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

Percentage Accurate: 96.0% → 97.5%

Time: 9.1s

Alternatives: 10

Speedup: 0.8×

• 21.3% 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: 96.0% 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: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.5e+103) (* x (+ 1.0 (* z (+ y -1.0)))) (* (+ y -1.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.5e+103) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (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 (z <= 1.5d+103) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = (y + (-1.0d0)) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.5e+103) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.5e+103:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = (y + -1.0) * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.5e+103)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.5e+103)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = (y + -1.0) * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.5e+103], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.5e103

   1. Initial program 98.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 1.5e103 < z

   1. Initial program 87.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 87.0%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 2: 66.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;z \leq -2.95 \cdot 10^{+184}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2900000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+143} \lor \neg \left(z \leq 9 \cdot 10^{+200}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* y (* z x))))
   (if (<= z -2.95e+184)
     t_0
     (if (<= z -2.4e+97)
       t_1
       (if (<= z -1.65e+38)
         t_0
         (if (<= z -2.4e-30)
           (* x (* z y))
           (if (<= z 2900000.0)
             x
             (if (or (<= z 7e+143) (not (<= z 9e+200))) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = y * (z * x);
	double tmp;
	if (z <= -2.95e+184) {
		tmp = t_0;
	} else if (z <= -2.4e+97) {
		tmp = t_1;
	} else if (z <= -1.65e+38) {
		tmp = t_0;
	} else if (z <= -2.4e-30) {
		tmp = x * (z * y);
	} else if (z <= 2900000.0) {
		tmp = x;
	} else if ((z <= 7e+143) || !(z <= 9e+200)) {
		tmp = t_0;
	} 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 = z * -x
    t_1 = y * (z * x)
    if (z <= (-2.95d+184)) then
        tmp = t_0
    else if (z <= (-2.4d+97)) then
        tmp = t_1
    else if (z <= (-1.65d+38)) then
        tmp = t_0
    else if (z <= (-2.4d-30)) then
        tmp = x * (z * y)
    else if (z <= 2900000.0d0) then
        tmp = x
    else if ((z <= 7d+143) .or. (.not. (z <= 9d+200))) then
        tmp = t_0
    else
        tmp = t_1
    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 = y * (z * x);
	double tmp;
	if (z <= -2.95e+184) {
		tmp = t_0;
	} else if (z <= -2.4e+97) {
		tmp = t_1;
	} else if (z <= -1.65e+38) {
		tmp = t_0;
	} else if (z <= -2.4e-30) {
		tmp = x * (z * y);
	} else if (z <= 2900000.0) {
		tmp = x;
	} else if ((z <= 7e+143) || !(z <= 9e+200)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = y * (z * x)
	tmp = 0
	if z <= -2.95e+184:
		tmp = t_0
	elif z <= -2.4e+97:
		tmp = t_1
	elif z <= -1.65e+38:
		tmp = t_0
	elif z <= -2.4e-30:
		tmp = x * (z * y)
	elif z <= 2900000.0:
		tmp = x
	elif (z <= 7e+143) or not (z <= 9e+200):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(y * Float64(z * x))
	tmp = 0.0
	if (z <= -2.95e+184)
		tmp = t_0;
	elseif (z <= -2.4e+97)
		tmp = t_1;
	elseif (z <= -1.65e+38)
		tmp = t_0;
	elseif (z <= -2.4e-30)
		tmp = Float64(x * Float64(z * y));
	elseif (z <= 2900000.0)
		tmp = x;
	elseif ((z <= 7e+143) || !(z <= 9e+200))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = y * (z * x);
	tmp = 0.0;
	if (z <= -2.95e+184)
		tmp = t_0;
	elseif (z <= -2.4e+97)
		tmp = t_1;
	elseif (z <= -1.65e+38)
		tmp = t_0;
	elseif (z <= -2.4e-30)
		tmp = x * (z * y);
	elseif (z <= 2900000.0)
		tmp = x;
	elseif ((z <= 7e+143) || ~((z <= 9e+200)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.95e+184], t$95$0, If[LessEqual[z, -2.4e+97], t$95$1, If[LessEqual[z, -1.65e+38], t$95$0, If[LessEqual[z, -2.4e-30], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2900000.0], x, If[Or[LessEqual[z, 7e+143], N[Not[LessEqual[z, 9e+200]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9500000000000001e184 or -2.4e97 < z < -1.65e38 or 2.9e6 < z < 7.00000000000000017e143 or 8.99999999999999939e200 < z

   1. Initial program 95.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 94.0%

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

   3. Taylor expanded in y around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. distribute-rgt-neg-in 75.2%

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

   5. Simplified 75.2%

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

   if -2.9500000000000001e184 < z < -2.4e97 or 7.00000000000000017e143 < z < 8.99999999999999939e200

