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

Percentage Accurate: 95.8% → 98.9%

Time: 8.2s

Alternatives: 10

Speedup: 0.6×

• 21.4% 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: 95.8% 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: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 0.084\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -23.0) (not (<= z 0.084)))
   (* z (* x (+ y -1.0)))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -23.0) || !(z <= 0.084)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-23.0d0)) .or. (.not. (z <= 0.084d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -23.0) || !(z <= 0.084)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -23.0) or not (z <= 0.084):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -23.0) || !(z <= 0.084))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -23.0) || ~((z <= 0.084)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -23.0], N[Not[LessEqual[z, 0.084]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -23 or 0.0840000000000000052 < z

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*r* 99.3%

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

      3. *-commutative 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -23 < z < 0.0840000000000000052

   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 98.7%

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

      1. *-commutative 98.7%

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

   6. Simplified 98.7%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 0.084\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 81.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+194} \lor \neg \left(y \leq -1.15 \cdot 10^{+137}\right) \land \left(y \leq -1.9 \cdot 10^{+90} \lor \neg \left(y \leq 8 \cdot 10^{+39}\right)\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.5e+194)
         (and (not (<= y -1.15e+137)) (or (<= y -1.9e+90) (not (<= y 8e+39)))))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.5e+194) || (!(y <= -1.15e+137) && ((y <= -1.9e+90) || !(y <= 8e+39)))) {
		tmp = x * (z * y);
	} 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 <= (-1.5d+194)) .or. (.not. (y <= (-1.15d+137))) .and. (y <= (-1.9d+90)) .or. (.not. (y <= 8d+39))) then
        tmp = x * (z * y)
    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 <= -1.5e+194) || (!(y <= -1.15e+137) && ((y <= -1.9e+90) || !(y <= 8e+39)))) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.5e+194) or (not (y <= -1.15e+137) and ((y <= -1.9e+90) or not (y <= 8e+39))):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.5e+194) || (!(y <= -1.15e+137) && ((y <= -1.9e+90) || !(y <= 8e+39))))
		tmp = Float64(x * Float64(z * y));
	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 <= -1.5e+194) || (~((y <= -1.15e+137)) && ((y <= -1.9e+90) || ~((y <= 8e+39)))))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.5e+194], And[N[Not[LessEqual[y, -1.15e+137]], $MachinePrecision], Or[LessEqual[y, -1.9e+90], N[Not[LessEqual[y, 8e+39]], $MachinePrecision]]]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5000000000000002e194 or -1.15e137 < y < -1.9000000000000001e90 or 7.99999999999999952e39 < y

   1. Initial program 91.9%

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

   3. Taylor expanded in y around inf 78.8%

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

      1. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   if -1.5000000000000002e194 < y < -1.15e137 or -1.9000000000000001e90 < y < 7.99999999999999952e39

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 92.3%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+194} \lor \neg \left(y \leq -1.15 \cdot 10^{+137}\right) \land \left(y \leq -1.9 \cdot 10^{+90} \lor \neg \left(y \leq 8 \cdot 10^{+39}\right)\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* z y))))
   (if (<= z -8e+33)
     t_0
     (if (<= z -1e-49)
       t_1
       (if (<= z 5.8e-46) x (if (<= z 4.8e+61) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -8e+33) {
		tmp = t_0;
	} else if (z <= -1e-49) {
		tmp = t_1;
	} else if (z <= 5.8e-46) {
		tmp = x;
	} else if (z <= 4.8e+61) {
		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 * (z * y)
    if (z <= (-8d+33)) then
        tmp = t_0
    else if (z <= (-1d-49)) then
        tmp = t_1
    else if (z <= 5.8d-46) then
        tmp = x
    else if (z <= 4.8d+61) 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 * (z * y);
	double tmp;
	if (z <= -8e+33) {
		tmp = t_0;
	} else if (z <= -1e-49) {
		tmp = t_1;
	} else if (z <= 5.8e-46) {
		tmp = x;
	} else if (z <= 4.8e+61) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (z * y)
	tmp = 0
	if z <= -8e+33:
		tmp = t_0
	elif z <= -1e-49:
		tmp = t_1
	elif z <= 5.8e-46:
		tmp = x
	elif z <= 4.8e+61:
		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(z * y))
	tmp = 0.0
	if (z <= -8e+33)
		tmp = t_0;
	elseif (z <= -1e-49)
		tmp = t_1;
	elseif (z <= 5.8e-46)
		tmp = x;
	elseif (z <= 4.8e+61)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -8e+33)
		tmp = t_0;
	elseif (z <= -1e-49)
		tmp = t_1;
	elseif (z <= 5.8e-46)
		tmp = x;
	elseif (z <= 4.8e+61)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+33], t$95$0, If[LessEqual[z, -1e-49], t$95$1, If[LessEqual[z, 5.8e-46], x, If[LessEqual[z, 4.8e+61], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999996e33 or 4.7999999999999998e61 < z

