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

Percentage Accurate: 96.3% → 99.5%

Time: 8.1s

Alternatives: 12

Speedup: 1.0×

• 20.8% 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: 96.3% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+71} \lor \neg \left(t\_0 \leq 2 \cdot 10^{+243}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (or (<= t_0 -4e+71) (not (<= t_0 2e+243)))
     (* z (* x (+ y -1.0)))
     (+ x (* x (* z (+ y -1.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if ((t_0 <= -4e+71) || !(t_0 <= 2e+243)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if ((t_0 <= (-4d+71)) .or. (.not. (t_0 <= 2d+243))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x + (x * (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if ((t_0 <= -4e+71) || !(t_0 <= 2e+243)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if (t_0 <= -4e+71) or not (t_0 <= 2e+243):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x + (x * (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((t_0 <= -4e+71) || !(t_0 <= 2e+243))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if ((t_0 <= -4e+71) || ~((t_0 <= 2e+243)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x + (x * (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -4e+71], N[Not[LessEqual[t$95$0, 2e+243]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -4.0000000000000002e71 or 2.0000000000000001e243 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf 89.3%

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

      1. *-commutative 89.3%

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

      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%

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

   if -4.0000000000000002e71 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 2.0000000000000001e243

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -4 \cdot 10^{+71} \lor \neg \left(z \cdot \left(1 - y\right) \leq 2 \cdot 10^{+243}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 60.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-z\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -3.55 \cdot 10^{+168}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{+61} \lor \neg \left(z \leq 5.1 \cdot 10^{+135}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- z))) (t_1 (* x (* z y))))
   (if (<= z -3.55e+168)
     t_0
     (if (<= z -1.8e-110)
       t_1
       (if (<= z 2.5e-34)
         x
         (if (or (<= z 1.24e+61) (not (<= z 5.1e+135))) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -3.55e+168) {
		tmp = t_0;
	} else if (z <= -1.8e-110) {
		tmp = t_1;
	} else if (z <= 2.5e-34) {
		tmp = x;
	} else if ((z <= 1.24e+61) || !(z <= 5.1e+135)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * -z
    t_1 = x * (z * y)
    if (z <= (-3.55d+168)) then
        tmp = t_0
    else if (z <= (-1.8d-110)) then
        tmp = t_1
    else if (z <= 2.5d-34) then
        tmp = x
    else if ((z <= 1.24d+61) .or. (.not. (z <= 5.1d+135))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * -z;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -3.55e+168) {
		tmp = t_0;
	} else if (z <= -1.8e-110) {
		tmp = t_1;
	} else if (z <= 2.5e-34) {
		tmp = x;
	} else if ((z <= 1.24e+61) || !(z <= 5.1e+135)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * -z
	t_1 = x * (z * y)
	tmp = 0
	if z <= -3.55e+168:
		tmp = t_0
	elif z <= -1.8e-110:
		tmp = t_1
	elif z <= 2.5e-34:
		tmp = x
	elif (z <= 1.24e+61) or not (z <= 5.1e+135):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-z))
	t_1 = Float64(x * Float64(z * y))
	tmp = 0.0
	if (z <= -3.55e+168)
		tmp = t_0;
	elseif (z <= -1.8e-110)
		tmp = t_1;
	elseif (z <= 2.5e-34)
		tmp = x;
	elseif ((z <= 1.24e+61) || !(z <= 5.1e+135))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * -z;
	t_1 = x * (z * y);
	tmp = 0.0;
	if (z <= -3.55e+168)
		tmp = t_0;
	elseif (z <= -1.8e-110)
		tmp = t_1;
	elseif (z <= 2.5e-34)
		tmp = x;
	elseif ((z <= 1.24e+61) || ~((z <= 5.1e+135)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * (-z)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.55e+168], t$95$0, If[LessEqual[z, -1.8e-110], t$95$1, If[LessEqual[z, 2.5e-34], x, If[Or[LessEqual[z, 1.24e+61], N[Not[LessEqual[z, 5.1e+135]], $MachinePrecision]], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.55000000000000006e168 or 1.24e61 < z < 5.09999999999999982e135

   1. Initial program 94.2%

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

   3. Taylor expanded in z around inf 94.2%

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

      1. *-commutative 94.2%

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

      2. associate-*r* 100.0%

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

      3. *-commutative 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 75.9%

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

      1. neg-mul-1 75.9%

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

   8. Simplified 75.9%

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

   if -3.55000000000000006e168 < z < -1.79999999999999997e-110 or 2.5000000000000001e-34 < z < 1.24e61 or 5.09999999999999982e135 < z

