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

Percentage Accurate: 97.2% → 97.2%

Time: 10.5s

Alternatives: 16

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * 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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * 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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{z - y} \cdot t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return ((x - y) / (z - y)) * 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 - y)) * t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

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

2. Final simplification 97.6%

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

Alternative 2: 59.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e+28)
   t
   (if (<= y -2.3e-13)
     (/ t (/ z x))
     (if (<= y -1.7e-47)
       (/ (* y (- t)) z)
       (if (<= y -2.5e-231)
         (/ x (/ z t))
         (if (<= y 5.4e-60)
           (/ (* x t) z)
           (if (<= y 1.15e+123) (* x (/ (- t) y)) t)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e+28) {
		tmp = t;
	} else if (y <= -2.3e-13) {
		tmp = t / (z / x);
	} else if (y <= -1.7e-47) {
		tmp = (y * -t) / z;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 5.4e-60) {
		tmp = (x * t) / z;
	} else if (y <= 1.15e+123) {
		tmp = x * (-t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.6d+28)) then
        tmp = t
    else if (y <= (-2.3d-13)) then
        tmp = t / (z / x)
    else if (y <= (-1.7d-47)) then
        tmp = (y * -t) / z
    else if (y <= (-2.5d-231)) then
        tmp = x / (z / t)
    else if (y <= 5.4d-60) then
        tmp = (x * t) / z
    else if (y <= 1.15d+123) then
        tmp = x * (-t / y)
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e+28) {
		tmp = t;
	} else if (y <= -2.3e-13) {
		tmp = t / (z / x);
	} else if (y <= -1.7e-47) {
		tmp = (y * -t) / z;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 5.4e-60) {
		tmp = (x * t) / z;
	} else if (y <= 1.15e+123) {
		tmp = x * (-t / y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e+28:
		tmp = t
	elif y <= -2.3e-13:
		tmp = t / (z / x)
	elif y <= -1.7e-47:
		tmp = (y * -t) / z
	elif y <= -2.5e-231:
		tmp = x / (z / t)
	elif y <= 5.4e-60:
		tmp = (x * t) / z
	elif y <= 1.15e+123:
		tmp = x * (-t / y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e+28)
		tmp = t;
	elseif (y <= -2.3e-13)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -1.7e-47)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (y <= -2.5e-231)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 5.4e-60)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 1.15e+123)
		tmp = Float64(x * Float64(Float64(-t) / y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.6e+28)
		tmp = t;
	elseif (y <= -2.3e-13)
		tmp = t / (z / x);
	elseif (y <= -1.7e-47)
		tmp = (y * -t) / z;
	elseif (y <= -2.5e-231)
		tmp = x / (z / t);
	elseif (y <= 5.4e-60)
		tmp = (x * t) / z;
	elseif (y <= 1.15e+123)
		tmp = x * (-t / y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e+28], t, If[LessEqual[y, -2.3e-13], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-47], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -2.5e-231], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-60], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.15e+123], N[(x * N[((-t) / y), $MachinePrecision]), $MachinePrecision], t]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.5999999999999999e28 or 1.14999999999999995e123 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.2%

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

      2. *-commutative 70.2%

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

      3. associate-*l/ 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in y around inf 62.4%

