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

Percentage Accurate: 96.8% → 96.8%

Time: 12.8s

Alternatives: 12

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: 96.8% 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: 96.8% 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 97.3%

   \[\frac{x - y}{z - y} \cdot t \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* (- x y) t) z)))
   (if (<= y -1.02e+32)
     (* t (- 1.0 (/ x y)))
     (if (<= y -4.8e-79)
       t_1
       (if (<= y 1.65e-60)
         (* x (/ t (- z y)))
         (if (<= y 7e+36)
           (* y (/ t (- y z)))
           (if (<= y 6.4e+47)
             t_1
             (if (<= y 5.6e+207)
               (* t (/ (- y x) y))
               (* t (/ y (- y z)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x - y) * t) / z;
	double tmp;
	if (y <= -1.02e+32) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4.8e-79) {
		tmp = t_1;
	} else if (y <= 1.65e-60) {
		tmp = x * (t / (z - y));
	} else if (y <= 7e+36) {
		tmp = y * (t / (y - z));
	} else if (y <= 6.4e+47) {
		tmp = t_1;
	} else if (y <= 5.6e+207) {
		tmp = t * ((y - x) / 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) :: t_1
    real(8) :: tmp
    t_1 = ((x - y) * t) / z
    if (y <= (-1.02d+32)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-4.8d-79)) then
        tmp = t_1
    else if (y <= 1.65d-60) then
        tmp = x * (t / (z - y))
    else if (y <= 7d+36) then
        tmp = y * (t / (y - z))
    else if (y <= 6.4d+47) then
        tmp = t_1
    else if (y <= 5.6d+207) then
        tmp = t * ((y - x) / 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 t_1 = ((x - y) * t) / z;
	double tmp;
	if (y <= -1.02e+32) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4.8e-79) {
		tmp = t_1;
	} else if (y <= 1.65e-60) {
		tmp = x * (t / (z - y));
	} else if (y <= 7e+36) {
		tmp = y * (t / (y - z));
	} else if (y <= 6.4e+47) {
		tmp = t_1;
	} else if (y <= 5.6e+207) {
		tmp = t * ((y - x) / y);
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x - y) * t) / z
	tmp = 0
	if y <= -1.02e+32:
		tmp = t * (1.0 - (x / y))
	elif y <= -4.8e-79:
		tmp = t_1
	elif y <= 1.65e-60:
		tmp = x * (t / (z - y))
	elif y <= 7e+36:
		tmp = y * (t / (y - z))
	elif y <= 6.4e+47:
		tmp = t_1
	elif y <= 5.6e+207:
		tmp = t * ((y - x) / y)
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x - y) * t) / z)
	tmp = 0.0
	if (y <= -1.02e+32)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -4.8e-79)
		tmp = t_1;
	elseif (y <= 1.65e-60)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 7e+36)
		tmp = Float64(y * Float64(t / Float64(y - z)));
	elseif (y <= 6.4e+47)
		tmp = t_1;
	elseif (y <= 5.6e+207)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x - y) * t) / z;
	tmp = 0.0;
	if (y <= -1.02e+32)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -4.8e-79)
		tmp = t_1;
	elseif (y <= 1.65e-60)
		tmp = x * (t / (z - y));
	elseif (y <= 7e+36)
		tmp = y * (t / (y - z));
	elseif (y <= 6.4e+47)
		tmp = t_1;
	elseif (y <= 5.6e+207)
		tmp = t * ((y - x) / y);
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -1.02e+32], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.8e-79], t$95$1, If[LessEqual[y, 1.65e-60], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+36], N[(y * N[(t / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+47], t$95$1, If[LessEqual[y, 5.6e+207], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.0199999999999999e32

   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. associate-/l* 79.1%

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

   3. Simplified 79.1%

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

      1. associate-*r/ 70.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-/l* 87.0%

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

      3. distribute-lft-neg-in 87.0%

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

      4. div-sub 87.0%

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

      5. *-inverses 87.0%

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

   9. Simplified 87.0%

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

   if -1.0199999999999999e32 < y < -4.80000000000000011e-79 or 6.9999999999999996e36 < y < 6.4e47

