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

Percentage Accurate: 96.2% → 97.5%

Time: 8.5s

Alternatives: 11

Speedup: 0.8×

• 21.1% 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: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+56}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 2e+56)
   (+ x (* x (* z (+ y -1.0))))
   (* (+ y -1.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+56) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= 2d+56) then
        tmp = x + (x * (z * (y + (-1.0d0))))
    else
        tmp = (y + (-1.0d0)) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+56) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 2e+56:
		tmp = x + (x * (z * (y + -1.0)))
	else:
		tmp = (y + -1.0) * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 2e+56)
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 2e+56)
		tmp = x + (x * (z * (y + -1.0)));
	else
		tmp = (y + -1.0) * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 2e+56], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < 2.00000000000000018e56

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 99.4%

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

   if 2.00000000000000018e56 < (*.f64 (-.f64 1 y) z)

   1. Initial program 89.2%

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

   2. Taylor expanded in z around inf 89.2%

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

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+56}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 2: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-168}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* y z))))
   (if (<= z -8.2e+169)
     t_0
     (if (<= z -3.9e+74)
       t_1
       (if (<= z -4.5e-6)
         t_0
         (if (<= z -1.6e-60)
           t_1
           (if (<= z -1.3e-168)
             x
             (if (<= z -3.8e-181)
               t_1
               (if (<= z 1.15e-49) x (if (<= z 15.0) t_1 t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -8.2e+169) {
		tmp = t_0;
	} else if (z <= -3.9e+74) {
		tmp = t_1;
	} else if (z <= -4.5e-6) {
		tmp = t_0;
	} else if (z <= -1.6e-60) {
		tmp = t_1;
	} else if (z <= -1.3e-168) {
		tmp = x;
	} else if (z <= -3.8e-181) {
		tmp = t_1;
	} else if (z <= 1.15e-49) {
		tmp = x;
	} else if (z <= 15.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * -x
    t_1 = x * (y * z)
    if (z <= (-8.2d+169)) then
        tmp = t_0
    else if (z <= (-3.9d+74)) then
        tmp = t_1
    else if (z <= (-4.5d-6)) then
        tmp = t_0
    else if (z <= (-1.6d-60)) then
        tmp = t_1
    else if (z <= (-1.3d-168)) then
        tmp = x
    else if (z <= (-3.8d-181)) then
        tmp = t_1
    else if (z <= 1.15d-49) then
        tmp = x
    else if (z <= 15.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -8.2e+169) {
		tmp = t_0;
	} else if (z <= -3.9e+74) {
		tmp = t_1;
	} else if (z <= -4.5e-6) {
		tmp = t_0;
	} else if (z <= -1.6e-60) {
		tmp = t_1;
	} else if (z <= -1.3e-168) {
		tmp = x;
	} else if (z <= -3.8e-181) {
		tmp = t_1;
	} else if (z <= 1.15e-49) {
		tmp = x;
	} else if (z <= 15.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (y * z)
	tmp = 0
	if z <= -8.2e+169:
		tmp = t_0
	elif z <= -3.9e+74:
		tmp = t_1
	elif z <= -4.5e-6:
		tmp = t_0
	elif z <= -1.6e-60:
		tmp = t_1
	elif z <= -1.3e-168:
		tmp = x
	elif z <= -3.8e-181:
		tmp = t_1
	elif z <= 1.15e-49:
		tmp = x
	elif z <= 15.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(-x))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -8.2e+169)
		tmp = t_0;
	elseif (z <= -3.9e+74)
		tmp = t_1;
	elseif (z <= -4.5e-6)
		tmp = t_0;
	elseif (z <= -1.6e-60)
		tmp = t_1;
	elseif (z <= -1.3e-168)
		tmp = x;
	elseif (z <= -3.8e-181)
		tmp = t_1;
	elseif (z <= 1.15e-49)
		tmp = x;
	elseif (z <= 15.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * -x;
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -8.2e+169)
		tmp = t_0;
	elseif (z <= -3.9e+74)
		tmp = t_1;
	elseif (z <= -4.5e-6)
		tmp = t_0;
	elseif (z <= -1.6e-60)
		tmp = t_1;
	elseif (z <= -1.3e-168)
		tmp = x;
	elseif (z <= -3.8e-181)
		tmp = t_1;
	elseif (z <= 1.15e-49)
		tmp = x;
	elseif (z <= 15.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * (-x)), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.2e+169], t$95$0, If[LessEqual[z, -3.9e+74], t$95$1, If[LessEqual[z, -4.5e-6], t$95$0, If[LessEqual[z, -1.6e-60], t$95$1, If[LessEqual[z, -1.3e-168], x, If[LessEqual[z, -3.8e-181], t$95$1, If[LessEqual[z, 1.15e-49], x, If[LessEqual[z, 15.0], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2000000000000006e169 or -3.90000000000000008e74 < z < -4.50000000000000011e-6 or 15 < z

