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

Percentage Accurate: 97.9% → 97.9%

Time: 6.8s

Alternatives: 11

Speedup: 1.0×

• 25.3% 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: 97.9% 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: 97.9% 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 98.0%

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

2. Final simplification 98.0%

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

Alternative 2: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+253}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+18} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+189}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e+253)
   (+ t (/ x (/ y z)))
   (if (or (<= (/ x y) -5e+18) (not (<= (/ x y) 2e+189)))
     (* (/ x y) (- t))
     (+ t (* (/ x y) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e+253) {
		tmp = t + (x / (y / z));
	} else if (((x / y) <= -5e+18) || !((x / y) <= 2e+189)) {
		tmp = (x / y) * -t;
	} 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+253)) then
        tmp = t + (x / (y / z))
    else if (((x / y) <= (-5d+18)) .or. (.not. ((x / y) <= 2d+189))) then
        tmp = (x / y) * -t
    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+253) {
		tmp = t + (x / (y / z));
	} else if (((x / y) <= -5e+18) || !((x / y) <= 2e+189)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e+253:
		tmp = t + (x / (y / z))
	elif ((x / y) <= -5e+18) or not ((x / y) <= 2e+189):
		tmp = (x / y) * -t
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e+253)
		tmp = Float64(t + Float64(x / Float64(y / z)));
	elseif ((Float64(x / y) <= -5e+18) || !(Float64(x / y) <= 2e+189))
		tmp = Float64(Float64(x / y) * Float64(-t));
	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+253)
		tmp = t + (x / (y / z));
	elseif (((x / y) <= -5e+18) || ~(((x / y) <= 2e+189)))
		tmp = (x / y) * -t;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e+253], N[(t + N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+18], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+189]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.9999999999999999e253

   1. Initial program 90.1%

      \[\frac{x}{y} \cdot \left(z - t\right) + t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

      2. associate-/l* 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in z around inf 76.0%

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

   if -1.9999999999999999e253 < (/.f64 x y) < -5e18 or 2e189 < (/.f64 x y)

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. associate-*r/ 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. *-commutative 67.2%

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

      3. neg-mul-1 67.2%

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

      4. distribute-rgt-neg-out 67.2%

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

      5. associate-*l/ 72.3%

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

   7. Simplified 72.3%

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

   if -5e18 < (/.f64 x y) < 2e189

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 89.1%

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

      1. associate-*r/ 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+253}:\\ \;\;\;\;t + \frac{x}{\frac{y}{z}}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{+18} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+189}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 3: 77.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+253} \lor \neg \left(\frac{x}{y} \leq -5 \cdot 10^{+18}\right) \land \frac{x}{y} \leq 2 \cdot 10^{+189}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2e+253)
         (and (not (<= (/ x y) -5e+18)) (<= (/ x y) 2e+189)))
   (+ t (/ z (/ y x)))
   (* (/ x y) (- t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2e+253) || (!((x / y) <= -5e+18) && ((x / y) <= 2e+189))) {
		tmp = t + (z / (y / x));
	} 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) <= (-2d+253)) .or. (.not. ((x / y) <= (-5d+18))) .and. ((x / y) <= 2d+189)) then
        tmp = t + (z / (y / x))
    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) <= -2e+253) || (!((x / y) <= -5e+18) && ((x / y) <= 2e+189))) {
		tmp = t + (z / (y / x));
	} else {
		tmp = (x / y) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2e+253) or (not ((x / y) <= -5e+18) and ((x / y) <= 2e+189)):
		tmp = t + (z / (y / x))
	else:
		tmp = (x / y) * -t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2e+253) || (!(Float64(x / y) <= -5e+18) && (Float64(x / y) <= 2e+189)))
		tmp = Float64(t + Float64(z / Float64(y / x)));
	else
		tmp = Float64(Float64(x / y) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2e+253) || (~(((x / y) <= -5e+18)) && ((x / y) <= 2e+189)))
		tmp = t + (z / (y / x));
	else
		tmp = (x / y) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2e+253], And[N[Not[LessEqual[N[(x / y), $MachinePrecision], -5e+18]], $MachinePrecision], LessEqual[N[(x / y), $MachinePrecision], 2e+189]]], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.9999999999999999e253 or -5e18 < (/.f64 x y) < 2e189

   1. Initial program 97.5%

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

   2. Taylor expanded in z around inf 87.3%

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

      1. associate-/l* 88.9%

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

   4. Simplified 88.9%

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

   if -1.9999999999999999e253 < (/.f64 x y) < -5e18 or 2e189 < (/.f64 x y)

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 67.2%

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

      1. mul-1-neg 67.2%

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

      2. unsub-neg 67.2%

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

      3. associate-*r/ 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around inf 67.2%

