Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 95.6% → 99.0%

Time: 9.0s

Alternatives: 12

Speedup: 0.5×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * 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 * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * 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 * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+47}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 -5e+118)
     (* z (- (* y x) x))
     (if (<= t_0 1e+47) (+ x (* x (* z (+ y -1.0)))) (* z (* x (+ y -1.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -5e+118) {
		tmp = z * ((y * x) - x);
	} else if (t_0 <= 1e+47) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - y) * z
    if (t_0 <= (-5d+118)) then
        tmp = z * ((y * x) - x)
    else if (t_0 <= 1d+47) then
        tmp = x + (x * (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -5e+118) {
		tmp = z * ((y * x) - x);
	} else if (t_0 <= 1e+47) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= -5e+118:
		tmp = z * ((y * x) - x)
	elif t_0 <= 1e+47:
		tmp = x + (x * (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= -5e+118)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (t_0 <= 1e+47)
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= -5e+118)
		tmp = z * ((y * x) - x);
	elseif (t_0 <= 1e+47)
		tmp = x + (x * (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+118], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+47], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -4.99999999999999972e118

   1. Initial program 91.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.1%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   6. Simplified 99.9%

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

   if -4.99999999999999972e118 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1e47

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

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

   if 1e47 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 89.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 10^{+47}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+47}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 -5e+118)
     (* z (- (* y x) x))
     (if (<= t_0 1e+47)
       (* x (+ 1.0 (* z (+ y -1.0))))
       (* z (* x (+ y -1.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -5e+118) {
		tmp = z * ((y * x) - x);
	} else if (t_0 <= 1e+47) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - y) * z
    if (t_0 <= (-5d+118)) then
        tmp = z * ((y * x) - x)
    else if (t_0 <= 1d+47) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -5e+118) {
		tmp = z * ((y * x) - x);
	} else if (t_0 <= 1e+47) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= -5e+118:
		tmp = z * ((y * x) - x)
	elif t_0 <= 1e+47:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= -5e+118)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (t_0 <= 1e+47)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= -5e+118)
		tmp = z * ((y * x) - x);
	elseif (t_0 <= 1e+47)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+118], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+47], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -4.99999999999999972e118

   1. Initial program 91.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 80.1%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   6. Simplified 99.9%

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

   if -4.99999999999999972e118 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1e47

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   if 1e47 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 89.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 10^{+47}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.46 \cdot 10^{+105}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-25}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -1.46e+105)
     t_0
     (if (<= z -4.4e-25)
       t_1
       (if (<= z 1.4e-59) x (if (<= z 3e+54) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -1.46e+105) {
		tmp = t_0;
	} else if (z <= -4.4e-25) {
		tmp = t_1;
	} else if (z <= 1.4e-59) {
		tmp = x;
	} else if (z <= 3e+54) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * -x
    t_1 = x * (y * z)
    if (z <= (-1.46d+105)) then
        tmp = t_0
    else if (z <= (-4.4d-25)) then
        tmp = t_1
    else if (z <= 1.4d-59) then
        tmp = x
    else if (z <= 3d+54) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -1.46e+105) {
		tmp = t_0;
	} else if (z <= -4.4e-25) {
		tmp = t_1;
	} else if (z <= 1.4e-59) {
		tmp = x;
	} else if (z <= 3e+54) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (y * z)
	tmp = 0
	if z <= -1.46e+105:
		tmp = t_0
	elif z <= -4.4e-25:
		tmp = t_1
	elif z <= 1.4e-59:
		tmp = x
	elif z <= 3e+54:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.46e+105)
		tmp = t_0;
	elseif (z <= -4.4e-25)
		tmp = t_1;
	elseif (z <= 1.4e-59)
		tmp = x;
	elseif (z <= 3e+54)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.46e+105)
		tmp = t_0;
	elseif (z <= -4.4e-25)
		tmp = t_1;
	elseif (z <= 1.4e-59)
		tmp = x;
	elseif (z <= 3e+54)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.46e+105], t$95$0, If[LessEqual[z, -4.4e-25], t$95$1, If[LessEqual[z, 1.4e-59], x, If[LessEqual[z, 3e+54], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4600000000000001e105 or 2.9999999999999999e54 < z

   1. Initial program 88.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.0%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. neg-mul-1 99.9%

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

      2. +-commutative 99.9%

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

      3. unsub-neg 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around 0 56.4%

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

      1. neg-mul-1 56.4%

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

   9. Simplified 56.4%

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

   if -1.4600000000000001e105 < z < -4.4000000000000004e-25 or 1.3999999999999999e-59 < z < 2.9999999999999999e54