   1. Initial program 99.6%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 76.1%

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

   if -4.80000000000000011e-79 < y < 1.6499999999999999e-60

   1. Initial program 94.0%

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

      1. associate-*l/ 87.4%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 81.1%

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

   if 1.6499999999999999e-60 < y < 6.9999999999999996e36

   1. Initial program 96.8%

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

      1. associate-*l/ 99.5%

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

      2. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 71.3%

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

      1. neg-mul-1 71.3%

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

   7. Simplified 71.3%

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

   if 6.4e47 < y < 5.60000000000000022e207

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

      3. neg-sub0 80.8%

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

      4. sub-neg 80.8%

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

      5. +-commutative 80.8%

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

      6. associate--r+ 80.8%

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

      7. neg-sub0 80.8%

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

      8. remove-double-neg 80.8%

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

   5. Simplified 80.8%

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

   if 5.60000000000000022e207 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-neg-frac2 99.8%

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

      3. neg-sub0 99.8%

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

      4. sub-neg 99.8%

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

      5. +-commutative 99.8%

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

      6. associate--r+ 99.8%

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

      7. neg-sub0 99.8%

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

      8. remove-double-neg 99.8%

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

   5. Simplified 99.8%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-79}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{t}{y - z}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+47}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+207}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{y - z}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-45} \lor \neg \left(y \leq 5 \cdot 10^{-38}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* t (/ y (- y z)))))
   (if (<= y -4e+108)
     t_1
     (if (<= y -1.8e+19)
       (* x (/ t (- z y)))
       (if (or (<= y -5e-45) (not (<= y 5e-38))) t_1 (* (- x y) (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t * (y / (y - z));
	double tmp;
	if (y <= -4e+108) {
		tmp = t_1;
	} else if (y <= -1.8e+19) {
		tmp = x * (t / (z - y));
	} else if ((y <= -5e-45) || !(y <= 5e-38)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / (y - z))
    if (y <= (-4d+108)) then
        tmp = t_1
    else if (y <= (-1.8d+19)) then
        tmp = x * (t / (z - y))
    else if ((y <= (-5d-45)) .or. (.not. (y <= 5d-38))) then
        tmp = t_1
    else
        tmp = (x - y) * (t / z)
    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 tmp;
	if (y <= -4e+108) {
		tmp = t_1;
	} else if (y <= -1.8e+19) {
		tmp = x * (t / (z - y));
	} else if ((y <= -5e-45) || !(y <= 5e-38)) {
		tmp = t_1;
	} else {
		tmp = (x - y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t * (y / (y - z))
	tmp = 0
	if y <= -4e+108:
		tmp = t_1
	elif y <= -1.8e+19:
		tmp = x * (t / (z - y))
	elif (y <= -5e-45) or not (y <= 5e-38):
		tmp = t_1
	else:
		tmp = (x - y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t * Float64(y / Float64(y - z)))
	tmp = 0.0
	if (y <= -4e+108)
		tmp = t_1;
	elseif (y <= -1.8e+19)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif ((y <= -5e-45) || !(y <= 5e-38))
		tmp = t_1;
	else
		tmp = Float64(Float64(x - y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t * (y / (y - z));
	tmp = 0.0;
	if (y <= -4e+108)
		tmp = t_1;
	elseif (y <= -1.8e+19)
		tmp = x * (t / (z - y));
	elseif ((y <= -5e-45) || ~((y <= 5e-38)))
		tmp = t_1;
	else
		tmp = (x - y) * (t / z);
	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]}, If[LessEqual[y, -4e+108], t$95$1, If[LessEqual[y, -1.8e+19], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5e-45], N[Not[LessEqual[y, 5e-38]], $MachinePrecision]], t$95$1, N[(N[(x - y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.0000000000000001e108 or -1.8e19 < y < -4.99999999999999976e-45 or 5.00000000000000033e-38 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.9%