   1. Initial program 94.6%

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

   2. Taylor expanded in z around inf 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*l* 95.0%

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

      3. sub-neg 95.0%

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

      4. metadata-eval 95.0%

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

   4. Simplified 95.0%

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

   5. Taylor expanded in y around 0 62.2%

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

      1. neg-mul-1 62.2%

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

   7. Simplified 62.2%

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

   if -8.2000000000000006e169 < z < -3.90000000000000008e74 or -4.50000000000000011e-6 < z < -1.6000000000000001e-60 or -1.3e-168 < z < -3.7999999999999998e-181 or 1.15e-49 < z < 15

   1. Initial program 96.1%

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

   2. Taylor expanded in y around inf 69.5%

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

      1. *-commutative 69.5%

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

   4. Simplified 69.5%

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

   if -1.6000000000000001e-60 < z < -1.3e-168 or -3.7999999999999998e-181 < z < 1.15e-49

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 86.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+169}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{+74}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-6}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-168}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-181}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 15:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]

Alternative 3: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) 2e+56)
   (* x (+ 1.0 (* z (+ y -1.0))))
   (* (+ y -1.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+56) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= 2d+56) then
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    else
        tmp = (y + (-1.0d0)) * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= 2e+56) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= 2e+56:
		tmp = x * (1.0 + (z * (y + -1.0)))
	else:
		tmp = (y + -1.0) * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= 2e+56)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= 2e+56)
		tmp = x * (1.0 + (z * (y + -1.0)));
	else
		tmp = (y + -1.0) * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], 2e+56], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < 2.00000000000000018e56

   1. Initial program 99.4%

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

   if 2.00000000000000018e56 < (*.f64 (-.f64 1 y) z)

   1. Initial program 89.2%

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

   2. Taylor expanded in z around inf 89.2%

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

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+56}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 4: 95.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0004\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.0004)))
   (* x (+ 1.0 (* y z)))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.0004)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 0.0004d0))) 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 <= -1.0) || !(y <= 0.0004)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.0004):
		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 <= -1.0) || !(y <= 0.0004))
		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 <= -1.0) || ~((y <= 0.0004)))
		tmp = x * (1.0 + (y * z));
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.0004]], $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 2 regimes

