Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 2.4s

Alternatives: 7

Speedup: 1.0×

• 20.1% 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-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. Add Preprocessing

Alternative 2: 62.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+285}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-9}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+68}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+213}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+285)
   (* y z)
   (if (<= y -2.5e+25)
     (* x y)
     (if (<= y -3e-9)
       (* y z)
       (if (<= y 1.55e-50)
         x
         (if (<= y 2.3e+18)
           (* y z)
           (if (<= y 7.5e+68)
             (* x y)
             (if (<= y 7.8e+213) (* y z) (* x y)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+285) {
		tmp = y * z;
	} else if (y <= -2.5e+25) {
		tmp = x * y;
	} else if (y <= -3e-9) {
		tmp = y * z;
	} else if (y <= 1.55e-50) {
		tmp = x;
	} else if (y <= 2.3e+18) {
		tmp = y * z;
	} else if (y <= 7.5e+68) {
		tmp = x * y;
	} else if (y <= 7.8e+213) {
		tmp = y * z;
	} 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 <= (-2d+285)) then
        tmp = y * z
    else if (y <= (-2.5d+25)) then
        tmp = x * y
    else if (y <= (-3d-9)) then
        tmp = y * z
    else if (y <= 1.55d-50) then
        tmp = x
    else if (y <= 2.3d+18) then
        tmp = y * z
    else if (y <= 7.5d+68) then
        tmp = x * y
    else if (y <= 7.8d+213) then
        tmp = y * z
    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 <= -2e+285) {
		tmp = y * z;
	} else if (y <= -2.5e+25) {
		tmp = x * y;
	} else if (y <= -3e-9) {
		tmp = y * z;
	} else if (y <= 1.55e-50) {
		tmp = x;
	} else if (y <= 2.3e+18) {
		tmp = y * z;
	} else if (y <= 7.5e+68) {
		tmp = x * y;
	} else if (y <= 7.8e+213) {
		tmp = y * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+285:
		tmp = y * z
	elif y <= -2.5e+25:
		tmp = x * y
	elif y <= -3e-9:
		tmp = y * z
	elif y <= 1.55e-50:
		tmp = x
	elif y <= 2.3e+18:
		tmp = y * z
	elif y <= 7.5e+68:
		tmp = x * y
	elif y <= 7.8e+213:
		tmp = y * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+285)
		tmp = Float64(y * z);
	elseif (y <= -2.5e+25)
		tmp = Float64(x * y);
	elseif (y <= -3e-9)
		tmp = Float64(y * z);
	elseif (y <= 1.55e-50)
		tmp = x;
	elseif (y <= 2.3e+18)
		tmp = Float64(y * z);
	elseif (y <= 7.5e+68)
		tmp = Float64(x * y);
	elseif (y <= 7.8e+213)
		tmp = Float64(y * z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+285)
		tmp = y * z;
	elseif (y <= -2.5e+25)
		tmp = x * y;
	elseif (y <= -3e-9)
		tmp = y * z;
	elseif (y <= 1.55e-50)
		tmp = x;
	elseif (y <= 2.3e+18)
		tmp = y * z;
	elseif (y <= 7.5e+68)
		tmp = x * y;
	elseif (y <= 7.8e+213)
		tmp = y * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+285], N[(y * z), $MachinePrecision], If[LessEqual[y, -2.5e+25], N[(x * y), $MachinePrecision], If[LessEqual[y, -3e-9], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.55e-50], x, If[LessEqual[y, 2.3e+18], N[(y * z), $MachinePrecision], If[LessEqual[y, 7.5e+68], N[(x * y), $MachinePrecision], If[LessEqual[y, 7.8e+213], N[(y * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2e285 or -2.50000000000000012e25 < y < -2.99999999999999998e-9 or 1.5500000000000001e-50 < y < 2.3e18 or 7.49999999999999959e68 < y < 7.8000000000000003e213

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 75.2%

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

   if -2e285 < y < -2.50000000000000012e25 or 2.3e18 < y < 7.49999999999999959e68 or 7.8000000000000003e213 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 68.3%

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

   4. Taylor expanded in y around inf 68.3%

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

   if -2.99999999999999998e-9 < y < 1.5500000000000001e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.2%

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

Alternative 3: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+72}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \left(1 + y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.5e+72) (* y z) (if (<= z 3.1e+31) (* x (+ 1.0 y)) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.5e+72) {
		tmp = y * z;
	} else if (z <= 3.1e+31) {
		tmp = x * (1.0 + y);
	} 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 <= (-5.5d+72)) then
        tmp = y * z
    else if (z <= 3.1d+31) then
        tmp = x * (1.0d0 + y)
    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 <= -5.5e+72) {
		tmp = y * z;
	} else if (z <= 3.1e+31) {
		tmp = x * (1.0 + y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.5e+72:
		tmp = y * z
	elif z <= 3.1e+31:
		tmp = x * (1.0 + y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.5e+72)
		tmp = Float64(y * z);
	elseif (z <= 3.1e+31)
		tmp = Float64(x * Float64(1.0 + y));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.5e+72)
		tmp = y * z;
	elseif (z <= 3.1e+31)
		tmp = x * (1.0 + y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.5e+72], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.1e+31], N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5e72 or 3.1000000000000002e31 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.7%

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

   if -5.5e72 < z < 3.1000000000000002e31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.4%

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

Alternative 4: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -19:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1700000:\\ \;\;\;\;x \cdot \left(1 + y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -19.0) t_0 (if (<= y 1700000.0) (* x (+ 1.0 y)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -19.0) {
		tmp = t_0;
	} else if (y <= 1700000.0) {
		tmp = x * (1.0 + 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 <= (-19.0d0)) then
        tmp = t_0
    else if (y <= 1700000.0d0) then
        tmp = x * (1.0d0 + 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 <= -19.0) {
		tmp = t_0;
	} else if (y <= 1700000.0) {
		tmp = x * (1.0 + y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -19.0:
		tmp = t_0
	elif y <= 1700000.0:
		tmp = x * (1.0 + 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 <= -19.0)
		tmp = t_0;
	elseif (y <= 1700000.0)
		tmp = Float64(x * Float64(1.0 + 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 <= -19.0)
		tmp = t_0;
	elseif (y <= 1700000.0)
		tmp = x * (1.0 + 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, -19.0], t$95$0, If[LessEqual[y, 1700000.0], N[(x * N[(1.0 + y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -19 or 1.7e6 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.4%

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

   if -19 < y < 1.7e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.6%

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

Alternative 5: 61.7% 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 100.0%

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

   3. Taylor expanded in x around inf 50.7%

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

   4. Taylor expanded in y around inf 49.2%

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

   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 73.8%

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

Alternative 6: 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]

Derivation

1. Initial program 100.0%

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

Alternative 7: 37.6% 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. Add Preprocessing

3. Taylor expanded in y around 0 37.0%

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

Reproduce

herbie shell --seed 2024034 -o generate:simplify
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))