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

Percentage Accurate: 95.6% → 98.7%

Time: 8.1s

Alternatives: 9

Speedup: 0.5×

• 20.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t\_0 \leq -5 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;t\_0 \leq 10^{+301}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (<= t_0 -5e+24)
     (* z (* x (+ y -1.0)))
     (if (<= t_0 1e+301) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* y x))))))

C

double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -5e+24) {
		tmp = z * (x * (y + -1.0));
	} else if (t_0 <= 1e+301) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - y) * z
    if (t_0 <= (-5d+24)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (t_0 <= 1d+301) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (1.0 - y) * z;
	double tmp;
	if (t_0 <= -5e+24) {
		tmp = z * (x * (y + -1.0));
	} else if (t_0 <= 1e+301) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (1.0 - y) * z
	tmp = 0
	if t_0 <= -5e+24:
		tmp = z * (x * (y + -1.0))
	elif t_0 <= 1e+301:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(1.0 - y) * z)
	tmp = 0.0
	if (t_0 <= -5e+24)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (t_0 <= 1e+301)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (1.0 - y) * z;
	tmp = 0.0;
	if (t_0 <= -5e+24)
		tmp = z * (x * (y + -1.0));
	elseif (t_0 <= 1e+301)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+24], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1e+301], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -5.00000000000000045e24

   1. Initial program 89.0%

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

   3. Taylor expanded in z around inf 89.0%

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

      1. associate-*r* 98.5%

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

      2. *-commutative 98.5%

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

      3. sub-neg 98.5%

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

      4. remove-double-neg 98.5%

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

      5. distribute-neg-in 98.5%

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

      6. +-commutative 98.5%

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

      7. sub-neg 98.5%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. *-commutative 99.9%

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

      11. neg-sub0 99.9%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(0 - \left(1 - y\right)\right)}\right) \]

      12. associate--r- 99.9%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(\left(0 - 1\right) + y\right)}\right) \]

      13. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -5.00000000000000045e24 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 1.00000000000000005e301

   1. Initial program 99.9%

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

   if 1.00000000000000005e301 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 70.3%

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

   3. Taylor expanded in y around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

      3. associate-*l* 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+24}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \leq 10^{+301}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.1e+149)
   (* z (* y x))
   (if (or (<= y -1.0) (not (<= y 1.0)))
     (* x (+ 1.0 (* y z)))
     (* x (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+149) {
		tmp = z * (y * x);
	} else if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4.1d+149)) then
        tmp = z * (y * x)
    else if ((y <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.1e+149) {
		tmp = z * (y * x);
	} else if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.1e+149:
		tmp = z * (y * x)
	elif (y <= -1.0) or not (y <= 1.0):
		tmp = x * (1.0 + (y * z))
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.1e+149)
		tmp = Float64(z * Float64(y * x));
	elseif ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4.1e+149)
		tmp = z * (y * x);
	elseif ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x * (1.0 + (y * z));
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.1e+149], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0999999999999996e149

   1. Initial program 74.6%

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

   3. Taylor expanded in y around inf 69.0%

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

      1. *-commutative 69.0%

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

      2. *-commutative 69.0%

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

      3. associate-*l* 90.7%

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

   5. Simplified 90.7%

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

   if -4.0999999999999996e149 < y < -1 or 1 < y

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 89.0%

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

      1. neg-mul-1 89.0%

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

   5. Simplified 89.0%

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

      1. cancel-sign-sub 89.0%

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

      2. +-commutative 89.0%

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

      3. *-commutative 89.0%

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

   7. Applied egg-rr 89.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.3%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+149}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+17} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.1e+17) (not (<= z 1.0)))
   (* z (* x (+ y -1.0)))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e+17) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.1d+17)) .or. (.not. (z <= 1.0d0))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.1e+17) || !(z <= 1.0)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.1e+17) or not (z <= 1.0):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.1e+17) || !(z <= 1.0))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.1e+17) || ~((z <= 1.0)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.1e+17], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e17 or 1 < z