   1. Initial program 92.6%

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

   3. Taylor expanded in z around inf 92.6%

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

      1. *-commutative 92.6%

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

      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%

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

   6. Taylor expanded in y around 0 63.1%

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

      1. neg-mul-1 63.1%

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

   8. Simplified 63.1%

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

   if -7.9999999999999996e33 < z < -9.99999999999999936e-50 or 5.80000000000000009e-46 < z < 4.7999999999999998e61

   1. Initial program 99.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   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 -9.99999999999999936e-50 < z < 5.80000000000000009e-46

   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 86.4%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+33}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+61}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot y\right)\\ t_1 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+194}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z y))) (t_1 (* x (- 1.0 z))))
   (if (<= y -1.45e+194)
     t_0
     (if (<= y -1.1e+137)
       t_1
       (if (<= y -2e+91) t_0 (if (<= y 8.2e+40) t_1 (* y (* z x))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double t_1 = x * (1.0 - z);
	double tmp;
	if (y <= -1.45e+194) {
		tmp = t_0;
	} else if (y <= -1.1e+137) {
		tmp = t_1;
	} else if (y <= -2e+91) {
		tmp = t_0;
	} else if (y <= 8.2e+40) {
		tmp = t_1;
	} else {
		tmp = y * (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * y)
    t_1 = x * (1.0d0 - z)
    if (y <= (-1.45d+194)) then
        tmp = t_0
    else if (y <= (-1.1d+137)) then
        tmp = t_1
    else if (y <= (-2d+91)) then
        tmp = t_0
    else if (y <= 8.2d+40) then
        tmp = t_1
    else
        tmp = y * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double t_1 = x * (1.0 - z);
	double tmp;
	if (y <= -1.45e+194) {
		tmp = t_0;
	} else if (y <= -1.1e+137) {
		tmp = t_1;
	} else if (y <= -2e+91) {
		tmp = t_0;
	} else if (y <= 8.2e+40) {
		tmp = t_1;
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * y)
	t_1 = x * (1.0 - z)
	tmp = 0
	if y <= -1.45e+194:
		tmp = t_0
	elif y <= -1.1e+137:
		tmp = t_1
	elif y <= -2e+91:
		tmp = t_0
	elif y <= 8.2e+40:
		tmp = t_1
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * y))
	t_1 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.45e+194)
		tmp = t_0;
	elseif (y <= -1.1e+137)
		tmp = t_1;
	elseif (y <= -2e+91)
		tmp = t_0;
	elseif (y <= 8.2e+40)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * y);
	t_1 = x * (1.0 - z);
	tmp = 0.0;
	if (y <= -1.45e+194)
		tmp = t_0;
	elseif (y <= -1.1e+137)
		tmp = t_1;
	elseif (y <= -2e+91)
		tmp = t_0;
	elseif (y <= 8.2e+40)
		tmp = t_1;
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+194], t$95$0, If[LessEqual[y, -1.1e+137], t$95$1, If[LessEqual[y, -2e+91], t$95$0, If[LessEqual[y, 8.2e+40], t$95$1, N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e194 or -1.10000000000000008e137 < y < -2.00000000000000016e91

