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

Percentage Accurate: 95.9% → 97.8%

Time: 7.5s

Alternatives: 12

Speedup: 0.5×

• 20.7% 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: 95.9% 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: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+199}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot z - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -5e+199)
   (* (* z x) (+ y -1.0))
   (* x (+ 1.0 (- (* y z) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -5e+199) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + ((y * z) - 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 (((1.0d0 - y) * z) <= (-5d+199)) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x * (1.0d0 + ((y * z) - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -5e+199) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + ((y * z) - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -5e+199:
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x * (1.0 + ((y * z) - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -5e+199)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x * Float64(1.0 + Float64(Float64(y * z) - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -5e+199)
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x * (1.0 + ((y * z) - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -5e+199], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(N[(y * z), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -4.9999999999999998e199

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. sub-neg 78.1%

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

      3. distribute-rgt-in 78.1%

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

      4. *-un-lft-identity 78.1%

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

   4. Applied egg-rr 78.1%

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

   5. Taylor expanded in z around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. *-commutative 78.1%

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

      3. mul-1-neg 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

      6. associate-*r* 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. mul-1-neg 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. mul-1-neg 99.9%

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

      13. remove-double-neg 99.9%

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

   7. Simplified 99.9%

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

   if -4.9999999999999998e199 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

      2. sub-neg 98.5%

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

      3. distribute-rgt-in 98.5%

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

      4. *-un-lft-identity 98.5%

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

   4. Applied egg-rr 98.5%

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

   5. Taylor expanded in x around 0 98.5%

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

      1. mul-1-neg 98.5%

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

      2. *-commutative 98.5%

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

      3. sub-neg 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+199}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \left(y \cdot z - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+199}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -5e+199)
   (* (* z x) (+ y -1.0))
   (* x (+ 1.0 (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -5e+199) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= (-5d+199)) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x * (1.0d0 + (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -5e+199) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x * (1.0 + (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -5e+199:
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x * (1.0 + (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -5e+199)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -5e+199)
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x * (1.0 + (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -5e+199], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -4.9999999999999998e199

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. sub-neg 78.1%

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

      3. distribute-rgt-in 78.1%

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

      4. *-un-lft-identity 78.1%

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

   4. Applied egg-rr 78.1%

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

   5. Taylor expanded in z around inf 78.1%

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

      1. mul-1-neg 78.1%

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

      2. *-commutative 78.1%

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

      3. mul-1-neg 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

      6. associate-*r* 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. sub-neg 99.9%

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

      9. mul-1-neg 99.9%

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

      10. distribute-neg-in 99.9%

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

      11. metadata-eval 99.9%

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

      12. mul-1-neg 99.9%

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

      13. remove-double-neg 99.9%

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

   7. Simplified 99.9%

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

   if -4.9999999999999998e199 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 98.5%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -5 \cdot 10^{+199}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-34} \lor \neg \left(z \leq 5.5 \cdot 10^{-85}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e-34) (not (<= z 5.5e-85))) (* z (* x (+ y -1.0))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-34) || !(z <= 5.5e-85)) {
		tmp = z * (x * (y + -1.0));
	} 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 <= (-2.4d-34)) .or. (.not. (z <= 5.5d-85))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-34) || !(z <= 5.5e-85)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.4e-34) or not (z <= 5.5e-85):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e-34) || !(z <= 5.5e-85))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.4e-34) || ~((z <= 5.5e-85)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.4e-34], N[Not[LessEqual[z, 5.5e-85]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999991e-34 or 5.4999999999999997e-85 < z

   1. Initial program 91.7%

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

   3. Taylor expanded in z around inf 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-*r* 91.7%

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

      3. *-commutative 91.7%

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

      4. sub-neg 91.7%

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

      5. metadata-eval 91.7%

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

   5. Simplified 91.7%

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

   if -2.39999999999999991e-34 < z < 5.4999999999999997e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-34} \lor \neg \left(z \leq 5.5 \cdot 10^{-85}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6500:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6500.0)
   (* z (* x (+ y -1.0)))
   (if (<= z 1.0) (+ x (* x (* y z))) (* (* z x) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6500.0) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x + (x * (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 <= (-6500.0d0)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 1.0d0) then
        tmp = x + (x * (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 <= -6500.0) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 1.0) {
		tmp = x + (x * (y * z));
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6500.0:
		tmp = z * (x * (y + -1.0))
	elif z <= 1.0:
		tmp = x + (x * (y * z))
	else:
		tmp = (z * x) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6500.0)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6500.0)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 1.0)
		tmp = x + (x * (y * z));
	else
		tmp = (z * x) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6500.0], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], N[(x + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6500

