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

Percentage Accurate: 95.5% → 98.8%

Time: 6.2s

Alternatives: 11

Speedup: 1.0×

• 20.6% 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: 95.5% 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: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5200000 \lor \neg \left(z \leq 0.0025\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5200000.0) (not (<= z 0.0025)))
   (* z (* x (+ -1.0 y)))
   (* x (+ 1.0 (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5200000.0) || !(z <= 0.0025)) {
		tmp = z * (x * (-1.0 + y));
	} 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 <= (-5200000.0d0)) .or. (.not. (z <= 0.0025d0))) then
        tmp = z * (x * ((-1.0d0) + y))
    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 <= -5200000.0) || !(z <= 0.0025)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x * (1.0 + (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5200000.0) or not (z <= 0.0025):
		tmp = z * (x * (-1.0 + y))
	else:
		tmp = x * (1.0 + (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5200000.0) || !(z <= 0.0025))
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	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 <= -5200000.0) || ~((z <= 0.0025)))
		tmp = z * (x * (-1.0 + y));
	else
		tmp = x * (1.0 + (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5200000.0], N[Not[LessEqual[z, 0.0025]], $MachinePrecision]], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e6 or 0.00250000000000000005 < z

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*r* 98.9%

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

      3. *-commutative 98.9%

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

      4. sub-neg 98.9%

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

      5. metadata-eval 98.9%

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

   4. Simplified 98.9%

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

   if -5.2e6 < z < 0.00250000000000000005

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in y around inf 98.9%

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

      1. *-commutative 98.9%

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

   5. Simplified 98.9%

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

      1. *-commutative 98.9%

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

      2. distribute-rgt1-in 98.9%

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

   7. Applied egg-rr 98.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5200000 \lor \neg \left(z \leq 0.0025\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \]

Alternative 2: 61.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+184}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5200000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 11500 \lor \neg \left(z \leq 7.1 \cdot 10^{+152}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* z y))))
   (if (<= z -1.22e+232)
     t_0
     (if (<= z -2.1e+204)
       t_1
       (if (<= z -1.25e+184)
         t_0
         (if (<= z -5.6e+138)
           t_1
           (if (<= z -5200000.0)
             t_0
             (if (<= z 5.8e-61)
               x
               (if (or (<= z 11500.0) (not (<= z 7.1e+152))) 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 <= -1.22e+232) {
		tmp = t_0;
	} else if (z <= -2.1e+204) {
		tmp = t_1;
	} else if (z <= -1.25e+184) {
		tmp = t_0;
	} else if (z <= -5.6e+138) {
		tmp = t_1;
	} else if (z <= -5200000.0) {
		tmp = t_0;
	} else if (z <= 5.8e-61) {
		tmp = x;
	} else if ((z <= 11500.0) || !(z <= 7.1e+152)) {
		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 <= (-1.22d+232)) then
        tmp = t_0
    else if (z <= (-2.1d+204)) then
        tmp = t_1
    else if (z <= (-1.25d+184)) then
        tmp = t_0
    else if (z <= (-5.6d+138)) then
        tmp = t_1
    else if (z <= (-5200000.0d0)) then
        tmp = t_0
    else if (z <= 5.8d-61) then
        tmp = x
    else if ((z <= 11500.0d0) .or. (.not. (z <= 7.1d+152))) 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 <= -1.22e+232) {
		tmp = t_0;
	} else if (z <= -2.1e+204) {
		tmp = t_1;
	} else if (z <= -1.25e+184) {
		tmp = t_0;
	} else if (z <= -5.6e+138) {
		tmp = t_1;
	} else if (z <= -5200000.0) {
		tmp = t_0;
	} else if (z <= 5.8e-61) {
		tmp = x;
	} else if ((z <= 11500.0) || !(z <= 7.1e+152)) {
		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 <= -1.22e+232:
		tmp = t_0
	elif z <= -2.1e+204:
		tmp = t_1
	elif z <= -1.25e+184:
		tmp = t_0
	elif z <= -5.6e+138:
		tmp = t_1
	elif z <= -5200000.0:
		tmp = t_0
	elif z <= 5.8e-61:
		tmp = x
	elif (z <= 11500.0) or not (z <= 7.1e+152):
		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 <= -1.22e+232)
		tmp = t_0;
	elseif (z <= -2.1e+204)
		tmp = t_1;
	elseif (z <= -1.25e+184)
		tmp = t_0;
	elseif (z <= -5.6e+138)
		tmp = t_1;
	elseif (z <= -5200000.0)
		tmp = t_0;
	elseif (z <= 5.8e-61)
		tmp = x;
	elseif ((z <= 11500.0) || !(z <= 7.1e+152))
		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 <= -1.22e+232)
		tmp = t_0;
	elseif (z <= -2.1e+204)
		tmp = t_1;
	elseif (z <= -1.25e+184)
		tmp = t_0;
	elseif (z <= -5.6e+138)
		tmp = t_1;
	elseif (z <= -5200000.0)
		tmp = t_0;
	elseif (z <= 5.8e-61)
		tmp = x;
	elseif ((z <= 11500.0) || ~((z <= 7.1e+152)))
		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, -1.22e+232], t$95$0, If[LessEqual[z, -2.1e+204], t$95$1, If[LessEqual[z, -1.25e+184], t$95$0, If[LessEqual[z, -5.6e+138], t$95$1, If[LessEqual[z, -5200000.0], t$95$0, If[LessEqual[z, 5.8e-61], x, If[Or[LessEqual[z, 11500.0], N[Not[LessEqual[z, 7.1e+152]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.21999999999999994e232 or -2.1e204 < z < -1.25e184 or -5.6000000000000002e138 < z < -5.2e6 or 11500 < z < 7.10000000000000017e152

