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

Percentage Accurate: 96.2% → 99.5%

Time: 7.1s

Alternatives: 12

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x + x \cdot \left(z \cdot y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 -5e+224)
     (* (* z x) (+ y -1.0))
     (if (<= t_0 5e+296) (+ x (* x (- (* z y) z))) (* z (* x y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+224) {
		tmp = (z * x) * (y + -1.0);
	} else if (t_0 <= 5e+296) {
		tmp = x + (x * ((z * y) - z));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if (t_0 <= (-5d+224)) then
        tmp = (z * x) * (y + (-1.0d0))
    else if (t_0 <= 5d+296) then
        tmp = x + (x * ((z * y) - z))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+224) {
		tmp = (z * x) * (y + -1.0);
	} else if (t_0 <= 5e+296) {
		tmp = x + (x * ((z * y) - z));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -5e+224:
		tmp = (z * x) * (y + -1.0)
	elif t_0 <= 5e+296:
		tmp = x + (x * ((z * y) - z))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -5e+224)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	elseif (t_0 <= 5e+296)
		tmp = Float64(x + Float64(x * Float64(Float64(z * y) - z)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -5e+224)
		tmp = (z * x) * (y + -1.0);
	elseif (t_0 <= 5e+296)
		tmp = x + (x * ((z * y) - z));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+224], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+296], N[(x + N[(x * N[(N[(z * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.99999999999999964e224

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -4.99999999999999964e224 < (*.f64 (-.f64 1 y) z) < 5.0000000000000001e296

   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-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. *-commutative 99.9%

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

   6. Simplified 99.9%

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

   if 5.0000000000000001e296 < (*.f64 (-.f64 1 y) z)

   1. Initial program 62.6%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. associate-*r* 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*l* 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x + x \cdot \left(z \cdot y - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 -5e+224)
     (* (* z x) (+ y -1.0))
     (if (<= t_0 5e+296) (* x (- 1.0 t_0)) (* z (* x y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+224) {
		tmp = (z * x) * (y + -1.0);
	} else if (t_0 <= 5e+296) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if (t_0 <= (-5d+224)) then
        tmp = (z * x) * (y + (-1.0d0))
    else if (t_0 <= 5d+296) then
        tmp = x * (1.0d0 - t_0)
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+224) {
		tmp = (z * x) * (y + -1.0);
	} else if (t_0 <= 5e+296) {
		tmp = x * (1.0 - t_0);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -5e+224:
		tmp = (z * x) * (y + -1.0)
	elif t_0 <= 5e+296:
		tmp = x * (1.0 - t_0)
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -5e+224)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	elseif (t_0 <= 5e+296)
		tmp = Float64(x * Float64(1.0 - t_0));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -5e+224)
		tmp = (z * x) * (y + -1.0);
	elseif (t_0 <= 5e+296)
		tmp = x * (1.0 - t_0);
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+224], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+296], N[(x * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.99999999999999964e224

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -4.99999999999999964e224 < (*.f64 (-.f64 1 y) z) < 5.0000000000000001e296

   1. Initial program 99.9%

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

   if 5.0000000000000001e296 < (*.f64 (-.f64 1 y) z)

   1. Initial program 62.6%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. associate-*r* 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*l* 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(1 - z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3: 99.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(1 + \left(z \cdot y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 -5e+224)
     (* (* z x) (+ y -1.0))
     (if (<= t_0 5e+296) (* x (+ 1.0 (- (* z y) z))) (* z (* x y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+224) {
		tmp = (z * x) * (y + -1.0);
	} else if (t_0 <= 5e+296) {
		tmp = x * (1.0 + ((z * y) - z));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (1.0d0 - y)
    if (t_0 <= (-5d+224)) then
        tmp = (z * x) * (y + (-1.0d0))
    else if (t_0 <= 5d+296) then
        tmp = x * (1.0d0 + ((z * y) - z))
    else
        tmp = z * (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -5e+224) {
		tmp = (z * x) * (y + -1.0);
	} else if (t_0 <= 5e+296) {
		tmp = x * (1.0 + ((z * y) - z));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -5e+224:
		tmp = (z * x) * (y + -1.0)
	elif t_0 <= 5e+296:
		tmp = x * (1.0 + ((z * y) - z))
	else:
		tmp = z * (x * y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (t_0 <= -5e+224)
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	elseif (t_0 <= 5e+296)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(z * y) - z)));
	else
		tmp = Float64(z * Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (1.0 - y);
	tmp = 0.0;
	if (t_0 <= -5e+224)
		tmp = (z * x) * (y + -1.0);
	elseif (t_0 <= 5e+296)
		tmp = x * (1.0 + ((z * y) - z));
	else
		tmp = z * (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+224], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+296], N[(x * N[(1.0 + N[(N[(z * y), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -4.99999999999999964e224