   1. Initial program 92.8%

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

   3. Taylor expanded in z around inf 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-*r* 99.6%

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

      3. *-commutative 99.6%

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

      4. sub-neg 99.6%

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

      5. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

   if -6500 < 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 98.6%

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

      1. mul-1-neg 98.6%

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

      2. distribute-lft-neg-out 98.6%

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

      3. *-commutative 98.6%

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

   5. Simplified 98.6%

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

      1. sub-neg 98.6%

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

      2. distribute-rgt-in 98.6%

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

      3. *-un-lft-identity 98.6%

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

      4. distribute-rgt-neg-out 98.6%

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

      5. remove-double-neg 98.6%

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

   7. Applied egg-rr 98.6%

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

   if 1 < z

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

      2. sub-neg 86.7%

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

      3. distribute-rgt-in 86.7%

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

      4. *-un-lft-identity 86.7%

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

   4. Applied egg-rr 86.7%

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

   5. Taylor expanded in z around inf 84.3%

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

      1. mul-1-neg 84.3%

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

      2. *-commutative 84.3%

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

      3. mul-1-neg 84.3%

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

      4. sub-neg 84.3%

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

      5. *-commutative 84.3%

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

      6. associate-*r* 97.4%

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

      7. distribute-rgt-neg-in 97.4%

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

      8. sub-neg 97.4%

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

      9. mul-1-neg 97.4%

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

      10. distribute-neg-in 97.4%

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

      11. metadata-eval 97.4%

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

      12. mul-1-neg 97.4%

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

      13. remove-double-neg 97.4%

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

   7. Simplified 97.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6500:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-37}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e-37)
   (* z (* x (+ y -1.0)))
   (if (<= z 5.5e-85) x (* (* z x) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-37) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 5.5e-85) {
		tmp = x;
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2d-37)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 5.5d-85) then
        tmp = x
    else
        tmp = (z * x) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e-37) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 5.5e-85) {
		tmp = x;
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e-37:
		tmp = z * (x * (y + -1.0))
	elif z <= 5.5e-85:
		tmp = x
	else:
		tmp = (z * x) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e-37)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 5.5e-85)
		tmp = x;
	else
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e-37)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 5.5e-85)
		tmp = x;
	else
		tmp = (z * x) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e-37], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-85], x, N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000013e-37

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*r* 96.1%

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

      3. *-commutative 96.1%

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

      4. sub-neg 96.1%

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

      5. metadata-eval 96.1%

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

   5. Simplified 96.1%

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

   if -2.00000000000000013e-37 < z < 5.4999999999999997e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

   if 5.4999999999999997e-85 < z

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

      2. sub-neg 90.2%

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

      3. distribute-rgt-in 90.2%

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

      4. *-un-lft-identity 90.2%

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

   4. Applied egg-rr 90.2%

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

   5. Taylor expanded in z around inf 79.4%

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

      1. mul-1-neg 79.4%

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

      2. *-commutative 79.4%

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

      3. mul-1-neg 79.4%

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

      4. sub-neg 79.4%

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

      5. *-commutative 79.4%

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

      6. associate-*r* 88.1%

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

      7. distribute-rgt-neg-in 88.1%

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

      8. sub-neg 88.1%

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

      9. mul-1-neg 88.1%

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

      10. distribute-neg-in 88.1%

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

      11. metadata-eval 88.1%

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

      12. mul-1-neg 88.1%

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

      13. remove-double-neg 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-37}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e-36)
   (* z (* x (+ y -1.0)))
   (if (<= z 5.5e-85) x (* z (- (* y x) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e-36) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 5.5e-85) {
		tmp = x;
	} else {
		tmp = z * ((y * x) - 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 <= (-1.9d-36)) then
        tmp = z * (x * (y + (-1.0d0)))
    else if (z <= 5.5d-85) then
        tmp = x
    else
        tmp = z * ((y * x) - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e-36) {
		tmp = z * (x * (y + -1.0));
	} else if (z <= 5.5e-85) {
		tmp = x;
	} else {
		tmp = z * ((y * x) - x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e-36:
		tmp = z * (x * (y + -1.0))
	elif z <= 5.5e-85:
		tmp = x
	else:
		tmp = z * ((y * x) - x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e-36)
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	elseif (z <= 5.5e-85)
		tmp = x;
	else
		tmp = Float64(z * Float64(Float64(y * x) - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e-36)
		tmp = z * (x * (y + -1.0));
	elseif (z <= 5.5e-85)
		tmp = x;
	else
		tmp = z * ((y * x) - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e-36], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e-85], x, N[(z * N[(N[(y * x), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.89999999999999985e-36