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

   if -3.5999999999999999e28 < y < -2.29999999999999979e-13

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. associate-/l* 63.5%

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

   6. Simplified 63.5%

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

   if -2.29999999999999979e-13 < y < -1.7000000000000001e-47

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around 0 36.0%

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

      1. mul-1-neg 36.0%

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

      2. associate-*l/ 35.7%

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

      3. *-commutative 35.7%

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

   7. Simplified 35.7%

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

   8. Taylor expanded in y around 0 36.0%

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

   if -1.7000000000000001e-47 < y < -2.50000000000000012e-231

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. associate-*l/ 54.1%

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

      2. associate-/l* 63.2%

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

   4. Applied egg-rr 63.2%

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

   if -2.50000000000000012e-231 < y < 5.40000000000000001e-60

   1. Initial program 95.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around 0 79.4%

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

   if 5.40000000000000001e-60 < y < 1.14999999999999995e123

   1. Initial program 99.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 49.7%

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

      1. associate-/l* 59.1%

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

   6. Simplified 59.1%

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

      1. associate-/r/ 56.6%

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

   8. Applied egg-rr 56.6%

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

   9. Taylor expanded in z around 0 46.0%

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

       1. associate-*r/ 46.0%

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

       2. neg-mul-1 46.0%

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

   11. Simplified 46.0%

       \[\leadsto \color{blue}{\frac{-t}{y}} \cdot x \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-47}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \frac{-t}{y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 3: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.56 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ x z))))
   (if (<= y -1.56e+29)
     t
     (if (<= y -6.5e-28)
       t_1
       (if (<= y -1.08e-48)
         t
         (if (<= y -2.5e-231) (* x (/ t z)) (if (<= y 3.5e+70) t_1 t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -1.56e+29) {
		tmp = t;
	} else if (y <= -6.5e-28) {
		tmp = t_1;
	} else if (y <= -1.08e-48) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x * (t / z);
	} else if (y <= 3.5e+70) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = t * (x / z)
    if (y <= (-1.56d+29)) then
        tmp = t
    else if (y <= (-6.5d-28)) then
        tmp = t_1
    else if (y <= (-1.08d-48)) then
        tmp = t
    else if (y <= (-2.5d-231)) then
        tmp = x * (t / z)
    else if (y <= 3.5d+70) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (x / z);
	double tmp;
	if (y <= -1.56e+29) {
		tmp = t;
	} else if (y <= -6.5e-28) {
		tmp = t_1;
	} else if (y <= -1.08e-48) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x * (t / z);
	} else if (y <= 3.5e+70) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (x / z)
	tmp = 0
	if y <= -1.56e+29:
		tmp = t
	elif y <= -6.5e-28:
		tmp = t_1
	elif y <= -1.08e-48:
		tmp = t
	elif y <= -2.5e-231:
		tmp = x * (t / z)
	elif y <= 3.5e+70:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(x / z))
	tmp = 0.0
	if (y <= -1.56e+29)
		tmp = t;
	elseif (y <= -6.5e-28)
		tmp = t_1;
	elseif (y <= -1.08e-48)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 3.5e+70)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (x / z);
	tmp = 0.0;
	if (y <= -1.56e+29)
		tmp = t;
	elseif (y <= -6.5e-28)
		tmp = t_1;
	elseif (y <= -1.08e-48)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = x * (t / z);
	elseif (y <= 3.5e+70)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.56e+29], t, If[LessEqual[y, -6.5e-28], t$95$1, If[LessEqual[y, -1.08e-48], t, If[LessEqual[y, -2.5e-231], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+70], t$95$1, t]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5599999999999999e29 or -6.50000000000000043e-28 < y < -1.08e-48 or 3.50000000000000002e70 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*l/ 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in y around inf 59.3%

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

   if -1.5599999999999999e29 < y < -6.50000000000000043e-28 or -2.50000000000000012e-231 < y < 3.50000000000000002e70

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 61.6%

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

   if -1.08e-48 < y < -2.50000000000000012e-231

   1. Initial program 90.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around 0 54.1%

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

      1. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

      1. associate-/r/ 63.1%

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

   8. Applied egg-rr 63.1%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 4: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e+29)
   t
   (if (<= y -3.65e-28)
     (/ t (/ z x))
     (if (<= y -2.1e-47)
       t
       (if (<= y -2.5e-231)
         (* x (/ t z))
         (if (<= y 4.2e+70) (* t (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+29) {
		tmp = t;
	} else if (y <= -3.65e-28) {
		tmp = t / (z / x);
	} else if (y <= -2.1e-47) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x * (t / z);
	} else if (y <= 4.2e+70) {
		tmp = t * (x / 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 (y <= (-5.8d+29)) then
        tmp = t
    else if (y <= (-3.65d-28)) then
        tmp = t / (z / x)
    else if (y <= (-2.1d-47)) then
        tmp = t
    else if (y <= (-2.5d-231)) then
        tmp = x * (t / z)
    else if (y <= 4.2d+70) then
        tmp = t * (x / 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 (y <= -5.8e+29) {
		tmp = t;
	} else if (y <= -3.65e-28) {
		tmp = t / (z / x);
	} else if (y <= -2.1e-47) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x * (t / z);
	} else if (y <= 4.2e+70) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e+29:
		tmp = t
	elif y <= -3.65e-28:
		tmp = t / (z / x)
	elif y <= -2.1e-47:
		tmp = t
	elif y <= -2.5e-231:
		tmp = x * (t / z)
	elif y <= 4.2e+70:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e+29)
		tmp = t;
	elseif (y <= -3.65e-28)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -2.1e-47)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = Float64(x * Float64(t / z));
	elseif (y <= 4.2e+70)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.8e+29)
		tmp = t;
	elseif (y <= -3.65e-28)
		tmp = t / (z / x);
	elseif (y <= -2.1e-47)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = x * (t / z);
	elseif (y <= 4.2e+70)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.8e+29], t, If[LessEqual[y, -3.65e-28], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-47], t, If[LessEqual[y, -2.5e-231], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+70], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.7999999999999999e29 or -3.6499999999999998e-28 < y < -2.1000000000000001e-47 or 4.20000000000000015e70 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*l/ 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in y around inf 59.3%

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

   if -5.7999999999999999e29 < y < -3.6499999999999998e-28

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*l/ 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in y around 0 46.2%