   1. Initial program 96.2%

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

   3. Taylor expanded in y around inf 88.4%

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

      1. *-commutative 88.4%

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

   5. Simplified 88.4%

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

   if -1.45e194 < y < -1.10000000000000008e137 or -2.00000000000000016e91 < y < 8.2000000000000003e40

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 92.3%

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

   if 8.2000000000000003e40 < y

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf 80.4%

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

   4. Taylor expanded in y around inf 79.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+91}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot y\right)\\ t_1 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;y \leq -1.45 \cdot 10^{+194}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z y))) (t_1 (* x (- 1.0 z))))
   (if (<= y -1.45e+194)
     t_0
     (if (<= y -1.02e+137)
       t_1
       (if (<= y -8.5e+90) t_0 (if (<= y 1.05e+40) t_1 (* z (* x y))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double t_1 = x * (1.0 - z);
	double tmp;
	if (y <= -1.45e+194) {
		tmp = t_0;
	} else if (y <= -1.02e+137) {
		tmp = t_1;
	} else if (y <= -8.5e+90) {
		tmp = t_0;
	} else if (y <= 1.05e+40) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * y)
    t_1 = x * (1.0d0 - z)
    if (y <= (-1.45d+194)) then
        tmp = t_0
    else if (y <= (-1.02d+137)) then
        tmp = t_1
    else if (y <= (-8.5d+90)) then
        tmp = t_0
    else if (y <= 1.05d+40) then
        tmp = t_1
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double t_1 = x * (1.0 - z);
	double tmp;
	if (y <= -1.45e+194) {
		tmp = t_0;
	} else if (y <= -1.02e+137) {
		tmp = t_1;
	} else if (y <= -8.5e+90) {
		tmp = t_0;
	} else if (y <= 1.05e+40) {
		tmp = t_1;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * y)
	t_1 = x * (1.0 - z)
	tmp = 0
	if y <= -1.45e+194:
		tmp = t_0
	elif y <= -1.02e+137:
		tmp = t_1
	elif y <= -8.5e+90:
		tmp = t_0
	elif y <= 1.05e+40:
		tmp = t_1
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * y))
	t_1 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.45e+194)
		tmp = t_0;
	elseif (y <= -1.02e+137)
		tmp = t_1;
	elseif (y <= -8.5e+90)
		tmp = t_0;
	elseif (y <= 1.05e+40)
		tmp = t_1;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * y);
	t_1 = x * (1.0 - z);
	tmp = 0.0;
	if (y <= -1.45e+194)
		tmp = t_0;
	elseif (y <= -1.02e+137)
		tmp = t_1;
	elseif (y <= -8.5e+90)
		tmp = t_0;
	elseif (y <= 1.05e+40)
		tmp = t_1;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.45e+194], t$95$0, If[LessEqual[y, -1.02e+137], t$95$1, If[LessEqual[y, -8.5e+90], t$95$0, If[LessEqual[y, 1.05e+40], t$95$1, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e194 or -1.02000000000000004e137 < y < -8.5000000000000002e90

   1. Initial program 96.2%

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

   3. Taylor expanded in y around inf 88.4%

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

      1. *-commutative 88.4%

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

   5. Simplified 88.4%

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

   if -1.45e194 < y < -1.02000000000000004e137 or -8.5000000000000002e90 < y < 1.05000000000000005e40