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 59.2%

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

      1. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   if -1.79999999999999997e-110 < z < 2.5000000000000001e-34

   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 85.8%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.55 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.24 \cdot 10^{+61} \lor \neg \left(z \leq 5.1 \cdot 10^{+135}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{if}\;z \leq -220000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-52}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x (+ y -1.0)))))
   (if (<= z -220000000000.0)
     t_0
     (if (<= z -1e-52)
       (- x (* x z))
       (if (<= z -9e-111) (* x (* z y)) (if (<= z 3.25e-34) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * (y + -1.0));
	double tmp;
	if (z <= -220000000000.0) {
		tmp = t_0;
	} else if (z <= -1e-52) {
		tmp = x - (x * z);
	} else if (z <= -9e-111) {
		tmp = x * (z * y);
	} else if (z <= 3.25e-34) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * (y + (-1.0d0)))
    if (z <= (-220000000000.0d0)) then
        tmp = t_0
    else if (z <= (-1d-52)) then
        tmp = x - (x * z)
    else if (z <= (-9d-111)) then
        tmp = x * (z * y)
    else if (z <= 3.25d-34) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * (y + -1.0));
	double tmp;
	if (z <= -220000000000.0) {
		tmp = t_0;
	} else if (z <= -1e-52) {
		tmp = x - (x * z);
	} else if (z <= -9e-111) {
		tmp = x * (z * y);
	} else if (z <= 3.25e-34) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * (y + -1.0))
	tmp = 0
	if z <= -220000000000.0:
		tmp = t_0
	elif z <= -1e-52:
		tmp = x - (x * z)
	elif z <= -9e-111:
		tmp = x * (z * y)
	elif z <= 3.25e-34:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * Float64(y + -1.0)))
	tmp = 0.0
	if (z <= -220000000000.0)
		tmp = t_0;
	elseif (z <= -1e-52)
		tmp = Float64(x - Float64(x * z));
	elseif (z <= -9e-111)
		tmp = Float64(x * Float64(z * y));
	elseif (z <= 3.25e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * (y + -1.0));
	tmp = 0.0;
	if (z <= -220000000000.0)
		tmp = t_0;
	elseif (z <= -1e-52)
		tmp = x - (x * z);
	elseif (z <= -9e-111)
		tmp = x * (z * y);
	elseif (z <= 3.25e-34)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -220000000000.0], t$95$0, If[LessEqual[z, -1e-52], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-111], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.25e-34], x, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.2e11 or 3.24999999999999993e-34 < z

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r* 99.3%

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

      3. *-commutative 99.3%

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

      4. sub-neg 99.3%

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

      5. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   if -2.2e11 < z < -1e-52

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. add-cube-cbrt 99.2%

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

      3. fma-define 99.2%

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

   5. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}\right)}^{2}, \sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}, x\right)} \]

   6. Taylor expanded in y around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. sub-neg 76.0%

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

   8. Simplified 76.0%

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

   if -1e-52 < z < -8.99999999999999987e-111

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 73.7%

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

      1. *-commutative 73.7%

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

   5. Simplified 73.7%

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

   if -8.99999999999999987e-111 < z < 3.24999999999999993e-34

   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 85.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -220000000000:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-52}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+71} \lor \neg \left(t\_0 \leq 2 \cdot 10^{+243}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (or (<= t_0 -4e+71) (not (<= t_0 2e+243)))
     (* z (* x (+ y -1.0)))
     (* x (+ 1.0 (* z (+ y -1.0)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if ((t_0 <= -4e+71) || !(t_0 <= 2e+243)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if ((t_0 <= (-4d+71)) .or. (.not. (t_0 <= 2d+243))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if ((t_0 <= -4e+71) || !(t_0 <= 2e+243)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if (t_0 <= -4e+71) or not (t_0 <= 2e+243):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if ((t_0 <= -4e+71) || !(t_0 <= 2e+243))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if ((t_0 <= -4e+71) || ~((t_0 <= 2e+243)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -4e+71], N[Not[LessEqual[t$95$0, 2e+243]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -4.0000000000000002e71 or 2.0000000000000001e243 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 89.3%

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

   3. Taylor expanded in z around inf 89.3%

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

      1. *-commutative 89.3%

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

      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%

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

   if -4.0000000000000002e71 < (*.f64 (-.f64 #s(literal 1 binary64) y) z) < 2.0000000000000001e243