   1. Initial program 88.1%

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

   3. Taylor expanded in z around inf 88.1%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. +-commutative 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r* 99.8%

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

      9. *-commutative 99.8%

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

      10. *-commutative 99.8%

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

      11. neg-sub0 99.8%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(0 - \left(1 - y\right)\right)}\right) \]

      12. associate--r- 99.8%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(\left(0 - 1\right) + y\right)}\right) \]

      13. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   if -1.1e17 < 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 y around inf 99.6%

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

      1. neg-mul-1 99.6%

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

   5. Simplified 99.6%

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

      1. cancel-sign-sub 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+17} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+17)
   (* z (* x (+ y -1.0)))
   (if (<= z 1.0) (* x (+ 1.0 (* y z))) (* (* z x) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+17) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.1d+17)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 1.0d0) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = (z * x) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+17) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+17:
		tmp = z * (x * (y + -1.0))
	elif z <= 1.0:
		tmp = x * (1.0 + (y * z))
	else:
		tmp = (z * x) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+17)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 1.0)
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+17)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 1.0)
		tmp = x * (1.0 + (y * z));
	else
		tmp = (z * x) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+17], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e17

   1. Initial program 88.5%

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

   3. Taylor expanded in z around inf 88.5%

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

      1. associate-*r* 99.8%

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

      2. *-commutative 99.8%

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

      3. sub-neg 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-neg-in 99.8%

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

      6. +-commutative 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. *-commutative 99.9%

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

      11. neg-sub0 99.9%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(0 - \left(1 - y\right)\right)}\right) \]

      12. associate--r- 99.9%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(\left(0 - 1\right) + y\right)}\right) \]

      13. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

   if -1.1e17 < 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 y around inf 99.6%

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

      1. neg-mul-1 99.6%

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

   5. Simplified 99.6%

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

      1. cancel-sign-sub 99.6%

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

      2. +-commutative 99.6%

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

      3. *-commutative 99.6%

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

   7. Applied egg-rr 99.6%

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

   if 1 < z

   1. Initial program 87.6%

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

   3. Taylor expanded in z around inf 87.6%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. metadata-eval 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+26} \lor \neg \left(y \leq 1.2 \cdot 10^{+38}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.7e+26) (not (<= y 1.2e+38))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.7e+26) || !(y <= 1.2e+38)) {
		tmp = z * (y * 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 <= (-4.7d+26)) .or. (.not. (y <= 1.2d+38))) then
        tmp = z * (y * 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 <= -4.7e+26) || !(y <= 1.2e+38)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.7e+26) or not (y <= 1.2e+38):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.7e+26) || !(y <= 1.2e+38))
		tmp = Float64(z * Float64(y * 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 <= -4.7e+26) || ~((y <= 1.2e+38)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.7e+26], N[Not[LessEqual[y, 1.2e+38]], $MachinePrecision]], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6999999999999998e26 or 1.20000000000000009e38 < y

   1. Initial program 86.9%

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

   3. Taylor expanded in y around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*l* 78.8%

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

   5. Simplified 78.8%

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

   if -4.6999999999999998e26 < y < 1.20000000000000009e38

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 94.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+26} \lor \neg \left(y \leq 1.2 \cdot 10^{+38}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -390000 \lor \neg \left(z \leq 9 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -390000.0) (not (<= z 9e+24))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -390000.0) || !(z <= 9e+24)) {
		tmp = x * -z;
	} 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 <= (-390000.0d0)) .or. (.not. (z <= 9d+24))) then
        tmp = x * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -390000.0) || !(z <= 9e+24)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -390000.0) or not (z <= 9e+24):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -390000.0) || !(z <= 9e+24))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -390000.0) || ~((z <= 9e+24)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -390000.0], N[Not[LessEqual[z, 9e+24]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.9e5 or 9.00000000000000039e24 < z

