Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 8

Speedup: 1.0×

• 20.9% 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: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-64)
   (* y z)
   (if (<= y -2.25e-91)
     x
     (if (<= y -9.2e-111)
       (* y z)
       (if (<= y 2.6e-50) x (if (<= y 1.25e+67) (* y z) (* y x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-64) {
		tmp = y * z;
	} else if (y <= -2.25e-91) {
		tmp = x;
	} else if (y <= -9.2e-111) {
		tmp = y * z;
	} else if (y <= 2.6e-50) {
		tmp = x;
	} else if (y <= 1.25e+67) {
		tmp = y * z;
	} else {
		tmp = y * 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 <= (-3.8d-64)) then
        tmp = y * z
    else if (y <= (-2.25d-91)) then
        tmp = x
    else if (y <= (-9.2d-111)) then
        tmp = y * z
    else if (y <= 2.6d-50) then
        tmp = x
    else if (y <= 1.25d+67) then
        tmp = y * z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-64) {
		tmp = y * z;
	} else if (y <= -2.25e-91) {
		tmp = x;
	} else if (y <= -9.2e-111) {
		tmp = y * z;
	} else if (y <= 2.6e-50) {
		tmp = x;
	} else if (y <= 1.25e+67) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.8e-64:
		tmp = y * z
	elif y <= -2.25e-91:
		tmp = x
	elif y <= -9.2e-111:
		tmp = y * z
	elif y <= 2.6e-50:
		tmp = x
	elif y <= 1.25e+67:
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e-64)
		tmp = Float64(y * z);
	elseif (y <= -2.25e-91)
		tmp = x;
	elseif (y <= -9.2e-111)
		tmp = Float64(y * z);
	elseif (y <= 2.6e-50)
		tmp = x;
	elseif (y <= 1.25e+67)
		tmp = Float64(y * z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e-64)
		tmp = y * z;
	elseif (y <= -2.25e-91)
		tmp = x;
	elseif (y <= -9.2e-111)
		tmp = y * z;
	elseif (y <= 2.6e-50)
		tmp = x;
	elseif (y <= 1.25e+67)
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.8e-64], N[(y * z), $MachinePrecision], If[LessEqual[y, -2.25e-91], x, If[LessEqual[y, -9.2e-111], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.6e-50], x, If[LessEqual[y, 1.25e+67], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000002e-64 or -2.24999999999999988e-91 < y < -9.2e-111 or 2.6000000000000001e-50 < y < 1.24999999999999994e67

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.9%

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

      1. fma-define 98.9%

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

      2. +-commutative 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in x around 0 64.9%

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

   if -3.8000000000000002e-64 < y < -2.24999999999999988e-91 or -9.2e-111 < y < 2.6000000000000001e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.8%

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

   if 1.24999999999999994e67 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 59.3%

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

      1. *-commutative 59.3%

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

   5. Simplified 59.3%

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

   6. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   8. Simplified 59.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-64}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-91}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-111}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-65} \lor \neg \left(y \leq -1.3 \cdot 10^{-89}\right) \land \left(y \leq -6 \cdot 10^{-111} \lor \neg \left(y \leq 1.02 \cdot 10^{-50}\right)\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.3e-65)
         (and (not (<= y -1.3e-89)) (or (<= y -6e-111) (not (<= y 1.02e-50)))))
   (* y (+ x z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.3e-65) || (!(y <= -1.3e-89) && ((y <= -6e-111) || !(y <= 1.02e-50)))) {
		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 <= (-4.3d-65)) .or. (.not. (y <= (-1.3d-89))) .and. (y <= (-6d-111)) .or. (.not. (y <= 1.02d-50))) 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 <= -4.3e-65) || (!(y <= -1.3e-89) && ((y <= -6e-111) || !(y <= 1.02e-50)))) {
		tmp = y * (x + z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.3e-65) or (not (y <= -1.3e-89) and ((y <= -6e-111) or not (y <= 1.02e-50))):
		tmp = y * (x + z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.3e-65) || (!(y <= -1.3e-89) && ((y <= -6e-111) || !(y <= 1.02e-50))))
		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 <= -4.3e-65) || (~((y <= -1.3e-89)) && ((y <= -6e-111) || ~((y <= 1.02e-50)))))
		tmp = y * (x + z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.3e-65], And[N[Not[LessEqual[y, -1.3e-89]], $MachinePrecision], Or[LessEqual[y, -6e-111], N[Not[LessEqual[y, 1.02e-50]], $MachinePrecision]]]], N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.30000000000000024e-65 or -1.2999999999999999e-89 < y < -6.00000000000000016e-111 or 1.0199999999999999e-50 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. fma-define 98.6%