   1. Initial program 82.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. add-cube-cbrt 81.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)} \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right) \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}} \]

      2. pow3 81.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   3. Applied egg-rr 81.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   4. Taylor expanded in y around inf 57.6%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot \left(y \cdot z\right)}}\right)}^{3} \]
   5. Step-by-step derivation

      1. *-commutative 57.9%

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

   6. Simplified 57.6%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot \left(z \cdot y\right)}}\right)}^{3} \]
   7. Step-by-step derivation

      1. rem-cube-cbrt 57.9%

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

      2. *-commutative 57.9%

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

      3. associate-*r* 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-*r* 82.4%

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

   8. Applied egg-rr 82.4%

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

   if -1.65e38 < z < -2.39999999999999985e-30

   1. Initial program 99.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 89.9%

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

      1. *-commutative 89.9%

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

   4. Simplified 89.9%

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

   if -2.39999999999999985e-30 < z < 2.9e6

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 78.6%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.95 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+97}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-30}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2900000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+143} \lor \neg \left(z \leq 9 \cdot 10^{+200}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 3: 65.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2900000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+157} \lor \neg \left(z \leq 9 \cdot 10^{+200}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -7.8e+38)
     t_0
     (if (<= z -3.4e-15)
       (* x (* z y))
       (if (<= z 2900000.0)
         x
         (if (or (<= z 8.8e+157) (not (<= z 9e+200))) t_0 (* z (* x y))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -7.8e+38) {
		tmp = t_0;
	} else if (z <= -3.4e-15) {
		tmp = x * (z * y);
	} else if (z <= 2900000.0) {
		tmp = x;
	} else if ((z <= 8.8e+157) || !(z <= 9e+200)) {
		tmp = t_0;
	} 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) :: tmp
    t_0 = z * -x
    if (z <= (-7.8d+38)) then
        tmp = t_0
    else if (z <= (-3.4d-15)) then
        tmp = x * (z * y)
    else if (z <= 2900000.0d0) then
        tmp = x
    else if ((z <= 8.8d+157) .or. (.not. (z <= 9d+200))) then
        tmp = t_0
    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 = z * -x;
	double tmp;
	if (z <= -7.8e+38) {
		tmp = t_0;
	} else if (z <= -3.4e-15) {
		tmp = x * (z * y);
	} else if (z <= 2900000.0) {
		tmp = x;
	} else if ((z <= 8.8e+157) || !(z <= 9e+200)) {
		tmp = t_0;
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -7.8e+38:
		tmp = t_0
	elif z <= -3.4e-15:
		tmp = x * (z * y)
	elif z <= 2900000.0:
		tmp = x
	elif (z <= 8.8e+157) or not (z <= 9e+200):
		tmp = t_0
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -7.8e+38)
		tmp = t_0;
	elseif (z <= -3.4e-15)
		tmp = Float64(x * Float64(z * y));
	elseif (z <= 2900000.0)
		tmp = x;
	elseif ((z <= 8.8e+157) || !(z <= 9e+200))
		tmp = t_0;
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -7.8e+38)
		tmp = t_0;
	elseif (z <= -3.4e-15)
		tmp = x * (z * y);
	elseif (z <= 2900000.0)
		tmp = x;
	elseif ((z <= 8.8e+157) || ~((z <= 9e+200)))
		tmp = t_0;
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -7.8e+38], t$95$0, If[LessEqual[z, -3.4e-15], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2900000.0], x, If[Or[LessEqual[z, 8.8e+157], N[Not[LessEqual[z, 9e+200]], $MachinePrecision]], t$95$0, N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.80000000000000047e38 or 2.9e6 < z < 8.8000000000000005e157 or 8.99999999999999939e200 < z

