Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 8

Speedup: 1.0×

• 21.5% 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. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, x + z, x\right) \]
6. Add Preprocessing

Alternative 2: 62.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+268}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+118}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-16} \lor \neg \left(y \leq -9.5 \cdot 10^{-56}\right) \land \left(y \leq -1.3 \cdot 10^{-77} \lor \neg \left(y \leq 1.32 \cdot 10^{-45}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.2e+268)
   (* y z)
   (if (<= y -1.15e+118)
     (* y x)
     (if (or (<= y -2.55e-16)
             (and (not (<= y -9.5e-56))
                  (or (<= y -1.3e-77) (not (<= y 1.32e-45)))))
       (* y z)
       x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.2e+268) {
		tmp = y * z;
	} else if (y <= -1.15e+118) {
		tmp = y * x;
	} else if ((y <= -2.55e-16) || (!(y <= -9.5e-56) && ((y <= -1.3e-77) || !(y <= 1.32e-45)))) {
		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 <= (-6.2d+268)) then
        tmp = y * z
    else if (y <= (-1.15d+118)) then
        tmp = y * x
    else if ((y <= (-2.55d-16)) .or. (.not. (y <= (-9.5d-56))) .and. (y <= (-1.3d-77)) .or. (.not. (y <= 1.32d-45))) 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 <= -6.2e+268) {
		tmp = y * z;
	} else if (y <= -1.15e+118) {
		tmp = y * x;
	} else if ((y <= -2.55e-16) || (!(y <= -9.5e-56) && ((y <= -1.3e-77) || !(y <= 1.32e-45)))) {
		tmp = y * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.2e+268:
		tmp = y * z
	elif y <= -1.15e+118:
		tmp = y * x
	elif (y <= -2.55e-16) or (not (y <= -9.5e-56) and ((y <= -1.3e-77) or not (y <= 1.32e-45))):
		tmp = y * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.2e+268)
		tmp = Float64(y * z);
	elseif (y <= -1.15e+118)
		tmp = Float64(y * x);
	elseif ((y <= -2.55e-16) || (!(y <= -9.5e-56) && ((y <= -1.3e-77) || !(y <= 1.32e-45))))
		tmp = Float64(y * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.2e+268)
		tmp = y * z;
	elseif (y <= -1.15e+118)
		tmp = y * x;
	elseif ((y <= -2.55e-16) || (~((y <= -9.5e-56)) && ((y <= -1.3e-77) || ~((y <= 1.32e-45)))))
		tmp = y * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.2e+268], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.15e+118], N[(y * x), $MachinePrecision], If[Or[LessEqual[y, -2.55e-16], And[N[Not[LessEqual[y, -9.5e-56]], $MachinePrecision], Or[LessEqual[y, -1.3e-77], N[Not[LessEqual[y, 1.32e-45]], $MachinePrecision]]]], N[(y * z), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2000000000000002e268 or -1.15000000000000008e118 < y < -2.55e-16 or -9.4999999999999991e-56 < y < -1.3000000000000001e-77 or 1.32000000000000005e-45 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 60.0%

