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

Percentage Accurate: 97.7% → 95.2%

Time: 8.9s

Alternatives: 10

Speedup: 1.0×

• 24.2% 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: 97.7% 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: 95.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40000:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -40000.0)
   (/ (* x (- z t)) y)
   (if (<= (/ x y) 2e-10)
     (+ t (/ z (/ y x)))
     (if (<= (/ x y) 2000000000000.0)
       (* t (- 1.0 (/ x y)))
       (if (<= (/ x y) 2e+69) (* (/ x y) (- z t)) (* x (/ (- z t) y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -40000.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z / (y / x));
	} else if ((x / y) <= 2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 2e+69) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = x * ((z - t) / 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) <= (-40000.0d0)) then
        tmp = (x * (z - t)) / y
    else if ((x / y) <= 2d-10) then
        tmp = t + (z / (y / x))
    else if ((x / y) <= 2000000000000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else if ((x / y) <= 2d+69) then
        tmp = (x / y) * (z - t)
    else
        tmp = x * ((z - t) / 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) <= -40000.0) {
		tmp = (x * (z - t)) / y;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z / (y / x));
	} else if ((x / y) <= 2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 2e+69) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -40000.0:
		tmp = (x * (z - t)) / y
	elif (x / y) <= 2e-10:
		tmp = t + (z / (y / x))
	elif (x / y) <= 2000000000000.0:
		tmp = t * (1.0 - (x / y))
	elif (x / y) <= 2e+69:
		tmp = (x / y) * (z - t)
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -40000.0)
		tmp = Float64(Float64(x * Float64(z - t)) / y);
	elseif (Float64(x / y) <= 2e-10)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (Float64(x / y) <= 2000000000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (Float64(x / y) <= 2e+69)
		tmp = Float64(Float64(x / y) * Float64(z - t));
	else
		tmp = Float64(x * Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -40000.0)
		tmp = (x * (z - t)) / y;
	elseif ((x / y) <= 2e-10)
		tmp = t + (z / (y / x));
	elseif ((x / y) <= 2000000000000.0)
		tmp = t * (1.0 - (x / y));
	elseif ((x / y) <= 2e+69)
		tmp = (x / y) * (z - t);
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -40000.0], N[(N[(x * N[(z - t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-10], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2000000000000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+69], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 x y) < -4e4

   1. Initial program 95.5%

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

   2. Taylor expanded in x around 0 95.5%

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

   3. Taylor expanded in x around -inf 94.6%

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

   if -4e4 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 93.6%

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

      1. associate-/l* 98.9%

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

   4. Simplified 98.9%

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

   if 2.00000000000000007e-10 < (/.f64 x y) < 2e12

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 78.1%

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

   3. Taylor expanded in z around 0 78.1%

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

      1. associate-*r/ 99.6%

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

      2. neg-mul-1 99.6%

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

      3. distribute-lft-neg-in 99.6%

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

      4. cancel-sign-sub-inv 99.6%

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

      5. *-rgt-identity 99.6%

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

      6. distribute-lft-out-- 99.6%

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

   5. Simplified 99.6%

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

   if 2e12 < (/.f64 x y) < 2.0000000000000001e69

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.7%

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

   3. Taylor expanded in x around -inf 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

      1. associate-*r/ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. neg-mul-1 99.7%

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

      4. distribute-lft-neg-in 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. sub-neg 99.7%

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

   6. Simplified 99.7%

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

   if 2.0000000000000001e69 < (/.f64 x y)