   1. Initial program 77.4%

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

   2. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -4.99999999999999964e224 < (*.f64 (-.f64 1 y) z) < 5.0000000000000001e296

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-lft-neg-out 99.9%

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

      3. +-commutative 99.9%

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

      4. cancel-sign-sub-inv 99.9%

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

      5. *-commutative 99.9%

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

   4. Simplified 99.9%

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

   if 5.0000000000000001e296 < (*.f64 (-.f64 1 y) z)

   1. Initial program 62.6%

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

   2. Taylor expanded in y around inf 99.8%

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

      1. associate-*r* 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*l* 99.8%

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

   4. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -5 \cdot 10^{+224}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot \left(1 + \left(z \cdot y - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4: 96.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-284}:\\ \;\;\;\;x + \left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq 0.2:\\ \;\;\;\;x + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z x) (+ y -1.0))))
   (if (<= z -1.0)
     t_0
     (if (<= z 1.18e-284)
       (+ x (* (* z x) y))
       (if (<= z 0.2) (+ x (* z (* x y))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = (z * x) * (y + -1.0);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.18e-284) {
		tmp = x + ((z * x) * y);
	} else if (z <= 0.2) {
		tmp = x + (z * (x * y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (z * x) * (y + (-1.0d0))
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1.18d-284) then
        tmp = x + ((z * x) * y)
    else if (z <= 0.2d0) then
        tmp = x + (z * (x * y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * x) * (y + -1.0);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.18e-284) {
		tmp = x + ((z * x) * y);
	} else if (z <= 0.2) {
		tmp = x + (z * (x * y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * x) * (y + -1.0)
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 1.18e-284:
		tmp = x + ((z * x) * y)
	elif z <= 0.2:
		tmp = x + (z * (x * y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * x) * Float64(y + -1.0))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.18e-284)
		tmp = Float64(x + Float64(Float64(z * x) * y));
	elseif (z <= 0.2)
		tmp = Float64(x + Float64(z * Float64(x * y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * x) * (y + -1.0);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 1.18e-284)
		tmp = x + ((z * x) * y);
	elseif (z <= 0.2)
		tmp = x + (z * (x * y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 1.18e-284], N[(x + N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.2], N[(x + N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 0.20000000000000001 < z

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*l* 98.1%

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

      3. sub-neg 98.1%

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

      4. metadata-eval 98.1%

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

      5. *-commutative 98.1%

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

   4. Simplified 98.1%

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

   if -1 < z < 1.17999999999999993e-284

   1. Initial program 99.9%

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

      1. distribute-rgt-out-- 100.0%

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

      2. *-lft-identity 100.0%

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

      3. cancel-sign-sub-inv 100.0%

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

      4. +-commutative 100.0%

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

      5. distribute-lft-neg-in 100.0%

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

      6. associate-*l* 98.4%

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

      7. fma-def 98.4%

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

      8. neg-sub0 98.4%

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

      9. associate--r- 98.4%

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

      10. metadata-eval 98.4%

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

      11. +-commutative 98.4%

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

      12. *-commutative 98.4%

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

   3. Simplified 98.4%

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

      1. fma-udef 98.4%

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

      2. associate-*r* 87.3%

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

   5. Applied egg-rr 87.3%

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

   6. Taylor expanded in y around inf 97.4%

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

   if 1.17999999999999993e-284 < z < 0.20000000000000001

   1. Initial program 99.9%

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

      1. distribute-rgt-out-- 99.9%

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

      2. *-lft-identity 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. associate-*l* 91.3%