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

      1. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

   if -2.1000000000000001e-47 < y < -2.50000000000000012e-231

   1. Initial program 90.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in y around 0 54.1%

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

      1. associate-/l* 57.4%

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

   6. Simplified 57.4%

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

      1. associate-/r/ 63.1%

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

   8. Applied egg-rr 63.1%

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

   if -2.50000000000000012e-231 < y < 4.20000000000000015e70

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 63.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -3.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-47}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 5: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.95e+27)
   t
   (if (<= y -4.8e-25)
     (/ t (/ z x))
     (if (<= y -9e-48)
       t
       (if (<= y -2.5e-231)
         (/ x (/ z t))
         (if (<= y 1.8e+70) (* t (/ x z)) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.95e+27) {
		tmp = t;
	} else if (y <= -4.8e-25) {
		tmp = t / (z / x);
	} else if (y <= -9e-48) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 1.8e+70) {
		tmp = t * (x / 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 (y <= (-1.95d+27)) then
        tmp = t
    else if (y <= (-4.8d-25)) then
        tmp = t / (z / x)
    else if (y <= (-9d-48)) then
        tmp = t
    else if (y <= (-2.5d-231)) then
        tmp = x / (z / t)
    else if (y <= 1.8d+70) then
        tmp = t * (x / 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 (y <= -1.95e+27) {
		tmp = t;
	} else if (y <= -4.8e-25) {
		tmp = t / (z / x);
	} else if (y <= -9e-48) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 1.8e+70) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.95e+27:
		tmp = t
	elif y <= -4.8e-25:
		tmp = t / (z / x)
	elif y <= -9e-48:
		tmp = t
	elif y <= -2.5e-231:
		tmp = x / (z / t)
	elif y <= 1.8e+70:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.95e+27)
		tmp = t;
	elseif (y <= -4.8e-25)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -9e-48)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 1.8e+70)
		tmp = Float64(t * Float64(x / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.95e+27)
		tmp = t;
	elseif (y <= -4.8e-25)
		tmp = t / (z / x);
	elseif (y <= -9e-48)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = x / (z / t);
	elseif (y <= 1.8e+70)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.95e+27], t, If[LessEqual[y, -4.8e-25], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-48], t, If[LessEqual[y, -2.5e-231], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+70], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.9499999999999999e27 or -4.80000000000000018e-25 < y < -8.99999999999999977e-48 or 1.8e70 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*l/ 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in y around inf 59.3%

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

   if -1.9499999999999999e27 < y < -4.80000000000000018e-25

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*l/ 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in y around 0 46.2%

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

      1. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

   if -8.99999999999999977e-48 < y < -2.50000000000000012e-231

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. associate-*l/ 54.1%

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

      2. associate-/l* 63.2%

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

   4. Applied egg-rr 63.2%

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

   if -2.50000000000000012e-231 < y < 1.8e70

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 63.0%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+70}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 6: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+27)
   t
   (if (<= y -1.65e-23)
     (/ t (/ z x))
     (if (<= y -4.5e-48)
       t
       (if (<= y -2.5e-231)
         (/ x (/ z t))
         (if (<= y 3.8e+70) (/ (* x t) z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+27) {
		tmp = t;
	} else if (y <= -1.65e-23) {
		tmp = t / (z / x);
	} else if (y <= -4.5e-48) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 3.8e+70) {
		tmp = (x * t) / 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 (y <= (-7.5d+27)) then
        tmp = t
    else if (y <= (-1.65d-23)) then
        tmp = t / (z / x)
    else if (y <= (-4.5d-48)) then
        tmp = t
    else if (y <= (-2.5d-231)) then
        tmp = x / (z / t)
    else if (y <= 3.8d+70) then
        tmp = (x * t) / 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 (y <= -7.5e+27) {
		tmp = t;
	} else if (y <= -1.65e-23) {
		tmp = t / (z / x);
	} else if (y <= -4.5e-48) {
		tmp = t;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 3.8e+70) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+27:
		tmp = t
	elif y <= -1.65e-23:
		tmp = t / (z / x)
	elif y <= -4.5e-48:
		tmp = t
	elif y <= -2.5e-231:
		tmp = x / (z / t)
	elif y <= 3.8e+70:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+27)
		tmp = t;
	elseif (y <= -1.65e-23)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -4.5e-48)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 3.8e+70)
		tmp = Float64(Float64(x * t) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.5e+27)
		tmp = t;
	elseif (y <= -1.65e-23)
		tmp = t / (z / x);
	elseif (y <= -4.5e-48)
		tmp = t;
	elseif (y <= -2.5e-231)
		tmp = x / (z / t);
	elseif (y <= 3.8e+70)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+27], t, If[LessEqual[y, -1.65e-23], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.5e-48], t, If[LessEqual[y, -2.5e-231], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+70], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.5000000000000002e27 or -1.6500000000000001e-23 < y < -4.49999999999999988e-48 or 3.7999999999999998e70 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

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

      2. *-commutative 72.6%

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

      3. associate-*l/ 77.4%

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

   3. Simplified 77.4%

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

   4. Taylor expanded in y around inf 59.3%

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

   if -7.5000000000000002e27 < y < -1.6500000000000001e-23

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 93.4%

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

      2. *-commutative 93.4%

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

      3. associate-*l/ 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in y around 0 46.2%