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

      1. neg-mul-1 80.9%

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

      2. distribute-neg-frac2 80.9%

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

      3. neg-sub0 80.9%

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

      4. sub-neg 80.9%

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

      5. +-commutative 80.9%

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

      6. associate--r+ 80.9%

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

      7. neg-sub0 80.9%

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

      8. remove-double-neg 80.9%

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

   5. Simplified 80.9%

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

   if -4.0000000000000001e108 < y < -1.8e19

   1. Initial program 99.6%

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

      1. associate-*l/ 83.9%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 63.6%

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

   if -4.99999999999999976e-45 < y < 5.00000000000000033e-38

   1. Initial program 94.3%

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

      1. associate-*l/ 89.0%

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

      2. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in z around inf 79.2%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-45} \lor \neg \left(y \leq 5 \cdot 10^{-38}\right):\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))))
   (if (<= y -1.65e+36)
     (* t (/ (- y x) y))
     (if (<= y -1.7e-200)
       t_1
       (if (<= y 2.65e-188)
         (/ x (/ (- z y) t))
         (if (<= y 3.5e-40) t_1 (* t (/ y (- y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -1.65e+36) {
		tmp = t * ((y - x) / y);
	} else if (y <= -1.7e-200) {
		tmp = t_1;
	} else if (y <= 2.65e-188) {
		tmp = x / ((z - y) / t);
	} else if (y <= 3.5e-40) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    if (y <= (-1.65d+36)) then
        tmp = t * ((y - x) / y)
    else if (y <= (-1.7d-200)) then
        tmp = t_1
    else if (y <= 2.65d-188) then
        tmp = x / ((z - y) / t)
    else if (y <= 3.5d-40) then
        tmp = t_1
    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 t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -1.65e+36) {
		tmp = t * ((y - x) / y);
	} else if (y <= -1.7e-200) {
		tmp = t_1;
	} else if (y <= 2.65e-188) {
		tmp = x / ((z - y) / t);
	} else if (y <= 3.5e-40) {
		tmp = t_1;
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	tmp = 0
	if y <= -1.65e+36:
		tmp = t * ((y - x) / y)
	elif y <= -1.7e-200:
		tmp = t_1
	elif y <= 2.65e-188:
		tmp = x / ((z - y) / t)
	elif y <= 3.5e-40:
		tmp = t_1
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	tmp = 0.0
	if (y <= -1.65e+36)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= -1.7e-200)
		tmp = t_1;
	elseif (y <= 2.65e-188)
		tmp = Float64(x / Float64(Float64(z - y) / t));
	elseif (y <= 3.5e-40)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	tmp = 0.0;
	if (y <= -1.65e+36)
		tmp = t * ((y - x) / y);
	elseif (y <= -1.7e-200)
		tmp = t_1;
	elseif (y <= 2.65e-188)
		tmp = x / ((z - y) / t);
	elseif (y <= 3.5e-40)
		tmp = t_1;
	else
		tmp = t * (y / (y - z));
	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, -1.65e+36], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-200], t$95$1, If[LessEqual[y, 2.65e-188], N[(x / N[(N[(z - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-40], t$95$1, N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6499999999999999e36

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

      3. neg-sub0 87.0%

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

      4. sub-neg 87.0%

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

      5. +-commutative 87.0%

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

      6. associate--r+ 87.0%

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

      7. neg-sub0 87.0%

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

      8. remove-double-neg 87.0%

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

   5. Simplified 87.0%

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

   if -1.6499999999999999e36 < y < -1.7000000000000001e-200 or 2.65000000000000007e-188 < y < 3.5000000000000002e-40

   1. Initial program 96.8%

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

      1. associate-*l/ 89.4%

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

      2. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in z around inf 72.0%

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

   if -1.7000000000000001e-200 < y < 2.65000000000000007e-188

   1. Initial program 92.1%

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

      1. associate-*l/ 92.2%

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

      2. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.2%

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

   6. Applied egg-rr 96.2%

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

   7. Taylor expanded in x around inf 91.1%

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

   if 3.5000000000000002e-40 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.8%