   1. Initial program 93.5%

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

   3. Taylor expanded in z around inf 89.7%

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

      1. *-commutative 89.7%

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

      2. associate-*r* 96.1%

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

      3. *-commutative 96.1%

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

      4. sub-neg 96.1%

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

      5. metadata-eval 96.1%

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

   5. Simplified 96.1%

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

   if -1.89999999999999985e-36 < z < 5.4999999999999997e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

   if 5.4999999999999997e-85 < z

   1. Initial program 90.2%

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

   3. Taylor expanded in z around inf 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-*r* 88.0%

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

      3. *-commutative 88.0%

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

      4. sub-neg 88.0%

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

      5. metadata-eval 88.0%

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

   5. Simplified 88.0%

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

      1. distribute-lft-in 88.0%

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

      2. *-commutative 88.0%

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

      3. mul-1-neg 88.0%

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

   7. Applied egg-rr 88.0%

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

   8. Taylor expanded in z around 0 88.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -34000 \lor \neg \left(y \leq 3.8 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -34000.0) (not (<= y 3.8e+28))) (* z (* y x)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -34000.0) || !(y <= 3.8e+28)) {
		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 <= (-34000.0d0)) .or. (.not. (y <= 3.8d+28))) 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 <= -34000.0) || !(y <= 3.8e+28)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -34000.0) or not (y <= 3.8e+28):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -34000.0) || !(y <= 3.8e+28))
		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 <= -34000.0) || ~((y <= 3.8e+28)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -34000.0], N[Not[LessEqual[y, 3.8e+28]], $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 < -34000 or 3.7999999999999999e28 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in z around inf 72.4%

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

      1. *-commutative 72.4%

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

      2. associate-*r* 79.9%

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

      3. *-commutative 79.9%

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

      4. sub-neg 79.9%

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

      5. metadata-eval 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in y around inf 79.2%

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

   if -34000 < y < 3.7999999999999999e28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -34000 \lor \neg \left(y \leq 3.8 \cdot 10^{+28}\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -34000 \lor \neg \left(y \leq 9 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -34000.0) (not (<= y 9e+28))) (* x (* y z)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -34000.0) || !(y <= 9e+28)) {
		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 <= (-34000.0d0)) .or. (.not. (y <= 9d+28))) 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 <= -34000.0) || !(y <= 9e+28)) {
		tmp = x * (y * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -34000.0) or not (y <= 9e+28):
		tmp = x * (y * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -34000.0) || !(y <= 9e+28))
		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 <= -34000.0) || ~((y <= 9e+28)))
		tmp = x * (y * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -34000.0], N[Not[LessEqual[y, 9e+28]], $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 < -34000 or 8.9999999999999994e28 < y

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 71.8%

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

      1. *-commutative 71.8%

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

   5. Simplified 71.8%

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

   if -34000 < y < 8.9999999999999994e28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -34000 \lor \neg \left(y \leq 9 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 59.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-35} \lor \neg \left(z \leq 5.5 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.8e-35) (not (<= z 5.5e-85))) (* x (* y z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-35) || !(z <= 5.5e-85)) {
		tmp = x * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.8d-35)) .or. (.not. (z <= 5.5d-85))) then
        tmp = x * (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.8e-35) || !(z <= 5.5e-85)) {
		tmp = x * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.8e-35) or not (z <= 5.5e-85):
		tmp = x * (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.8e-35) || !(z <= 5.5e-85))
		tmp = Float64(x * Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.8e-35) || ~((z <= 5.5e-85)))
		tmp = x * (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.8e-35], N[Not[LessEqual[z, 5.5e-85]], $MachinePrecision]], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.8000000000000003e-35 or 5.4999999999999997e-85 < z