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

      1. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

   if -4.49999999999999988e-48 < y < -2.50000000000000012e-231

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. associate-*l/ 54.1%

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

      2. associate-/l* 63.2%

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

   4. Applied egg-rr 63.2%

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

   if -2.50000000000000012e-231 < y < 3.7999999999999998e70

   1. Initial program 97.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around 0 63.6%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-48}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 7: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 10^{+73}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.65e+28)
   t
   (if (<= y -8.2e-13)
     (/ t (/ z x))
     (if (<= y -1.9e-47)
       (* (/ t z) (- y))
       (if (<= y -2.5e-231)
         (/ x (/ z t))
         (if (<= y 1e+73) (/ (* x t) z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.65e+28) {
		tmp = t;
	} else if (y <= -8.2e-13) {
		tmp = t / (z / x);
	} else if (y <= -1.9e-47) {
		tmp = (t / z) * -y;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 1e+73) {
		tmp = (x * t) / 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 (y <= (-3.65d+28)) then
        tmp = t
    else if (y <= (-8.2d-13)) then
        tmp = t / (z / x)
    else if (y <= (-1.9d-47)) then
        tmp = (t / z) * -y
    else if (y <= (-2.5d-231)) then
        tmp = x / (z / t)
    else if (y <= 1d+73) then
        tmp = (x * t) / 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 (y <= -3.65e+28) {
		tmp = t;
	} else if (y <= -8.2e-13) {
		tmp = t / (z / x);
	} else if (y <= -1.9e-47) {
		tmp = (t / z) * -y;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 1e+73) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.65e+28:
		tmp = t
	elif y <= -8.2e-13:
		tmp = t / (z / x)
	elif y <= -1.9e-47:
		tmp = (t / z) * -y
	elif y <= -2.5e-231:
		tmp = x / (z / t)
	elif y <= 1e+73:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.65e+28)
		tmp = t;
	elseif (y <= -8.2e-13)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -1.9e-47)
		tmp = Float64(Float64(t / z) * Float64(-y));
	elseif (y <= -2.5e-231)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 1e+73)
		tmp = Float64(Float64(x * t) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.65e+28)
		tmp = t;
	elseif (y <= -8.2e-13)
		tmp = t / (z / x);
	elseif (y <= -1.9e-47)
		tmp = (t / z) * -y;
	elseif (y <= -2.5e-231)
		tmp = x / (z / t);
	elseif (y <= 1e+73)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.65e+28], t, If[LessEqual[y, -8.2e-13], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-47], N[(N[(t / z), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, -2.5e-231], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+73], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.6499999999999999e28 or 9.99999999999999983e72 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around inf 61.3%

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

   if -3.6499999999999999e28 < y < -8.2000000000000004e-13

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. associate-/l* 63.5%

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

   6. Simplified 63.5%

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

   if -8.2000000000000004e-13 < y < -1.90000000000000007e-47

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around 0 36.0%

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

      1. mul-1-neg 36.0%

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

      2. associate-*l/ 35.7%

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

      3. *-commutative 35.7%

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

   7. Simplified 35.7%

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

   if -1.90000000000000007e-47 < y < -2.50000000000000012e-231

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. associate-*l/ 54.1%

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

      2. associate-/l* 63.2%

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

   4. Applied egg-rr 63.2%

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

   if -2.50000000000000012e-231 < y < 9.99999999999999983e72

   1. Initial program 97.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around 0 63.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.65 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-47}:\\ \;\;\;\;\frac{t}{z} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 10^{+73}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 8: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e+28)
   t
   (if (<= y -1.15e-12)
     (/ t (/ z x))
     (if (<= y -1.9e-48)
       (/ (* y (- t)) z)
       (if (<= y -2.5e-231)
         (/ x (/ z t))
         (if (<= y 2.7e+72) (/ (* x t) z) t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+28) {
		tmp = t;
	} else if (y <= -1.15e-12) {
		tmp = t / (z / x);
	} else if (y <= -1.9e-48) {
		tmp = (y * -t) / z;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 2.7e+72) {
		tmp = (x * t) / 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 (y <= (-4.2d+28)) then
        tmp = t
    else if (y <= (-1.15d-12)) then
        tmp = t / (z / x)
    else if (y <= (-1.9d-48)) then
        tmp = (y * -t) / z
    else if (y <= (-2.5d-231)) then
        tmp = x / (z / t)
    else if (y <= 2.7d+72) then
        tmp = (x * t) / 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 (y <= -4.2e+28) {
		tmp = t;
	} else if (y <= -1.15e-12) {
		tmp = t / (z / x);
	} else if (y <= -1.9e-48) {
		tmp = (y * -t) / z;
	} else if (y <= -2.5e-231) {
		tmp = x / (z / t);
	} else if (y <= 2.7e+72) {
		tmp = (x * t) / z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e+28:
		tmp = t
	elif y <= -1.15e-12:
		tmp = t / (z / x)
	elif y <= -1.9e-48:
		tmp = (y * -t) / z
	elif y <= -2.5e-231:
		tmp = x / (z / t)
	elif y <= 2.7e+72:
		tmp = (x * t) / z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e+28)
		tmp = t;
	elseif (y <= -1.15e-12)
		tmp = Float64(t / Float64(z / x));
	elseif (y <= -1.9e-48)
		tmp = Float64(Float64(y * Float64(-t)) / z);
	elseif (y <= -2.5e-231)
		tmp = Float64(x / Float64(z / t));
	elseif (y <= 2.7e+72)
		tmp = Float64(Float64(x * t) / z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e+28)
		tmp = t;
	elseif (y <= -1.15e-12)
		tmp = t / (z / x);
	elseif (y <= -1.9e-48)
		tmp = (y * -t) / z;
	elseif (y <= -2.5e-231)
		tmp = x / (z / t);
	elseif (y <= 2.7e+72)
		tmp = (x * t) / z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e+28], t, If[LessEqual[y, -1.15e-12], N[(t / N[(z / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-48], N[(N[(y * (-t)), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -2.5e-231], N[(x / N[(z / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+72], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], t]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.19999999999999978e28 or 2.7000000000000001e72 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around inf 61.3%