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

      7. fma-def 91.3%

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

      8. neg-sub0 91.3%

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

      9. associate--r- 91.3%

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

      10. metadata-eval 91.3%

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

      11. +-commutative 91.3%

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

      12. *-commutative 91.3%

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

   3. Simplified 91.3%

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

      1. fma-udef 91.3%

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

      2. associate-*r* 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in y around inf 97.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{elif}\;z \leq 1.18 \cdot 10^{-284}:\\ \;\;\;\;x + \left(z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq 0.2:\\ \;\;\;\;x + z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 5: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.39\right):\\ \;\;\;\;x + \left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.39))) (+ x (* (* z x) y)) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.39)) {
		tmp = x + ((z * x) * y);
	} 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 <= (-1.0d0)) .or. (.not. (y <= 0.39d0))) then
        tmp = x + ((z * x) * y)
    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 <= -1.0) || !(y <= 0.39)) {
		tmp = x + ((z * x) * y);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.39):
		tmp = x + ((z * x) * y)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.39))
		tmp = Float64(x + Float64(Float64(z * x) * y));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.39)))
		tmp = x + ((z * x) * y);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.39]], $MachinePrecision]], N[(x + N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.39000000000000001 < y

   1. Initial program 88.4%

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

      1. distribute-rgt-out-- 88.4%

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

      2. *-lft-identity 88.4%

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

      3. cancel-sign-sub-inv 88.4%

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

      4. +-commutative 88.4%

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

      5. distribute-lft-neg-in 88.4%

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

      6. associate-*l* 94.6%

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

      7. fma-def 94.6%

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

      8. neg-sub0 94.6%

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

      9. associate--r- 94.6%

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

      10. metadata-eval 94.6%

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

      11. +-commutative 94.6%

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

      12. *-commutative 94.6%

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

   3. Simplified 94.6%

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

      1. fma-udef 94.6%

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

      2. associate-*r* 93.2%

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

   5. Applied egg-rr 93.2%

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

   6. Taylor expanded in y around inf 93.4%

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

   if -1 < y < 0.39000000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 98.7%

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

      1. *-commutative 98.7%

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

      2. distribute-rgt-out-- 98.7%

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

      3. *-lft-identity 98.7%

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

   4. Simplified 98.7%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.39\right):\\ \;\;\;\;x + \left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.9 \lor \neg \left(z \leq 0.2\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.9) (not (<= z 0.2)))
   (* (* z x) (+ y -1.0))
   (+ x (* x (* z y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.9) || !(z <= 0.2)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.9d0)) .or. (.not. (z <= 0.2d0))) then
        tmp = (z * x) * (y + (-1.0d0))
    else
        tmp = x + (x * (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.9) || !(z <= 0.2)) {
		tmp = (z * x) * (y + -1.0);
	} else {
		tmp = x + (x * (z * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.9) or not (z <= 0.2):
		tmp = (z * x) * (y + -1.0)
	else:
		tmp = x + (x * (z * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.9) || !(z <= 0.2))
		tmp = Float64(Float64(z * x) * Float64(y + -1.0));
	else
		tmp = Float64(x + Float64(x * Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.9) || ~((z <= 0.2)))
		tmp = (z * x) * (y + -1.0);
	else
		tmp = x + (x * (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.9], N[Not[LessEqual[z, 0.2]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.900000000000000022 or 0.20000000000000001 < z