   1. Initial program 95.5%

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

   2. Taylor expanded in z around inf 93.9%

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

   3. Taylor expanded in y around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-lft-neg-out 76.9%

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

      3. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -1.21999999999999994e232 < z < -2.1e204 or -1.25e184 < z < -5.6000000000000002e138 or 5.7999999999999999e-61 < z < 11500 or 7.10000000000000017e152 < z

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 77.5%

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

      1. *-commutative 77.5%

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

   4. Simplified 77.5%

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

   if -5.2e6 < z < 5.7999999999999999e-61

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.9%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.22 \cdot 10^{+232}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+204}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+184}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -5200000:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 11500 \lor \neg \left(z \leq 7.1 \cdot 10^{+152}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-15} \lor \neg \left(z \leq 5.8 \cdot 10^{-61}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e-15) (not (<= z 5.8e-61))) (* z (* x (+ -1.0 y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e-15) || !(z <= 5.8e-61)) {
		tmp = z * (x * (-1.0 + y));
	} 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 <= (-1.3d-15)) .or. (.not. (z <= 5.8d-61))) then
        tmp = z * (x * ((-1.0d0) + y))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e-15) || !(z <= 5.8e-61)) {
		tmp = z * (x * (-1.0 + y));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e-15) or not (z <= 5.8e-61):
		tmp = z * (x * (-1.0 + y))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e-15) || !(z <= 5.8e-61))
		tmp = Float64(z * Float64(x * Float64(-1.0 + y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e-15) || ~((z <= 5.8e-61)))
		tmp = z * (x * (-1.0 + y));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e-15], N[Not[LessEqual[z, 5.8e-61]], $MachinePrecision]], N[(z * N[(x * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000002e-15 or 5.7999999999999999e-61 < z

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*r* 96.4%

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

      3. *-commutative 96.4%

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

      4. sub-neg 96.4%

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

      5. metadata-eval 96.4%

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

   4. Simplified 96.4%

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

   if -1.30000000000000002e-15 < z < 5.7999999999999999e-61

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 76.9%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-15} \lor \neg \left(z \leq 5.8 \cdot 10^{-61}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(-1 + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 83.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.8e+140)
   (* z (* x y))
   (if (<= y 1.6e-8) (* x (- 1.0 z)) (* x (* z (+ -1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.8e+140) {
		tmp = z * (x * y);
	} else if (y <= 1.6e-8) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * (-1.0 + 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 <= (-8.8d+140)) then
        tmp = z * (x * y)
    else if (y <= 1.6d-8) then
        tmp = x * (1.0d0 - z)
    else
        tmp = x * (z * ((-1.0d0) + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.8e+140) {
		tmp = z * (x * y);
	} else if (y <= 1.6e-8) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * (-1.0 + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.8e+140:
		tmp = z * (x * y)
	elif y <= 1.6e-8:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (z * (-1.0 + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.8e+140)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 1.6e-8)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x * Float64(z * Float64(-1.0 + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.8e+140)
		tmp = z * (x * y);
	elseif (y <= 1.6e-8)
		tmp = x * (1.0 - z);
	else
		tmp = x * (z * (-1.0 + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.8e+140], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-8], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.7999999999999993e140

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 88.0%

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

      1. associate-*r* 91.5%

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

      2. *-commutative 91.5%

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

   4. Simplified 91.5%

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

   if -8.7999999999999993e140 < y < 1.6000000000000001e-8

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 93.5%

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

   if 1.6000000000000001e-8 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 72.9%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+140}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot \left(-1 + y\right)\right)\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(-1 + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e+139)
   (* z (* x y))
   (if (<= y 1.6e-8) (* x (- 1.0 z)) (* (* x z) (+ -1.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+139) {
		tmp = z * (x * y);
	} else if (y <= 1.6e-8) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (x * z) * (-1.0 + 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 <= (-1.8d+139)) then
        tmp = z * (x * y)
    else if (y <= 1.6d-8) then
        tmp = x * (1.0d0 - z)
    else
        tmp = (x * z) * ((-1.0d0) + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+139) {
		tmp = z * (x * y);
	} else if (y <= 1.6e-8) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (x * z) * (-1.0 + y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.8e+139:
		tmp = z * (x * y)
	elif y <= 1.6e-8:
		tmp = x * (1.0 - z)
	else:
		tmp = (x * z) * (-1.0 + y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+139)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 1.6e-8)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(Float64(x * z) * Float64(-1.0 + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.8e+139)
		tmp = z * (x * y);
	elseif (y <= 1.6e-8)
		tmp = x * (1.0 - z);
	else
		tmp = (x * z) * (-1.0 + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.8e+139], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-8], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] * N[(-1.0 + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999993e139

