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

Percentage Accurate: 95.9% → 98.8%

Time: 10.6s

Alternatives: 12

Speedup: 0.6×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 (- INFINITY))
     (* y (* x z))
     (if (<= t_0 5e+281) (+ x (* x (* z (+ y -1.0)))) (* z (* x y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y * (x * z);
	} else if (t_0 <= 5e+281) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x * z);
	} else if (t_0 <= 5e+281) {
		tmp = x + (x * (z * (y + -1.0)));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y * (x * z)
	elif t_0 <= 5e+281:
		tmp = x + (x * (z * (y + -1.0)))
	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 <= Float64(-Inf))
		tmp = Float64(y * Float64(x * z));
	elseif (t_0 <= 5e+281)
		tmp = Float64(x + Float64(x * Float64(z * Float64(y + -1.0))));
	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 <= -Inf)
		tmp = y * (x * z);
	elseif (t_0 <= 5e+281)
		tmp = x + (x * (z * (y + -1.0)));
	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, (-Infinity)], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+281], N[(x + N[(x * N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 67.6%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-*l* 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 5.00000000000000016e281

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

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

   if 5.00000000000000016e281 < (*.f64 (-.f64 1 y) z)

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0 78.5%

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

   4. Taylor expanded in z around -inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*l* 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot y\right)\\ t_1 := x \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+237}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+174}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z y))) (t_1 (* x (- z))))
   (if (<= z -4e+237)
     t_0
     (if (<= z -9.8e+123)
       t_1
       (if (<= z -1.9e-15)
         t_0
         (if (<= z 1.0) x (if (<= z 8e+174) t_1 t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double t_1 = x * -z;
	double tmp;
	if (z <= -4e+237) {
		tmp = t_0;
	} else if (z <= -9.8e+123) {
		tmp = t_1;
	} else if (z <= -1.9e-15) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 8e+174) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (z * y)
    t_1 = x * -z
    if (z <= (-4d+237)) then
        tmp = t_0
    else if (z <= (-9.8d+123)) then
        tmp = t_1
    else if (z <= (-1.9d-15)) then
        tmp = t_0
    else if (z <= 1.0d0) then
        tmp = x
    else if (z <= 8d+174) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * y);
	double t_1 = x * -z;
	double tmp;
	if (z <= -4e+237) {
		tmp = t_0;
	} else if (z <= -9.8e+123) {
		tmp = t_1;
	} else if (z <= -1.9e-15) {
		tmp = t_0;
	} else if (z <= 1.0) {
		tmp = x;
	} else if (z <= 8e+174) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * y)
	t_1 = x * -z
	tmp = 0
	if z <= -4e+237:
		tmp = t_0
	elif z <= -9.8e+123:
		tmp = t_1
	elif z <= -1.9e-15:
		tmp = t_0
	elif z <= 1.0:
		tmp = x
	elif z <= 8e+174:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * y))
	t_1 = Float64(x * Float64(-z))
	tmp = 0.0
	if (z <= -4e+237)
		tmp = t_0;
	elseif (z <= -9.8e+123)
		tmp = t_1;
	elseif (z <= -1.9e-15)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 8e+174)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * y);
	t_1 = x * -z;
	tmp = 0.0;
	if (z <= -4e+237)
		tmp = t_0;
	elseif (z <= -9.8e+123)
		tmp = t_1;
	elseif (z <= -1.9e-15)
		tmp = t_0;
	elseif (z <= 1.0)
		tmp = x;
	elseif (z <= 8e+174)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * (-z)), $MachinePrecision]}, If[LessEqual[z, -4e+237], t$95$0, If[LessEqual[z, -9.8e+123], t$95$1, If[LessEqual[z, -1.9e-15], t$95$0, If[LessEqual[z, 1.0], x, If[LessEqual[z, 8e+174], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999976e237 or -9.79999999999999952e123 < z < -1.9000000000000001e-15 or 8.00000000000000055e174 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if -3.99999999999999976e237 < z < -9.79999999999999952e123 or 1 < z < 8.00000000000000055e174

