Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

Alternatives: 6

Speedup: 1.0×

• 21.2% 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. Final simplification 100.0%

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

Alternative 2: 62.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+231}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+146}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+47}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-27} \lor \neg \left(y \leq 2.1 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+231)
   (* x y)
   (if (<= y -1.45e+146)
     (* y z)
     (if (<= y -2e+47)
       (* x y)
       (if (or (<= y -3.6e-27) (not (<= y 2.1e-11))) (* y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+231) {
		tmp = x * y;
	} else if (y <= -1.45e+146) {
		tmp = y * z;
	} else if (y <= -2e+47) {
		tmp = x * y;
	} else if ((y <= -3.6e-27) || !(y <= 2.1e-11)) {
		tmp = y * 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 <= (-2.7d+231)) then
        tmp = x * y
    else if (y <= (-1.45d+146)) then
        tmp = y * z
    else if (y <= (-2d+47)) then
        tmp = x * y
    else if ((y <= (-3.6d-27)) .or. (.not. (y <= 2.1d-11))) then
        tmp = y * 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 <= -2.7e+231) {
		tmp = x * y;
	} else if (y <= -1.45e+146) {
		tmp = y * z;
	} else if (y <= -2e+47) {
		tmp = x * y;
	} else if ((y <= -3.6e-27) || !(y <= 2.1e-11)) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+231:
		tmp = x * y
	elif y <= -1.45e+146:
		tmp = y * z
	elif y <= -2e+47:
		tmp = x * y
	elif (y <= -3.6e-27) or not (y <= 2.1e-11):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+231)
		tmp = Float64(x * y);
	elseif (y <= -1.45e+146)
		tmp = Float64(y * z);
	elseif (y <= -2e+47)
		tmp = Float64(x * y);
	elseif ((y <= -3.6e-27) || !(y <= 2.1e-11))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+231)
		tmp = x * y;
	elseif (y <= -1.45e+146)
		tmp = y * z;
	elseif (y <= -2e+47)
		tmp = x * y;
	elseif ((y <= -3.6e-27) || ~((y <= 2.1e-11)))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+231], N[(x * y), $MachinePrecision], If[LessEqual[y, -1.45e+146], N[(y * z), $MachinePrecision], If[LessEqual[y, -2e+47], N[(x * y), $MachinePrecision], If[Or[LessEqual[y, -3.6e-27], N[Not[LessEqual[y, 2.1e-11]], $MachinePrecision]], N[(y * z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999999e231 or -1.4499999999999999e146 < y < -2.0000000000000001e47

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 70.7%

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

      1. *-commutative 70.7%

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

   4. Simplified 70.7%

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

   5. Taylor expanded in y around inf 70.7%

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

   if -2.6999999999999999e231 < y < -1.4499999999999999e146 or -2.0000000000000001e47 < y < -3.5999999999999999e-27 or 2.0999999999999999e-11 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 63.4%

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

   3. Taylor expanded in x around 0 61.0%

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

   if -3.5999999999999999e-27 < y < 2.0999999999999999e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 77.1%

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

      1. *-commutative 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in y around 0 77.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+231}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{+146}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+47}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-27} \lor \neg \left(y \leq 2.1 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-66} \lor \neg \left(x \leq 4.6 \cdot 10^{-135}\right):\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.8e-66) (not (<= x 4.6e-135))) (+ x (* x y)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.8e-66) || !(x <= 4.6e-135)) {
		tmp = x + (x * 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 ((x <= (-3.8d-66)) .or. (.not. (x <= 4.6d-135))) then
        tmp = x + (x * 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 ((x <= -3.8e-66) || !(x <= 4.6e-135)) {
		tmp = x + (x * y);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.8e-66) or not (x <= 4.6e-135):
		tmp = x + (x * y)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.8e-66) || !(x <= 4.6e-135))
		tmp = Float64(x + Float64(x * y));
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.8e-66) || ~((x <= 4.6e-135)))
		tmp = x + (x * y);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.8e-66], N[Not[LessEqual[x, 4.6e-135]], $MachinePrecision]], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998e-66 or 4.5999999999999998e-135 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 84.2%

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

      1. *-commutative 84.2%

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

   4. Simplified 84.2%

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

   if -3.7999999999999998e-66 < x < 4.5999999999999998e-135

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 92.4%

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

   3. Taylor expanded in x around 0 71.4%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-66} \lor \neg \left(x \leq 4.6 \cdot 10^{-135}\right):\\ \;\;\;\;x + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 4: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -122 \lor \neg \left(z \leq 8.8 \cdot 10^{-32}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -122.0) (not (<= z 8.8e-32))) (+ x (* y z)) (+ x (* x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -122.0) || !(z <= 8.8e-32)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (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 ((z <= (-122.0d0)) .or. (.not. (z <= 8.8d-32))) then
        tmp = x + (y * z)
    else
        tmp = x + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -122.0) || !(z <= 8.8e-32)) {
		tmp = x + (y * z);
	} else {
		tmp = x + (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -122.0) or not (z <= 8.8e-32):
		tmp = x + (y * z)
	else:
		tmp = x + (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -122.0) || !(z <= 8.8e-32))
		tmp = Float64(x + Float64(y * z));
	else
		tmp = Float64(x + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -122.0) || ~((z <= 8.8e-32)))
		tmp = x + (y * z);
	else
		tmp = x + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -122.0], N[Not[LessEqual[z, 8.8e-32]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -122 or 8.7999999999999999e-32 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 90.4%

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

   if -122 < z < 8.7999999999999999e-32

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 87.7%

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

      1. *-commutative 87.7%

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

   4. Simplified 87.7%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -122 \lor \neg \left(z \leq 8.8 \cdot 10^{-32}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot y\\ \end{array} \]

Alternative 5: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -480000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -480000000.0) (not (<= y 1.0))) (* x y) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -480000000.0) || !(y <= 1.0)) {
		tmp = x * y;
	} 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 <= (-480000000.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -480000000.0) || !(y <= 1.0)) {
		tmp = x * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -480000000.0) or not (y <= 1.0):
		tmp = x * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -480000000.0) || !(y <= 1.0))
		tmp = Float64(x * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -480000000.0) || ~((y <= 1.0)))
		tmp = x * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -480000000.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e8 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 51.7%

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

      1. *-commutative 51.7%

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

   4. Simplified 51.7%

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

   5. Taylor expanded in y around inf 51.7%

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

   if -4.8e8 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 74.6%

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

      1. *-commutative 74.6%

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

   4. Simplified 74.6%

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

   5. Taylor expanded in y around 0 74.2%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -480000000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 36.5% 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 z around 0 63.5%

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

   1. *-commutative 63.5%

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

4. Simplified 63.5%

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

5. Taylor expanded in y around 0 39.4%

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

6. Final simplification 39.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023309 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))