Main:bigenough2 from A

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

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-def 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: 61.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+250}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -700000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+87} \lor \neg \left(y \leq 5 \cdot 10^{+168}\right) \land y \leq 1.08 \cdot 10^{+225}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.6e+250)
   (* y x)
   (if (<= y -6.8e+50)
     (* y z)
     (if (<= y -700000.0)
       (* y x)
       (if (<= y -1.3e-18)
         (* y z)
         (if (<= y -1.65e-65)
           x
           (if (<= y -3e-102)
             (* y z)
             (if (<= y 1.05e-53)
               x
               (if (or (<= y 1.3e+87)
                       (and (not (<= y 5e+168)) (<= y 1.08e+225)))
                 (* y z)
                 (* y x))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.6e+250) {
		tmp = y * x;
	} else if (y <= -6.8e+50) {
		tmp = y * z;
	} else if (y <= -700000.0) {
		tmp = y * x;
	} else if (y <= -1.3e-18) {
		tmp = y * z;
	} else if (y <= -1.65e-65) {
		tmp = x;
	} else if (y <= -3e-102) {
		tmp = y * z;
	} else if (y <= 1.05e-53) {
		tmp = x;
	} else if ((y <= 1.3e+87) || (!(y <= 5e+168) && (y <= 1.08e+225))) {
		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 <= (-5.6d+250)) then
        tmp = y * x
    else if (y <= (-6.8d+50)) then
        tmp = y * z
    else if (y <= (-700000.0d0)) then
        tmp = y * x
    else if (y <= (-1.3d-18)) then
        tmp = y * z
    else if (y <= (-1.65d-65)) then
        tmp = x
    else if (y <= (-3d-102)) then
        tmp = y * z
    else if (y <= 1.05d-53) then
        tmp = x
    else if ((y <= 1.3d+87) .or. (.not. (y <= 5d+168)) .and. (y <= 1.08d+225)) 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 <= -5.6e+250) {
		tmp = y * x;
	} else if (y <= -6.8e+50) {
		tmp = y * z;
	} else if (y <= -700000.0) {
		tmp = y * x;
	} else if (y <= -1.3e-18) {
		tmp = y * z;
	} else if (y <= -1.65e-65) {
		tmp = x;
	} else if (y <= -3e-102) {
		tmp = y * z;
	} else if (y <= 1.05e-53) {
		tmp = x;
	} else if ((y <= 1.3e+87) || (!(y <= 5e+168) && (y <= 1.08e+225))) {
		tmp = y * z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.6e+250:
		tmp = y * x
	elif y <= -6.8e+50:
		tmp = y * z
	elif y <= -700000.0:
		tmp = y * x
	elif y <= -1.3e-18:
		tmp = y * z
	elif y <= -1.65e-65:
		tmp = x
	elif y <= -3e-102:
		tmp = y * z
	elif y <= 1.05e-53:
		tmp = x
	elif (y <= 1.3e+87) or (not (y <= 5e+168) and (y <= 1.08e+225)):
		tmp = y * z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.6e+250)
		tmp = Float64(y * x);
	elseif (y <= -6.8e+50)
		tmp = Float64(y * z);
	elseif (y <= -700000.0)
		tmp = Float64(y * x);
	elseif (y <= -1.3e-18)
		tmp = Float64(y * z);
	elseif (y <= -1.65e-65)
		tmp = x;
	elseif (y <= -3e-102)
		tmp = Float64(y * z);
	elseif (y <= 1.05e-53)
		tmp = x;
	elseif ((y <= 1.3e+87) || (!(y <= 5e+168) && (y <= 1.08e+225)))
		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 <= -5.6e+250)
		tmp = y * x;
	elseif (y <= -6.8e+50)
		tmp = y * z;
	elseif (y <= -700000.0)
		tmp = y * x;
	elseif (y <= -1.3e-18)
		tmp = y * z;
	elseif (y <= -1.65e-65)
		tmp = x;
	elseif (y <= -3e-102)
		tmp = y * z;
	elseif (y <= 1.05e-53)
		tmp = x;
	elseif ((y <= 1.3e+87) || (~((y <= 5e+168)) && (y <= 1.08e+225)))
		tmp = y * z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.6e+250], N[(y * x), $MachinePrecision], If[LessEqual[y, -6.8e+50], N[(y * z), $MachinePrecision], If[LessEqual[y, -700000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, -1.3e-18], N[(y * z), $MachinePrecision], If[LessEqual[y, -1.65e-65], x, If[LessEqual[y, -3e-102], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.05e-53], x, If[Or[LessEqual[y, 1.3e+87], And[N[Not[LessEqual[y, 5e+168]], $MachinePrecision], LessEqual[y, 1.08e+225]]], N[(y * z), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000019e250 or -6.7999999999999997e50 < y < -7e5 or 1.29999999999999999e87 < y < 4.99999999999999967e168 or 1.0799999999999999e225 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 80.6%

