Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Percentage Accurate: 97.8% → 97.8%

Time: 8.9s

Alternatives: 12

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (z - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((x / y) * (z - t)) + t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = t + ((x / y) * (z - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Final simplification 98.7%

   \[\leadsto t + \frac{x}{y} \cdot \left(z - t\right) \]
4. Add Preprocessing

Alternative 2: 64.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+44)
   (* (/ x y) (- t))
   (if (<= (/ x y) -5e-65)
     (* (/ x y) z)
     (if (<= (/ x y) 5e-19) t (/ (* x z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+44) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= -5e-65) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 5e-19) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-2d+44)) then
        tmp = (x / y) * -t
    else if ((x / y) <= (-5d-65)) then
        tmp = (x / y) * z
    else if ((x / y) <= 5d-19) then
        tmp = t
    else
        tmp = (x * z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+44) {
		tmp = (x / y) * -t;
	} else if ((x / y) <= -5e-65) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 5e-19) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+44:
		tmp = (x / y) * -t
	elif (x / y) <= -5e-65:
		tmp = (x / y) * z
	elif (x / y) <= 5e-19:
		tmp = t
	else:
		tmp = (x * z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+44)
		tmp = Float64(Float64(x / y) * Float64(-t));
	elseif (Float64(x / y) <= -5e-65)
		tmp = Float64(Float64(x / y) * z);
	elseif (Float64(x / y) <= 5e-19)
		tmp = t;
	else
		tmp = Float64(Float64(x * z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2e+44)
		tmp = (x / y) * -t;
	elseif ((x / y) <= -5e-65)
		tmp = (x / y) * z;
	elseif ((x / y) <= 5e-19)
		tmp = t;
	else
		tmp = (x * z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+44], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -5e-65], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-19], t, N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -2.0000000000000002e44

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 61.5%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   4. Step-by-step derivation

      1. *-rgt-identity 61.5%

         \[\leadsto \color{blue}{t \cdot 1} + -1 \cdot \frac{t \cdot x}{y} \]

      2. mul-1-neg 61.5%

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

      3. associate-/l* 66.8%

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

      4. distribute-rgt-neg-in 66.8%

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

      5. mul-1-neg 66.8%

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

      6. distribute-lft-in 66.8%

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

      7. mul-1-neg 66.8%

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

      8. unsub-neg 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in x around inf 66.8%

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

      1. associate-*r/ 66.8%

         \[\leadsto t \cdot \color{blue}{\frac{-1 \cdot x}{y}} \]

      2. neg-mul-1 66.8%

         \[\leadsto t \cdot \frac{\color{blue}{-x}}{y} \]

   8. Simplified 66.8%

      \[\leadsto t \cdot \color{blue}{\frac{-x}{y}} \]

   if -2.0000000000000002e44 < (/.f64 x y) < -4.99999999999999983e-65

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.3%

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

   4. Taylor expanded in x around -inf 69.7%

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

   5. Taylor expanded in z around inf 51.4%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 51.4%

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

      2. associate-*r/ 67.1%

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

   7. Simplified 67.1%

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

   if -4.99999999999999983e-65 < (/.f64 x y) < 5.0000000000000004e-19

   1. Initial program 98.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.2%

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

   if 5.0000000000000004e-19 < (/.f64 x y)

   1. Initial program 98.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in x around -inf 96.5%

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

   5. Taylor expanded in z around inf 69.4%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+44} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+44) (not (<= (/ x y) 4e+30)))
   (/ (* x (- z t)) y)
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+44) || !((x / y) <= 4e+30)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-2d+44)) .or. (.not. ((x / y) <= 4d+30))) then
        tmp = (x * (z - t)) / y
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+44) || !((x / y) <= 4e+30)) {
		tmp = (x * (z - t)) / y;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+44) or not ((x / y) <= 4e+30):
		tmp = (x * (z - t)) / y
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+44) || !(Float64(x / y) <= 4e+30))
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+44) || ~(((x / y) <= 4e+30)))
		tmp = (x * (z - t)) / y;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+44], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+30]], $MachinePrecision]], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.0000000000000002e44 or 4.0000000000000001e30 < (/.f64 x y)