2. if y < -1 or 4.00000000000000019e-4 < y

   1. Initial program 93.9%

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

   2. Taylor expanded in y around inf 92.9%

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

      1. mul-1-neg 92.9%

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

      2. distribute-lft-neg-out 92.9%

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

      3. *-commutative 92.9%

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

   4. Simplified 92.9%

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

      1. *-commutative 92.9%

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

      2. cancel-sign-sub 92.9%

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

      3. *-commutative 92.9%

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

      4. distribute-rgt-in 92.9%

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

      5. *-un-lft-identity 92.9%

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

      6. associate-*l* 90.8%

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

   6. Applied egg-rr 90.8%

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

      1. *-un-lft-identity 90.8%

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

      2. associate-*r* 92.9%

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

      3. distribute-rgt-out 92.9%

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

   8. Applied egg-rr 92.9%

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

   if -1 < y < 4.00000000000000019e-4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.3%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.0004\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 5: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.98 \lor \neg \left(z \leq 1.6 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.98) (not (<= z 1.6e-16)))
   (* z (* x (+ y -1.0)))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.98) || !(z <= 1.6e-16)) {
		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 <= (-0.98d0)) .or. (.not. (z <= 1.6d-16))) 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 <= -0.98) || !(z <= 1.6e-16)) {
		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 <= -0.98) or not (z <= 1.6e-16):
		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 <= -0.98) || !(z <= 1.6e-16))
		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 <= -0.98) || ~((z <= 1.6e-16)))
		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, -0.98], N[Not[LessEqual[z, 1.6e-16]], $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 < -0.97999999999999998 or 1.60000000000000011e-16 < z

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l* 97.8%

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

      3. sub-neg 97.8%

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

      4. metadata-eval 97.8%

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

   4. Simplified 97.8%

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

   if -0.97999999999999998 < z < 1.60000000000000011e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-lft-neg-out 97.8%

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

      3. *-commutative 97.8%

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

   4. Simplified 97.8%

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

      1. *-commutative 97.8%

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

      2. cancel-sign-sub 97.8%

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

      3. *-commutative 97.8%

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

      4. distribute-rgt-in 97.8%

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

      5. *-un-lft-identity 97.8%

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

      6. associate-*l* 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. *-un-lft-identity 89.8%

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

      2. associate-*r* 97.8%

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

      3. distribute-rgt-out 97.8%

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

   8. Applied egg-rr 97.8%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.98 \lor \neg \left(z \leq 1.6 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 6: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.05)
   (* (+ y -1.0) (* z x))
   (if (<= z 1.6e-16) (* x (+ 1.0 (* y z))) (* z (* x (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.05) {
		tmp = (y + -1.0) * (z * x);
	} else if (z <= 1.6e-16) {
		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 <= (-1.05d0)) then
        tmp = (y + (-1.0d0)) * (z * x)
    else if (z <= 1.6d-16) 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 <= -1.05) {
		tmp = (y + -1.0) * (z * x);
	} else if (z <= 1.6e-16) {
		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 <= -1.05:
		tmp = (y + -1.0) * (z * x)
	elif z <= 1.6e-16:
		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 <= -1.05)
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	elseif (z <= 1.6e-16)
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.05)
		tmp = (y + -1.0) * (z * x);
	elseif (z <= 1.6e-16)
		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, -1.05], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e-16], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004

   1. Initial program 93.8%

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

   2. Taylor expanded in z around inf 90.8%

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

      1. associate-*r* 96.9%

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

      2. *-commutative 96.9%

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

      3. sub-neg 96.9%

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

      4. metadata-eval 96.9%

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

   4. Simplified 96.9%

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

   if -1.05000000000000004 < z < 1.60000000000000011e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-lft-neg-out 97.8%

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

      3. *-commutative 97.8%

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

   4. Simplified 97.8%

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

      1. *-commutative 97.8%

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

      2. cancel-sign-sub 97.8%

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

      3. *-commutative 97.8%

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

      4. distribute-rgt-in 97.8%

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

      5. *-un-lft-identity 97.8%

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

      6. associate-*l* 89.8%

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

   6. Applied egg-rr 89.8%

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

      1. *-un-lft-identity 89.8%

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

      2. associate-*r* 97.8%

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

      3. distribute-rgt-out 97.8%

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

   8. Applied egg-rr 97.8%

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

   if 1.60000000000000011e-16 < z

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 92.9%

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

      1. *-commutative 92.9%

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

      2. associate-*l* 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

   4. Simplified 98.7%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 7: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+34} \lor \neg \left(y \leq 5 \cdot 10^{+155}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.5e+34) (not (<= y 5e+155))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+34) || !(y <= 5e+155)) {
		tmp = x * (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 <= (-5.5d+34)) .or. (.not. (y <= 5d+155))) then
        tmp = x * (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 <= -5.5e+34) || !(y <= 5e+155)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+34) or not (y <= 5e+155):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+34) || !(y <= 5e+155))
		tmp = Float64(x * 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 <= -5.5e+34) || ~((y <= 5e+155)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+34], N[Not[LessEqual[y, 5e+155]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999996e34 or 4.9999999999999999e155 < y