   1. Initial program 88.0%

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

   3. Taylor expanded in z around inf 88.0%

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

      1. associate-*r* 99.9%

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

      2. *-commutative 99.9%

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

      3. sub-neg 99.9%

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

      4. remove-double-neg 99.9%

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

      5. distribute-neg-in 99.9%

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

      6. +-commutative 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-*r* 99.8%

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

      9. *-commutative 99.8%

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

      10. *-commutative 99.8%

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

      11. neg-sub0 99.8%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(0 - \left(1 - y\right)\right)}\right) \]

      12. associate--r- 99.8%

          \[\leadsto z \cdot \left(x \cdot \color{blue}{\left(\left(0 - 1\right) + y\right)}\right) \]

      13. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in y around 0 48.9%

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

      1. neg-mul-1 48.9%

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

   8. Simplified 48.9%

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

   if -3.9e5 < z < 9.00000000000000039e24

   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 74.0%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -390000 \lor \neg \left(z \leq 9 \cdot 10^{+24}\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 4.2e+104) (* x (- 1.0 z)) (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.2e+104) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 4.2d+104) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 4.2e+104) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 4.2e+104:
		tmp = x * (1.0 - z)
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 4.2e+104)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 4.2e+104)
		tmp = x * (1.0 - z);
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 4.2e+104], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.1999999999999997e104

   1. Initial program 94.6%

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

   3. Taylor expanded in y around 0 69.7%

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

   if 4.1999999999999997e104 < y

   1. Initial program 86.8%

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

   3. Taylor expanded in z around 0 86.8%

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

   4. Taylor expanded in y around 0 13.7%

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

      1. mul-1-neg 13.7%

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

      2. unsub-neg 13.7%

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

   6. Simplified 13.7%

      \[\leadsto \color{blue}{x - x \cdot z} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 13.7%

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

      2. *-commutative 13.7%

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

      3. +-commutative 13.7%

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

      4. *-commutative 13.7%

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

      5. add-sqr-sqrt 4.8%

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

      6. sqrt-unprod 30.8%

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

      7. sqr-neg 30.8%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot z + x \]

      8. sqrt-unprod 23.2%

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

      9. add-sqr-sqrt 36.0%

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

   8. Applied egg-rr 36.0%

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

   9. Taylor expanded in z around inf 24.2%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{+104}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+62}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z -5.4e+62) (* z x) x))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e+62) {
		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 <= (-5.4d+62)) 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 <= -5.4e+62) {
		tmp = z * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4e+62:
		tmp = z * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4e+62)
		tmp = Float64(z * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4e+62)
		tmp = z * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4e+62], N[(z * x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.4e62

   1. Initial program 85.7%

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

   3. Taylor expanded in z around 0 85.7%

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

   4. Taylor expanded in y around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. unsub-neg 39.2%

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

   6. Simplified 39.2%

      \[\leadsto \color{blue}{x - x \cdot z} \]
   7. Step-by-step derivation

      1. cancel-sign-sub-inv 39.2%

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

      2. *-commutative 39.2%

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

      3. +-commutative 39.2%

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

      4. *-commutative 39.2%

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

      5. add-sqr-sqrt 21.9%

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

      6. sqrt-unprod 28.9%

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

      7. sqr-neg 28.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot x}} \cdot z + x \]

      8. sqrt-unprod 10.7%

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

      9. add-sqr-sqrt 18.8%

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

   8. Applied egg-rr 18.8%

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

   9. Taylor expanded in z around inf 18.8%

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

   if -5.4e62 < z

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0 43.8%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+62}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 93.3%

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

3. Taylor expanded in z around 0 34.3%

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

Developer Target 1: 99.8% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024157 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (* x (- 1 (* (- 1 y) z))) -161819597360704900000000000000000000000000000000000) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 389223764966390300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x))))))

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