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 96.2%

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

   3. Taylor expanded in z around 0 96.2%

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

      1. mul-1-neg 96.2%

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

      2. distribute-frac-neg 96.2%

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

      3. +-commutative 96.2%

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

      4. distribute-frac-neg 96.2%

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

      5. sub-neg 96.2%

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

      6. div-sub 99.9%

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

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{z - t}{y}} \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40000:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 2: 96.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{if}\;\frac{x}{y} \leq -40000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x y) (- z t))))
   (if (<= (/ x y) -40000.0)
     t_1
     (if (<= (/ x y) 2e-10)
       (+ t (/ z (/ y x)))
       (if (<= (/ x y) 2000000000000.0)
         (* t (- 1.0 (/ x y)))
         (if (<= (/ x y) 2e+69) t_1 (* x (/ (- z t) y))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (z - t);
	double tmp;
	if ((x / y) <= -40000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z / (y / x));
	} else if ((x / y) <= 2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 2e+69) {
		tmp = t_1;
	} else {
		tmp = x * ((z - t) / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) * (z - t)
    if ((x / y) <= (-40000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 2d-10) then
        tmp = t + (z / (y / x))
    else if ((x / y) <= 2000000000000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else if ((x / y) <= 2d+69) then
        tmp = t_1
    else
        tmp = x * ((z - t) / y)
    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);
	double tmp;
	if ((x / y) <= -40000.0) {
		tmp = t_1;
	} else if ((x / y) <= 2e-10) {
		tmp = t + (z / (y / x));
	} else if ((x / y) <= 2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else if ((x / y) <= 2e+69) {
		tmp = t_1;
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) * (z - t)
	tmp = 0
	if (x / y) <= -40000.0:
		tmp = t_1
	elif (x / y) <= 2e-10:
		tmp = t + (z / (y / x))
	elif (x / y) <= 2000000000000.0:
		tmp = t * (1.0 - (x / y))
	elif (x / y) <= 2e+69:
		tmp = t_1
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) * Float64(z - t))
	tmp = 0.0
	if (Float64(x / y) <= -40000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 2e-10)
		tmp = Float64(t + Float64(z / Float64(y / x)));
	elseif (Float64(x / y) <= 2000000000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (Float64(x / y) <= 2e+69)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) * (z - t);
	tmp = 0.0;
	if ((x / y) <= -40000.0)
		tmp = t_1;
	elseif ((x / y) <= 2e-10)
		tmp = t + (z / (y / x));
	elseif ((x / y) <= 2000000000000.0)
		tmp = t * (1.0 - (x / y));
	elseif ((x / y) <= 2e+69)
		tmp = t_1;
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -40000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2e-10], N[(t + N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2000000000000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e+69], t$95$1, N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -4e4 or 2e12 < (/.f64 x y) < 2.0000000000000001e69

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 95.8%

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

   3. Taylor expanded in x around -inf 95.0%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. associate-*r/ 74.8%

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

      2. associate-*r/ 76.6%

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

      3. neg-mul-1 76.6%

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

      4. distribute-lft-neg-in 76.6%

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

      5. distribute-rgt-in 94.3%

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

      6. sub-neg 94.3%

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

   6. Simplified 94.3%

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

   if -4e4 < (/.f64 x y) < 2.00000000000000007e-10

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 93.6%

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

      1. associate-/l* 98.9%

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

   4. Simplified 98.9%

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

   if 2.00000000000000007e-10 < (/.f64 x y) < 2e12

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 78.1%

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

   3. Taylor expanded in z around 0 78.1%

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

      1. associate-*r/ 99.6%

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

      2. neg-mul-1 99.6%

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

      3. distribute-lft-neg-in 99.6%

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

      4. cancel-sign-sub-inv 99.6%

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

      5. *-rgt-identity 99.6%

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

      6. distribute-lft-out-- 99.6%

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

   5. Simplified 99.6%

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

   if 2.0000000000000001e69 < (/.f64 x y)