   1. Initial program 99.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.1%

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

   4. Taylor expanded in x around -inf 98.1%

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

   if -2.0000000000000002e44 < (/.f64 x y) < 4.0000000000000001e30

   1. Initial program 98.5%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 94.9%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+44} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+30}\right):\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-65} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-65) (not (<= (/ x y) 5e-19))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-65) || !((x / y) <= 5e-19)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d-65)) .or. (.not. ((x / y) <= 5d-19))) then
        tmp = (x / y) * z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-65) || !((x / y) <= 5e-19)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-65) or not ((x / y) <= 5e-19):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-65) || !(Float64(x / y) <= 5e-19))
		tmp = Float64(Float64(x / y) * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-65) || ~(((x / y) <= 5e-19)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-65], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-19]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999983e-65 or 5.0000000000000004e-19 < (/.f64 x y)

   1. Initial program 99.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.1%

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

   4. Taylor expanded in x around -inf 92.5%

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

   5. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 61.9%

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

      2. associate-*r/ 64.3%

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

   7. Simplified 64.3%

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

   if -4.99999999999999983e-65 < (/.f64 x y) < 5.0000000000000004e-19

   1. Initial program 98.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.2%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-65} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-65} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-65) (not (<= (/ x y) 5e-19))) (* x (/ z y)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-65) || !((x / y) <= 5e-19)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5d-65)) .or. (.not. ((x / y) <= 5d-19))) then
        tmp = x * (z / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-65) || !((x / y) <= 5e-19)) {
		tmp = x * (z / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-65) or not ((x / y) <= 5e-19):
		tmp = x * (z / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-65) || !(Float64(x / y) <= 5e-19))
		tmp = Float64(x * Float64(z / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e-65) || ~(((x / y) <= 5e-19)))
		tmp = x * (z / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-65], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e-19]], $MachinePrecision]], N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.99999999999999983e-65 or 5.0000000000000004e-19 < (/.f64 x y)

   1. Initial program 99.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 95.1%

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

   4. Taylor expanded in x around -inf 92.5%

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

   5. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   6. Step-by-step derivation

      1. associate-*r/ 60.3%

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

   7. Simplified 60.3%

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

   if -4.99999999999999983e-65 < (/.f64 x y) < 5.0000000000000004e-19

   1. Initial program 98.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.2%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-65} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{-19}\right):\\ \;\;\;\;x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-65)
   (* (/ x y) z)
   (if (<= (/ x y) 5e-19) t (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-65) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 5e-19) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5d-65)) then
        tmp = (x / y) * z
    else if ((x / y) <= 5d-19) then
        tmp = t
    else
        tmp = (x * z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-65) {
		tmp = (x / y) * z;
	} else if ((x / y) <= 5e-19) {
		tmp = t;
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-65:
		tmp = (x / y) * z
	elif (x / y) <= 5e-19:
		tmp = t
	else:
		tmp = (x * z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-65)
		tmp = Float64(Float64(x / y) * z);
	elseif (Float64(x / y) <= 5e-19)
		tmp = t;
	else
		tmp = Float64(Float64(x * z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-65)
		tmp = (x / y) * z;
	elseif ((x / y) <= 5e-19)
		tmp = t;
	else
		tmp = (x * z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-65], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e-19], t, N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.99999999999999983e-65

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 92.6%

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

   4. Taylor expanded in x around -inf 89.3%

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

   5. Taylor expanded in z around inf 55.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 55.9%

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

      2. associate-*r/ 60.8%

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

   7. Simplified 60.8%

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

   if -4.99999999999999983e-65 < (/.f64 x y) < 5.0000000000000004e-19

   1. Initial program 98.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.2%

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

   if 5.0000000000000004e-19 < (/.f64 x y)