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf 98.1%

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

      1. *-commutative 98.1%

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

      2. associate-*l* 98.1%

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

      3. sub-neg 98.1%

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

      4. metadata-eval 98.1%

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

      5. *-commutative 98.1%

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

   4. Simplified 98.1%

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

   if -0.900000000000000022 < z < 0.20000000000000001

   1. Initial program 99.9%

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

      1. distribute-rgt-out-- 99.9%

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

      2. *-lft-identity 99.9%

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

      3. cancel-sign-sub-inv 99.9%

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

      4. +-commutative 99.9%

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

      5. distribute-lft-neg-in 99.9%

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

      6. associate-*l* 94.7%

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

      7. fma-def 94.7%

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

      8. neg-sub0 94.7%

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

      9. associate--r- 94.7%

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

      10. metadata-eval 94.7%

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

      11. +-commutative 94.7%

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

      12. *-commutative 94.7%

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

   3. Simplified 94.7%

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

      1. fma-udef 94.7%

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

      2. associate-*r* 93.2%

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

   5. Applied egg-rr 93.2%

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

      1. add-cube-cbrt 92.8%

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

      2. pow3 92.8%

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

   7. Applied egg-rr 92.8%

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

   8. Taylor expanded in y around inf 93.6%

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

      1. associate-*r* 98.9%

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

   10. Simplified 98.9%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.9 \lor \neg \left(z \leq 0.2\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 7: 97.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.3 \cdot 10^{-283}:\\ \;\;\;\;x + \left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(x \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 3.3e-283) (+ x (* (* z x) (+ y -1.0))) (- x (* z (* x (- 1.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.3e-283) {
		tmp = x + ((z * x) * (y + -1.0));
	} else {
		tmp = x - (z * (x * (1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 3.3d-283) then
        tmp = x + ((z * x) * (y + (-1.0d0)))
    else
        tmp = x - (z * (x * (1.0d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 3.3e-283) {
		tmp = x + ((z * x) * (y + -1.0));
	} else {
		tmp = x - (z * (x * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 3.3e-283:
		tmp = x + ((z * x) * (y + -1.0))
	else:
		tmp = x - (z * (x * (1.0 - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 3.3e-283)
		tmp = Float64(x + Float64(Float64(z * x) * Float64(y + -1.0)));
	else
		tmp = Float64(x - Float64(z * Float64(x * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 3.3e-283)
		tmp = x + ((z * x) * (y + -1.0));
	else
		tmp = x - (z * (x * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 3.3e-283], N[(x + N[(N[(z * x), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.30000000000000019e-283

   1. Initial program 95.1%

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

   2. Taylor expanded in y around 0 92.3%

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

      1. *-commutative 92.3%

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

      2. sub-neg 92.3%

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

      3. distribute-rgt-in 92.3%

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

      4. *-un-lft-identity 92.3%

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

   4. Applied egg-rr 92.3%

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

   5. Taylor expanded in y around 0 92.3%

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

      1. associate-+r+ 92.3%

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

      2. distribute-rgt-out 99.1%

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

   7. Simplified 99.1%

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

   if 3.30000000000000019e-283 < z

   1. Initial program 93.2%

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

      1. distribute-rgt-out-- 93.2%

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

      2. *-lft-identity 93.2%

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

      3. cancel-sign-sub-inv 93.2%

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

      4. +-commutative 93.2%

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

      5. distribute-lft-neg-in 93.2%

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

      6. associate-*l* 95.7%

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

      7. fma-def 95.7%

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

      8. neg-sub0 95.7%

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

      9. associate--r- 95.7%

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

      10. metadata-eval 95.7%

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

      11. +-commutative 95.7%

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

      12. *-commutative 95.7%

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

   3. Simplified 95.7%

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

      1. fma-udef 95.7%

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

      2. associate-*r* 99.2%

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

   5. Applied egg-rr 99.2%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.3 \cdot 10^{-283}:\\ \;\;\;\;x + \left(z \cdot x\right) \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(x \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 8: 53.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-143} \lor \neg \left(y \leq 4.8 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e-143) (not (<= y 4.8e+82))) (* x (* z y)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e-143) || !(y <= 4.8e+82)) {
		tmp = x * (z * y);
	} 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 ((y <= (-9.5d-143)) .or. (.not. (y <= 4.8d+82))) then
        tmp = x * (z * y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e-143) || !(y <= 4.8e+82)) {
		tmp = x * (z * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.5e-143) or not (y <= 4.8e+82):
		tmp = x * (z * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e-143) || !(y <= 4.8e+82))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.5e-143) || ~((y <= 4.8e+82)))
		tmp = x * (z * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.5e-143], N[Not[LessEqual[y, 4.8e+82]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999993e-143 or 4.79999999999999996e82 < y