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 96.2%

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

   3. Taylor expanded in z around 0 96.2%

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

      1. mul-1-neg 96.2%

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

      2. distribute-frac-neg 96.2%

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

      3. +-commutative 96.2%

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

      4. distribute-frac-neg 96.2%

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

      5. sub-neg 96.2%

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

      6. div-sub 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -40000:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-10}:\\ \;\;\;\;t + \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 3: 63.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-155} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+81)
   (* t (/ x (- y)))
   (if (or (<= (/ x y) -5e-155) (not (<= (/ x y) 2e-20))) (* (/ x y) z) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+81) {
		tmp = t * (x / -y);
	} else if (((x / y) <= -5e-155) || !((x / y) <= 2e-20)) {
		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) <= (-1d+81)) then
        tmp = t * (x / -y)
    else if (((x / y) <= (-5d-155)) .or. (.not. ((x / y) <= 2d-20))) 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) <= -1e+81) {
		tmp = t * (x / -y);
	} else if (((x / y) <= -5e-155) || !((x / y) <= 2e-20)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+81:
		tmp = t * (x / -y)
	elif ((x / y) <= -5e-155) or not ((x / y) <= 2e-20):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1e+81)
		tmp = Float64(t * Float64(x / Float64(-y)));
	elseif ((Float64(x / y) <= -5e-155) || !(Float64(x / y) <= 2e-20))
		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) <= -1e+81)
		tmp = t * (x / -y);
	elseif (((x / y) <= -5e-155) || ~(((x / y) <= 2e-20)))
		tmp = (x / y) * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1e+81], N[(t * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-155], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-20]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.99999999999999921e80

   1. Initial program 94.4%

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

   2. Taylor expanded in x around inf 94.1%

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

   3. Taylor expanded in z around 0 67.1%

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

      1. mul-1-neg 67.1%

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

      2. distribute-frac-neg 67.1%

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

   5. Simplified 67.1%

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

      1. *-commutative 67.1%

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

      2. frac-2neg 67.1%

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

      3. remove-double-neg 67.1%

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

      4. associate-*r/ 67.1%

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

   7. Applied egg-rr 67.1%

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

      1. associate-/l* 67.1%

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

      2. associate-/r/ 69.1%

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

   9. Simplified 69.1%

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

   if -9.99999999999999921e80 < (/.f64 x y) < -4.9999999999999999e-155 or 1.99999999999999989e-20 < (/.f64 x y)

   1. Initial program 98.2%

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

   2. Taylor expanded in x around inf 72.6%

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

   3. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. clear-num 47.9%

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

      3. un-div-inv 47.9%

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

   5. Applied egg-rr 47.9%

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

      1. associate-/r/ 53.6%

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

   7. Applied egg-rr 53.6%

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

   if -4.9999999999999999e-155 < (/.f64 x y) < 1.99999999999999989e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+81}:\\ \;\;\;\;t \cdot \frac{x}{-y}\\ \mathbf{elif}\;\frac{x}{y} \leq -5 \cdot 10^{-155} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 83.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155} \lor \neg \left(\frac{x}{y} \leq 2000000000000\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-155) (not (<= (/ x y) 2000000000000.0)))
   (* (/ x y) (- z t))
   (* t (- 1.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-155) || !((x / y) <= 2000000000000.0)) {
		tmp = (x / y) * (z - t);
	} 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 (((x / y) <= (-5d-155)) .or. (.not. ((x / y) <= 2000000000000.0d0))) then
        tmp = (x / y) * (z - t)
    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 (((x / y) <= -5e-155) || !((x / y) <= 2000000000000.0)) {
		tmp = (x / y) * (z - t);
	} else {
		tmp = t * (1.0 - (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-155) or not ((x / y) <= 2000000000000.0):
		tmp = (x / y) * (z - t)
	else:
		tmp = t * (1.0 - (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-155) || !(Float64(x / y) <= 2000000000000.0))
		tmp = Float64(Float64(x / y) * Float64(z - t));
	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 (((x / y) <= -5e-155) || ~(((x / y) <= 2000000000000.0)))
		tmp = (x / y) * (z - t);
	else
		tmp = t * (1.0 - (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e-155], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2000000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e-155 or 2e12 < (/.f64 x y)

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 93.8%

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

   3. Taylor expanded in x around -inf 87.0%

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

   4. Taylor expanded in z around 0 76.2%

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

      1. associate-*r/ 71.1%

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

      2. associate-*r/ 73.8%

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

      3. neg-mul-1 73.8%

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

      4. distribute-lft-neg-in 73.8%

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

      5. distribute-rgt-in 87.8%

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

      6. sub-neg 87.8%

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

   6. Simplified 87.8%

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

   if -4.9999999999999999e-155 < (/.f64 x y) < 2e12

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 90.1%

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

   3. Taylor expanded in z around 0 76.0%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

      3. distribute-lft-neg-in 81.3%

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

      4. cancel-sign-sub-inv 81.3%

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

      5. *-rgt-identity 81.3%

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

      6. distribute-lft-out-- 81.3%

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

   5. Simplified 81.3%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155} \lor \neg \left(\frac{x}{y} \leq 2000000000000\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \end{array} \]

