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

Percentage Accurate: 96.1% → 97.9%

Time: 7.1s

Alternatives: 11

Speedup: 0.6×

• 20.2% 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: 96.1% 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: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+16}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2e+16) (+ x (* x (* z (+ y -1.0)))) (* z (* x (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e+16) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 2d+16) then
        tmp = x + (x * (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e+16) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2e+16:
		tmp = x + (x * (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2e+16)
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2e+16)
		tmp = x + (x * (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2e+16], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2e16

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 98.9%

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

   if 2e16 < z

   1. Initial program 86.4%

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

   3. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+16}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -7 \cdot 10^{+35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+144} \lor \neg \left(z \leq 6.2 \cdot 10^{+189}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* z y))))
   (if (<= z -7e+35)
     t_0
     (if (<= z -6e-6)
       t_1
       (if (<= z 1.0)
         x
         (if (or (<= z 2.3e+144) (not (<= z 6.2e+189))) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -7e+35) {
		tmp = t_0;
	} else if (z <= -6e-6) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 2.3e+144) || !(z <= 6.2e+189)) {
		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 = x * (z * y)
    if (z <= (-7d+35)) then
        tmp = t_0
    else if (z <= (-6d-6)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x
    else if ((z <= 2.3d+144) .or. (.not. (z <= 6.2d+189))) 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 = x * (z * y);
	double tmp;
	if (z <= -7e+35) {
		tmp = t_0;
	} else if (z <= -6e-6) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 2.3e+144) || !(z <= 6.2e+189)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (z * y)
	tmp = 0
	if z <= -7e+35:
		tmp = t_0
	elif z <= -6e-6:
		tmp = t_1
	elif z <= 1.0:
		tmp = x
	elif (z <= 2.3e+144) or not (z <= 6.2e+189):
		tmp = t_0
	else:
		tmp = t_1
	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 <= -7e+35)
		tmp = t_0;
	elseif (z <= -6e-6)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 2.3e+144) || !(z <= 6.2e+189))
		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 = x * (z * y);
	tmp = 0.0;
	if (z <= -7e+35)
		tmp = t_0;
	elseif (z <= -6e-6)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 2.3e+144) || ~((z <= 6.2e+189)))
		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[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7e+35], t$95$0, If[LessEqual[z, -6e-6], t$95$1, If[LessEqual[z, 1.0], x, If[Or[LessEqual[z, 2.3e+144], N[Not[LessEqual[z, 6.2e+189]], $MachinePrecision]], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.0000000000000001e35 or 1 < z < 2.3000000000000001e144 or 6.1999999999999999e189 < z

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 93.6%

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

   4. Taylor expanded in y around inf 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. unsub-neg 73.3%

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

      4. *-commutative 73.3%

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

      5. *-commutative 73.3%

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

      6. associate-/l* 74.9%

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

      7. distribute-lft-out-- 85.3%

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

   6. Simplified 85.3%

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

   7. Taylor expanded in y around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. sub-neg 67.5%

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

   9. Simplified 67.5%

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

   10. Taylor expanded in z around inf 66.5%

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

       1. associate-*r* 66.5%

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

       2. neg-mul-1 66.5%

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

       3. *-commutative 66.5%

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

   12. Simplified 66.5%

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

   if -7.0000000000000001e35 < z < -6.0000000000000002e-6 or 2.3000000000000001e144 < z < 6.1999999999999999e189

   1. Initial program 81.7%

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

   3. Taylor expanded in y around inf 63.9%

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

      1. *-commutative 63.9%

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

   5. Simplified 63.9%

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

   if -6.0000000000000002e-6 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 79.5%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+144} \lor \neg \left(z \leq 6.2 \cdot 10^{+189}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+148} \lor \neg \left(y \leq -1.85 \cdot 10^{+53}\right) \land \left(y \leq -7.2 \cdot 10^{+29} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right)\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e+148)
         (and (not (<= y -1.85e+53))
              (or (<= y -7.2e+29) (not (<= y 1.5e+18)))))
   (* y (* z x))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+148) || (!(y <= -1.85e+53) && ((y <= -7.2e+29) || !(y <= 1.5e+18)))) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-9.5d+148)) .or. (.not. (y <= (-1.85d+53))) .and. (y <= (-7.2d+29)) .or. (.not. (y <= 1.5d+18))) then
        tmp = y * (z * x)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e+148) || (!(y <= -1.85e+53) && ((y <= -7.2e+29) || !(y <= 1.5e+18)))) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.5e+148) or (not (y <= -1.85e+53) and ((y <= -7.2e+29) or not (y <= 1.5e+18))):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e+148) || (!(y <= -1.85e+53) && ((y <= -7.2e+29) || !(y <= 1.5e+18))))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.5e+148) || (~((y <= -1.85e+53)) && ((y <= -7.2e+29) || ~((y <= 1.5e+18)))))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.5e+148], And[N[Not[LessEqual[y, -1.85e+53]], $MachinePrecision], Or[LessEqual[y, -7.2e+29], N[Not[LessEqual[y, 1.5e+18]], $MachinePrecision]]]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000002e148 or -1.85e53 < y < -7.19999999999999952e29 or 1.5e18 < y

