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

Percentage Accurate: 96.1% → 97.4%

Time: 7.9s

Alternatives: 11

Speedup: 0.5×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.1% 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: 97.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+16)
   (* (* z x) (+ y -1.0))
   (+ x (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+16) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((1.0d0 - y) * z) <= (-1d+16)) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x + (x * (z * (y + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((1.0 - y) * z) <= -1e+16) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((1.0 - y) * z) <= -1e+16:
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x + (x * (z * (y + -1.0)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(1.0 - y) * z) <= -1e+16)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((1.0 - y) * z) <= -1e+16)
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x + (x * (z * (y + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision], -1e+16], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) y) z) < -1e16

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf 91.3%

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

      1. distribute-rgt-out-- 91.4%

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

      2. *-lft-identity 91.4%

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

      3. sub-neg 91.4%

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

      4. +-commutative 91.4%

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

      5. +-commutative 91.4%

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

      6. neg-mul-1 91.4%

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

      7. distribute-rgt-in 91.3%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   if -1e16 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 97.8%

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

      1. sub-neg 97.8%

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

      2. distribute-rgt-neg-out 97.8%

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

      3. +-commutative 97.8%

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

      4. distribute-rgt-neg-out 97.8%

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

      5. *-commutative 97.8%

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

      6. distribute-rgt-neg-in 97.8%

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

      7. fma-define 97.8%

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

      8. neg-sub0 97.8%

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

      9. associate--r- 97.8%

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

      10. metadata-eval 97.8%

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

      11. +-commutative 97.8%

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

   3. Simplified 97.8%

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

      1. fma-undefine 97.8%

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

      2. distribute-rgt-in 97.8%

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

      3. *-un-lft-identity 97.8%

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

   6. Applied egg-rr 97.8%

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

4. Final simplification 98.4%

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

Alternative 2: 97.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (- 1.0 y) z) -1e+16)
   (* (* 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) <= -1e+16) {
		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) <= (-1d+16)) 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) <= -1e+16) {
		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) <= -1e+16:
		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) <= -1e+16)
		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) <= -1e+16)
		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], -1e+16], 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) < -1e16

   1. Initial program 91.3%

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

   3. Taylor expanded in z around inf 91.3%

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

      1. distribute-rgt-out-- 91.4%

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

      2. *-lft-identity 91.4%

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

      3. sub-neg 91.4%

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

      4. +-commutative 91.4%

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

      5. +-commutative 91.4%

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

      6. neg-mul-1 91.4%

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

      7. distribute-rgt-in 91.3%

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

      8. associate-*r* 99.9%

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

      9. *-commutative 99.9%

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

      10. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   if -1e16 < (*.f64 (-.f64 #s(literal 1 binary64) y) z)

   1. Initial program 97.8%

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

4. Final simplification 98.4%

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

Alternative 3: 98.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (* (* 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 <= -1.0) {
		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 <= (-1.0d0)) 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 <= -1.0) {
		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 <= -1.0:
		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 <= -1.0)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	elseif (z <= 1.0)
		tmp = Float64(x + Float64(x * Float64(y * z)));
	else
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

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

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 89.7%

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

   3. Taylor expanded in z around inf 88.3%

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

      1. distribute-rgt-out-- 88.3%

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

      2. *-lft-identity 88.3%

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

      3. sub-neg 88.3%

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

      4. +-commutative 88.3%

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

      5. +-commutative 88.3%

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

      6. neg-mul-1 88.3%

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

      7. distribute-rgt-in 88.3%

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

      8. associate-*r* 98.5%

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

      9. *-commutative 98.5%

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

      10. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   if -1 < z < 1

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-neg-out 99.8%

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

      3. +-commutative 99.8%

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

      4. distribute-rgt-neg-out 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-define 99.8%

