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

Percentage Accurate: 95.6% → 97.7%

Time: 9.1s

Alternatives: 11

Speedup: 0.6×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{+84}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1e+84) (+ x (* x (* z (+ y -1.0)))) (* (+ y -1.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1e+84) {
		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 (z <= 1d+84) 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 (z <= 1e+84) {
		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 z <= 1e+84:
		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 (z <= 1e+84)
		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 (z <= 1e+84)
		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[z, 1e+84], 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 z < 1.00000000000000006e84

   1. Initial program 98.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 98.5%

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

      2. distribute-rgt-neg-out 98.5%

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

      3. +-commutative 98.5%

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

      4. distribute-rgt-neg-out 98.5%

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

      5. *-commutative 98.5%

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

      6. distribute-rgt-neg-in 98.5%

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

      7. fma-define 98.5%

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

      8. neg-sub0 98.5%

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

      9. associate--r- 98.5%

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

      10. metadata-eval 98.5%

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

      11. +-commutative 98.5%

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

   3. Simplified 98.5%

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

      1. fma-undefine 98.5%

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

      2. distribute-rgt-in 98.5%

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

      3. *-un-lft-identity 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 1.00000000000000006e84 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in y around 0 85.6%

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

   4. Taylor expanded in z around inf 85.6%

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

      1. sub-neg 85.6%

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

      2. metadata-eval 85.6%

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

      3. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{+84}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 64.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(-x\right)\\ t_1 := x \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+108}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- x))) (t_1 (* x (* z y))))
   (if (<= z -1.35e+108)
     t_0
     (if (<= z -2.2e-40)
       t_1
       (if (<= z 2.6e-94) x (if (<= z 6000000000.0) t_1 t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * -x;
	double t_1 = x * (z * y);
	double tmp;
	if (z <= -1.35e+108) {
		tmp = t_0;
	} else if (z <= -2.2e-40) {
		tmp = t_1;
	} else if (z <= 2.6e-94) {
		tmp = x;
	} else if (z <= 6000000000.0) {
		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 * (z * y)
    if (z <= (-1.35d+108)) then
        tmp = t_0
    else if (z <= (-2.2d-40)) then
        tmp = t_1
    else if (z <= 2.6d-94) then
        tmp = x
    else if (z <= 6000000000.0d0) 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 * (z * y);
	double tmp;
	if (z <= -1.35e+108) {
		tmp = t_0;
	} else if (z <= -2.2e-40) {
		tmp = t_1;
	} else if (z <= 2.6e-94) {
		tmp = x;
	} else if (z <= 6000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * -x
	t_1 = x * (z * y)
	tmp = 0
	if z <= -1.35e+108:
		tmp = t_0
	elif z <= -2.2e-40:
		tmp = t_1
	elif z <= 2.6e-94:
		tmp = x
	elif z <= 6000000000.0:
		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(z * y))
	tmp = 0.0
	if (z <= -1.35e+108)
		tmp = t_0;
	elseif (z <= -2.2e-40)
		tmp = t_1;
	elseif (z <= 2.6e-94)
		tmp = x;
	elseif (z <= 6000000000.0)
		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 * (z * y);
	tmp = 0.0;
	if (z <= -1.35e+108)
		tmp = t_0;
	elseif (z <= -2.2e-40)
		tmp = t_1;
	elseif (z <= 2.6e-94)
		tmp = x;
	elseif (z <= 6000000000.0)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+108], t$95$0, If[LessEqual[z, -2.2e-40], t$95$1, If[LessEqual[z, 2.6e-94], x, If[LessEqual[z, 6000000000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e108 or 6e9 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 89.5%

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

   4. Taylor expanded in z around inf 89.2%

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

      1. sub-neg 89.2%

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

      2. metadata-eval 89.2%

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

      3. associate-*r* 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in y around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. *-commutative 60.3%

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

      3. distribute-rgt-neg-in 60.3%

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

   9. Simplified 60.3%

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

   if -1.35e108 < z < -2.20000000000000009e-40 or 2.59999999999999994e-94 < z < 6e9

   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 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -2.20000000000000009e-40 < z < 2.59999999999999994e-94