   1. Initial program 98.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 98.2%

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

   4. Taylor expanded in x around -inf 96.5%

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

   5. Taylor expanded in z around inf 69.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{-19}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+40} \lor \neg \left(t \leq 1.95 \cdot 10^{+135}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9e+40) (not (<= t 1.95e+135)))
   (* t (- 1.0 (/ x y)))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+40) || !(t <= 1.95e+135)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-9d+40)) .or. (.not. (t <= 1.95d+135))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + ((x / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9e+40) || !(t <= 1.95e+135)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9e+40) or not (t <= 1.95e+135):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9e+40) || !(t <= 1.95e+135))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(Float64(x / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9e+40) || ~((t <= 1.95e+135)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9e+40], N[Not[LessEqual[t, 1.95e+135]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.00000000000000064e40 or 1.95000000000000016e135 < t

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.7%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   4. Step-by-step derivation

      1. *-rgt-identity 89.7%

         \[\leadsto \color{blue}{t \cdot 1} + -1 \cdot \frac{t \cdot x}{y} \]

      2. mul-1-neg 89.7%

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

      3. associate-/l* 95.1%

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

      4. distribute-rgt-neg-in 95.1%

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

      5. mul-1-neg 95.1%

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

      6. distribute-lft-in 95.1%

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

      7. mul-1-neg 95.1%

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

      8. unsub-neg 95.1%

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

   5. Simplified 95.1%

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

   if -9.00000000000000064e40 < t < 1.95000000000000016e135

   1. Initial program 98.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+40} \lor \neg \left(t \leq 1.95 \cdot 10^{+135}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+43} \lor \neg \left(t \leq 1.95 \cdot 10^{+135}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e+43) (not (<= t 1.95e+135)))
   (* t (- 1.0 (/ x y)))
   (+ t (* x (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e+43) || !(t <= 1.95e+135)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.6d+43)) .or. (.not. (t <= 1.95d+135))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = t + (x * (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e+43) || !(t <= 1.95e+135)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = t + (x * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e+43) or not (t <= 1.95e+135):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = t + (x * (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e+43) || !(t <= 1.95e+135))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(t + Float64(x * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e+43) || ~((t <= 1.95e+135)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = t + (x * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e+43], N[Not[LessEqual[t, 1.95e+135]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.60000000000000007e43 or 1.95000000000000016e135 < t

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.7%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   4. Step-by-step derivation

      1. *-rgt-identity 89.7%

         \[\leadsto \color{blue}{t \cdot 1} + -1 \cdot \frac{t \cdot x}{y} \]

      2. mul-1-neg 89.7%

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

      3. associate-/l* 95.1%

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

      4. distribute-rgt-neg-in 95.1%

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

      5. mul-1-neg 95.1%

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

      6. distribute-lft-in 95.1%

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

      7. mul-1-neg 95.1%

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

      8. unsub-neg 95.1%

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

   5. Simplified 95.1%

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

   if -1.60000000000000007e43 < t < 1.95000000000000016e135

   1. Initial program 98.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 88.0%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} + t \]
   4. Step-by-step derivation

      1. associate-/l* 87.3%

         \[\leadsto \color{blue}{x \cdot \frac{z}{y}} + t \]

   5. Simplified 87.3%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+43} \lor \neg \left(t \leq 1.95 \cdot 10^{+135}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+135}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -9e+42)
   (- t (* (/ x y) t))
   (if (<= t 2.1e+135) (+ t (* (/ x y) z)) (* t (- 1.0 (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e+42) {
		tmp = t - ((x / y) * t);
	} else if (t <= 2.1e+135) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-9d+42)) then
        tmp = t - ((x / y) * t)
    else if (t <= 2.1d+135) then
        tmp = t + ((x / y) * z)
    else
        tmp = t * (1.0d0 - (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -9e+42) {
		tmp = t - ((x / y) * t);
	} else if (t <= 2.1e+135) {
		tmp = t + ((x / y) * z);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -9e+42:
		tmp = t - ((x / y) * t)
	elif t <= 2.1e+135:
		tmp = t + ((x / y) * z)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -9e+42)
		tmp = Float64(t - Float64(Float64(x / y) * t));
	elseif (t <= 2.1e+135)
		tmp = Float64(t + Float64(Float64(x / y) * z));
	else
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -9e+42)
		tmp = t - ((x / y) * t);
	elseif (t <= 2.1e+135)
		tmp = t + ((x / y) * z);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -9e+42], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e+135], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.00000000000000025e42