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

      8. neg-sub0 99.8%

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

      9. associate--r- 99.8%

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

      10. metadata-eval 99.8%

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

      11. +-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. fma-undefine 99.8%

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

      2. distribute-rgt-in 99.8%

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

      3. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 96.2%

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

      1. *-commutative 96.2%

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

   9. Simplified 96.2%

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

   if 1 < z

   1. Initial program 94.3%

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

   3. Taylor expanded in z around inf 92.8%

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

      1. *-commutative 92.8%

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

      2. sub-neg 92.8%

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

      3. metadata-eval 92.8%

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

      4. associate-*l* 98.5%

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

      5. +-commutative 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 97.4%

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

Alternative 4: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 560000000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.4e+17)
   (* y (* z x))
   (if (<= y 560000000.0) (- x (* z x)) (* (* z x) (+ y -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.4e+17) {
		tmp = y * (z * x);
	} else if (y <= 560000000.0) {
		tmp = x - (z * 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 (y <= (-8.4d+17)) then
        tmp = y * (z * x)
    else if (y <= 560000000.0d0) then
        tmp = x - (z * 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 (y <= -8.4e+17) {
		tmp = y * (z * x);
	} else if (y <= 560000000.0) {
		tmp = x - (z * x);
	} else {
		tmp = (z * x) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.4e+17:
		tmp = y * (z * x)
	elif y <= 560000000.0:
		tmp = x - (z * x)
	else:
		tmp = (z * x) * (y + -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.4e+17)
		tmp = Float64(y * Float64(z * x));
	elseif (y <= 560000000.0)
		tmp = Float64(x - Float64(z * 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 (y <= -8.4e+17)
		tmp = y * (z * x);
	elseif (y <= 560000000.0)
		tmp = x - (z * x);
	else
		tmp = (z * x) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.4e+17], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 560000000.0], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.4e17

   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 79.1%

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

      1. distribute-rgt-out-- 79.1%

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

      2. *-lft-identity 79.1%

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

      3. sub-neg 79.1%

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

      4. +-commutative 79.1%

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

      5. +-commutative 79.1%

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

      6. neg-mul-1 79.1%

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

      7. distribute-rgt-in 79.1%

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

      8. associate-*r* 85.0%

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

      9. *-commutative 85.0%

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

      10. +-commutative 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in y around inf 85.0%

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

   if -8.4e17 < y < 5.6e8

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-neg-out 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-rgt-neg-out 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-define 99.9%

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

      8. neg-sub0 99.9%

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

      9. associate--r- 99.9%

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

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

   9. Simplified 97.8%

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

   if 5.6e8 < y

   1. Initial program 90.5%

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

   3. Taylor expanded in z around inf 70.7%

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

      1. distribute-rgt-out-- 70.7%

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

      2. *-lft-identity 70.7%

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

      3. sub-neg 70.7%

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

      4. +-commutative 70.7%

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

      5. +-commutative 70.7%

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

      6. neg-mul-1 70.7%

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

      7. distribute-rgt-in 70.7%

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

      8. associate-*r* 73.8%

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

      9. *-commutative 73.8%

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

      10. +-commutative 73.8%

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

   5. Simplified 73.8%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 560000000:\\ \;\;\;\;x - z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+20} \lor \neg \left(y \leq 36000000000\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e+20) (not (<= y 36000000000.0)))
   (* y (* z x))
   (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+20) || !(y <= 36000000000.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x - (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 <= (-3.7d+20)) .or. (.not. (y <= 36000000000.0d0))) then
        tmp = y * (z * x)
    else
        tmp = x - (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e+20) || !(y <= 36000000000.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e+20) or not (y <= 36000000000.0):
		tmp = y * (z * x)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e+20) || !(y <= 36000000000.0))
		tmp = Float64(y * Float64(z * x));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.7e+20) || ~((y <= 36000000000.0)))
		tmp = y * (z * x);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e+20], N[Not[LessEqual[y, 36000000000.0]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.7e20 or 3.6e10 < y

   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 74.4%

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

      1. distribute-rgt-out-- 74.4%

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

      2. *-lft-identity 74.4%

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

      3. sub-neg 74.4%

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

      4. +-commutative 74.4%

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

      5. +-commutative 74.4%

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

      6. neg-mul-1 74.4%

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

      7. distribute-rgt-in 74.4%

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

      8. associate-*r* 78.7%

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

      9. *-commutative 78.7%

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

      10. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in y around inf 78.6%

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

   if -3.7e20 < y < 3.6e10

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-neg-out 99.9%

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

      3. +-commutative 99.9%

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

      4. distribute-rgt-neg-out 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-rgt-neg-in 99.9%

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

      7. fma-define 99.9%

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

      8. neg-sub0 99.9%

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

      9. associate--r- 99.9%

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

      10. metadata-eval 99.9%

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

      11. +-commutative 99.9%

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

   3. Simplified 99.9%

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

      1. fma-undefine 99.9%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

   9. Simplified 97.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+20} \lor \neg \left(y \leq 36000000000\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+18} \lor \neg \left(y \leq 66000000000\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.2e+18) (not (<= y 66000000000.0)))
   (* y (* z x))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.2e+18) || !(y <= 66000000000.0)) {
		tmp = y * (z * 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 <= (-2.2d+18)) .or. (.not. (y <= 66000000000.0d0))) then
        tmp = y * (z * 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 <= -2.2e+18) || !(y <= 66000000000.0)) {
		tmp = y * (z * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.2e+18) or not (y <= 66000000000.0):
		tmp = y * (z * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.2e+18) || !(y <= 66000000000.0))
		tmp = Float64(y * Float64(z * 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 <= -2.2e+18) || ~((y <= 66000000000.0)))
		tmp = y * (z * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.2e+18], N[Not[LessEqual[y, 66000000000.0]], $MachinePrecision]], N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e18 or 6.6e10 < y