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

      1. *-commutative 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

   8. Simplified 78.5%

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

   if -5.60000000000000019e250 < y < -6.7999999999999997e50 or -7e5 < y < -1.3e-18 or -1.6500000000000001e-65 < y < -3e-102 or 1.04999999999999989e-53 < y < 1.29999999999999999e87 or 4.99999999999999967e168 < y < 1.0799999999999999e225

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 95.6%

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

      1. fma-def 98.8%

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

      2. +-commutative 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in x around 0 65.2%

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

   if -1.3e-18 < y < -1.6500000000000001e-65 or -3e-102 < y < 1.04999999999999989e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.4%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+250}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -700000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-18}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-65}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+87} \lor \neg \left(y \leq 5 \cdot 10^{+168}\right) \land y \leq 1.08 \cdot 10^{+225}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -3.5e-20)
     t_0
     (if (<= y -3.2e-66)
       x
       (if (<= y -6.2e-102) (* y z) (if (<= y 1.35e-53) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -3.5e-20) {
		tmp = t_0;
	} else if (y <= -3.2e-66) {
		tmp = x;
	} else if (y <= -6.2e-102) {
		tmp = y * z;
	} else if (y <= 1.35e-53) {
		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 <= (-3.5d-20)) then
        tmp = t_0
    else if (y <= (-3.2d-66)) then
        tmp = x
    else if (y <= (-6.2d-102)) then
        tmp = y * z
    else if (y <= 1.35d-53) 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 <= -3.5e-20) {
		tmp = t_0;
	} else if (y <= -3.2e-66) {
		tmp = x;
	} else if (y <= -6.2e-102) {
		tmp = y * z;
	} else if (y <= 1.35e-53) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -3.5e-20:
		tmp = t_0
	elif y <= -3.2e-66:
		tmp = x
	elif y <= -6.2e-102:
		tmp = y * z
	elif y <= 1.35e-53:
		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 <= -3.5e-20)
		tmp = t_0;
	elseif (y <= -3.2e-66)
		tmp = x;
	elseif (y <= -6.2e-102)
		tmp = Float64(y * z);
	elseif (y <= 1.35e-53)
		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 <= -3.5e-20)
		tmp = t_0;
	elseif (y <= -3.2e-66)
		tmp = x;
	elseif (y <= -6.2e-102)
		tmp = y * z;
	elseif (y <= 1.35e-53)
		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, -3.5e-20], t$95$0, If[LessEqual[y, -3.2e-66], x, If[LessEqual[y, -6.2e-102], N[(y * z), $MachinePrecision], If[LessEqual[y, 1.35e-53], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000003e-20 or 1.35e-53 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.0%

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

      1. fma-def 99.2%

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

      2. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf 94.5%

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

      1. +-commutative 94.5%

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

   8. Simplified 94.5%

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

   if -3.50000000000000003e-20 < y < -3.19999999999999982e-66 or -6.20000000000000026e-102 < y < 1.35e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.4%