   1. Initial program 92.4%

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

   3. Taylor expanded in z around inf 90.2%

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

   4. Taylor expanded in y around 0 63.4%

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

      1. mul-1-neg 63.4%

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

      2. distribute-rgt-neg-out 63.4%

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

   6. Simplified 63.4%

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

   if -1.9000000000000001e-15 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.9%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+237}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 (- INFINITY))
     (* y (* x z))
     (if (<= t_0 5e+281) (* x (+ 1.0 (* z (+ y -1.0)))) (* z (* x y))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = y * (x * z);
	} else if (t_0 <= 5e+281) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x * z);
	} else if (t_0 <= 5e+281) {
		tmp = x * (1.0 + (z * (y + -1.0)));
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (1.0 - y)
	tmp = 0
	if t_0 <= -math.inf:
		tmp = y * (x * z)
	elif t_0 <= 5e+281:
		tmp = x * (1.0 + (z * (y + -1.0)))
	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 <= Float64(-Inf))
		tmp = Float64(y * Float64(x * z));
	elseif (t_0 <= 5e+281)
		tmp = Float64(x * Float64(1.0 + Float64(z * Float64(y + -1.0))));
	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 <= -Inf)
		tmp = y * (x * z);
	elseif (t_0 <= 5e+281)
		tmp = x * (1.0 + (z * (y + -1.0)));
	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, (-Infinity)], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+281], N[(x * N[(1.0 + N[(z * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 67.6%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-*l* 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 5.00000000000000016e281

   1. Initial program 99.9%

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

   if 5.00000000000000016e281 < (*.f64 (-.f64 1 y) z)

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0 78.5%

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

   4. Taylor expanded in z around -inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*l* 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x \cdot \left(1 + z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (- 1.0 y))))
   (if (<= t_0 (- INFINITY))
     (* y (* x z))
     (if (<= t_0 5e+281) (* 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 <= -((double) INFINITY)) {
		tmp = y * (x * z);
	} else if (t_0 <= 5e+281) {
		tmp = x * ((1.0 + (z * y)) - z);
	} else {
		tmp = z * (x * y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (1.0 - y);
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = y * (x * z);
	} else if (t_0 <= 5e+281) {
		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 <= -math.inf:
		tmp = y * (x * z)
	elif t_0 <= 5e+281:
		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 <= Float64(-Inf))
		tmp = Float64(y * Float64(x * z));
	elseif (t_0 <= 5e+281)
		tmp = Float64(x * Float64(Float64(1.0 + 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 <= -Inf)
		tmp = y * (x * z);
	elseif (t_0 <= 5e+281)
		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, (-Infinity)], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+281], N[(x * N[(N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 1 y) z) < -inf.0

   1. Initial program 67.6%

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

   3. Taylor expanded in y around inf 67.6%

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

      1. *-commutative 67.6%

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

      2. associate-*l* 100.0%

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

      3. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -inf.0 < (*.f64 (-.f64 1 y) z) < 5.00000000000000016e281

   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 99.9%

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

   if 5.00000000000000016e281 < (*.f64 (-.f64 1 y) z)

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0 78.5%

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

   4. Taylor expanded in z around -inf 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

      3. *-commutative 78.5%

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

      4. associate-*l* 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(1 - y\right) \leq -\infty:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \cdot \left(1 - y\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x \cdot \left(\left(1 + z \cdot y\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+101} \lor \neg \left(y \leq -1.1 \cdot 10^{+71} \lor \neg \left(y \leq -4.6 \cdot 10^{+21}\right) \land y \leq 860000000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.3e+101)
         (not
          (or (<= y -1.1e+71)
              (and (not (<= y -4.6e+21)) (<= y 860000000000.0)))))
   (* x (* z y))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.3e+101) || !((y <= -1.1e+71) || (!(y <= -4.6e+21) && (y <= 860000000000.0)))) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.3d+101)) .or. (.not. (y <= (-1.1d+71)) .or. (.not. (y <= (-4.6d+21))) .and. (y <= 860000000000.0d0))) then
        tmp = x * (z * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.3e+101) || !((y <= -1.1e+71) || (!(y <= -4.6e+21) && (y <= 860000000000.0)))) {
		tmp = x * (z * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.3e+101) or not ((y <= -1.1e+71) or (not (y <= -4.6e+21) and (y <= 860000000000.0))):
		tmp = x * (z * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.3e+101) || !((y <= -1.1e+71) || (!(y <= -4.6e+21) && (y <= 860000000000.0))))
		tmp = Float64(x * Float64(z * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.3e+101) || ~(((y <= -1.1e+71) || (~((y <= -4.6e+21)) && (y <= 860000000000.0)))))
		tmp = x * (z * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.3e+101], N[Not[Or[LessEqual[y, -1.1e+71], And[N[Not[LessEqual[y, -4.6e+21]], $MachinePrecision], LessEqual[y, 860000000000.0]]]], $MachinePrecision]], N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.30000000000000004e101 or -1.09999999999999997e71 < y < -4.6e21 or 8.6e11 < 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 71.6%