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

      1. neg-mul-1 79.8%

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

      2. distribute-neg-frac2 79.8%

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

      3. neg-sub0 79.8%

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

      4. sub-neg 79.8%

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

      5. +-commutative 79.8%

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

      6. associate--r+ 79.8%

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

      7. neg-sub0 79.8%

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

      8. remove-double-neg 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+36}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-200}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-188}:\\ \;\;\;\;\frac{x}{\frac{z - y}{t}}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-40}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- x y) (/ t z))))
   (if (<= y -1.55e+35)
     (* t (/ (- y x) y))
     (if (<= y -3.4e-195)
       t_1
       (if (<= y 5.2e-176)
         (* x (/ t (- z y)))
         (if (<= y 1.16e-40) t_1 (* t (/ y (- y z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -1.55e+35) {
		tmp = t * ((y - x) / y);
	} else if (y <= -3.4e-195) {
		tmp = t_1;
	} else if (y <= 5.2e-176) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.16e-40) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x - y) * (t / z)
    if (y <= (-1.55d+35)) then
        tmp = t * ((y - x) / y)
    else if (y <= (-3.4d-195)) then
        tmp = t_1
    else if (y <= 5.2d-176) then
        tmp = x * (t / (z - y))
    else if (y <= 1.16d-40) then
        tmp = t_1
    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 t_1 = (x - y) * (t / z);
	double tmp;
	if (y <= -1.55e+35) {
		tmp = t * ((y - x) / y);
	} else if (y <= -3.4e-195) {
		tmp = t_1;
	} else if (y <= 5.2e-176) {
		tmp = x * (t / (z - y));
	} else if (y <= 1.16e-40) {
		tmp = t_1;
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - y) * (t / z)
	tmp = 0
	if y <= -1.55e+35:
		tmp = t * ((y - x) / y)
	elif y <= -3.4e-195:
		tmp = t_1
	elif y <= 5.2e-176:
		tmp = x * (t / (z - y))
	elif y <= 1.16e-40:
		tmp = t_1
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - y) * Float64(t / z))
	tmp = 0.0
	if (y <= -1.55e+35)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= -3.4e-195)
		tmp = t_1;
	elseif (y <= 5.2e-176)
		tmp = Float64(x * Float64(t / Float64(z - y)));
	elseif (y <= 1.16e-40)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(y - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - y) * (t / z);
	tmp = 0.0;
	if (y <= -1.55e+35)
		tmp = t * ((y - x) / y);
	elseif (y <= -3.4e-195)
		tmp = t_1;
	elseif (y <= 5.2e-176)
		tmp = x * (t / (z - y));
	elseif (y <= 1.16e-40)
		tmp = t_1;
	else
		tmp = t * (y / (y - z));
	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, -1.55e+35], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.4e-195], t$95$1, If[LessEqual[y, 5.2e-176], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.16e-40], t$95$1, N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.54999999999999993e35

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

      3. neg-sub0 87.0%

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

      4. sub-neg 87.0%

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

      5. +-commutative 87.0%

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

      6. associate--r+ 87.0%

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

      7. neg-sub0 87.0%

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

      8. remove-double-neg 87.0%

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

   5. Simplified 87.0%

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

   if -1.54999999999999993e35 < y < -3.40000000000000001e-195 or 5.19999999999999984e-176 < y < 1.15999999999999991e-40

   1. Initial program 96.7%

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

      1. associate-*l/ 90.1%

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

      2. associate-/l* 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around inf 71.7%

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

   if -3.40000000000000001e-195 < y < 5.19999999999999984e-176

   1. Initial program 92.7%

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

      1. associate-*l/ 91.0%

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

      2. associate-/l* 94.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in x around inf 90.0%