   1. Initial program 89.4%

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

   2. Taylor expanded in y around inf 79.6%

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

      1. mul-1-neg 79.6%

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

      2. distribute-lft-neg-out 79.6%

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

      3. *-commutative 79.6%

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

   4. Simplified 79.6%

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

   5. Taylor expanded in z around inf 61.4%

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

      1. *-commutative 61.4%

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

   7. Simplified 61.4%

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

   if -9.4999999999999993e-143 < y < 4.79999999999999996e82

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 58.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-143} \lor \neg \left(y \leq 4.8 \cdot 10^{+82}\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-30} \lor \neg \left(z \leq 1.4 \cdot 10^{-45}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4e-30) (not (<= z 1.4e-45))) (* (* z x) y) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-30) || !(z <= 1.4e-45)) {
		tmp = (z * x) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.4d-30)) .or. (.not. (z <= 1.4d-45))) then
        tmp = (z * x) * y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4e-30) || !(z <= 1.4e-45)) {
		tmp = (z * x) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.4e-30) or not (z <= 1.4e-45):
		tmp = (z * x) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.4e-30) || !(z <= 1.4e-45))
		tmp = Float64(Float64(z * x) * y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.4e-30) || ~((z <= 1.4e-45)))
		tmp = (z * x) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.4e-30], N[Not[LessEqual[z, 1.4e-45]], $MachinePrecision]], N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999994e-30 or 1.4000000000000001e-45 < z

   1. Initial program 89.7%

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

   2. Taylor expanded in y around inf 57.3%

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

   if -1.39999999999999994e-30 < z < 1.4000000000000001e-45

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 79.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-30} \lor \neg \left(z \leq 1.4 \cdot 10^{-45}\right):\\ \;\;\;\;\left(z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 84.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+44} \lor \neg \left(y \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e+44) (not (<= y 2.55e+79))) (* z (* x y)) (- x (* z x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+44) || !(y <= 2.55e+79)) {
		tmp = z * (x * y);
	} 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 <= (-6.2d+44)) .or. (.not. (y <= 2.55d+79))) then
        tmp = z * (x * y)
    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 <= -6.2e+44) || !(y <= 2.55e+79)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (z * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e+44) or not (y <= 2.55e+79):
		tmp = z * (x * y)
	else:
		tmp = x - (z * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e+44) || !(y <= 2.55e+79))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x - Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e+44) || ~((y <= 2.55e+79)))
		tmp = z * (x * y);
	else
		tmp = x - (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e+44], N[Not[LessEqual[y, 2.55e+79]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.19999999999999991e44 or 2.5500000000000001e79 < y

   1. Initial program 86.5%

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

   2. Taylor expanded in y around inf 76.9%

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

      1. associate-*r* 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*l* 82.3%

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

   4. Simplified 82.3%

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

   if -6.19999999999999991e44 < y < 2.5500000000000001e79

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 93.3%

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

      1. *-commutative 93.3%

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

      2. distribute-rgt-out-- 93.3%

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

      3. *-lft-identity 93.3%

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

   4. Simplified 93.3%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+44} \lor \neg \left(y \leq 2.55 \cdot 10^{+79}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot x\\ \end{array} \]

Alternative 11: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z * x) * (y + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

2. Taylor expanded in y around 0 91.8%

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

   1. *-commutative 91.8%

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

   2. sub-neg 91.8%

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

   3. distribute-rgt-in 91.8%

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

   4. *-un-lft-identity 91.8%

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

4. Applied egg-rr 91.8%

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

5. Taylor expanded in y around 0 91.8%

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

   1. associate-+r+ 91.8%

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

   2. distribute-rgt-out 97.2%

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

7. Simplified 97.2%

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

8. Final simplification 97.2%

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

Alternative 12: 39.1% 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 94.1%

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

2. Taylor expanded in z around 0 38.9%

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

3. Final simplification 38.9%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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