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

      1. *-commutative 71.6%

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

   5. Simplified 71.6%

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

   if -6.30000000000000004e101 < y < -1.09999999999999997e71 or -4.6e21 < y < 8.6e11

   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 97.5%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+101} \lor \neg \left(y \leq -1.1 \cdot 10^{+71} \lor \neg \left(y \leq -4.6 \cdot 10^{+21}\right) \land y \leq 860000000000\right):\\ \;\;\;\;x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+101} \lor \neg \left(y \leq -2.4 \cdot 10^{+70} \lor \neg \left(y \leq -4.3 \cdot 10^{+19}\right) \land y \leq 1200000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.3e+101)
         (not
          (or (<= y -2.4e+70)
              (and (not (<= y -4.3e+19)) (<= y 1200000000000.0)))))
   (* y (* x z))
   (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.3e+101) || !((y <= -2.4e+70) || (!(y <= -4.3e+19) && (y <= 1200000000000.0)))) {
		tmp = y * (x * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-6.3d+101)) .or. (.not. (y <= (-2.4d+70)) .or. (.not. (y <= (-4.3d+19))) .and. (y <= 1200000000000.0d0))) then
        tmp = y * (x * z)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.3e+101) || !((y <= -2.4e+70) || (!(y <= -4.3e+19) && (y <= 1200000000000.0)))) {
		tmp = y * (x * z);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.3e+101) or not ((y <= -2.4e+70) or (not (y <= -4.3e+19) and (y <= 1200000000000.0))):
		tmp = y * (x * z)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.3e+101) || !((y <= -2.4e+70) || (!(y <= -4.3e+19) && (y <= 1200000000000.0))))
		tmp = Float64(y * Float64(x * z));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.3e+101) || ~(((y <= -2.4e+70) || (~((y <= -4.3e+19)) && (y <= 1200000000000.0)))))
		tmp = y * (x * z);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.3e+101], N[Not[Or[LessEqual[y, -2.4e+70], And[N[Not[LessEqual[y, -4.3e+19]], $MachinePrecision], LessEqual[y, 1200000000000.0]]]], $MachinePrecision]], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.30000000000000004e101 or -2.39999999999999987e70 < y < -4.3e19 or 1.2e12 < 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 71.6%

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

      1. *-commutative 71.6%

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

      2. associate-*l* 77.0%

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

      3. *-commutative 77.0%

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

   5. Simplified 77.0%

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

   if -6.30000000000000004e101 < y < -2.39999999999999987e70 or -4.3e19 < y < 1.2e12

   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 97.5%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+101} \lor \neg \left(y \leq -2.4 \cdot 10^{+70} \lor \neg \left(y \leq -4.3 \cdot 10^{+19}\right) \land y \leq 1200000000000\right):\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot y\right)\\ t_1 := x \cdot \left(1 - z\right)\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+70}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 90000000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x y))) (t_1 (* x (- 1.0 z))))
   (if (<= y -6.2e+101)
     t_0
     (if (<= y -5e+70)
       t_1
       (if (<= y -5.4e+20)
         t_0
         (if (<= y 90000000000000.0) t_1 (* y (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double t_1 = x * (1.0 - z);
	double tmp;
	if (y <= -6.2e+101) {
		tmp = t_0;
	} else if (y <= -5e+70) {
		tmp = t_1;
	} else if (y <= -5.4e+20) {
		tmp = t_0;
	} else if (y <= 90000000000000.0) {
		tmp = t_1;
	} else {
		tmp = y * (x * 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = z * (x * y)
    t_1 = x * (1.0d0 - z)
    if (y <= (-6.2d+101)) then
        tmp = t_0
    else if (y <= (-5d+70)) then
        tmp = t_1
    else if (y <= (-5.4d+20)) then
        tmp = t_0
    else if (y <= 90000000000000.0d0) then
        tmp = t_1
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double t_1 = x * (1.0 - z);
	double tmp;
	if (y <= -6.2e+101) {
		tmp = t_0;
	} else if (y <= -5e+70) {
		tmp = t_1;
	} else if (y <= -5.4e+20) {
		tmp = t_0;
	} else if (y <= 90000000000000.0) {
		tmp = t_1;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * y)
	t_1 = x * (1.0 - z)
	tmp = 0
	if y <= -6.2e+101:
		tmp = t_0
	elif y <= -5e+70:
		tmp = t_1
	elif y <= -5.4e+20:
		tmp = t_0
	elif y <= 90000000000000.0:
		tmp = t_1
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * y))
	t_1 = Float64(x * Float64(1.0 - z))
	tmp = 0.0
	if (y <= -6.2e+101)
		tmp = t_0;
	elseif (y <= -5e+70)
		tmp = t_1;
	elseif (y <= -5.4e+20)
		tmp = t_0;
	elseif (y <= 90000000000000.0)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * y);
	t_1 = x * (1.0 - z);
	tmp = 0.0;
	if (y <= -6.2e+101)
		tmp = t_0;
	elseif (y <= -5e+70)
		tmp = t_1;
	elseif (y <= -5.4e+20)
		tmp = t_0;
	elseif (y <= 90000000000000.0)
		tmp = t_1;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.2e+101], t$95$0, If[LessEqual[y, -5e+70], t$95$1, If[LessEqual[y, -5.4e+20], t$95$0, If[LessEqual[y, 90000000000000.0], t$95$1, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999998e101 or -5.0000000000000002e70 < y < -5.4e20