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 88.0%

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

      1. associate-*r* 91.5%

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

      2. *-commutative 91.5%

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

   4. Simplified 91.5%

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

   if -1.79999999999999993e139 < y < 1.6000000000000001e-8

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 93.5%

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

   if 1.6000000000000001e-8 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 72.9%

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

   3. Taylor expanded in y around 0 56.5%

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

      1. associate-*r* 56.5%

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

      2. *-commutative 56.5%

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

      3. associate-*l* 60.7%

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

      4. distribute-rgt-in 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(-1 + y\right)\\ \end{array} \]

Alternative 6: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+139} \lor \neg \left(y \leq 420\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+139) (not (<= y 420.0))) (* x (* z y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+139) || !(y <= 420.0)) {
		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 <= (-5d+139)) .or. (.not. (y <= 420.0d0))) 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 <= -5e+139) || !(y <= 420.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+139) or not (y <= 420.0):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+139) || !(y <= 420.0))
		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 <= -5e+139) || ~((y <= 420.0)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+139], N[Not[LessEqual[y, 420.0]], $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 < -5.0000000000000003e139 or 420 < y

   1. Initial program 92.9%

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

   2. Taylor expanded in y around inf 76.7%

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

      1. *-commutative 76.7%

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

   4. Simplified 76.7%

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

   if -5.0000000000000003e139 < y < 420

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 93.3%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+139} \lor \neg \left(y \leq 420\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 7: 83.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 92000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+139)
   (* z (* x y))
   (if (<= y 92000.0) (* x (- 1.0 z)) (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+139) {
		tmp = z * (x * y);
	} else if (y <= 92000.0) {
		tmp = x * (1.0 - z);
	} 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 <= (-2.2d+139)) then
        tmp = z * (x * y)
    else if (y <= 92000.0d0) then
        tmp = x * (1.0d0 - z)
    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 <= -2.2e+139) {
		tmp = z * (x * y);
	} else if (y <= 92000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = x * (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.2e+139:
		tmp = z * (x * y)
	elif y <= 92000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = x * (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.2e+139)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 92000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(x * Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.2e+139)
		tmp = z * (x * y);
	elseif (y <= 92000.0)
		tmp = x * (1.0 - z);
	else
		tmp = x * (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.2e+139], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 92000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1999999999999999e139

   1. Initial program 93.2%

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

   2. Taylor expanded in y around inf 88.0%

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

      1. associate-*r* 91.5%

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

      2. *-commutative 91.5%

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

   4. Simplified 91.5%

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

   if -2.1999999999999999e139 < y < 92000

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 93.3%

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

   if 92000 < y

   1. Initial program 92.8%

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

   2. Taylor expanded in y around inf 71.9%

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

      1. *-commutative 71.9%

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

   4. Simplified 71.9%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+139}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 92000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 - ((x * z) * (1.0d0 - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Taylor expanded in z around 0 97.0%

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

3. Taylor expanded in y around 0 92.3%

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

   1. associate-*r* 58.6%

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

   2. *-commutative 58.6%

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

   3. associate-*l* 55.8%

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

   4. distribute-rgt-in 63.3%

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

5. Simplified 97.4%

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

6. Final simplification 97.4%

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

Alternative 9: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (z * ((-1.0d0) + y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.0%

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

2. Final simplification 97.0%

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

Alternative 10: 64.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5200000 \lor \neg \left(z \leq 0.0025\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5200000.0) (not (<= z 0.0025))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5200000.0) || !(z <= 0.0025)) {
		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 <= (-5200000.0d0)) .or. (.not. (z <= 0.0025d0))) 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 <= -5200000.0) || !(z <= 0.0025)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5200000.0) or not (z <= 0.0025):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5200000.0) || !(z <= 0.0025))
		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 <= -5200000.0) || ~((z <= 0.0025)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5200000.0], N[Not[LessEqual[z, 0.0025]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.2e6 or 0.00250000000000000005 < z

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 93.3%

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

   3. Taylor expanded in y around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. distribute-lft-neg-out 61.9%

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

      3. *-commutative 61.9%

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

   5. Simplified 61.9%

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

   if -5.2e6 < z < 0.00250000000000000005

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 71.0%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5200000 \lor \neg \left(z \leq 0.0025\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 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. Taylor expanded in z around 0 35.9%

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

3. Final simplification 35.9%

   \[\leadsto x \]

Developer target: 99.7% 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 2023308 
(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))))