Alternative 5: 82.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-155)
   (* (/ x y) (- z t))
   (if (<= (/ x y) 2000000000000.0)
     (* t (- 1.0 (/ x y)))
     (* x (/ (- z t) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-155) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * ((z - t) / 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-155)) then
        tmp = (x / y) * (z - t)
    else if ((x / y) <= 2000000000000.0d0) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = x * ((z - t) / 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-155) {
		tmp = (x / y) * (z - t);
	} else if ((x / y) <= 2000000000000.0) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = x * ((z - t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-155:
		tmp = (x / y) * (z - t)
	elif (x / y) <= 2000000000000.0:
		tmp = t * (1.0 - (x / y))
	else:
		tmp = x * ((z - t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-155)
		tmp = Float64(Float64(x / y) * Float64(z - t));
	elseif (Float64(x / y) <= 2000000000000.0)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(x * Float64(Float64(z - t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5e-155)
		tmp = (x / y) * (z - t);
	elseif ((x / y) <= 2000000000000.0)
		tmp = t * (1.0 - (x / y));
	else
		tmp = x * ((z - t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-155], N[(N[(x / y), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2000000000000.0], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999999e-155

   1. Initial program 96.8%

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

   2. Taylor expanded in x around 0 92.8%

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

   3. Taylor expanded in x around -inf 81.5%

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

   4. Taylor expanded in z around 0 72.6%

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

      1. associate-*r/ 67.4%

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

      2. associate-*r/ 68.8%

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

      3. neg-mul-1 68.8%

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

      4. distribute-lft-neg-in 68.8%

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

      5. distribute-rgt-in 82.0%

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

      6. sub-neg 82.0%

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

   6. Simplified 82.0%

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

   if -4.9999999999999999e-155 < (/.f64 x y) < 2e12

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 90.1%

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

   3. Taylor expanded in z around 0 76.0%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

      3. distribute-lft-neg-in 81.3%

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

      4. cancel-sign-sub-inv 81.3%

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

      5. *-rgt-identity 81.3%

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

      6. distribute-lft-out-- 81.3%

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

   5. Simplified 81.3%

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

   if 2e12 < (/.f64 x y)

   1. Initial program 96.7%

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

   2. Taylor expanded in x around inf 93.4%

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

   3. Taylor expanded in z around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. distribute-frac-neg 93.4%

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

      3. +-commutative 93.4%

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

      4. distribute-frac-neg 93.4%

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

      5. sub-neg 93.4%

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

      6. div-sub 96.8%

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

   5. Simplified 96.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right)\\ \mathbf{elif}\;\frac{x}{y} \leq 2000000000000:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y}\\ \end{array} \]

Alternative 6: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e-155) (not (<= (/ x y) 2e-20))) (* (/ x y) z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e-155) || !((x / y) <= 2e-20)) {
		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-155)) .or. (.not. ((x / y) <= 2d-20))) 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-155) || !((x / y) <= 2e-20)) {
		tmp = (x / y) * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e-155) or not ((x / y) <= 2e-20):
		tmp = (x / y) * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e-155) || !(Float64(x / y) <= 2e-20))
		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-155) || ~(((x / y) <= 2e-20)))
		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-155], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-20]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.9999999999999999e-155 or 1.99999999999999989e-20 < (/.f64 x y)