   1. Initial program 91.7%

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

   3. Taylor expanded in y around inf 56.5%

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

      1. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   if -4.8000000000000003e-35 < z < 5.4999999999999997e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 84.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-35} \lor \neg \left(z \leq 5.5 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -34000:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -34000.0)
   (* y (* z x))
   (if (<= y 3.5e+28) (* x (- 1.0 z)) (* z (* y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -34000.0) {
		tmp = y * (z * x);
	} else if (y <= 3.5e+28) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-34000.0d0)) then
        tmp = y * (z * x)
    else if (y <= 3.5d+28) then
        tmp = x * (1.0d0 - z)
    else
        tmp = z * (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -34000.0) {
		tmp = y * (z * x);
	} else if (y <= 3.5e+28) {
		tmp = x * (1.0 - z);
	} else {
		tmp = z * (y * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -34000.0:
		tmp = y * (z * x)
	elif y <= 3.5e+28:
		tmp = x * (1.0 - z)
	else:
		tmp = z * (y * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -34000.0)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 3.5e+28)
		tmp = Float64(x * Float64(1.0 - z));
	else
		tmp = Float64(z * Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -34000.0)
		tmp = y * (z * x);
	elseif (y <= 3.5e+28)
		tmp = x * (1.0 - z);
	else
		tmp = z * (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -34000.0], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+28], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -34000

   1. Initial program 89.5%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. *-commutative 75.1%

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

      2. associate-*r* 81.6%

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

      3. *-commutative 81.6%

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

      4. sub-neg 81.6%

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

      5. metadata-eval 81.6%

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

   5. Simplified 81.6%

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

      1. associate-*r* 82.3%

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

      2. *-commutative 82.3%

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

      3. +-commutative 82.3%

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

      4. flip3-+ 32.3%

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

      5. associate-*r/ 25.9%

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

      6. metadata-eval 25.9%

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

      7. metadata-eval 25.9%

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

      8. cancel-sign-sub-inv 25.9%

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

      9. pow2 25.9%

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

      10. metadata-eval 25.9%

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

      11. *-un-lft-identity 25.9%

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

   7. Applied egg-rr 25.9%

      \[\leadsto \color{blue}{\frac{\left(x \cdot z\right) \cdot \left(-1 + {y}^{3}\right)}{1 + \left({y}^{2} + y\right)}} \]
   8. Step-by-step derivation

      1. associate-+r+ 25.9%

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

      2. +-commutative 25.9%

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

      3. remove-double-neg 25.9%

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

      4. sub-neg 25.9%

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

      5. associate-+r- 25.9%

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

      6. unpow2 25.9%

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

      7. fma-undefine 26.0%

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

      8. associate-/l* 32.4%

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

      9. fma-undefine 32.3%

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

      10. unpow2 32.3%

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

      11. associate-+r- 32.3%

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

      12. sub-neg 32.3%

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

      13. +-commutative 32.3%

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

      14. remove-double-neg 32.3%

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

      15. associate-+r+ 32.3%

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

      16. unpow2 32.3%

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

      17. fma-define 32.4%

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

   9. Simplified 32.4%

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

   10. Taylor expanded in y around inf 81.1%

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

   if -34000 < y < 3.5e28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.7%

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

   if 3.5e28 < y

   1. Initial program 91.2%

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

   3. Taylor expanded in z around inf 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 78.0%

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

      3. *-commutative 78.0%

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

      4. sub-neg 78.0%

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

      5. metadata-eval 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in y around inf 78.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -34000:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.175) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.175) || !(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 <= (-0.175d0)) .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 <= -0.175) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.175) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.175) || !(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 <= -0.175) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.175], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.17499999999999999 or 1 < z

   1. Initial program 90.0%

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

   3. Taylor expanded in z around inf 88.6%

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

      1. *-commutative 88.6%

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

      2. associate-*r* 98.5%

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

      3. *-commutative 98.5%

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

      4. sub-neg 98.5%

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

      5. metadata-eval 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in y around 0 43.7%

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

      1. associate-*r* 43.7%

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

      2. neg-mul-1 43.7%

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

      3. *-commutative 43.7%

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

   8. Simplified 43.7%

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

   if -0.17499999999999999 < 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 72.1%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.175 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 94.7%

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

3. Taylor expanded in z around 0 35.9%

   \[\leadsto \color{blue}{x} \]
4. 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 2024091 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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