   1. Initial program 92.4%

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

   2. Taylor expanded in y around inf 79.6%

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

      1. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   if -5.4999999999999996e34 < y < 4.9999999999999999e155

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 91.4%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+34} \lor \neg \left(y \leq 5 \cdot 10^{+155}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 8: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+35} \lor \neg \left(y \leq 5 \cdot 10^{+155}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9e+35) (not (<= y 5e+155))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9e+35) || !(y <= 5e+155)) {
		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 <= (-9d+35)) .or. (.not. (y <= 5d+155))) 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 <= -9e+35) || !(y <= 5e+155)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9e+35) or not (y <= 5e+155):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9e+35) || !(y <= 5e+155))
		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 <= -9e+35) || ~((y <= 5e+155)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9e+35], N[Not[LessEqual[y, 5e+155]], $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 < -8.9999999999999993e35 or 4.9999999999999999e155 < y

   1. Initial program 92.4%

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

   2. Taylor expanded in z around inf 79.6%

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

      1. *-commutative 79.6%

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

      2. associate-*l* 80.9%

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

      3. sub-neg 80.9%

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

      4. metadata-eval 80.9%

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

   4. Simplified 80.9%

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

   5. Taylor expanded in y around inf 80.9%

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

   if -8.9999999999999993e35 < y < 4.9999999999999999e155

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 91.4%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+35} \lor \neg \left(y \leq 5 \cdot 10^{+155}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 9: 82.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.4e+32)
   (* z (* y x))
   (if (<= y 5e+155) (* x (- 1.0 z)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+32) {
		tmp = z * (y * x);
	} else if (y <= 5e+155) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-2.4d+32)) then
        tmp = z * (y * x)
    else if (y <= 5d+155) then
        tmp = x * (1.0d0 - z)
    else
        tmp = y * (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.4e+32) {
		tmp = z * (y * x);
	} else if (y <= 5e+155) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.4e+32:
		tmp = z * (y * x)
	elif y <= 5e+155:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.4e+32)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 5e+155)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(y * Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.4e+32)
		tmp = z * (y * x);
	elseif (y <= 5e+155)
		tmp = x * (1.0 - z);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.4e+32], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e+155], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999991e32

   1. Initial program 94.8%

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

   2. Taylor expanded in z around inf 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l* 80.3%

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

      3. sub-neg 80.3%

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

      4. metadata-eval 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in y around inf 80.3%

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

   if -2.39999999999999991e32 < y < 4.9999999999999999e155

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 91.4%

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

   if 4.9999999999999999e155 < y

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 81.8%

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

      1. *-commutative 81.8%

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

   4. Simplified 81.8%

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

      1. add-sqr-sqrt 34.3%

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

      2. pow2 34.3%

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

      3. *-commutative 34.3%

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

      4. associate-*l* 31.6%

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

   6. Applied egg-rr 31.6%

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

      1. unpow2 31.6%

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

      2. add-sqr-sqrt 82.0%

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

      3. *-commutative 82.0%

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

      4. associate-*r* 86.5%

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

   8. Applied egg-rr 86.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+32}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+155}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 10: 65.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.6 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.6e-16))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.6e-16)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 1.6d-16))) then
        tmp = z * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.6e-16)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.6e-16):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.6e-16))
		tmp = Float64(z * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.6e-16)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.6e-16]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.60000000000000011e-16 < z

   1. Initial program 94.0%

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

   2. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-*l* 97.8%

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

      3. sub-neg 97.8%

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

      4. metadata-eval 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in y around 0 57.5%

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

      1. neg-mul-1 57.5%

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

   7. Simplified 57.5%

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

   if -1 < z < 1.60000000000000011e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 73.6%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.6 \cdot 10^{-16}\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 97.0%

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

2. Taylor expanded in z around 0 38.6%

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

3. Final simplification 38.6%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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