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

      1. associate-*r/ 67.2%

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

      2. *-commutative 67.2%

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

      3. neg-mul-1 67.2%

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

      4. distribute-rgt-neg-out 67.2%

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

      5. associate-*l/ 72.3%

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

   7. Simplified 72.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{+253} \lor \neg \left(\frac{x}{y} \leq -5 \cdot 10^{+18}\right) \land \frac{x}{y} \leq 2 \cdot 10^{+189}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \end{array} \]

Alternative 4: 77.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+18} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+189}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+18) (not (<= (/ x y) 2e+189)))
   (* (/ x y) (- t))
   (+ t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+18) || !((x / y) <= 2e+189)) {
		tmp = (x / y) * -t;
	} 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) <= (-5d+18)) .or. (.not. ((x / y) <= 2d+189))) then
        tmp = (x / y) * -t
    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) <= -5e+18) || !((x / y) <= 2e+189)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t + ((x / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+18) or not ((x / y) <= 2e+189):
		tmp = (x / y) * -t
	else:
		tmp = t + ((x / y) * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+18) || !(Float64(x / y) <= 2e+189))
		tmp = Float64(Float64(x / y) * Float64(-t));
	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) <= -5e+18) || ~(((x / y) <= 2e+189)))
		tmp = (x / y) * -t;
	else
		tmp = t + ((x / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+18], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e+189]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], N[(t + N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e18 or 2e189 < (/.f64 x y)

   1. Initial program 96.5%

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

   2. Taylor expanded in z around 0 62.9%

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

      1. mul-1-neg 62.9%

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

      2. unsub-neg 62.9%

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

      3. associate-*r/ 68.6%

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

   4. Simplified 68.6%

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

   5. Taylor expanded in x around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. *-commutative 62.9%

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

      3. neg-mul-1 62.9%

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

      4. distribute-rgt-neg-out 62.9%

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

      5. associate-*l/ 68.6%

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

   7. Simplified 68.6%

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

   if -5e18 < (/.f64 x y) < 2e189

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 89.1%

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

      1. associate-*r/ 90.7%

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

   4. Simplified 90.7%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+18} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{+189}\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x}{y} \cdot z\\ \end{array} \]

Alternative 5: 62.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+23} \lor \neg \left(\frac{x}{y} \leq 0.004\right):\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+23) (not (<= (/ x y) 0.004))) (* (/ t y) (- x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+23) || !((x / y) <= 0.004)) {
		tmp = (t / y) * -x;
	} 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) <= (-1d+23)) .or. (.not. ((x / y) <= 0.004d0))) then
        tmp = (t / y) * -x
    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) <= -1e+23) || !((x / y) <= 0.004)) {
		tmp = (t / y) * -x;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+23) or not ((x / y) <= 0.004):
		tmp = (t / y) * -x
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+23) || !(Float64(x / y) <= 0.004))
		tmp = Float64(Float64(t / y) * Float64(-x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+23) || ~(((x / y) <= 0.004)))
		tmp = (t / y) * -x;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+23], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.004]], $MachinePrecision]], N[(N[(t / y), $MachinePrecision] * (-x)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.9999999999999992e22 or 0.0040000000000000001 < (/.f64 x y)

   1. Initial program 97.3%

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

   2. Taylor expanded in z around 0 53.8%

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

      1. mul-1-neg 53.8%

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

      2. unsub-neg 53.8%

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

      3. associate-*r/ 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-*l/ 52.0%

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

      3. *-commutative 52.0%

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

      4. distribute-rgt-neg-in 52.0%

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

      5. distribute-neg-frac 52.0%

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

   7. Simplified 52.0%

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

   if -9.9999999999999992e22 < (/.f64 x y) < 0.0040000000000000001

   1. Initial program 98.6%

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

   2. Taylor expanded in x around 0 71.1%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+23} \lor \neg \left(\frac{x}{y} \leq 0.004\right):\\ \;\;\;\;\frac{t}{y} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 65.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000 \lor \neg \left(\frac{x}{y} \leq 0.004\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -50000000.0) (not (<= (/ x y) 0.004)))
   (* (/ x y) (- t))
   t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -50000000.0) || !((x / y) <= 0.004)) {
		tmp = (x / y) * -t;
	} 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) <= (-50000000.0d0)) .or. (.not. ((x / y) <= 0.004d0))) then
        tmp = (x / y) * -t
    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) <= -50000000.0) || !((x / y) <= 0.004)) {
		tmp = (x / y) * -t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -50000000.0) or not ((x / y) <= 0.004):
		tmp = (x / y) * -t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -50000000.0) || !(Float64(x / y) <= 0.004))
		tmp = Float64(Float64(x / y) * Float64(-t));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -50000000.0) || ~(((x / y) <= 0.004)))
		tmp = (x / y) * -t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -50000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.004]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * (-t)), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e7 or 0.0040000000000000001 < (/.f64 x y)