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

   if -6.2000000000000002e268 < y < -1.15000000000000008e118

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in z around 0 70.5%

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

      1. *-commutative 70.5%

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

   8. Simplified 70.5%

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

   if -2.55e-16 < y < -9.4999999999999991e-56 or -1.3000000000000001e-77 < y < 1.32000000000000005e-45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.4%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+268}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+118}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-16} \lor \neg \left(y \leq -9.5 \cdot 10^{-56}\right) \land \left(y \leq -1.3 \cdot 10^{-77} \lor \neg \left(y \leq 1.32 \cdot 10^{-45}\right)\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-16}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-77}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -4.2e-16)
     t_0
     (if (<= y -2e-56)
       (* x (+ y 1.0))
       (if (<= y -1.3e-77) (* y z) (if (<= y 1.1e-41) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -4.2e-16) {
		tmp = t_0;
	} else if (y <= -2e-56) {
		tmp = x * (y + 1.0);
	} else if (y <= -1.3e-77) {
		tmp = y * z;
	} else if (y <= 1.1e-41) {
		tmp = x;
	} 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 <= (-4.2d-16)) then
        tmp = t_0
    else if (y <= (-2d-56)) then
        tmp = x * (y + 1.0d0)
    else if (y <= (-1.3d-77)) then
        tmp = y * z
    else if (y <= 1.1d-41) then
        tmp = x
    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 <= -4.2e-16) {
		tmp = t_0;
	} else if (y <= -2e-56) {
		tmp = x * (y + 1.0);
	} else if (y <= -1.3e-77) {
		tmp = y * z;
	} else if (y <= 1.1e-41) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -4.2e-16:
		tmp = t_0
	elif y <= -2e-56:
		tmp = x * (y + 1.0)
	elif y <= -1.3e-77:
		tmp = y * z
	elif y <= 1.1e-41:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -4.2e-16)
		tmp = t_0;
	elseif (y <= -2e-56)
		tmp = Float64(x * Float64(y + 1.0));
	elseif (y <= -1.3e-77)
		tmp = Float64(y * z);
	elseif (y <= 1.1e-41)
		tmp = x;
	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 <= -4.2e-16)
		tmp = t_0;
	elseif (y <= -2e-56)
		tmp = x * (y + 1.0);
	elseif (y <= -1.3e-77)
		tmp = y * z;
	elseif (y <= 1.1e-41)
		tmp = x;
	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, -4.2e-16], t$95$0, If[LessEqual[y, -2e-56], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.3e-77], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.1e-41], x, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2000000000000002e-16 or 1.1e-41 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 96.8%

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

      1. +-commutative 96.8%

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

   5. Simplified 96.8%

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

   if -4.2000000000000002e-16 < y < -2.0000000000000001e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -2.0000000000000001e-56 < y < -1.3000000000000001e-77

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 84.7%

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

   if -1.3000000000000001e-77 < y < 1.1e-41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 78.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-77}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-120} \lor \neg \left(x \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.5e-120) (not (<= x 4.7e-39))) (* x (+ y 1.0)) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.5e-120) || !(x <= 4.7e-39)) {
		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 ((x <= (-5.5d-120)) .or. (.not. (x <= 4.7d-39))) 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 ((x <= -5.5e-120) || !(x <= 4.7e-39)) {
		tmp = x * (y + 1.0);
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.5e-120) or not (x <= 4.7e-39):
		tmp = x * (y + 1.0)
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.5e-120) || !(x <= 4.7e-39))
		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 ((x <= -5.5e-120) || ~((x <= 4.7e-39)))
		tmp = x * (y + 1.0);
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.5e-120], N[Not[LessEqual[x, 4.7e-39]], $MachinePrecision]], N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5000000000000001e-120 or 4.7000000000000002e-39 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + y\right)} \]
   4. Step-by-step derivation

      1. +-commutative 82.2%

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

   5. Simplified 82.2%

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

   if -5.5000000000000001e-120 < x < 4.7000000000000002e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{-120} \lor \neg \left(x \leq 4.7 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(y + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.6) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.6) || !(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 <= (-5.6d0)) .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 <= -5.6) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.6) 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 <= -5.6) || !(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 <= -5.6) || ~((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, -5.6], 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 < -5.5999999999999996 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.0%

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

      1. +-commutative 98.0%

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

   5. Simplified 98.0%

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

   if -5.5999999999999996 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.4%

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

      1. associate-/l* 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in x around 0 98.7%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-16} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e-16) (not (<= y 1.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e-16) || !(y <= 1.0)) {
		tmp = y * x;
	} 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 <= (-5.8d-16)) .or. (.not. (y <= 1.0d0))) then
        tmp = y * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e-16) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.8e-16) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e-16) || !(y <= 1.0))
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.8e-16) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.8e-16], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.7999999999999996e-16 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.1%

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

      1. +-commutative 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in z around 0 50.8%

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

      1. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   if -5.7999999999999996e-16 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.9%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-16} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 8: 36.2% 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 33.1%

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

4. Final simplification 33.1%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))