   1. Initial program 99.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.1%

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

   4. Taylor expanded in z around 0 87.6%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   5. Step-by-step derivation

      1. mul-1-neg 87.6%

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

      2. associate-*r/ 91.4%

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

      3. distribute-lft-neg-in 91.4%

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

      4. cancel-sign-sub-inv 91.4%

         \[\leadsto \color{blue}{t - t \cdot \frac{x}{y}} \]

   6. Simplified 91.4%

      \[\leadsto \color{blue}{t - t \cdot \frac{x}{y}} \]

   if -9.00000000000000025e42 < t < 2.1000000000000001e135

   1. Initial program 98.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.4%

      \[\leadsto \frac{x}{y} \cdot \color{blue}{z} + t \]

   if 2.1000000000000001e135 < t

   1. Initial program 100.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 92.5%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   4. Step-by-step derivation

      1. *-rgt-identity 92.5%

         \[\leadsto \color{blue}{t \cdot 1} + -1 \cdot \frac{t \cdot x}{y} \]

      2. mul-1-neg 92.5%

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

      3. associate-/l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. mul-1-neg 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. mul-1-neg 100.0%

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

      8. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+42}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+135}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.32e-41)
   (* (/ x y) z)
   (if (<= z 4.8e+144) (* t (- 1.0 (/ x y))) (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e-41) {
		tmp = (x / y) * z;
	} else if (z <= 4.8e+144) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.32d-41)) then
        tmp = (x / y) * z
    else if (z <= 4.8d+144) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = (x * z) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.32e-41) {
		tmp = (x / y) * z;
	} else if (z <= 4.8e+144) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = (x * z) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.32e-41:
		tmp = (x / y) * z
	elif z <= 4.8e+144:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = (x * z) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.32e-41)
		tmp = Float64(Float64(x / y) * z);
	elseif (z <= 4.8e+144)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(Float64(x * z) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.32e-41)
		tmp = (x / y) * z;
	elseif (z <= 4.8e+144)
		tmp = t * (1.0 - (x / y));
	else
		tmp = (x * z) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.32e-41], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[z, 4.8e+144], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3200000000000001e-41

   1. Initial program 98.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.4%

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

   4. Taylor expanded in x around -inf 73.6%

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

   5. Taylor expanded in z around inf 70.1%

      \[\leadsto \color{blue}{\frac{x \cdot z}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 70.1%

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

      2. associate-*r/ 74.1%

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

   7. Simplified 74.1%

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

   if -1.3200000000000001e-41 < z < 4.8000000000000001e144

   1. Initial program 99.3%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 78.6%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   4. Step-by-step derivation

      1. *-rgt-identity 78.6%

         \[\leadsto \color{blue}{t \cdot 1} + -1 \cdot \frac{t \cdot x}{y} \]

      2. mul-1-neg 78.6%

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

      3. associate-/l* 81.7%

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

      4. distribute-rgt-neg-in 81.7%

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

      5. mul-1-neg 81.7%

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

      6. distribute-lft-in 81.7%

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

      7. mul-1-neg 81.7%

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

      8. unsub-neg 81.7%

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

   5. Simplified 81.7%

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

   if 4.8000000000000001e144 < z

   1. Initial program 97.0%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 93.6%

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

   4. Taylor expanded in x around -inf 77.1%

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

   5. Taylor expanded in z around inf 73.8%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.32 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+144}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 750000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) 750000000.0) t (* (/ x y) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 750000000.0) {
		tmp = t;
	} else {
		tmp = (x / y) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= 750000000.0d0) then
        tmp = t
    else
        tmp = (x / y) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= 750000000.0) {
		tmp = t;
	} else {
		tmp = (x / y) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= 750000000.0:
		tmp = t
	else:
		tmp = (x / y) * t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= 750000000.0)
		tmp = t;
	else
		tmp = Float64(Float64(x / y) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= 750000000.0)
		tmp = t;
	else
		tmp = (x / y) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], 750000000.0], t, N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < 7.5e8