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

      2. +-commutative 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in y around inf 93.0%

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

      1. +-commutative 93.0%

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

   8. Simplified 93.0%

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

   if -4.30000000000000024e-65 < y < -1.2999999999999999e-89 or -6.00000000000000016e-111 < y < 1.0199999999999999e-50

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-65} \lor \neg \left(y \leq -1.3 \cdot 10^{-89}\right) \land \left(y \leq -6 \cdot 10^{-111} \lor \neg \left(y \leq 1.02 \cdot 10^{-50}\right)\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-111} \lor \neg \left(y \leq 1.55 \cdot 10^{-50}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -6.8e-65)
     t_0
     (if (<= y -1.75e-91)
       (+ x (* y x))
       (if (or (<= y -9.2e-111) (not (<= y 1.55e-50))) t_0 x)))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -6.8e-65) {
		tmp = t_0;
	} else if (y <= -1.75e-91) {
		tmp = x + (y * x);
	} else if ((y <= -9.2e-111) || !(y <= 1.55e-50)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * (x + z)
    if (y <= (-6.8d-65)) then
        tmp = t_0
    else if (y <= (-1.75d-91)) then
        tmp = x + (y * x)
    else if ((y <= (-9.2d-111)) .or. (.not. (y <= 1.55d-50))) then
        tmp = t_0
    else
        tmp = x
    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 <= -6.8e-65) {
		tmp = t_0;
	} else if (y <= -1.75e-91) {
		tmp = x + (y * x);
	} else if ((y <= -9.2e-111) || !(y <= 1.55e-50)) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -6.8e-65:
		tmp = t_0
	elif y <= -1.75e-91:
		tmp = x + (y * x)
	elif (y <= -9.2e-111) or not (y <= 1.55e-50):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x + z))
	tmp = 0.0
	if (y <= -6.8e-65)
		tmp = t_0;
	elseif (y <= -1.75e-91)
		tmp = Float64(x + Float64(y * x));
	elseif ((y <= -9.2e-111) || !(y <= 1.55e-50))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x + z);
	tmp = 0.0;
	if (y <= -6.8e-65)
		tmp = t_0;
	elseif (y <= -1.75e-91)
		tmp = x + (y * x);
	elseif ((y <= -9.2e-111) || ~((y <= 1.55e-50)))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e-65], t$95$0, If[LessEqual[y, -1.75e-91], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -9.2e-111], N[Not[LessEqual[y, 1.55e-50]], $MachinePrecision]], t$95$0, x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.79999999999999973e-65 or -1.7499999999999999e-91 < y < -9.2e-111 or 1.5500000000000001e-50 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.3%

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

      1. fma-define 98.6%

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

      2. +-commutative 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in y around inf 93.0%

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

      1. +-commutative 93.0%

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

   8. Simplified 93.0%

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

   if -6.79999999999999973e-65 < y < -1.7499999999999999e-91

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 86.1%

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

      1. *-commutative 86.1%

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

   5. Simplified 86.1%

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

   if -9.2e-111 < 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 77.2%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-65}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-91}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-111} \lor \neg \left(y \leq 1.55 \cdot 10^{-50}\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1400000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1400000.0) (not (<= y 1.0))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1400000.0) || !(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 <= (-1400000.0d0)) .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 <= -1400000.0) || !(y <= 1.0)) {
		tmp = y * (x + z);
	} else {
		tmp = x + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1400000.0) 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 <= -1400000.0) || !(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 <= -1400000.0) || ~((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, -1400000.0], 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 < -1.4e6 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 96.5%

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

      1. fma-define 98.3%

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

      2. +-commutative 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 99.4%

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

      1. +-commutative 99.4%

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

   8. Simplified 99.4%

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

   if -1.4e6 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1400000 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-9} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.25e-9) (not (<= y 1.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.25e-9) || !(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 <= (-1.25d-9)) .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 <= -1.25e-9) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.25e-9) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.25e-9) || !(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 <= -1.25e-9) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.25e-9], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e-9 or 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 46.9%

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

      1. *-commutative 46.9%

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

   5. Simplified 46.9%

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

   6. Taylor expanded in y around inf 46.4%

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

      1. *-commutative 46.4%

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

   8. Simplified 46.4%

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

   if -1.25e-9 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 68.2%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-9} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 36.6% 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 37.6%

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

4. Final simplification 37.6%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024095 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))