   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 74.4%

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

      1. distribute-rgt-out-- 74.4%

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

      2. *-lft-identity 74.4%

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

      3. sub-neg 74.4%

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

      4. +-commutative 74.4%

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

      5. +-commutative 74.4%

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

      6. neg-mul-1 74.4%

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

      7. distribute-rgt-in 74.4%

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

      8. associate-*r* 78.7%

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

      9. *-commutative 78.7%

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

      10. +-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in y around inf 78.6%

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

   if -2.2e18 < y < 6.6e10

   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 0 97.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+18} \lor \neg \left(y \leq 66000000000\right):\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+20} \lor \neg \left(y \leq 76000000000\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+20) (not (<= y 76000000000.0)))
   (* z (* y x))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+20) || !(y <= 76000000000.0)) {
		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 <= (-6.5d+20)) .or. (.not. (y <= 76000000000.0d0))) 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 <= -6.5e+20) || !(y <= 76000000000.0)) {
		tmp = z * (y * x);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e+20) or not (y <= 76000000000.0):
		tmp = z * (y * x)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e+20) || !(y <= 76000000000.0))
		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 <= -6.5e+20) || ~((y <= 76000000000.0)))
		tmp = z * (y * x);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e+20], N[Not[LessEqual[y, 76000000000.0]], $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 < -6.5e20 or 7.6e10 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*l* 75.3%

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

   5. Simplified 75.3%

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

   if -6.5e20 < y < 7.6e10

   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 0 97.8%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+20} \lor \neg \left(y \leq 76000000000\right):\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 1.0))) (* z (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(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 <= (-0.58d0)) .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 <= -0.58) || !(z <= 1.0)) {
		tmp = z * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 1.0):
		tmp = z * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(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 <= -0.58) || ~((z <= 1.0)))
		tmp = z * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(z * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 1 < z

   1. Initial program 92.0%

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

   3. Taylor expanded in z around inf 90.6%

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

      1. *-commutative 90.6%

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

      2. sub-neg 90.6%

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

      3. metadata-eval 90.6%

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

      4. associate-*l* 98.5%

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

      5. +-commutative 98.5%

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

   5. Simplified 98.5%

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

   6. Taylor expanded in y around 0 62.2%

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

      1. mul-1-neg 62.2%

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

   8. Simplified 62.2%

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

   if -0.57999999999999996 < z < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 68.0%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 41.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.6e+19) x (* z x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.6e+19) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1.6d+19) then
        tmp = x
    else
        tmp = z * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.6e+19) {
		tmp = x;
	} else {
		tmp = z * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.6e+19:
		tmp = x
	else:
		tmp = z * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.6e+19)
		tmp = x;
	else
		tmp = Float64(z * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.6e+19)
		tmp = x;
	else
		tmp = z * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.6e+19], x, N[(z * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.6e19

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 45.5%

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

   if 1.6e19 < z

   1. Initial program 94.0%

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

   3. Taylor expanded in z around inf 94.0%

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

      1. *-commutative 94.0%

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

      2. sub-neg 94.0%

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

      3. metadata-eval 94.0%

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

      4. associate-*l* 99.9%

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

      5. +-commutative 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 68.0%

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

      1. mul-1-neg 68.0%

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

   8. Simplified 68.0%

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

      1. add-sqr-sqrt 33.6%

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

      2. sqrt-unprod 31.4%

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

      3. sqr-neg 31.4%

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

      4. sqrt-unprod 0.8%

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

      5. add-sqr-sqrt 8.2%

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

      6. pow1 8.2%

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

   10. Applied egg-rr 8.2%

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

       1. unpow1 8.2%

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

       2. *-commutative 8.2%

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

   12. Simplified 8.2%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.6 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.9% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.8%

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

3. Taylor expanded in y around 0 67.3%

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

Alternative 11: 39.9% 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 95.8%

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

3. Taylor expanded in z around 0 34.9%

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

Developer Target 1: 99.8% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024165 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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