996e96 < z

   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 76.9%

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

   5. Simplified 76.9%

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

   if -8.4999999999999999e-6 < z < 7.4999999999999996e96

   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 80.5%

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

   5. Simplified 80.5%

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

Alternative 7: 59.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 1.0) {
		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 <= 1.0d0) 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 <= 1.0) {
		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 <= 1.0:
		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 <= 1.0)
		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 <= 1.0)
		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, 1.0], x, N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 99.9%

      \[x + y \cdot \left(z + x\right) \]
   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 46.5%

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

   5. Simplified 46.5%

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

   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 45.4%

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

   8. Simplified 45.4%

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

   if -1 < y < 1

   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 65.8%

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

4. Final simplification 56.0%

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

Alternative 8: 35.8% 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

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

5. Simplified 35.5%

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

Reproduce

herbie shell --seed 2024150 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))