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0 87.6%

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

   4. Taylor expanded in z around -inf 87.6%

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

      1. mul-1-neg 87.6%

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

      2. unsub-neg 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l* 90.6%

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

      5. mul-1-neg 90.6%

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

      6. unsub-neg 90.6%

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

   6. Simplified 90.6%

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

   7. Taylor expanded in y around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 81.2%

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

      4. *-commutative 81.2%

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

   9. Simplified 81.2%

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

   if -6.19999999999999998e101 < y < -5.0000000000000002e70 or -5.4e20 < y < 9e13

   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 97.5%

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

   if 9e13 < y

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   5. Simplified 75.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{+20}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 90000000000000:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+101}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 86000000000:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x y))))
   (if (<= y -6.5e+101)
     t_0
     (if (<= y -2.2e+70)
       (* x (- 1.0 z))
       (if (<= y -1.25e+21)
         t_0
         (if (<= y 86000000000.0) (- x (* x z)) (* y (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -6.5e+101) {
		tmp = t_0;
	} else if (y <= -2.2e+70) {
		tmp = x * (1.0 - z);
	} else if (y <= -1.25e+21) {
		tmp = t_0;
	} else if (y <= 86000000000.0) {
		tmp = x - (x * z);
	} else {
		tmp = y * (x * 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) :: t_0
    real(8) :: tmp
    t_0 = z * (x * y)
    if (y <= (-6.5d+101)) then
        tmp = t_0
    else if (y <= (-2.2d+70)) then
        tmp = x * (1.0d0 - z)
    else if (y <= (-1.25d+21)) then
        tmp = t_0
    else if (y <= 86000000000.0d0) then
        tmp = x - (x * z)
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * y);
	double tmp;
	if (y <= -6.5e+101) {
		tmp = t_0;
	} else if (y <= -2.2e+70) {
		tmp = x * (1.0 - z);
	} else if (y <= -1.25e+21) {
		tmp = t_0;
	} else if (y <= 86000000000.0) {
		tmp = x - (x * z);
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * y)
	tmp = 0
	if y <= -6.5e+101:
		tmp = t_0
	elif y <= -2.2e+70:
		tmp = x * (1.0 - z)
	elif y <= -1.25e+21:
		tmp = t_0
	elif y <= 86000000000.0:
		tmp = x - (x * z)
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (y <= -6.5e+101)
		tmp = t_0;
	elseif (y <= -2.2e+70)
		tmp = Float64(x * Float64(1.0 - z));
	elseif (y <= -1.25e+21)
		tmp = t_0;
	elseif (y <= 86000000000.0)
		tmp = Float64(x - Float64(x * z));
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * y);
	tmp = 0.0;
	if (y <= -6.5e+101)
		tmp = t_0;
	elseif (y <= -2.2e+70)
		tmp = x * (1.0 - z);
	elseif (y <= -1.25e+21)
		tmp = t_0;
	elseif (y <= 86000000000.0)
		tmp = x - (x * z);
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+101], t$95$0, If[LessEqual[y, -2.2e+70], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e+21], t$95$0, If[LessEqual[y, 86000000000.0], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.50000000000000016e101 or -2.20000000000000001e70 < y < -1.25e21