   1. Initial program 98.9%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 50.0%

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

   if 7.5e8 < (/.f64 x y)

   1. Initial program 98.2%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 39.7%

      \[\leadsto \color{blue}{t + -1 \cdot \frac{t \cdot x}{y}} \]
   4. Step-by-step derivation

      1. *-rgt-identity 39.7%

         \[\leadsto \color{blue}{t \cdot 1} + -1 \cdot \frac{t \cdot x}{y} \]

      2. mul-1-neg 39.7%

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

      3. associate-/l* 44.6%

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

      4. distribute-rgt-neg-in 44.6%

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

      5. mul-1-neg 44.6%

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

      6. distribute-lft-in 44.6%

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

      7. mul-1-neg 44.6%

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

      8. unsub-neg 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in x around inf 44.6%

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

      1. associate-*r/ 44.6%

         \[\leadsto t \cdot \color{blue}{\frac{-1 \cdot x}{y}} \]

      2. neg-mul-1 44.6%

         \[\leadsto t \cdot \frac{\color{blue}{-x}}{y} \]

   8. Simplified 44.6%

      \[\leadsto t \cdot \color{blue}{\frac{-x}{y}} \]
   9. Step-by-step derivation

      1. div-inv 44.6%

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

      2. add-sqr-sqrt 20.8%

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

      3. sqrt-unprod 19.3%

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

      4. sqr-neg 19.3%

         \[\leadsto t \cdot \left(\sqrt{\color{blue}{x \cdot x}} \cdot \frac{1}{y}\right) \]

      5. sqrt-unprod 0.4%

         \[\leadsto t \cdot \left(\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{y}\right) \]

      6. add-sqr-sqrt 9.0%

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

   10. Applied egg-rr 9.0%

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

       1. associate-*r/ 9.0%

          \[\leadsto t \cdot \color{blue}{\frac{x \cdot 1}{y}} \]

       2. *-rgt-identity 9.0%

          \[\leadsto t \cdot \frac{\color{blue}{x}}{y} \]

   12. Simplified 9.0%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq 750000000:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 98.7%

   \[\frac{x}{y} \cdot \left(z - t\right) + t \]
2. Add Preprocessing

3. Taylor expanded in x around 0 39.4%

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

Developer Target 1: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{if}\;z < 2.759456554562692 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (* (/ x y) (- z t)) t)))
   (if (< z 2.759456554562692e-282)
     t_1
     (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x / y) * (z - t)) + t
    if (z < 2.759456554562692d-282) then
        tmp = t_1
    else if (z < 2.326994450874436d-110) then
        tmp = (x * ((z - t) / y)) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x / y) * (z - t)) + t;
	double tmp;
	if (z < 2.759456554562692e-282) {
		tmp = t_1;
	} else if (z < 2.326994450874436e-110) {
		tmp = (x * ((z - t) / y)) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x / y) * (z - t)) + t
	tmp = 0
	if z < 2.759456554562692e-282:
		tmp = t_1
	elif z < 2.326994450874436e-110:
		tmp = (x * ((z - t) / y)) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x / y) * Float64(z - t)) + t)
	tmp = 0.0
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = Float64(Float64(x * Float64(Float64(z - t) / y)) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x / y) * (z - t)) + t;
	tmp = 0.0;
	if (z < 2.759456554562692e-282)
		tmp = t_1;
	elseif (z < 2.326994450874436e-110)
		tmp = (x * ((z - t) / y)) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision]}, If[Less[z, 2.759456554562692e-282], t$95$1, If[Less[z, 2.326994450874436e-110], N[(N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 689864138640673/250000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* (/ x y) (- z t)) t) (if (< z 581748612718609/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t))))

  (+ (* (/ x y) (- z t)) t))