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

   if -3.19999999999999982e-66 < y < -6.20000000000000026e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 86.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + z\right)\\ \mathbf{if}\;y \leq -1.82:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ x z))))
   (if (<= y -1.82)
     t_0
     (if (<= y -1.8e-57)
       (+ x (* y x))
       (if (<= y -5.9e-102) (* y z) (if (<= y 2.8e-53) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x + z);
	double tmp;
	if (y <= -1.82) {
		tmp = t_0;
	} else if (y <= -1.8e-57) {
		tmp = x + (y * x);
	} else if (y <= -5.9e-102) {
		tmp = y * z;
	} else if (y <= 2.8e-53) {
		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 <= (-1.82d0)) then
        tmp = t_0
    else if (y <= (-1.8d-57)) then
        tmp = x + (y * x)
    else if (y <= (-5.9d-102)) then
        tmp = y * z
    else if (y <= 2.8d-53) 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 <= -1.82) {
		tmp = t_0;
	} else if (y <= -1.8e-57) {
		tmp = x + (y * x);
	} else if (y <= -5.9e-102) {
		tmp = y * z;
	} else if (y <= 2.8e-53) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x + z)
	tmp = 0
	if y <= -1.82:
		tmp = t_0
	elif y <= -1.8e-57:
		tmp = x + (y * x)
	elif y <= -5.9e-102:
		tmp = y * z
	elif y <= 2.8e-53:
		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 <= -1.82)
		tmp = t_0;
	elseif (y <= -1.8e-57)
		tmp = Float64(x + Float64(y * x));
	elseif (y <= -5.9e-102)
		tmp = Float64(y * z);
	elseif (y <= 2.8e-53)
		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 <= -1.82)
		tmp = t_0;
	elseif (y <= -1.8e-57)
		tmp = x + (y * x);
	elseif (y <= -5.9e-102)
		tmp = y * z;
	elseif (y <= 2.8e-53)
		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, -1.82], t$95$0, If[LessEqual[y, -1.8e-57], N[(x + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.9e-102], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.8e-53], x, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.82000000000000006 or 2.79999999999999985e-53 < y

   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-def 99.2%

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

      2. +-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around inf 95.1%

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

      1. +-commutative 95.1%

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

   8. Simplified 95.1%

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

   if -1.82000000000000006 < y < -1.8000000000000001e-57

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if -1.8000000000000001e-57 < y < -5.9000000000000003e-102

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

      1. fma-def 100.0%

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

      2. +-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around 0 86.0%

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

   if -5.9000000000000003e-102 < y < 2.79999999999999985e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.82:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-57}:\\ \;\;\;\;x + y \cdot x\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{-102}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.019\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.019))) (* y (+ x z)) (+ x (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.019)) {
		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 <= 0.019d0))) 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 <= 0.019)) {
		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 <= 0.019):
		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 <= 0.019))
		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 <= 0.019)))
		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, 0.019]], $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 0.0189999999999999995 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.7%

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

      1. fma-def 99.1%

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

      2. +-commutative 99.1%

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

   5. Simplified 99.1%

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

   6. Taylor expanded in y around inf 98.4%

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

      1. +-commutative 98.4%

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

   8. Simplified 98.4%

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

   if -1 < y < 0.0189999999999999995

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.019\right):\\ \;\;\;\;y \cdot \left(x + z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8200 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8200.0) (not (<= y 1.0))) (* y x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8200.0) || !(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 <= (-8200.0d0)) .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 <= -8200.0) || !(y <= 1.0)) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8200.0) or not (y <= 1.0):
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8200.0) || !(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 <= -8200.0) || ~((y <= 1.0)))
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8200.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8200 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 54.3%

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

      1. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in y around inf 53.2%

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

      1. *-commutative 53.2%

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

   8. Simplified 53.2%

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

   if -8200 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.6%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8200 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
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: 36.4% 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 y around 0 40.0%

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

4. Final simplification 40.0%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024026 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))