   1. Initial program 97.4%

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

   2. Taylor expanded in z around 0 53.7%

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

      1. mul-1-neg 53.7%

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

      2. unsub-neg 53.7%

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

      3. associate-*r/ 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in x around inf 53.2%

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

      1. associate-*r/ 53.2%

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

      2. *-commutative 53.2%

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

      3. neg-mul-1 53.2%

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

      4. distribute-rgt-neg-out 53.2%

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

      5. associate-*l/ 58.9%

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

   7. Simplified 58.9%

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

   if -5e7 < (/.f64 x y) < 0.0040000000000000001

   1. Initial program 98.5%

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

   2. Taylor expanded in x around 0 72.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -50000000 \lor \neg \left(\frac{x}{y} \leq 0.004\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+49} \lor \neg \left(t \leq 1.55 \cdot 10^{-82}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.4e+49) (not (<= t 1.55e-82)))
   (- t (* (/ x y) t))
   (+ t (/ (* x z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.4e+49) || !(t <= 1.55e-82)) {
		tmp = t - ((x / y) * t);
	} 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 <= (-1.4d+49)) .or. (.not. (t <= 1.55d-82))) then
        tmp = t - ((x / y) * t)
    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 <= -1.4e+49) || !(t <= 1.55e-82)) {
		tmp = t - ((x / y) * t);
	} else {
		tmp = t + ((x * z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.4e+49) or not (t <= 1.55e-82):
		tmp = t - ((x / y) * t)
	else:
		tmp = t + ((x * z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.4e+49) || !(t <= 1.55e-82))
		tmp = Float64(t - Float64(Float64(x / y) * t));
	else
		tmp = Float64(t + Float64(Float64(x * z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.4e+49) || ~((t <= 1.55e-82)))
		tmp = t - ((x / y) * t);
	else
		tmp = t + ((x * z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.4e+49], N[Not[LessEqual[t, 1.55e-82]], $MachinePrecision]], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3999999999999999e49 or 1.55e-82 < t

   1. Initial program 99.2%

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

   2. Taylor expanded in z around 0 83.6%

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

      1. mul-1-neg 83.6%

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

      2. unsub-neg 83.6%

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

      3. associate-*r/ 86.4%

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

   4. Simplified 86.4%

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

   if -1.3999999999999999e49 < t < 1.55e-82

   1. Initial program 96.6%

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

   2. Taylor expanded in z around inf 93.4%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+49} \lor \neg \left(t \leq 1.55 \cdot 10^{-82}\right):\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \end{array} \]

Alternative 8: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -6.8e+50)
   (- t (* (/ x y) t))
   (if (<= t 4.4e-82) (+ t (/ (* x z) y)) (- t (/ t (/ y x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.8e+50) {
		tmp = t - ((x / y) * t);
	} else if (t <= 4.4e-82) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = t - (t / (y / x));
	}
	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 <= (-6.8d+50)) then
        tmp = t - ((x / y) * t)
    else if (t <= 4.4d-82) then
        tmp = t + ((x * z) / y)
    else
        tmp = t - (t / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -6.8e+50) {
		tmp = t - ((x / y) * t);
	} else if (t <= 4.4e-82) {
		tmp = t + ((x * z) / y);
	} else {
		tmp = t - (t / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -6.8e+50:
		tmp = t - ((x / y) * t)
	elif t <= 4.4e-82:
		tmp = t + ((x * z) / y)
	else:
		tmp = t - (t / (y / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -6.8e+50)
		tmp = Float64(t - Float64(Float64(x / y) * t));
	elseif (t <= 4.4e-82)
		tmp = Float64(t + Float64(Float64(x * z) / y));
	else
		tmp = Float64(t - Float64(t / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -6.8e+50)
		tmp = t - ((x / y) * t);
	elseif (t <= 4.4e-82)
		tmp = t + ((x * z) / y);
	else
		tmp = t - (t / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -6.8e+50], N[(t - N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-82], N[(t + N[(N[(x * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t - N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.7999999999999997e50

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 84.0%

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

      1. mul-1-neg 84.0%

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

      2. unsub-neg 84.0%

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

      3. associate-*r/ 87.5%

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

   4. Simplified 87.5%

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

   if -6.7999999999999997e50 < t < 4.39999999999999971e-82

   1. Initial program 96.6%

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

   2. Taylor expanded in z around inf 93.4%

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

   if 4.39999999999999971e-82 < t

   1. Initial program 98.8%

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

   2. Taylor expanded in z around 0 83.4%

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

      1. mul-1-neg 83.4%

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

      2. associate-/l* 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+50}:\\ \;\;\;\;t - \frac{x}{y} \cdot t\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;t + \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;t - \frac{t}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 40.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -9.5e+117) (* (/ x y) t) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9.5e+117) {
		tmp = (x / y) * t;
	} 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) <= (-9.5d+117)) then
        tmp = (x / y) * t
    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) <= -9.5e+117) {
		tmp = (x / y) * t;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -9.5e+117:
		tmp = (x / y) * t
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -9.5e+117)
		tmp = Float64(Float64(x / y) * t);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -9.5e+117)
		tmp = (x / y) * t;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -9.5e+117], N[(N[(x / y), $MachinePrecision] * t), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.50000000000000041e117