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 92.3%

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

   if 1.05000000000000005e40 < y

   1. Initial program 89.8%

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

   3. Taylor expanded in z around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-*r* 80.7%

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

      3. *-commutative 80.7%

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

      4. sub-neg 80.7%

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

      5. metadata-eval 80.7%

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

   5. Simplified 80.7%

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

   6. Taylor expanded in y around inf 80.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+194}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+90}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-50} \lor \neg \left(z \leq 2.7 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -9e-50) (not (<= z 2.7e-47))) (* x (* z (+ y -1.0))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9e-50) || !(z <= 2.7e-47)) {
		tmp = x * (z * (y + -1.0));
	} 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) :: tmp
    if ((z <= (-9d-50)) .or. (.not. (z <= 2.7d-47))) then
        tmp = x * (z * (y + (-1.0d0)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -9e-50) || !(z <= 2.7e-47)) {
		tmp = x * (z * (y + -1.0));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -9e-50) or not (z <= 2.7e-47):
		tmp = x * (z * (y + -1.0))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -9e-50) || !(z <= 2.7e-47))
		tmp = Float64(x * Float64(z * Float64(y + -1.0)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -9e-50) || ~((z <= 2.7e-47)))
		tmp = x * (z * (y + -1.0));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -9e-50], N[Not[LessEqual[z, 2.7e-47]], $MachinePrecision]], N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999924e-50 or 2.6999999999999998e-47 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 89.2%

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

   if -8.99999999999999924e-50 < z < 2.6999999999999998e-47

   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 86.4%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-50} \lor \neg \left(z \leq 2.7 \cdot 10^{-47}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-50} \lor \neg \left(z \leq 2.2 \cdot 10^{-45}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.9e-50) (not (<= z 2.2e-45))) (* z (* x (+ y -1.0))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.9e-50) || !(z <= 2.2e-45)) {
		tmp = z * (x * (y + -1.0));
	} 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) :: tmp
    if ((z <= (-2.9d-50)) .or. (.not. (z <= 2.2d-45))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.9e-50) || !(z <= 2.2e-45)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.9e-50) or not (z <= 2.2e-45):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.9e-50) || !(z <= 2.2e-45))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.9e-50) || ~((z <= 2.2e-45)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.9e-50], N[Not[LessEqual[z, 2.2e-45]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.90000000000000008e-50 or 2.19999999999999993e-45 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in z around inf 89.2%

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

      1. *-commutative 89.2%

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

      2. associate-*r* 94.3%

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

      3. *-commutative 94.3%

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

      4. sub-neg 94.3%

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

      5. metadata-eval 94.3%

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

   5. Simplified 94.3%

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

   if -2.90000000000000008e-50 < z < 2.19999999999999993e-45

   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 86.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-50} \lor \neg \left(z \leq 2.2 \cdot 10^{-45}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 0.084\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -23.0) (not (<= z 0.084))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -23.0) || !(z <= 0.084)) {
		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 <= (-23.0d0)) .or. (.not. (z <= 0.084d0))) 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 <= -23.0) || !(z <= 0.084)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -23.0) or not (z <= 0.084):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -23.0) || !(z <= 0.084))
		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 <= -23.0) || ~((z <= 0.084)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -23.0], N[Not[LessEqual[z, 0.084]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -23 or 0.0840000000000000052 < z

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 93.5%

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

      1. *-commutative 93.5%

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

      2. associate-*r* 99.3%

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

      3. *-commutative 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in y around 0 57.1%

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

      1. neg-mul-1 57.1%

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

   8. Simplified 57.1%

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

   if -23 < z < 0.0840000000000000052

   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 78.3%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23 \lor \neg \left(z \leq 0.084\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+130) (* z (* x (+ y -1.0))) (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+130) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * (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 <= (-5.8d+130)) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+130) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+130:
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+130)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+130)
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+130], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.7999999999999998e130

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf 88.0%

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

      1. *-commutative 88.0%

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

      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%

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

   if -5.7999999999999998e130 < z

   1. Initial program 98.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+130}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.3% 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 97.0%

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

3. Taylor expanded in z around 0 41.0%

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

4. Final simplification 41.0%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.8% 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 2024055 
(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))))