   1. Initial program 96.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.8%

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

      1. *-commutative 65.8%

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

   5. Simplified 65.8%

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

   if -4.4000000000000004e-25 < z < 1.3999999999999999e-59

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 81.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{+105}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-25}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 8.8 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1) (not (<= z 8.8e-31)))
   (* z (* x (+ y -1.0)))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 8.8e-31)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (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 ((z <= (-1.1d0)) .or. (.not. (z <= 8.8d-31))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1) || !(z <= 8.8e-31)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1) or not (z <= 8.8e-31):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1) || !(z <= 8.8e-31))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1) || ~((z <= 8.8e-31)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1], N[Not[LessEqual[z, 8.8e-31]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1000000000000001 or 8.80000000000000038e-31 < z

   1. Initial program 90.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*r* 98.1%

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

      3. *-commutative 98.1%

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

      4. sub-neg 98.1%

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

      5. metadata-eval 98.1%

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

   5. Simplified 98.1%

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

   if -1.1000000000000001 < z < 8.80000000000000038e-31

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around inf 99.8%

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

      1. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 99.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \lor \neg \left(z \leq 8.8 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -105 \lor \neg \left(y \leq 0.0069\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -105.0) (not (<= y 0.0069)))
   (* x (+ 1.0 (* y z)))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -105.0) || !(y <= 0.0069)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x - (z * 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 <= (-105.0d0)) .or. (.not. (y <= 0.0069d0))) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -105.0) || !(y <= 0.0069)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -105.0) or not (y <= 0.0069):
		tmp = x * (1.0 + (y * z))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -105.0) || !(y <= 0.0069))
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -105.0) || ~((y <= 0.0069)))
		tmp = x * (1.0 + (y * z));
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -105.0], N[Not[LessEqual[y, 0.0069]], $MachinePrecision]], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -105 or 0.0068999999999999999 < y

   1. Initial program 91.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 91.3%

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

   4. Taylor expanded in y around inf 90.1%

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

      1. *-commutative 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in x around 0 90.1%

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

   if -105 < y < 0.0068999999999999999

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*r/ 100.0%

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

      4. metadata-eval 100.0%

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

      5. fma-neg 100.0%

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

      6. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in y around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. sub-neg 100.0%

         \[\leadsto \color{blue}{x - x \cdot z} \]

   8. Simplified 100.0%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -105 \lor \neg \left(y \leq 0.0069\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.9:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.9)
   (* z (- (* y x) x))
   (if (<= z 8.8e-31) (* x (+ 1.0 (* y z))) (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.9) {
		tmp = z * ((y * x) - x);
	} else if (z <= 8.8e-31) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.9d0)) then
        tmp = z * ((y * x) - x)
    else if (z <= 8.8d-31) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.9) {
		tmp = z * ((y * x) - x);
	} else if (z <= 8.8e-31) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.9:
		tmp = z * ((y * x) - x)
	elif z <= 8.8e-31:
		tmp = x * (1.0 + (y * z))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.9)
		tmp = Float64(z * Float64(Float64(y * x) - x));
	elseif (z <= 8.8e-31)
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.9)
		tmp = z * ((y * x) - x);
	elseif (z <= 8.8e-31)
		tmp = x * (1.0 + (y * z));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.9], N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-31], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.900000000000000022

   1. Initial program 89.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.2%

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

   4. Taylor expanded in z around inf 98.4%

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

      1. neg-mul-1 98.4%

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

      2. +-commutative 98.4%

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

      3. unsub-neg 98.4%

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

   6. Simplified 98.4%

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

   if -0.900000000000000022 < z < 8.80000000000000038e-31

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around inf 99.8%

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

      1. *-commutative 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 99.8%

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

   if 8.80000000000000038e-31 < z

   1. Initial program 92.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. associate-*r* 97.8%

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

      3. *-commutative 97.8%

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

      4. sub-neg 97.8%

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

      5. metadata-eval 97.8%

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

   5. Simplified 97.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.9:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+43} \lor \neg \left(y \leq 3.1 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+43) (not (<= y 3.1e+33))) (* y (* z x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+43) || !(y <= 3.1e+33)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - 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 <= (-2.4d+43)) .or. (.not. (y <= 3.1d+33))) then
        tmp = y * (z * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+43) || !(y <= 3.1e+33)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+43) or not (y <= 3.1e+33):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+43) || !(y <= 3.1e+33))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+43) || ~((y <= 3.1e+33)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+43], N[Not[LessEqual[y, 3.1e+33]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.40000000000000023e43 or 3.1e33 < y