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

   if -4.19999999999999978e28 < y < -1.14999999999999995e-12

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

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

      2. *-commutative 91.2%

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

      3. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around 0 54.9%

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

      1. associate-/l* 63.5%

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

   6. Simplified 63.5%

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

   if -1.14999999999999995e-12 < y < -1.90000000000000001e-48

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around inf 49.4%

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

   5. Taylor expanded in x around 0 36.0%

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

      1. mul-1-neg 36.0%

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

      2. associate-*l/ 35.7%

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

      3. *-commutative 35.7%

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

   7. Simplified 35.7%

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

   8. Taylor expanded in y around 0 36.0%

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

   if -1.90000000000000001e-48 < y < -2.50000000000000012e-231

   1. Initial program 90.1%

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

   2. Taylor expanded in y around 0 57.3%

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

      1. associate-*l/ 54.1%

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

      2. associate-/l* 63.2%

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

   4. Applied egg-rr 63.2%

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

   if -2.50000000000000012e-231 < y < 2.7000000000000001e72

   1. Initial program 97.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-*l/ 91.6%

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

   3. Simplified 91.6%

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

   4. Taylor expanded in y around 0 63.6%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-12}:\\ \;\;\;\;\frac{t}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-48}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{z}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-231}:\\ \;\;\;\;\frac{x}{\frac{z}{t}}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 9: 66.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-249}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))))
   (if (<= y -4.8e+29)
     t
     (if (<= y -5.8e-218)
       t_1
       (if (<= y 7.2e-249) (/ (* x t) z) (if (<= y 2.55e+79) t_1 t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -4.8e+29) {
		tmp = t;
	} else if (y <= -5.8e-218) {
		tmp = t_1;
	} else if (y <= 7.2e-249) {
		tmp = (x * t) / z;
	} else if (y <= 2.55e+79) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    if (y <= (-4.8d+29)) then
        tmp = t
    else if (y <= (-5.8d-218)) then
        tmp = t_1
    else if (y <= 7.2d-249) then
        tmp = (x * t) / z
    else if (y <= 2.55d+79) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -4.8e+29) {
		tmp = t;
	} else if (y <= -5.8e-218) {
		tmp = t_1;
	} else if (y <= 7.2e-249) {
		tmp = (x * t) / z;
	} else if (y <= 2.55e+79) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	tmp = 0
	if y <= -4.8e+29:
		tmp = t
	elif y <= -5.8e-218:
		tmp = t_1
	elif y <= 7.2e-249:
		tmp = (x * t) / z
	elif y <= 2.55e+79:
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	tmp = 0.0
	if (y <= -4.8e+29)
		tmp = t;
	elseif (y <= -5.8e-218)
		tmp = t_1;
	elseif (y <= 7.2e-249)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 2.55e+79)
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	tmp = 0.0;
	if (y <= -4.8e+29)
		tmp = t;
	elseif (y <= -5.8e-218)
		tmp = t_1;
	elseif (y <= 7.2e-249)
		tmp = (x * t) / z;
	elseif (y <= 2.55e+79)
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+29], t, If[LessEqual[y, -5.8e-218], t$95$1, If[LessEqual[y, 7.2e-249], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.55e+79], t$95$1, t]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000002e29 or 2.5500000000000001e79 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around inf 61.3%

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

   if -4.8000000000000002e29 < y < -5.8000000000000004e-218 or 7.19999999999999989e-249 < y < 2.5500000000000001e79

   1. Initial program 96.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 92.8%

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

      2. *-commutative 92.8%

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

      3. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around inf 65.0%

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

   if -5.8000000000000004e-218 < y < 7.19999999999999989e-249

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around 0 95.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-218}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-249}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{+79}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 10: 65.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-218}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.36e+29)
   t
   (if (<= y -4.1e-218)
     (* (- x y) (/ t z))
     (if (<= y 1.95e-245)
       (/ (* x t) z)
       (if (<= y 6.8e+177) (* x (/ t (- z y))) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e+29) {
		tmp = t;
	} else if (y <= -4.1e-218) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.95e-245) {
		tmp = (x * t) / z;
	} else if (y <= 6.8e+177) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.36d+29)) then
        tmp = t
    else if (y <= (-4.1d-218)) then
        tmp = (x - y) * (t / z)
    else if (y <= 1.95d-245) then
        tmp = (x * t) / z
    else if (y <= 6.8d+177) then
        tmp = x * (t / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.36e+29) {
		tmp = t;
	} else if (y <= -4.1e-218) {
		tmp = (x - y) * (t / z);
	} else if (y <= 1.95e-245) {
		tmp = (x * t) / z;
	} else if (y <= 6.8e+177) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.36e+29:
		tmp = t
	elif y <= -4.1e-218:
		tmp = (x - y) * (t / z)
	elif y <= 1.95e-245:
		tmp = (x * t) / z
	elif y <= 6.8e+177:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.36e+29)
		tmp = t;
	elseif (y <= -4.1e-218)
		tmp = Float64(Float64(x - y) * Float64(t / z));
	elseif (y <= 1.95e-245)
		tmp = Float64(Float64(x * t) / z);
	elseif (y <= 6.8e+177)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.36e+29)
		tmp = t;
	elseif (y <= -4.1e-218)
		tmp = (x - y) * (t / z);
	elseif (y <= 1.95e-245)
		tmp = (x * t) / z;
	elseif (y <= 6.8e+177)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.36e+29], t, If[LessEqual[y, -4.1e-218], N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-245], N[(N[(x * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.8e+177], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.36e29 or 6.7999999999999996e177 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in y around inf 64.5%