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

      3. associate-*r/ 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in x around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. associate-*l/ 56.4%

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

      3. *-commutative 56.4%

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

      4. distribute-rgt-neg-in 56.4%

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

      5. distribute-neg-frac 56.4%

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

   7. Simplified 56.4%

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

      1. add-log-exp 56.0%

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

      2. associate-*r/ 56.0%

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

      3. associate-*l/ 56.0%

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

      4. *-un-lft-identity 56.0%

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

      5. log-prod 56.0%

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

      6. metadata-eval 56.0%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{x}{y} \cdot \left(-t\right)}\right) \]

      7. add-log-exp 60.9%

         \[\leadsto 0 + \color{blue}{\frac{x}{y} \cdot \left(-t\right)} \]

      8. associate-*l/ 56.4%

         \[\leadsto 0 + \color{blue}{\frac{x \cdot \left(-t\right)}{y}} \]

      9. associate-/l* 56.4%

         \[\leadsto 0 + \color{blue}{\frac{x}{\frac{y}{-t}}} \]

      10. add-sqr-sqrt 17.7%

          \[\leadsto 0 + \frac{x}{\frac{y}{\color{blue}{\sqrt{-t} \cdot \sqrt{-t}}}} \]

      11. sqrt-unprod 20.8%

          \[\leadsto 0 + \frac{x}{\frac{y}{\color{blue}{\sqrt{\left(-t\right) \cdot \left(-t\right)}}}} \]

      12. sqr-neg 20.8%

          \[\leadsto 0 + \frac{x}{\frac{y}{\sqrt{\color{blue}{t \cdot t}}}} \]

      13. sqrt-unprod 3.2%

          \[\leadsto 0 + \frac{x}{\frac{y}{\color{blue}{\sqrt{t} \cdot \sqrt{t}}}} \]

      14. add-sqr-sqrt 10.9%

          \[\leadsto 0 + \frac{x}{\frac{y}{\color{blue}{t}}} \]

   9. Applied egg-rr 10.9%

      \[\leadsto \color{blue}{0 + \frac{x}{\frac{y}{t}}} \]
   10. Step-by-step derivation

       1. +-lft-identity 10.9%

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

       2. associate-/r/ 13.2%

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

   11. Simplified 13.2%

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

   if -9.50000000000000041e117 < (/.f64 x y)

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 48.7%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.5 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 40.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+121}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e+121) (/ t (/ y x)) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e+121) {
		tmp = t / (y / x);
	} 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+121)) then
        tmp = t / (y / x)
    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+121) {
		tmp = t / (y / x);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e+121:
		tmp = t / (y / x)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e+121)
		tmp = Float64(t / Float64(y / x));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e+121)
		tmp = t / (y / x);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e+121], N[(t / N[(y / x), $MachinePrecision]), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.00000000000000007e121

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 56.4%

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

      1. mul-1-neg 56.4%

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

      2. unsub-neg 56.4%

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

      3. associate-*r/ 60.9%

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

   4. Simplified 60.9%

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

   5. Taylor expanded in x around inf 56.4%

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

      1. mul-1-neg 56.4%

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

      2. associate-*l/ 56.4%

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

      3. *-commutative 56.4%

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

      4. distribute-rgt-neg-in 56.4%

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

      5. distribute-neg-frac 56.4%

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

   7. Simplified 56.4%

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

      1. associate-*r/ 56.4%

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

      2. associate-*l/ 60.9%

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

      3. *-commutative 60.9%

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

      4. clear-num 61.0%

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

      5. un-div-inv 61.0%

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

      6. add-sqr-sqrt 22.2%

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

      7. sqrt-unprod 22.9%

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

      8. sqr-neg 22.9%

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

      9. sqrt-unprod 3.3%

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

      10. add-sqr-sqrt 13.3%

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

   9. Applied egg-rr 13.3%

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

   if -5.00000000000000007e121 < (/.f64 x y)

   1. Initial program 99.0%

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

   2. Taylor expanded in x around 0 48.7%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+121}:\\ \;\;\;\;\frac{t}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 38.8% 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 98.0%

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

2. Taylor expanded in x around 0 41.3%

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

3. Final simplification 41.3%

   \[\leadsto t \]

Developer target: 97.7% accurate, 0.7× 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 2023195 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.759456554562692e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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