Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

Alternatives: 6

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, 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: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-38}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+62} \lor \neg \left(y \leq 1.5 \cdot 10^{+201}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e-38)
   (* y z)
   (if (<= y 8.2e-17)
     x
     (if (or (<= y 5.7e+62) (not (<= y 1.5e+201))) (* y z) (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e-38) {
		tmp = y * z;
	} else if (y <= 8.2e-17) {
		tmp = x;
	} else if ((y <= 5.7e+62) || !(y <= 1.5e+201)) {
		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 <= (-2.7d-38)) then
        tmp = y * z
    else if (y <= 8.2d-17) then
        tmp = x
    else if ((y <= 5.7d+62) .or. (.not. (y <= 1.5d+201))) 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 <= -2.7e-38) {
		tmp = y * z;
	} else if (y <= 8.2e-17) {
		tmp = x;
	} else if ((y <= 5.7e+62) || !(y <= 1.5e+201)) {
		tmp = y * z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e-38:
		tmp = y * z
	elif y <= 8.2e-17:
		tmp = x
	elif (y <= 5.7e+62) or not (y <= 1.5e+201):
		tmp = y * z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e-38)
		tmp = Float64(y * z);
	elseif (y <= 8.2e-17)
		tmp = x;
	elseif ((y <= 5.7e+62) || !(y <= 1.5e+201))
		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 <= -2.7e-38)
		tmp = y * z;
	elseif (y <= 8.2e-17)
		tmp = x;
	elseif ((y <= 5.7e+62) || ~((y <= 1.5e+201)))
		tmp = y * z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e-38], N[(y * z), $MachinePrecision], If[LessEqual[y, 8.2e-17], x, If[Or[LessEqual[y, 5.7e+62], N[Not[LessEqual[y, 1.5e+201]], $MachinePrecision]], N[(y * z), $MachinePrecision], N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.70000000000000005e-38 or 8.2000000000000001e-17 < y < 5.69999999999999998e62 or 1.50000000000000012e201 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 66.7%

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

   4. Taylor expanded in x around 0 64.9%

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

   if -2.70000000000000005e-38 < y < 8.2000000000000001e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 78.5%

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

      1. *-commutative 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in y around 0 78.5%

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

   if 5.69999999999999998e62 < y < 1.50000000000000012e201

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.1%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in x around inf 70.1%

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

      1. *-commutative 70.1%

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

   7. Simplified 70.1%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-38}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+62} \lor \neg \left(y \leq 1.5 \cdot 10^{+201}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * z), $MachinePrecision]), $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 0 94.3%

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

   4. Taylor expanded in y around inf 98.6%

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

   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 98.7%

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

4. Final simplification 98.6%

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

Alternative 4: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-37} \lor \neg \left(y \leq 1.45 \cdot 10^{-59}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.15e-37) (not (<= y 1.45e-59))) (* y (+ x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.15e-37) || !(y <= 1.45e-59)) {
		tmp = y * (x + 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 <= (-1.15d-37)) .or. (.not. (y <= 1.45d-59))) then
        tmp = y * (x + 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 <= -1.15e-37) || !(y <= 1.45e-59)) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.15e-37) or not (y <= 1.45e-59):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.15e-37) || !(y <= 1.45e-59))
		tmp = Float64(y * Float64(x + z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.15e-37) || ~((y <= 1.45e-59)))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.15e-37], N[Not[LessEqual[y, 1.45e-59]], $MachinePrecision]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-37 or 1.45000000000000008e-59 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.9%

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

   4. Taylor expanded in y around inf 95.5%

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

   if -1.15e-37 < y < 1.45000000000000008e-59

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. *-commutative 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in y around 0 79.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-37} \lor \neg \left(y \leq 1.45 \cdot 10^{-59}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.5 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.5e+15))) (* x y) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.5e+15)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 1.5d+15))) 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 <= -1.0) || !(y <= 1.5e+15)) {
		tmp = x * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.5e+15):
		tmp = x * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.5e+15))
		tmp = Float64(x * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.5e+15)))
		tmp = x * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.5e+15]], $MachinePrecision]], N[(x * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.5e15 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.2%

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

   4. Taylor expanded in y around inf 98.5%

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

   5. Taylor expanded in x around inf 50.9%

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

      1. *-commutative 50.9%

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

   7. Simplified 50.9%

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

   if -1 < y < 1.5e15

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   6. Taylor expanded in y around 0 71.7%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.5 \cdot 10^{+15}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 37.8% 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 z around 0 63.3%

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

   1. *-commutative 63.3%

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

5. Simplified 63.3%

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

6. Taylor expanded in y around 0 39.5%

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

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))