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

   if 1.15999999999999991e-40 < y

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.8%

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

      1. neg-mul-1 79.8%

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

      2. distribute-neg-frac2 79.8%

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

      3. neg-sub0 79.8%

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

      4. sub-neg 79.8%

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

      5. +-commutative 79.8%

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

      6. associate--r+ 79.8%

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

      7. neg-sub0 79.8%

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

      8. remove-double-neg 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-195}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{-40}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-79}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e+32)
   (* t (- 1.0 (/ x y)))
   (if (<= y -4e-79)
     (/ (* (- x y) t) z)
     (if (<= y 2.15e-60) (* x (/ t (- z y))) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e+32) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4e-79) {
		tmp = ((x - y) * t) / z;
	} else if (y <= 2.15e-60) {
		tmp = x * (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 (y <= (-6.5d+32)) then
        tmp = t * (1.0d0 - (x / y))
    else if (y <= (-4d-79)) then
        tmp = ((x - y) * t) / z
    else if (y <= 2.15d-60) then
        tmp = x * (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 (y <= -6.5e+32) {
		tmp = t * (1.0 - (x / y));
	} else if (y <= -4e-79) {
		tmp = ((x - y) * t) / z;
	} else if (y <= 2.15e-60) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e+32:
		tmp = t * (1.0 - (x / y))
	elif y <= -4e-79:
		tmp = ((x - y) * t) / z
	elif y <= 2.15e-60:
		tmp = x * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e+32)
		tmp = Float64(t * Float64(1.0 - Float64(x / y)));
	elseif (y <= -4e-79)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (y <= 2.15e-60)
		tmp = Float64(x * 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 (y <= -6.5e+32)
		tmp = t * (1.0 - (x / y));
	elseif (y <= -4e-79)
		tmp = ((x - y) * t) / z;
	elseif (y <= 2.15e-60)
		tmp = x * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+32], N[(t * N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-79], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.15e-60], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.4999999999999994e32

   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. associate-/l* 79.1%

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

   3. Simplified 79.1%

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

      1. associate-*r/ 70.1%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. clear-num 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 58.9%

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

      1. mul-1-neg 58.9%

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

      2. associate-/l* 87.0%

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

      3. distribute-lft-neg-in 87.0%

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

      4. div-sub 87.0%

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

      5. *-inverses 87.0%

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

   9. Simplified 87.0%

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

   if -6.4999999999999994e32 < y < -4e-79

   1. Initial program 99.5%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around inf 73.7%

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

   if -4e-79 < y < 2.15e-60

   1. Initial program 94.0%

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

      1. associate-*l/ 87.4%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 81.1%

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

   if 2.15e-60 < y

   1. Initial program 99.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.8%

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

      1. neg-mul-1 78.8%

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

      2. distribute-neg-frac2 78.8%

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

      3. neg-sub0 78.8%

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

      4. sub-neg 78.8%

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

      5. +-commutative 78.8%

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

      6. associate--r+ 78.8%

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

      7. neg-sub0 78.8%

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

      8. remove-double-neg 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+32}:\\ \;\;\;\;t \cdot \left(1 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-79}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-79}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.32e+35)
   (* t (/ (- y x) y))
   (if (<= y -2.9e-79)
     (/ (* (- x y) t) z)
     (if (<= y 1.1e-58) (* x (/ t (- z y))) (* t (/ y (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.32e+35) {
		tmp = t * ((y - x) / y);
	} else if (y <= -2.9e-79) {
		tmp = ((x - y) * t) / z;
	} else if (y <= 1.1e-58) {
		tmp = x * (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 (y <= (-1.32d+35)) then
        tmp = t * ((y - x) / y)
    else if (y <= (-2.9d-79)) then
        tmp = ((x - y) * t) / z
    else if (y <= 1.1d-58) then
        tmp = x * (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 (y <= -1.32e+35) {
		tmp = t * ((y - x) / y);
	} else if (y <= -2.9e-79) {
		tmp = ((x - y) * t) / z;
	} else if (y <= 1.1e-58) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.32e+35:
		tmp = t * ((y - x) / y)
	elif y <= -2.9e-79:
		tmp = ((x - y) * t) / z
	elif y <= 1.1e-58:
		tmp = x * (t / (z - y))
	else:
		tmp = t * (y / (y - z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.32e+35)
		tmp = Float64(t * Float64(Float64(y - x) / y));
	elseif (y <= -2.9e-79)
		tmp = Float64(Float64(Float64(x - y) * t) / z);
	elseif (y <= 1.1e-58)
		tmp = Float64(x * 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 (y <= -1.32e+35)
		tmp = t * ((y - x) / y);
	elseif (y <= -2.9e-79)
		tmp = ((x - y) * t) / z;
	elseif (y <= 1.1e-58)
		tmp = x * (t / (z - y));
	else
		tmp = t * (y / (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.32e+35], N[(t * N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.9e-79], N[(N[(N[(x - y), $MachinePrecision] * t), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 1.1e-58], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.31999999999999995e35