   1. Initial program 87.6%

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

   3. Taylor expanded in y around 0 87.6%

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

   4. Taylor expanded in z around -inf 87.6%

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

      1. mul-1-neg 87.6%

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

      2. unsub-neg 87.6%

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

      3. *-commutative 87.6%

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

      4. associate-*l* 90.6%

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

      5. mul-1-neg 90.6%

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

      6. unsub-neg 90.6%

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

   6. Simplified 90.6%

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

   7. Taylor expanded in y around inf 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-*r* 81.2%

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

      4. *-commutative 81.2%

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

   9. Simplified 81.2%

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

   if -6.50000000000000016e101 < y < -2.20000000000000001e70

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 80.6%

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

   if -1.25e21 < y < 8.6e10

   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 99.9%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 98.8%

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

   if 8.6e10 < y

   1. Initial program 92.7%

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

   3. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-*l* 75.3%

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

      3. *-commutative 75.3%

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

   5. Simplified 75.3%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+70}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 86000000000:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 6.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 6.7e-6))) (+ x (* x (* z y))) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 6.7e-6)) {
		tmp = x + (x * (z * y));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 6.7d-6))) then
        tmp = x + (x * (z * y))
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.0) || !(y <= 6.7e-6)) {
		tmp = x + (x * (z * y));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.0) or not (y <= 6.7e-6):
		tmp = x + (x * (z * y))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 6.7e-6))
		tmp = Float64(x + Float64(x * Float64(z * y)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 6.7e-6)))
		tmp = x + (x * (z * y));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 6.7e-6]], $MachinePrecision]], N[(x + N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 6.7e-6 < y

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 91.2%

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

   4. Taylor expanded in y around inf 90.8%

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

      1. *-commutative 90.8%

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

   6. Simplified 90.8%

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

   if -1 < y < 6.7e-6

   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 99.9%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-*l* 100.0%

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

      5. mul-1-neg 100.0%

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

      6. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 99.6%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 6.7 \cdot 10^{-6}\right):\\ \;\;\;\;x + x \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e-15) (not (<= z 1.0))) (* x (- z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-15) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-3.5d-15)) .or. (.not. (z <= 1.0d0))) then
        tmp = x * -z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-15) || !(z <= 1.0)) {
		tmp = x * -z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e-15) or not (z <= 1.0):
		tmp = x * -z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e-15) || !(z <= 1.0))
		tmp = Float64(x * Float64(-z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.5e-15) || ~((z <= 1.0)))
		tmp = x * -z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e-15], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x * (-z)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000001e-15 or 1 < z

   1. Initial program 90.6%

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

   3. Taylor expanded in z around inf 89.1%

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

   4. Taylor expanded in y around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. distribute-rgt-neg-out 50.8%

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

   6. Simplified 50.8%

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

   if -3.5000000000000001e-15 < z < 1

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.9%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-15} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 4.4e-89) (+ x (* z (* x (+ y -1.0)))) (+ x (* x (* z (+ y -1.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.4e-89) {
		tmp = x + (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 (x <= 4.4d-89) then
        tmp = x + (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 (x <= 4.4e-89) {
		tmp = x + (z * (x * (y + -1.0)));
	} else {
		tmp = x + (x * (z * (y + -1.0)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 4.4e-89:
		tmp = x + (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 (x <= 4.4e-89)
		tmp = Float64(x + Float64(z * Float64(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 (x <= 4.4e-89)
		tmp = x + (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[x, 4.4e-89], N[(x + N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $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 x < 4.40000000000000024e-89

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 93.0%

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

   4. Taylor expanded in z around -inf 93.0%

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

      1. mul-1-neg 93.0%

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

      2. unsub-neg 93.0%

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

      3. *-commutative 93.0%

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

      4. associate-*l* 96.1%

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

      5. mul-1-neg 96.1%

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

      6. unsub-neg 96.1%

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

   6. Simplified 96.1%

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

   if 4.40000000000000024e-89 < x

   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 99.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{-89}:\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 95.1%

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

3. Taylor expanded in z around 0 37.8%

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

4. Final simplification 37.8%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.8% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

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

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