   1. Initial program 94.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 93.2%

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

   3. Taylor expanded in y around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. distribute-rgt-neg-in 70.1%

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

   5. Simplified 70.1%

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

   if -7.80000000000000047e38 < z < -3.4e-15

   1. Initial program 99.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 89.9%

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

      1. *-commutative 89.9%

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

   4. Simplified 89.9%

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

   if -3.4e-15 < z < 2.9e6

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 78.6%

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

   if 8.8000000000000005e157 < z < 8.99999999999999939e200

   1. Initial program 68.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 68.3%

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

      1. *-commutative 68.3%

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

      2. associate-*l* 99.7%

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

      3. sub-neg 99.7%

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

      4. metadata-eval 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 99.7%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2900000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+157} \lor \neg \left(z \leq 9 \cdot 10^{+200}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4: 94.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+29} \lor \neg \left(y \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.2e+29) (not (<= y 2.85e-5)))
   (* x (+ 1.0 (* z y)))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e+29) || !(y <= 2.85e-5)) {
		tmp = x * (1.0 + (z * y));
	} 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 <= (-2.2d+29)) .or. (.not. (y <= 2.85d-5))) then
        tmp = x * (1.0d0 + (z * y))
    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 <= -2.2e+29) || !(y <= 2.85e-5)) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.2e+29) or not (y <= 2.85e-5):
		tmp = x * (1.0 + (z * y))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.2e+29) || !(y <= 2.85e-5))
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.2e+29) || ~((y <= 2.85e-5)))
		tmp = x * (1.0 + (z * y));
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.2e+29], N[Not[LessEqual[y, 2.85e-5]], $MachinePrecision]], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000001e29 or 2.8500000000000002e-5 < y

   1. Initial program 93.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 93.0%

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

      2. flip-- 69.5%

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

      3. associate-*r/ 66.0%

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

      4. metadata-eval 66.0%

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

   3. Applied egg-rr 66.0%

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

      1. associate-*l/ 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in y around inf 66.6%

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

   7. Taylor expanded in y around inf 92.7%

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

      1. *-commutative 92.7%

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

   9. Simplified 92.7%

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

   if -2.2000000000000001e29 < y < 2.8500000000000002e-5

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 98.2%

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

      1. sub-neg 98.2%

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

      2. distribute-rgt-in 98.2%

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

      3. *-lft-identity 98.2%

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

      4. distribute-lft-neg-out 98.2%

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

      5. *-commutative 98.2%

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

      6. unsub-neg 98.2%

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

   4. Simplified 98.2%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+29} \lor \neg \left(y \leq 2.85 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 5: 98.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 92.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 91.4%

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

      1. *-commutative 91.4%

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

      2. associate-*l* 98.3%

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

      3. sub-neg 98.3%

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

      4. metadata-eval 98.3%

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

   4. Simplified 98.3%

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

   if -1 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. flip-- 81.5%

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

      3. associate-*r/ 81.5%

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

      4. metadata-eval 81.5%

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

   3. Applied egg-rr 81.5%

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

      1. associate-*l/ 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in y around inf 48.0%

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

   7. Taylor expanded in y around inf 98.8%

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

      1. *-commutative 98.8%

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

   9. Simplified 98.8%

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

4. Final simplification 98.6%

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

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05)
   (* z (* x (+ y -1.0)))
   (if (<= z 1.0) (* x (+ 1.0 (* z y))) (* (+ y -1.0) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = (y + -1.0) * (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 (z <= (-1.05d0)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 1.0d0) then
        tmp = x * (1.0d0 + (z * y))
    else
        tmp = (y + (-1.0d0)) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (z * y));
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.05:
		tmp = z * (x * (y + -1.0))
	elif z <= 1.0:
		tmp = x * (1.0 + (z * y))
	else:
		tmp = (y + -1.0) * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.05)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(1.0 + Float64(z * y)));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 1.0)
		tmp = x * (1.0 + (z * y));
	else
		tmp = (y + -1.0) * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.05], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 94.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 93.9%

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

      1. *-commutative 93.9%

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

      2. associate-*l* 99.0%

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

      3. sub-neg 99.0%

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

      4. metadata-eval 99.0%

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

   4. Simplified 99.0%

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

   if -1.05000000000000004 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. flip-- 81.5%

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

      3. associate-*r/ 81.5%

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

      4. metadata-eval 81.5%

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

   3. Applied egg-rr 81.5%

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

      1. associate-*l/ 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in y around inf 48.0%

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

   7. Taylor expanded in y around inf 98.8%

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

      1. *-commutative 98.8%

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

   9. Simplified 98.8%

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

   if 1 < z

   1. Initial program 91.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 89.4%

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

      1. associate-*r* 97.9%

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

      2. *-commutative 97.9%

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

      3. sub-neg 97.9%

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

      4. metadata-eval 97.9%

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

   4. Simplified 97.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 7: 65.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2900000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))))
   (if (<= z -1.6e+38)
     t_0
     (if (<= z -8e-24) (* x (* z y)) (if (<= z 2900000.0) x t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1.6e+38) {
		tmp = t_0;
	} else if (z <= -8e-24) {
		tmp = x * (z * y);
	} else if (z <= 2900000.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * -x
    if (z <= (-1.6d+38)) then
        tmp = t_0
    else if (z <= (-8d-24)) then
        tmp = x * (z * y)
    else if (z <= 2900000.0d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double tmp;
	if (z <= -1.6e+38) {
		tmp = t_0;
	} else if (z <= -8e-24) {
		tmp = x * (z * y);
	} else if (z <= 2900000.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	tmp = 0
	if z <= -1.6e+38:
		tmp = t_0
	elif z <= -8e-24:
		tmp = x * (z * y)
	elif z <= 2900000.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	tmp = 0.0
	if (z <= -1.6e+38)
		tmp = t_0;
	elseif (z <= -8e-24)
		tmp = Float64(x * Float64(z * y));
	elseif (z <= 2900000.0)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	tmp = 0.0;
	if (z <= -1.6e+38)
		tmp = t_0;
	elseif (z <= -8e-24)
		tmp = x * (z * y);
	elseif (z <= 2900000.0)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, If[LessEqual[z, -1.6e+38], t$95$0, If[LessEqual[z, -8e-24], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2900000.0], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999993e38 or 2.9e6 < z