   1. Initial program 99.8%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. neg-mul-1 87.0%

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

      3. neg-sub0 87.0%

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

      4. sub-neg 87.0%

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

      5. +-commutative 87.0%

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

      6. associate--r+ 87.0%

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

      7. neg-sub0 87.0%

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

      8. remove-double-neg 87.0%

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

   5. Simplified 87.0%

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

   if -1.31999999999999995e35 < y < -2.9000000000000001e-79

   1. Initial program 99.5%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around inf 73.7%

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

   if -2.9000000000000001e-79 < y < 1.10000000000000003e-58

   1. Initial program 94.0%

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

      1. associate-*l/ 87.4%

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

      2. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 81.1%

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

   if 1.10000000000000003e-58 < y

   1. Initial program 99.1%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.8%

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

      1. neg-mul-1 78.8%

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

      2. distribute-neg-frac2 78.8%

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

      3. neg-sub0 78.8%

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

      4. sub-neg 78.8%

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

      5. +-commutative 78.8%

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

      6. associate--r+ 78.8%

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

      7. neg-sub0 78.8%

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

      8. remove-double-neg 78.8%

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

   5. Simplified 78.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+35}:\\ \;\;\;\;t \cdot \frac{y - x}{y}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-79}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+160}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+186}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+160)
   (/ t (- 1.0 (/ z y)))
   (if (<= y 1.6e+186) (* (- x y) (/ t (- z y))) (* t (/ y (- y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+160) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.6e+186) {
		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 (y <= (-7.5d+160)) then
        tmp = t / (1.0d0 - (z / y))
    else if (y <= 1.6d+186) 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 (y <= -7.5e+160) {
		tmp = t / (1.0 - (z / y));
	} else if (y <= 1.6e+186) {
		tmp = (x - y) * (t / (z - y));
	} else {
		tmp = t * (y / (y - z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+160:
		tmp = t / (1.0 - (z / y))
	elif y <= 1.6e+186:
		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 (y <= -7.5e+160)
		tmp = Float64(t / Float64(1.0 - Float64(z / y)));
	elseif (y <= 1.6e+186)
		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 (y <= -7.5e+160)
		tmp = t / (1.0 - (z / y));
	elseif (y <= 1.6e+186)
		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[y, -7.5e+160], N[(t / N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+186], 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 y < -7.50000000000000028e160

   1. Initial program 99.9%

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

      1. associate-*l/ 63.3%

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

      2. associate-/l* 67.8%

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

   3. Simplified 67.8%

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

      1. associate-*r/ 63.3%

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

      2. associate-*l/ 99.9%

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

      3. *-commutative 99.9%

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

      4. clear-num 99.9%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. associate-/r/ 67.8%