   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 82.8%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-40}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6000000000:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.96 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.96) (not (<= z 1.0)))
   (* (+ y -1.0) (* z x))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.96) || !(z <= 1.0)) {
		tmp = (y + -1.0) * (z * x);
	} 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 <= (-0.96d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y + (-1.0d0)) * (z * x)
    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 <= -0.96) || !(z <= 1.0)) {
		tmp = (y + -1.0) * (z * x);
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.96) or not (z <= 1.0):
		tmp = (y + -1.0) * (z * x)
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.96) || !(z <= 1.0))
		tmp = Float64(Float64(y + -1.0) * Float64(z * x));
	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 <= -0.96) || ~((z <= 1.0)))
		tmp = (y + -1.0) * (z * x);
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.96], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.95999999999999996 or 1 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 91.3%

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

   4. Taylor expanded in z around inf 89.9%

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

      1. sub-neg 89.9%

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

      2. metadata-eval 89.9%

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

      3. associate-*r* 98.5%

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

   6. Simplified 98.5%

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

   if -0.95999999999999996 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.2%

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

      1. mul-1-neg 98.2%

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

      2. distribute-lft-neg-out 98.2%

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

      3. *-commutative 98.2%

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

   5. Simplified 98.2%

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

      1. sub-neg 98.2%

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

      2. distribute-rgt-neg-out 98.2%

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

      3. remove-double-neg 98.2%

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

      4. distribute-lft-in 98.2%

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

      5. *-commutative 98.2%

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

      6. *-un-lft-identity 98.2%

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

   7. Applied egg-rr 98.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.96 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+97)
   (* z (* y x))
   (if (<= y 2.9e+26) (* x (- 1.0 z)) (* (+ y -1.0) (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+97) {
		tmp = z * (y * x);
	} else if (y <= 2.9e+26) {
		tmp = x * (1.0 - z);
	} 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 (y <= (-2.7d+97)) then
        tmp = z * (y * x)
    else if (y <= 2.9d+26) then
        tmp = x * (1.0d0 - z)
    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 (y <= -2.7e+97) {
		tmp = z * (y * x);
	} else if (y <= 2.9e+26) {
		tmp = x * (1.0 - z);
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.7e+97:
		tmp = z * (y * x)
	elif y <= 2.9e+26:
		tmp = x * (1.0 - z)
	else:
		tmp = (y + -1.0) * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+97)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 2.9e+26)
		tmp = Float64(x * Float64(1.0 - z));
	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 (y <= -2.7e+97)
		tmp = z * (y * x);
	elseif (y <= 2.9e+26)
		tmp = x * (1.0 - z);
	else
		tmp = (y + -1.0) * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.7e+97], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+26], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.69999999999999993e97

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. associate-*r* 85.6%

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

      2. *-commutative 85.6%

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

   5. Simplified 85.6%

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

   if -2.69999999999999993e97 < y < 2.9e26

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 95.6%

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

   if 2.9e26 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in y around 0 90.6%

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

   4. Taylor expanded in z around inf 70.0%

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

      1. sub-neg 70.0%

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

      2. metadata-eval 70.0%

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

      3. associate-*r* 75.8%

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

   6. Simplified 75.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+26}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+97} \lor \neg \left(y \leq 2.6 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.7e+97) (not (<= y 2.6e+23))) (* x (* z y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+97) || !(y <= 2.6e+23)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.7d+97)) .or. (.not. (y <= 2.6d+23))) then
        tmp = x * (z * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.7e+97) || !(y <= 2.6e+23)) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.7e+97) or not (y <= 2.6e+23):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.7e+97) || !(y <= 2.6e+23))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.7e+97) || ~((y <= 2.6e+23)))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.7e+97], N[Not[LessEqual[y, 2.6e+23]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.69999999999999993e97 or 2.59999999999999992e23 < y

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 73.2%

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

      1. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -2.69999999999999993e97 < y < 2.59999999999999992e23

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 95.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+97} \lor \neg \left(y \leq 2.6 \cdot 10^{+23}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+96} \lor \neg \left(y \leq 9.6 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.9e+96) (not (<= y 9.6e+29))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.9e+96) || !(y <= 9.6e+29)) {
		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 <= (-5.9d+96)) .or. (.not. (y <= 9.6d+29))) 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 <= -5.9e+96) || !(y <= 9.6e+29)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.9e+96) or not (y <= 9.6e+29):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.9e+96) || !(y <= 9.6e+29))
		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 <= -5.9e+96) || ~((y <= 9.6e+29)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.9e+96], N[Not[LessEqual[y, 9.6e+29]], $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 < -5.90000000000000028e96 or 9.6000000000000003e29 < y