   1. Initial program 89.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 82.3%

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

   4. Taylor expanded in y around inf 73.4%

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

   if -2.40000000000000023e43 < y < 3.1e33

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+43} \lor \neg \left(y \leq 3.1 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+38} \lor \neg \left(y \leq 1.4 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.4e+38) (not (<= y 1.4e+34))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+38) || !(y <= 1.4e+34)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - 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 <= (-2.4d+38)) .or. (.not. (y <= 1.4d+34))) then
        tmp = x * (y * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.4e+38) || !(y <= 1.4e+34)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.4e+38) or not (y <= 1.4e+34):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.4e+38) || !(y <= 1.4e+34))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.4e+38) || ~((y <= 1.4e+34)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.4e+38], N[Not[LessEqual[y, 1.4e+34]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.40000000000000017e38 or 1.40000000000000004e34 < y

   1. Initial program 89.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

   5. Simplified 67.0%

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

   if -2.40000000000000017e38 < y < 1.40000000000000004e34

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+38} \lor \neg \left(y \leq 1.4 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+33}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+43)
   (* y (* z x))
   (if (<= y 1.6e+33) (- x (* z x)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+43) {
		tmp = y * (z * x);
	} else if (y <= 1.6e+33) {
		tmp = x - (z * x);
	} else {
		tmp = z * (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 <= (-1.35d+43)) then
        tmp = y * (z * x)
    else if (y <= 1.6d+33) then
        tmp = x - (z * x)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+43) {
		tmp = y * (z * x);
	} else if (y <= 1.6e+33) {
		tmp = x - (z * x);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+43:
		tmp = y * (z * x)
	elif y <= 1.6e+33:
		tmp = x - (z * x)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+43)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 1.6e+33)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e+43)
		tmp = y * (z * x);
	elseif (y <= 1.6e+33)
		tmp = x - (z * x);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+43], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+33], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3500000000000001e43

   1. Initial program 90.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.9%

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

   4. Taylor expanded in y around inf 73.1%

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

   if -1.3500000000000001e43 < y < 1.60000000000000009e33

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 100.0%

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

      1. associate-*r* 100.0%

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

      2. flip-- 100.0%

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

      3. associate-*r/ 99.2%

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

      4. metadata-eval 99.2%

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

      5. fma-neg 99.2%

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

      6. metadata-eval 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in y around 0 95.1%

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

      1. mul-1-neg 95.1%

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

      2. sub-neg 95.1%

         \[\leadsto \color{blue}{x - x \cdot z} \]

   8. Simplified 95.1%

      \[\leadsto \color{blue}{x - x \cdot z} \]

   if 1.60000000000000009e33 < y

   1. Initial program 89.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.6%

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

   4. Taylor expanded in y around inf 65.0%

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

      1. associate-*r* 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+33}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.45e+44)
   (* y (* z x))
   (if (<= y 6.2e+33) (* x (- 1.0 z)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.45e+44) {
		tmp = y * (z * x);
	} else if (y <= 6.2e+33) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (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 <= (-1.45d+44)) then
        tmp = y * (z * x)
    else if (y <= 6.2d+33) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.45e+44) {
		tmp = y * (z * x);
	} else if (y <= 6.2e+33) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.45e+44:
		tmp = y * (z * x)
	elif y <= 6.2e+33:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.45e+44)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 6.2e+33)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.45e+44)
		tmp = y * (z * x);
	elseif (y <= 6.2e+33)
		tmp = x * (1.0 - z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.45e+44], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e+33], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4500000000000001e44

   1. Initial program 90.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 87.9%

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

   4. Taylor expanded in y around inf 73.1%

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

   if -1.4500000000000001e44 < y < 6.2e33

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.0%

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

   if 6.2e33 < y

   1. Initial program 89.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.6%

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

   4. Taylor expanded in y around inf 65.0%

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

      1. associate-*r* 76.0%

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

   6. Simplified 76.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-13} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.1e-13) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-13) || !(z <= 1.0)) {
		tmp = z * -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 ((z <= (-4.1d-13)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-13) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.1e-13) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.1e-13) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.1e-13) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.1e-13], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.1000000000000002e-13 or 1 < z

   1. Initial program 90.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.9%

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

   4. Taylor expanded in z around inf 98.1%

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

      1. neg-mul-1 98.1%

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

      2. +-commutative 98.1%

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

      3. unsub-neg 98.1%

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

   6. Simplified 98.1%

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

   7. Taylor expanded in y around 0 49.6%

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

      1. neg-mul-1 49.6%

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

   9. Simplified 49.6%

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

   if -4.1000000000000002e-13 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 73.9%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-13} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.6% accurate, 9.0× 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 95.1%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in z around 0 39.7%

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

Developer target: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t\_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))