   1. Initial program 97.0%

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

   2. Taylor expanded in x around inf 79.4%

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

   3. Taylor expanded in z around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. clear-num 46.5%

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

      3. un-div-inv 46.6%

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

   5. Applied egg-rr 46.6%

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

      1. associate-/r/ 50.8%

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

   7. Applied egg-rr 50.8%

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

   if -4.9999999999999999e-155 < (/.f64 x y) < 1.99999999999999989e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.3%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5e-155)
   (/ z (/ y x))
   (if (<= (/ x y) 2e-20) t (* (/ x y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5e-155) {
		tmp = z / (y / x);
	} else if ((x / y) <= 2e-20) {
		tmp = t;
	} else {
		tmp = (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-155)) then
        tmp = z / (y / x)
    else if ((x / y) <= 2d-20) then
        tmp = t
    else
        tmp = (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-155) {
		tmp = z / (y / x);
	} else if ((x / y) <= 2e-20) {
		tmp = t;
	} else {
		tmp = (x / y) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5e-155:
		tmp = z / (y / x)
	elif (x / y) <= 2e-20:
		tmp = t
	else:
		tmp = (x / y) * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5e-155)
		tmp = Float64(z / Float64(y / x));
	elseif (Float64(x / y) <= 2e-20)
		tmp = t;
	else
		tmp = 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-155)
		tmp = z / (y / x);
	elseif ((x / y) <= 2e-20)
		tmp = t;
	else
		tmp = (x / y) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5e-155], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-20], t, N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.9999999999999999e-155

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 75.3%

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

   3. Taylor expanded in z around inf 43.0%

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

      1. associate-*l/ 46.1%

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

      2. associate-/l* 48.8%

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

   5. Applied egg-rr 48.8%

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

   if -4.9999999999999999e-155 < (/.f64 x y) < 1.99999999999999989e-20

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 82.3%

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

   if 1.99999999999999989e-20 < (/.f64 x y)

   1. Initial program 97.2%

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

   2. Taylor expanded in x around inf 84.8%

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

   3. Taylor expanded in z around inf 51.6%

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

      1. *-commutative 51.6%

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

      2. clear-num 51.5%

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

      3. un-div-inv 51.6%

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

   5. Applied egg-rr 51.6%

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

      1. associate-/r/ 54.8%

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

   7. Applied egg-rr 54.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-20}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot z\\ \end{array} \]

Alternative 8: 73.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-46} \lor \neg \left(t \leq 1.85 \cdot 10^{-49}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8.5e-46) (not (<= t 1.85e-49)))
   (* t (- 1.0 (/ x y)))
   (/ z (/ y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8.5e-46) || !(t <= 1.85e-49)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (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 <= (-8.5d-46)) .or. (.not. (t <= 1.85d-49))) then
        tmp = t * (1.0d0 - (x / y))
    else
        tmp = z / (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 <= -8.5e-46) || !(t <= 1.85e-49)) {
		tmp = t * (1.0 - (x / y));
	} else {
		tmp = z / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8.5e-46) or not (t <= 1.85e-49):
		tmp = t * (1.0 - (x / y))
	else:
		tmp = z / (y / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8.5e-46) || !(t <= 1.85e-49))
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(z / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8.5e-46) || ~((t <= 1.85e-49)))
		tmp = t * (1.0 - (x / y));
	else
		tmp = z / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8.5e-46], N[Not[LessEqual[t, 1.85e-49]], $MachinePrecision]], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5000000000000001e-46 or 1.85e-49 < t

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 91.1%

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

   3. Taylor expanded in z around 0 79.0%

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

      1. associate-*r/ 86.0%

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

      2. neg-mul-1 86.0%

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

      3. distribute-lft-neg-in 86.0%

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

      4. cancel-sign-sub-inv 86.0%

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

      5. *-rgt-identity 86.0%

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

      6. distribute-lft-out-- 86.0%

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

   5. Simplified 86.0%

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

   if -8.5000000000000001e-46 < t < 1.85e-49

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 70.3%

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

   3. Taylor expanded in z around inf 60.2%

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

      1. associate-*l/ 61.9%

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

      2. associate-/l* 65.5%

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

   5. Applied egg-rr 65.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-46} \lor \neg \left(t \leq 1.85 \cdot 10^{-49}\right):\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 97.7% 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 10: 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 37.3%

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

3. Final simplification 37.3%

   \[\leadsto t \]

Developer target: 97.3% 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 2023274 
(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))