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

   if -1.36e29 < y < -4.0999999999999998e-218

   1. Initial program 95.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 88.3%

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

      2. *-commutative 88.3%

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

      3. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in z around inf 62.2%

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

   if -4.0999999999999998e-218 < y < 1.9499999999999999e-245

   1. Initial program 94.7%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*l/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around 0 95.0%

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

   if 1.9499999999999999e-245 < y < 6.7999999999999996e177

   1. Initial program 97.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 97.7%

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

      2. associate-/r/ 97.6%

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

   3. Applied egg-rr 97.6%

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

   4. Taylor expanded in x around inf 61.6%

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

      1. associate-/l* 67.6%

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

   6. Simplified 67.6%

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

      1. associate-/r/ 66.4%

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

   8. Applied egg-rr 66.4%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+29}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-218}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot t}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+177}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 11: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := t \cdot \frac{x}{z - y}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 9200000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (* t (/ x (- z y)))))
   (if (<= x -1.85e+31)
     t_2
     (if (<= x -7.5e-26)
       t_1
       (if (<= x -1.6e-116)
         (* x (/ t (- z y)))
         (if (<= x 9200000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -1.85e+31) {
		tmp = t_2;
	} else if (x <= -7.5e-26) {
		tmp = t_1;
	} else if (x <= -1.6e-116) {
		tmp = x * (t / (z - y));
	} else if (x <= 9200000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = t * (x / (z - y))
    if (x <= (-1.85d+31)) then
        tmp = t_2
    else if (x <= (-7.5d-26)) then
        tmp = t_1
    else if (x <= (-1.6d-116)) then
        tmp = x * (t / (z - y))
    else if (x <= 9200000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t * (x / (z - y));
	double tmp;
	if (x <= -1.85e+31) {
		tmp = t_2;
	} else if (x <= -7.5e-26) {
		tmp = t_1;
	} else if (x <= -1.6e-116) {
		tmp = x * (t / (z - y));
	} else if (x <= 9200000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t * (x / (z - y))
	tmp = 0
	if x <= -1.85e+31:
		tmp = t_2
	elif x <= -7.5e-26:
		tmp = t_1
	elif x <= -1.6e-116:
		tmp = x * (t / (z - y))
	elif x <= 9200000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t * Float64(x / Float64(z - y)))
	tmp = 0.0
	if (x <= -1.85e+31)
		tmp = t_2;
	elseif (x <= -7.5e-26)
		tmp = t_1;
	elseif (x <= -1.6e-116)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (x <= 9200000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t * (x / (z - y));
	tmp = 0.0;
	if (x <= -1.85e+31)
		tmp = t_2;
	elseif (x <= -7.5e-26)
		tmp = t_1;
	elseif (x <= -1.6e-116)
		tmp = x * (t / (z - y));
	elseif (x <= 9200000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.85e+31], t$95$2, If[LessEqual[x, -7.5e-26], t$95$1, If[LessEqual[x, -1.6e-116], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9200000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8499999999999999e31 or 9.2e9 < x

   1. Initial program 99.0%

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

   2. Taylor expanded in x around inf 82.9%

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

   if -1.8499999999999999e31 < x < -7.4999999999999994e-26 or -1.60000000000000005e-116 < x < 9.2e9

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 80.4%

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

      1. neg-mul-1 80.4%

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

      2. distribute-neg-frac 80.4%

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

   4. Simplified 80.4%

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

      1. frac-2neg 80.4%

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

      2. div-inv 80.2%

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

      3. remove-double-neg 80.2%

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

      4. sub-neg 80.2%

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

      5. distribute-neg-in 80.2%

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

      6. remove-double-neg 80.2%

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

   6. Applied egg-rr 80.2%

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

      1. associate-*r/ 80.4%

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

      2. *-rgt-identity 80.4%

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

      3. +-commutative 80.4%

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

      4. unsub-neg 80.4%

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

   8. Simplified 80.4%

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

   if -7.4999999999999994e-26 < x < -1.60000000000000005e-116

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 99.4%

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

      2. associate-/r/ 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in x around inf 76.9%

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

      1. associate-/l* 78.0%

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

   6. Simplified 78.0%

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

      1. associate-/r/ 78.0%

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

   8. Applied egg-rr 78.0%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-26}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 9200000000:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \end{array} \]