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 88.3%

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

   4. Taylor expanded in y around inf 88.3%

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

      1. *-commutative 88.3%

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

   6. Simplified 88.3%

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

      1. *-commutative 88.3%

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

      2. distribute-rgt1-in 88.3%

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

   8. Applied egg-rr 88.3%

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

   9. Taylor expanded in z around inf 68.1%

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

       1. associate-*r* 76.7%

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

       2. *-commutative 76.7%

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

       3. associate-*r* 75.9%

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

   11. Simplified 75.9%

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

   if -9.5000000000000002e148 < y < -1.85e53 or -7.19999999999999952e29 < y < 1.5e18

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 96.5%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+148} \lor \neg \left(y \leq -1.85 \cdot 10^{+53}\right) \land \left(y \leq -7.2 \cdot 10^{+29} \lor \neg \left(y \leq 1.5 \cdot 10^{+18}\right)\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+148}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{+28} \lor \neg \left(y \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z x))))
   (if (<= y -9.5e+148)
     t_0
     (if (<= y -1.05e+57)
       (* x (- 1.0 z))
       (if (or (<= y -3.35e+28) (not (<= y 2.5e+18))) t_0 (- x (* z x)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * x);
	double tmp;
	if (y <= -9.5e+148) {
		tmp = t_0;
	} else if (y <= -1.05e+57) {
		tmp = x * (1.0 - z);
	} else if ((y <= -3.35e+28) || !(y <= 2.5e+18)) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = y * (z * x)
    if (y <= (-9.5d+148)) then
        tmp = t_0
    else if (y <= (-1.05d+57)) then
        tmp = x * (1.0d0 - z)
    else if ((y <= (-3.35d+28)) .or. (.not. (y <= 2.5d+18))) then
        tmp = t_0
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * x);
	double tmp;
	if (y <= -9.5e+148) {
		tmp = t_0;
	} else if (y <= -1.05e+57) {
		tmp = x * (1.0 - z);
	} else if ((y <= -3.35e+28) || !(y <= 2.5e+18)) {
		tmp = t_0;
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * x)
	tmp = 0
	if y <= -9.5e+148:
		tmp = t_0
	elif y <= -1.05e+57:
		tmp = x * (1.0 - z)
	elif (y <= -3.35e+28) or not (y <= 2.5e+18):
		tmp = t_0
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * x))
	tmp = 0.0
	if (y <= -9.5e+148)
		tmp = t_0;
	elseif (y <= -1.05e+57)
		tmp = Float64(x * Float64(1.0 - z));
	elseif ((y <= -3.35e+28) || !(y <= 2.5e+18))
		tmp = t_0;
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * x);
	tmp = 0.0;
	if (y <= -9.5e+148)
		tmp = t_0;
	elseif (y <= -1.05e+57)
		tmp = x * (1.0 - z);
	elseif ((y <= -3.35e+28) || ~((y <= 2.5e+18)))
		tmp = t_0;
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9.5e+148], t$95$0, If[LessEqual[y, -1.05e+57], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -3.35e+28], N[Not[LessEqual[y, 2.5e+18]], $MachinePrecision]], t$95$0, N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000002e148 or -1.04999999999999995e57 < y < -3.35e28 or 2.5e18 < y

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 88.3%

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

   4. Taylor expanded in y around inf 88.3%

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

      1. *-commutative 88.3%

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

   6. Simplified 88.3%

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

      1. *-commutative 88.3%

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

      2. distribute-rgt1-in 88.3%

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

   8. Applied egg-rr 88.3%

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

   9. Taylor expanded in z around inf 68.1%

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

       1. associate-*r* 76.7%

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

       2. *-commutative 76.7%

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

       3. associate-*r* 75.9%

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

   11. Simplified 75.9%

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

   if -9.5000000000000002e148 < y < -1.04999999999999995e57

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0 75.1%

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

   if -3.35e28 < y < 2.5e18

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around inf 77.1%

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

      1. +-commutative 77.1%

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

      2. mul-1-neg 77.1%

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

      3. unsub-neg 77.1%

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

      4. *-commutative 77.1%

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

      5. *-commutative 77.1%

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

      6. associate-/l* 72.4%

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

      7. distribute-lft-out-- 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in y around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. sub-neg 98.7%