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -4 \cdot 10^{+71} \lor \neg \left(z \cdot \left(1 - y\right) \leq 2 \cdot 10^{+243}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 2.45 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.95) (not (<= z 2.45e-31)))
   (* z (* x (+ y -1.0)))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.95) || !(z <= 2.45e-31)) {
		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 <= (-0.95d0)) .or. (.not. (z <= 2.45d-31))) 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 <= -0.95) || !(z <= 2.45e-31)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.95) or not (z <= 2.45e-31):
		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 <= -0.95) || !(z <= 2.45e-31))
		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 <= -0.95) || ~((z <= 2.45e-31)))
		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, -0.95], N[Not[LessEqual[z, 2.45e-31]], $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 < -0.94999999999999996 or 2.45000000000000012e-31 < z

   1. Initial program 92.5%

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

   3. Taylor expanded in z around inf 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*r* 98.8%

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

      3. *-commutative 98.8%

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

      4. sub-neg 98.8%

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

      5. metadata-eval 98.8%

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

   5. Simplified 98.8%

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

   if -0.94999999999999996 < z < 2.45000000000000012e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in y around inf 99.4%

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

      1. *-commutative 99.4%

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

   6. Simplified 99.4%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.95 \lor \neg \left(z \leq 2.45 \cdot 10^{-31}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{z}{\frac{1}{x \cdot \left(y + -1\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.02e-94)
   (+ x (/ z (/ 1.0 (* x (+ y -1.0)))))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.02e-94) {
		tmp = x + (z / (1.0 / (x * (y + -1.0))));
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.02d-94) then
        tmp = x + (z / (1.0d0 / (x * (y + (-1.0d0)))))
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.02e-94) {
		tmp = x + (z / (1.0 / (x * (y + -1.0))));
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.02e-94:
		tmp = x + (z / (1.0 / (x * (y + -1.0))))
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.02e-94)
		tmp = Float64(x + Float64(z / Float64(1.0 / Float64(x * Float64(y + -1.0)))));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 1.02e-94)
		tmp = x + (z / (1.0 / (x * (y + -1.0))));
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.02e-94], N[(x + N[(z / N[(1.0 / N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.02e-94

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 94.2%

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

      1. +-commutative 94.2%

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

      2. add-cube-cbrt 93.4%

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

      3. fma-define 93.4%

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

   5. Applied egg-rr 96.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}\right)}^{2}, \sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}, x\right)} \]
   6. Step-by-step derivation

      1. fma-undefine 96.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}\right)}^{2} \cdot \sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)} + x} \]

      2. unpow2 96.7%

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

      3. add-cube-cbrt 97.5%

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

   7. Applied egg-rr 97.5%

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

      1. associate-*r* 96.3%

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

      2. metadata-eval 96.3%

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

      3. sub-neg 96.3%

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

      4. flip-- 82.4%

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

      5. metadata-eval 82.4%

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

      6. fma-neg 82.4%

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

      7. metadata-eval 82.4%

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

      8. associate-*l/ 81.4%

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

      9. clear-num 81.4%

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

      10. associate-*l/ 81.3%

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

      11. *-un-lft-identity 81.3%

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

      12. clear-num 81.3%

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

      13. associate-*l/ 82.4%

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

      14. metadata-eval 82.4%

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

      15. fma-neg 82.4%

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

      16. metadata-eval 82.4%

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

      17. flip-- 96.2%

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

      18. sub-neg 96.2%

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

      19. metadata-eval 96.2%

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

   9. Applied egg-rr 96.2%

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

   if 1.02e-94 < x

   1. Initial program 99.9%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.02 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{z}{\frac{1}{x \cdot \left(y + -1\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58} \lor \neg \left(y \leq 360000000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e+58) (not (<= y 360000000000.0)))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+58) || !(y <= 360000000000.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.1d+58)) .or. (.not. (y <= 360000000000.0d0))) then
        tmp = x * (z * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+58) || !(y <= 360000000000.0)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e+58) or not (y <= 360000000000.0):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e+58) || !(y <= 360000000000.0))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.1e+58) || ~((y <= 360000000000.0)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e+58], N[Not[LessEqual[y, 360000000000.0]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e58 or 3.6e11 < y

   1. Initial program 91.1%

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

   3. Taylor expanded in y around inf 70.4%

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

      1. *-commutative 70.4%

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

   5. Simplified 70.4%

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

   if -3.0999999999999999e58 < y < 3.6e11

   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 96.2%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58} \lor \neg \left(y \leq 360000000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58} \lor \neg \left(y \leq 280000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e+58) (not (<= y 280000000000.0)))
   (* z (* x y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+58) || !(y <= 280000000000.0)) {
		tmp = z * (x * 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 <= (-3.1d+58)) .or. (.not. (y <= 280000000000.0d0))) then
        tmp = z * (x * 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 <= -3.1e+58) || !(y <= 280000000000.0)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.1e+58) or not (y <= 280000000000.0):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e+58) || !(y <= 280000000000.0))
		tmp = Float64(z * Float64(x * 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 <= -3.1e+58) || ~((y <= 280000000000.0)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.1e+58], N[Not[LessEqual[y, 280000000000.0]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e58 or 2.8e11 < y