   1. Initial program 92.4%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 91.2%

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

   3. Taylor expanded in y around 0 66.4%

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

      1. mul-1-neg 66.4%

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

      2. distribute-rgt-neg-in 66.4%

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

   5. Simplified 66.4%

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

   if -1.59999999999999993e38 < z < -7.99999999999999939e-24

   1. Initial program 99.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 89.9%

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

      1. *-commutative 89.9%

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

   4. Simplified 89.9%

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

   if -7.99999999999999939e-24 < z < 2.9e6

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 78.6%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2900000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 8: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+50}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+28)
   (* y (* z x))
   (if (<= y 5.6e+50) (- x (* z x)) (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+28) {
		tmp = y * (z * x);
	} else if (y <= 5.6e+50) {
		tmp = x - (z * x);
	} else {
		tmp = 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 (y <= (-6d+28)) then
        tmp = y * (z * x)
    else if (y <= 5.6d+50) then
        tmp = x - (z * x)
    else
        tmp = x * (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+28) {
		tmp = y * (z * x);
	} else if (y <= 5.6e+50) {
		tmp = x - (z * x);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+28:
		tmp = y * (z * x)
	elif y <= 5.6e+50:
		tmp = x - (z * x)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+28)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 5.6e+50)
		tmp = Float64(x - Float64(z * x));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e+28)
		tmp = y * (z * x);
	elseif (y <= 5.6e+50)
		tmp = x - (z * x);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+28], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+50], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.0000000000000002e28

   1. Initial program 89.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. add-cube-cbrt 87.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)} \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right) \cdot \sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}} \]

      2. pow3 87.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   3. Applied egg-rr 87.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \left(1 - \left(1 - y\right) \cdot z\right)}\right)}^{3}} \]

   4. Taylor expanded in y around inf 63.2%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot \left(y \cdot z\right)}}\right)}^{3} \]
   5. Step-by-step derivation

      1. *-commutative 63.8%

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

   6. Simplified 63.2%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot \left(z \cdot y\right)}}\right)}^{3} \]
   7. Step-by-step derivation

      1. rem-cube-cbrt 63.8%

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

      2. *-commutative 63.8%

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

      3. associate-*r* 68.5%

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

      4. *-commutative 68.5%

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

      5. associate-*r* 69.2%

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

   8. Applied egg-rr 69.2%

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

   if -6.0000000000000002e28 < y < 5.5999999999999996e50

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 97.0%

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

      1. sub-neg 97.0%

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

      2. distribute-rgt-in 97.0%

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

      3. *-lft-identity 97.0%

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

      4. distribute-lft-neg-out 97.0%

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

      5. *-commutative 97.0%

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

      6. unsub-neg 97.0%

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

   4. Simplified 97.0%

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

   if 5.5999999999999996e50 < y

   1. Initial program 95.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 75.8%

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

      1. *-commutative 75.8%

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

   4. Simplified 75.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+28}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+50}:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 9: 65.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-11} \lor \neg \left(z \leq 2900000\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e-11) (not (<= z 2900000.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-11) || !(z <= 2900000.0)) {
		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 <= (-3.4d-11)) .or. (.not. (z <= 2900000.0d0))) 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 <= -3.4e-11) || !(z <= 2900000.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e-11) or not (z <= 2900000.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e-11) || !(z <= 2900000.0))
		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 <= -3.4e-11) || ~((z <= 2900000.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e-11], N[Not[LessEqual[z, 2900000.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.3999999999999999e-11 or 2.9e6 < z

   1. Initial program 92.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 91.4%

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

   3. Taylor expanded in y around 0 62.1%

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

      1. mul-1-neg 62.1%

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

      2. distribute-rgt-neg-in 62.1%

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

   5. Simplified 62.1%

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

   if -3.3999999999999999e-11 < z < 2.9e6

   1. Initial program 100.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 78.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-11} \lor \neg \left(z \leq 2900000\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 38.7% 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 96.6%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in z around 0 42.6%

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

3. Final simplification 42.6%

   \[\leadsto x \]

Developer target: 99.8% accurate, 0.3× 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 2023271 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (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))))