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 73.2%

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

      1. associate-*r* 78.3%

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

      2. *-commutative 78.3%

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

   5. Simplified 78.3%

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

   if -5.90000000000000028e96 < y < 9.6000000000000003e29

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 95.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+96} \lor \neg \left(y \leq 9.6 \cdot 10^{+29}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3e+95)
   (* z (* y x))
   (if (<= y 2.8e+27) (* x (- 1.0 z)) (* y (* z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3e+95) {
		tmp = z * (y * x);
	} else if (y <= 2.8e+27) {
		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 <= (-3d+95)) then
        tmp = z * (y * x)
    else if (y <= 2.8d+27) 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 <= -3e+95) {
		tmp = z * (y * x);
	} else if (y <= 2.8e+27) {
		tmp = x * (1.0 - z);
	} else {
		tmp = y * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3e+95:
		tmp = z * (y * x)
	elif y <= 2.8e+27:
		tmp = x * (1.0 - z)
	else:
		tmp = y * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3e+95)
		tmp = Float64(z * Float64(y * x));
	elseif (y <= 2.8e+27)
		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 <= -3e+95)
		tmp = z * (y * x);
	elseif (y <= 2.8e+27)
		tmp = x * (1.0 - z);
	else
		tmp = y * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3e+95], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+27], 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 < -2.99999999999999991e95

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 77.5%

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

      1. associate-*r* 85.6%

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

      2. *-commutative 85.6%

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

   5. Simplified 85.6%

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

   if -2.99999999999999991e95 < y < 2.7999999999999999e27

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 95.6%

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

   if 2.7999999999999999e27 < y

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 90.6%

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

      1. mul-1-neg 90.6%

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

      2. distribute-lft-neg-out 90.6%

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

      3. *-commutative 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in z around inf 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-*r* 75.8%

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

   8. Simplified 75.8%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+95}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.0)))
		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, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 91.3%

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

   3. Taylor expanded in y around 0 91.3%

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

   4. Taylor expanded in z around inf 89.9%

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

      1. sub-neg 89.9%

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

      2. metadata-eval 89.9%

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

      3. associate-*r* 98.5%

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

   6. Simplified 98.5%

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

   7. Taylor expanded in y around 0 55.5%

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

      1. mul-1-neg 55.5%

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

      2. *-commutative 55.5%

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

      3. distribute-rgt-neg-in 55.5%

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

   9. Simplified 55.5%

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

   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 72.6%

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

4. Final simplification 64.7%

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

Alternative 9: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.2e+83) (* x (+ 1.0 (* z (+ y -1.0)))) (* (+ y -1.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.2e+83) {
		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 (z <= 1.2d+83) 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 (z <= 1.2e+83) {
		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 z <= 1.2e+83:
		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 (z <= 1.2e+83)
		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 (z <= 1.2e+83)
		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[z, 1.2e+83], 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 z < 1.19999999999999996e83

   1. Initial program 98.5%

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

   if 1.19999999999999996e83 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in y around 0 85.6%

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

   4. Taylor expanded in z around inf 85.6%

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

      1. sub-neg 85.6%

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

      2. metadata-eval 85.6%

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

      3. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2e+83) (* x (- (+ 1.0 (* z y)) z)) (* (+ y -1.0) (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2e+83) {
		tmp = x * ((1.0 + (z * y)) - z);
	} 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 (z <= 2d+83) then
        tmp = x * ((1.0d0 + (z * y)) - z)
    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 (z <= 2e+83) {
		tmp = x * ((1.0 + (z * y)) - z);
	} else {
		tmp = (y + -1.0) * (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2e+83:
		tmp = x * ((1.0 + (z * y)) - z)
	else:
		tmp = (y + -1.0) * (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2e+83)
		tmp = Float64(x * Float64(Float64(1.0 + Float64(z * y)) - z));
	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 (z <= 2e+83)
		tmp = x * ((1.0 + (z * y)) - z);
	else
		tmp = (y + -1.0) * (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2e+83], N[(x * N[(N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.00000000000000006e83

   1. Initial program 98.5%

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

   3. Taylor expanded in y around 0 98.5%

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

   if 2.00000000000000006e83 < z

   1. Initial program 85.6%

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

   3. Taylor expanded in y around 0 85.6%

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

   4. Taylor expanded in z around inf 85.6%

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

      1. sub-neg 85.6%

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

      2. metadata-eval 85.6%

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

      3. associate-*r* 99.8%

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

   6. Simplified 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(z \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.9%

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

3. Taylor expanded in z around 0 40.4%

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

4. Final simplification 40.4%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.8% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(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))))