Alternative 12: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ t_2 := \frac{t}{\frac{z - y}{x}}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 3400000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))) (t_2 (/ t (/ (- z y) x))))
   (if (<= x -2e+31)
     t_2
     (if (<= x -1.9e-25)
       t_1
       (if (<= x -1.6e-116)
         (* x (/ t (- z y)))
         (if (<= x 3400000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t / ((z - y) / x);
	double tmp;
	if (x <= -2e+31) {
		tmp = t_2;
	} else if (x <= -1.9e-25) {
		tmp = t_1;
	} else if (x <= -1.6e-116) {
		tmp = x * (t / (z - y));
	} else if (x <= 3400000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    t_2 = t / ((z - y) / x)
    if (x <= (-2d+31)) then
        tmp = t_2
    else if (x <= (-1.9d-25)) then
        tmp = t_1
    else if (x <= (-1.6d-116)) then
        tmp = x * (t / (z - y))
    else if (x <= 3400000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double t_2 = t / ((z - y) / x);
	double tmp;
	if (x <= -2e+31) {
		tmp = t_2;
	} else if (x <= -1.9e-25) {
		tmp = t_1;
	} else if (x <= -1.6e-116) {
		tmp = x * (t / (z - y));
	} else if (x <= 3400000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	t_2 = t / ((z - y) / x)
	tmp = 0
	if x <= -2e+31:
		tmp = t_2
	elif x <= -1.9e-25:
		tmp = t_1
	elif x <= -1.6e-116:
		tmp = x * (t / (z - y))
	elif x <= 3400000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	t_2 = Float64(t / Float64(Float64(z - y) / x))
	tmp = 0.0
	if (x <= -2e+31)
		tmp = t_2;
	elseif (x <= -1.9e-25)
		tmp = t_1;
	elseif (x <= -1.6e-116)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (x <= 3400000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	t_2 = t / ((z - y) / x);
	tmp = 0.0;
	if (x <= -2e+31)
		tmp = t_2;
	elseif (x <= -1.9e-25)
		tmp = t_1;
	elseif (x <= -1.6e-116)
		tmp = x * (t / (z - y));
	elseif (x <= 3400000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+31], t$95$2, If[LessEqual[x, -1.9e-25], t$95$1, If[LessEqual[x, -1.6e-116], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3400000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9999999999999999e31 or 3.4e9 < x

   1. Initial program 99.0%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 99.0%

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

      2. associate-/r/ 98.9%

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

   3. Applied egg-rr 98.9%

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

   4. Taylor expanded in x around inf 71.5%

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

      1. associate-/l* 82.9%

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

   6. Simplified 82.9%

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

   if -1.9999999999999999e31 < x < -1.8999999999999999e-25 or -1.60000000000000005e-116 < x < 3.4e9

   1. Initial program 95.8%

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

   2. Taylor expanded in x around 0 80.4%

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

      1. neg-mul-1 80.4%

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

      2. distribute-neg-frac 80.4%

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

   4. Simplified 80.4%

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

      1. frac-2neg 80.4%

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

      2. div-inv 80.2%

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

      3. remove-double-neg 80.2%

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

      4. sub-neg 80.2%

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

      5. distribute-neg-in 80.2%

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

      6. remove-double-neg 80.2%

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

   6. Applied egg-rr 80.2%

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

      1. associate-*r/ 80.4%

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

      2. *-rgt-identity 80.4%

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

      3. +-commutative 80.4%

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

      4. unsub-neg 80.4%

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

   8. Simplified 80.4%

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

   if -1.8999999999999999e-25 < x < -1.60000000000000005e-116

   1. Initial program 99.6%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 99.4%

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

      2. associate-/r/ 99.4%

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

   3. Applied egg-rr 99.4%

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

   4. Taylor expanded in x around inf 76.9%

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

      1. associate-/l* 78.0%

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

   6. Simplified 78.0%

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

      1. associate-/r/ 78.0%

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

   8. Applied egg-rr 78.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-25}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-116}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;x \leq 3400000000:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \end{array} \]

Alternative 13: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+227}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-223} \lor \neg \left(x \leq 1.4 \cdot 10^{-209}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.5e+227)
   (/ t (/ (- z y) x))
   (if (or (<= x -5.8e-223) (not (<= x 1.4e-209)))
     (* (- x y) (/ t (- z y)))
     (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e+227) {
		tmp = t / ((z - y) / x);
	} else if ((x <= -5.8e-223) || !(x <= 1.4e-209)) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (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 <= (-6.5d+227)) then
        tmp = t / ((z - y) / x)
    else if ((x <= (-5.8d-223)) .or. (.not. (x <= 1.4d-209))) then
        tmp = (x - y) * (t / (z - y))
    else
        tmp = t * (y / (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 <= -6.5e+227) {
		tmp = t / ((z - y) / x);
	} else if ((x <= -5.8e-223) || !(x <= 1.4e-209)) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.5e+227:
		tmp = t / ((z - y) / x)
	elif (x <= -5.8e-223) or not (x <= 1.4e-209):
		tmp = (x - y) * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.5e+227)
		tmp = Float64(t / Float64(Float64(z - y) / x));
	elseif ((x <= -5.8e-223) || !(x <= 1.4e-209))
		tmp = Float64(Float64(x - y) * Float64(t / Float64(z - y)));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.5e+227)
		tmp = t / ((z - y) / x);
	elseif ((x <= -5.8e-223) || ~((x <= 1.4e-209)))
		tmp = (x - y) * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.5e+227], N[(t / N[(N[(z - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -5.8e-223], N[Not[LessEqual[x, 1.4e-209]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.50000000000000018e227