   1. Initial program 91.1%

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

   3. Taylor expanded in z around inf 70.4%

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

      1. *-commutative 70.4%

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

      2. associate-*r* 76.1%

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

      3. *-commutative 76.1%

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

      4. sub-neg 76.1%

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

      5. metadata-eval 76.1%

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

   5. Simplified 76.1%

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

   6. Taylor expanded in y around inf 76.1%

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

   if -3.0999999999999999e58 < y < 2.8e11

   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 96.2%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+58} \lor \neg \left(y \leq 280000000000\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 210000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+58)
   (* y (* x z))
   (if (<= y 210000000000.0) (* x (- 1.0 z)) (* z (* x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+58) {
		tmp = y * (x * z);
	} else if (y <= 210000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.4d+58)) then
        tmp = y * (x * z)
    else if (y <= 210000000000.0d0) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+58) {
		tmp = y * (x * z);
	} else if (y <= 210000000000.0) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.4e+58:
		tmp = y * (x * z)
	elif y <= 210000000000.0:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+58)
		tmp = Float64(y * Float64(x * z));
	elseif (y <= 210000000000.0)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+58)
		tmp = y * (x * z);
	elseif (y <= 210000000000.0)
		tmp = x * (1.0 - z);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.4e+58], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 210000000000.0], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4000000000000001e58

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 71.7%

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

      1. *-commutative 71.7%

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

   5. Simplified 71.7%

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

      1. add-sqr-sqrt 39.3%

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

      2. pow2 39.3%

         \[\leadsto \color{blue}{{\left(\sqrt{x \cdot \left(z \cdot y\right)}\right)}^{2}} \]

      3. associate-*r* 43.0%

         \[\leadsto {\left(\sqrt{\color{blue}{\left(x \cdot z\right) \cdot y}}\right)}^{2} \]

      4. *-commutative 43.0%

         \[\leadsto {\left(\sqrt{\color{blue}{y \cdot \left(x \cdot z\right)}}\right)}^{2} \]

   7. Applied egg-rr 43.0%

      \[\leadsto \color{blue}{{\left(\sqrt{y \cdot \left(x \cdot z\right)}\right)}^{2}} \]
   8. Step-by-step derivation

      1. unpow2 43.0%

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

      2. add-sqr-sqrt 80.3%

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

      3. *-commutative 80.3%

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

   9. Applied egg-rr 80.3%

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

   if -3.4000000000000001e58 < y < 2.1e11

   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 96.2%

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

   if 2.1e11 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 69.3%

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

      1. *-commutative 69.3%

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

      2. associate-*r* 75.3%

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

      3. *-commutative 75.3%

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

      4. sub-neg 75.3%

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

      5. metadata-eval 75.3%

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

   5. Simplified 75.3%

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

   6. Taylor expanded in y around inf 75.3%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;y \leq 210000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*r* 98.8%

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

      3. *-commutative 98.8%

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

      4. sub-neg 98.8%

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

      5. metadata-eval 98.8%

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

   5. Simplified 98.8%

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

   6. Taylor expanded in y around 0 51.8%

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

      1. neg-mul-1 51.8%

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

   8. Simplified 51.8%

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

   if -1 < 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 76.4%

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

4. Final simplification 63.3%

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

Alternative 11: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y + -1.0) * (x * 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 + ((y + (-1.0d0)) * (x * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.9%

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

3. Taylor expanded in z around 0 95.9%

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

   1. +-commutative 95.9%

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

   2. add-cube-cbrt 95.2%

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

   3. fma-define 95.2%

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

5. Applied egg-rr 97.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left({\left(\sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}\right)}^{2}, \sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}, x\right)} \]
6. Step-by-step derivation

   1. fma-undefine 97.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)}\right)}^{2} \cdot \sqrt[3]{\left(y + -1\right) \cdot \left(x \cdot z\right)} + x} \]

   2. unpow2 97.5%

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

   3. add-cube-cbrt 98.2%

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

7. Applied egg-rr 98.2%

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

8. Final simplification 98.2%

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

Alternative 12: 37.7% 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 95.9%

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

3. Taylor expanded in z around 0 37.5%

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

4. Final simplification 37.5%

   \[\leadsto x \]
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 2024077 
(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))))