Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 5

Speedup: 1.0×

• 20.6% 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: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.76 \cdot 10^{-72} \lor \neg \left(z \leq 4.3 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.76e-72) (not (<= z 4.3e+21))) (+ x (* y z)) (* x (+ y 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.76e-72) || !(z <= 4.3e+21)) {
		tmp = x + (y * 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 ((z <= (-1.76d-72)) .or. (.not. (z <= 4.3d+21))) then
        tmp = x + (y * 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 ((z <= -1.76e-72) || !(z <= 4.3e+21)) {
		tmp = x + (y * z);
	} else {
		tmp = x * (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.76e-72) or not (z <= 4.3e+21):
		tmp = x + (y * z)
	else:
		tmp = x * (y + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.76e-72) || !(z <= 4.3e+21))
		tmp = Float64(x + Float64(y * 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 ((z <= -1.76e-72) || ~((z <= 4.3e+21)))
		tmp = x + (y * z);
	else
		tmp = x * (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.76e-72], N[Not[LessEqual[z, 4.3e+21]], $MachinePrecision]], N[(x + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.76e-72 or 4.3e21 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 94.0%

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

   if -1.76e-72 < z < 4.3e21

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.4%

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

      1. *-commutative 89.4%

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

   5. Simplified 89.4%

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

      1. distribute-rgt1-in 89.4%

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

   7. Applied egg-rr 89.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.76 \cdot 10^{-72} \lor \neg \left(z \leq 4.3 \cdot 10^{+21}\right):\\ \;\;\;\;x + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -82 \lor \neg \left(y \leq 250000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -82.0) (not (<= y 250000.0))) (* x y) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -82.0) || !(y <= 250000.0)) {
		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 <= (-82.0d0)) .or. (.not. (y <= 250000.0d0))) 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 <= -82.0) || !(y <= 250000.0)) {
		tmp = x * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -82.0) or not (y <= 250000.0):
		tmp = x * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -82.0) || !(y <= 250000.0))
		tmp = Float64(x * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -82.0) || ~((y <= 250000.0)))
		tmp = x * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -82.0], N[Not[LessEqual[y, 250000.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -82 or 2.5e5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 61.9%

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

      1. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in y around inf 61.3%

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

   if -82 < y < 2.5e5

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 68.2%

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

      1. *-commutative 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in y around 0 67.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -82 \lor \neg \left(y \leq 250000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + 1\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (+ y 1.0)))

C

double code(double x, double y, double z) {
	return x * (y + 1.0);
}

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 + 1.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * (y + 1.0);
}

Python

def code(x, y, z):
	return x * (y + 1.0)

Julia

function code(x, y, z)
	return Float64(x * Float64(y + 1.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (y + 1.0);
end

Wolfram

code[x_, y_, z_] := N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in z around 0 65.1%

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

   1. *-commutative 65.1%

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

5. Simplified 65.1%

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

   1. distribute-rgt1-in 65.1%

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

7. Applied egg-rr 65.1%

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

8. Final simplification 65.1%

   \[\leadsto x \cdot \left(y + 1\right) \]
9. Add Preprocessing

Alternative 5: 36.4% 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 z around 0 65.1%

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

   1. *-commutative 65.1%

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

5. Simplified 65.1%

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

6. Taylor expanded in y around 0 35.5%

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

7. Final simplification 35.5%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))