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

   9. Simplified 98.7%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+148}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{+28} \lor \neg \left(y \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-5} \lor \neg \left(z \leq 8200\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e-5) (not (<= z 8200.0)))
   (* z (* x (+ y -1.0)))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e-5) || !(z <= 8200.0)) {
		tmp = z * (x * (y + -1.0));
	} 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 ((z <= (-2d-5)) .or. (.not. (z <= 8200.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    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 ((z <= -2e-5) || !(z <= 8200.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e-5) or not (z <= 8200.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2e-5) || !(z <= 8200.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2e-5) || ~((z <= 8200.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2e-5], N[Not[LessEqual[z, 8200.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000016e-5 or 8200 < z

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 90.7%

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

      1. *-commutative 90.7%

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

      2. associate-*r* 99.0%

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

      3. *-commutative 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   if -2.00000000000000016e-5 < z < 8200

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around inf 87.7%

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

      1. +-commutative 87.7%

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

      2. mul-1-neg 87.7%

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

      3. unsub-neg 87.7%

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

      4. *-commutative 87.7%

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

      5. *-commutative 87.7%

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

      6. associate-/l* 81.9%

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

      7. distribute-lft-out-- 81.9%

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

   6. Simplified 81.9%

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

   7. Taylor expanded in y around 0 81.6%

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

      1. mul-1-neg 81.6%

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

      2. sub-neg 81.6%

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

   9. Simplified 81.6%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-5} \lor \neg \left(z \leq 8200\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+24) (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 <= -1.5e+24) || !(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 <= (-1.5d+24)) .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 <= -1.5e+24) || !(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 <= -1.5e+24) 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 <= -1.5e+24) || !(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 <= -1.5e+24) || ~((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, -1.5e+24], 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 < -1.49999999999999997e24 or 1 < z

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*r* 99.0%

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

      3. *-commutative 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   if -1.49999999999999997e24 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around inf 97.6%

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

      1. *-commutative 97.6%

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

   6. Simplified 97.6%

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

      1. *-commutative 97.6%

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

      2. distribute-rgt1-in 97.6%

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

   8. Applied egg-rr 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+24) (not (<= z 1.0)))
   (* z (* x (+ y -1.0)))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+24) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.5d+24)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+24) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e+24) or not (z <= 1.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e+24) || !(z <= 1.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e+24) || ~((z <= 1.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e+24], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999997e24 or 1 < z

   1. Initial program 91.4%

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

   3. Taylor expanded in z around inf 90.5%

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

      1. *-commutative 90.5%

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

      2. associate-*r* 99.0%

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

      3. *-commutative 99.0%

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

      4. sub-neg 99.0%

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

      5. metadata-eval 99.0%

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

   5. Simplified 99.0%

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

   if -1.49999999999999997e24 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 100.0%

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

   4. Taylor expanded in y around inf 97.6%

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

      1. *-commutative 97.6%

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

   6. Simplified 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+120} \lor \neg \left(y \leq 1.6 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.05e+120) (not (<= y 1.6e+18)))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.05e+120) || !(y <= 1.6e+18)) {
		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 <= (-2.05d+120)) .or. (.not. (y <= 1.6d+18))) 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 <= -2.05e+120) || !(y <= 1.6e+18)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.05e+120) or not (y <= 1.6e+18):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.05e+120) || !(y <= 1.6e+18))
		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 <= -2.05e+120) || ~((y <= 1.6e+18)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.05e+120], N[Not[LessEqual[y, 1.6e+18]], $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 < -2.05e120 or 1.6e18 < y

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if -2.05e120 < y < 1.6e18

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 94.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+120} \lor \neg \left(y \leq 1.6 \cdot 10^{+18}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e+24) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+24) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.5d+24)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e+24) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e+24) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e+24) || !(z <= 1.0))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.5e+24) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e+24], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999997e24 or 1 < z

   1. Initial program 91.4%

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

   3. Taylor expanded in z around 0 91.4%

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

   4. Taylor expanded in y around inf 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. *-commutative 76.4%

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

      5. *-commutative 76.4%

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

      6. associate-/l* 77.8%

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

      7. distribute-lft-out-- 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in y around 0 63.0%

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

      1. mul-1-neg 63.0%

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

      2. sub-neg 63.0%

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

   9. Simplified 63.0%

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

   10. Taylor expanded in z around inf 62.1%

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

       1. associate-*r* 62.1%

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

       2. neg-mul-1 62.1%

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

       3. *-commutative 62.1%

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

   12. Simplified 62.1%

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

   if -1.49999999999999997e24 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 76.0%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+24} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2e+16) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* x (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e+16) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 2d+16) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (x * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e+16) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2e+16:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (x * (y + -1.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2e+16)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2e+16)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (x * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2e+16], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2e16

   1. Initial program 98.9%

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

   if 2e16 < z

   1. Initial program 86.4%

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

   3. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. associate-*r* 99.9%

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

      3. *-commutative 99.9%

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

      4. sub-neg 99.9%

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

      5. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.5%

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

3. Taylor expanded in z around 0 38.7%

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

4. Final simplification 38.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.7% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024054 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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