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. clear-num 96.1%

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

      2. associate-/r/ 96.1%

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

   3. Applied egg-rr 96.1%

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

   4. Taylor expanded in x around inf 77.4%

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

      1. associate-/l* 92.2%

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

   6. Simplified 92.2%

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

   if -6.50000000000000018e227 < x < -5.8000000000000001e-223 or 1.40000000000000006e-209 < x

   1. Initial program 97.4%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-*l/ 88.1%

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

   3. Simplified 88.1%

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

   if -5.8000000000000001e-223 < x < 1.40000000000000006e-209

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 97.0%

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

      1. neg-mul-1 97.0%

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

      2. distribute-neg-frac 97.0%

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

   4. Simplified 97.0%

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

      1. frac-2neg 97.0%

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

      2. div-inv 96.8%

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

      3. remove-double-neg 96.8%

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

      4. sub-neg 96.8%

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

      5. distribute-neg-in 96.8%

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

      6. remove-double-neg 96.8%

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

   6. Applied egg-rr 96.8%

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

      1. associate-*r/ 97.0%

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

      2. *-rgt-identity 97.0%

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

      3. +-commutative 97.0%

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

      4. unsub-neg 97.0%

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

   8. Simplified 97.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+227}:\\ \;\;\;\;\frac{t}{\frac{z - y}{x}}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-223} \lor \neg \left(x \leq 1.4 \cdot 10^{-209}\right):\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]

Alternative 14: 67.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+30) t (if (<= y 7.2e+177) (* t (/ x (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+30) {
		tmp = t;
	} else if (y <= 7.2e+177) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.05d+30)) then
        tmp = t
    else if (y <= 7.2d+177) then
        tmp = t * (x / (z - y))
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+30) {
		tmp = t;
	} else if (y <= 7.2e+177) {
		tmp = t * (x / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+30:
		tmp = t
	elif y <= 7.2e+177:
		tmp = t * (x / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+30)
		tmp = t;
	elseif (y <= 7.2e+177)
		tmp = Float64(t * Float64(x / Float64(z - y)));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e+30)
		tmp = t;
	elseif (y <= 7.2e+177)
		tmp = t * (x / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+30], t, If[LessEqual[y, 7.2e+177], N[(t * N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e30 or 7.20000000000000005e177 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 70.1%

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

      2. *-commutative 70.1%

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

      3. associate-*l/ 72.2%

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

   3. Simplified 72.2%

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

   4. Taylor expanded in y around inf 64.5%

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

   if -1.05e30 < y < 7.20000000000000005e177

   1. Initial program 96.5%

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

   2. Taylor expanded in x around inf 71.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+30}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+177}:\\ \;\;\;\;t \cdot \frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 15: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e+27) t (if (<= y 2.3e+80) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e+27) {
		tmp = t;
	} else if (y <= 2.3e+80) {
		tmp = x * (t / 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 (y <= (-2.05d+27)) then
        tmp = t
    else if (y <= 2.3d+80) then
        tmp = x * (t / 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 (y <= -2.05e+27) {
		tmp = t;
	} else if (y <= 2.3e+80) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.05e+27:
		tmp = t
	elif y <= 2.3e+80:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e+27)
		tmp = t;
	elseif (y <= 2.3e+80)
		tmp = Float64(x * Float64(t / z));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.05e+27)
		tmp = t;
	elseif (y <= 2.3e+80)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e+27], t, If[LessEqual[y, 2.3e+80], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.0500000000000001e27 or 2.30000000000000004e80 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 69.9%

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

      2. *-commutative 69.9%

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

      3. associate-*l/ 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in y around inf 61.3%

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

   if -2.0500000000000001e27 < y < 2.30000000000000004e80

   1. Initial program 96.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Step-by-step derivation

      1. associate-*l/ 94.3%

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

      2. *-commutative 94.3%

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

      3. associate-*l/ 91.9%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in y around 0 57.0%

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

      1. associate-/l* 57.8%

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

   6. Simplified 57.8%

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

      1. associate-/r/ 55.5%

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

   8. Applied egg-rr 55.5%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+27}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]

Alternative 16: 35.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.6%

   \[\frac{x - y}{z - y} \cdot t \]
2. Step-by-step derivation

   1. associate-*l/ 84.7%

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

   2. *-commutative 84.7%

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

   3. associate-*l/ 85.4%

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

3. Simplified 85.4%

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

4. Taylor expanded in y around inf 31.6%

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

5. Final simplification 31.6%

   \[\leadsto t \]

Developer target: 97.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{t}{\frac{z - y}{x - y}} \end{array} \]

FPCore

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

C

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

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 / ((z - y) / (x - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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