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

      2. clear-num 65.4%

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

      3. associate-/r/ 65.4%

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

      4. clear-num 65.7%

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

      5. div-inv 65.4%

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

      6. *-un-lft-identity 65.4%

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

      7. times-frac 63.1%

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

   8. Applied egg-rr 63.1%

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

   9. Taylor expanded in x around 0 62.7%

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

       1. mul-1-neg 62.7%

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

       2. distribute-neg-frac2 62.7%

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

       3. *-commutative 62.7%

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

       4. sub-neg 62.7%

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

       5. distribute-neg-in 62.7%

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

       6. remove-double-neg 62.7%

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

       7. +-commutative 62.7%

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

       8. sub-neg 62.7%

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

       9. associate-*r/ 62.0%

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

       10. *-commutative 62.0%

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

       11. associate-/r/ 93.9%

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

       12. div-sub 93.9%

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

       13. *-inverses 93.9%

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

   11. Simplified 93.9%

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

   if -7.50000000000000028e160 < y < 1.6e186

   1. Initial program 96.5%

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

      1. associate-*l/ 89.6%

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

      2. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   if 1.6e186 < y

   1. Initial program 99.9%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.1%

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

      1. neg-mul-1 96.1%

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

      2. distribute-neg-frac2 96.1%

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

      3. neg-sub0 96.1%

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

      4. sub-neg 96.1%

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

      5. +-commutative 96.1%

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

      6. associate--r+ 96.1%

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

      7. neg-sub0 96.1%

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

      8. remove-double-neg 96.1%

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

   5. Simplified 96.1%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+160}:\\ \;\;\;\;\frac{t}{1 - \frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+186}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+65}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.58 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \frac{t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.9e+65) t (if (<= y 1.58e+53) (* x (/ t (- z y))) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.9e+65) {
		tmp = t;
	} else if (y <= 1.58e+53) {
		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 <= (-2.9d+65)) then
        tmp = t
    else if (y <= 1.58d+53) 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 <= -2.9e+65) {
		tmp = t;
	} else if (y <= 1.58e+53) {
		tmp = x * (t / (z - y));
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.9e+65:
		tmp = t
	elif y <= 1.58e+53:
		tmp = x * (t / (z - y))
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.9e+65)
		tmp = t;
	elseif (y <= 1.58e+53)
		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 <= -2.9e+65)
		tmp = t;
	elseif (y <= 1.58e+53)
		tmp = x * (t / (z - y));
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.9e+65], t, If[LessEqual[y, 1.58e+53], N[(x * N[(t / N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e65 or 1.57999999999999999e53 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 66.2%

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

      2. associate-/l* 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in y around inf 73.8%

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

   if -2.9e65 < y < 1.57999999999999999e53

   1. Initial program 95.7%

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

      1. associate-*l/ 91.8%

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

      2. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around inf 70.6%

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

Alternative 10: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e+64) t (if (<= y 5.8e-38) (* t (/ x z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+64) {
		tmp = t;
	} else if (y <= 5.8e-38) {
		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 <= (-7d+64)) then
        tmp = t
    else if (y <= 5.8d-38) 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 <= -7e+64) {
		tmp = t;
	} else if (y <= 5.8e-38) {
		tmp = t * (x / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e+64:
		tmp = t
	elif y <= 5.8e-38:
		tmp = t * (x / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e+64)
		tmp = t;
	elseif (y <= 5.8e-38)
		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 <= -7e+64)
		tmp = t;
	elseif (y <= 5.8e-38)
		tmp = t * (x / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e+64], t, If[LessEqual[y, 5.8e-38], N[(t * N[(x / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999997e64 or 5.79999999999999988e-38 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 71.1%

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

      2. associate-/l* 78.0%

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

   3. Simplified 78.0%

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

   5. Taylor expanded in y around inf 68.1%

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

   if -6.9999999999999997e64 < y < 5.79999999999999988e-38

   1. Initial program 95.2%

      \[\frac{x - y}{z - y} \cdot t \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 63.7%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-38}:\\ \;\;\;\;t \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+64}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.5e+64) t (if (<= y 3.2e-51) (* x (/ t z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.5e+64) {
		tmp = t;
	} else if (y <= 3.2e-51) {
		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+64)) then
        tmp = t
    else if (y <= 3.2d-51) 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+64) {
		tmp = t;
	} else if (y <= 3.2e-51) {
		tmp = x * (t / z);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7.5e+64:
		tmp = t
	elif y <= 3.2e-51:
		tmp = x * (t / z)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7.5e+64)
		tmp = t;
	elseif (y <= 3.2e-51)
		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 <= -7.5e+64)
		tmp = t;
	elseif (y <= 3.2e-51)
		tmp = x * (t / z);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7.5e+64], t, If[LessEqual[y, 3.2e-51], N[(x * N[(t / z), $MachinePrecision]), $MachinePrecision], t]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5000000000000005e64 or 3.2e-51 < y

   1. Initial program 99.8%

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

      1. associate-*l/ 71.5%

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

      2. associate-/l* 78.4%

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

   3. Simplified 78.4%

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

   5. Taylor expanded in y around inf 67.8%

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

   if -7.5000000000000005e64 < y < 3.2e-51

   1. Initial program 95.2%

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

      1. associate-*l/ 90.8%

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

      2. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in z around inf 74.1%

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

   6. Taylor expanded in x around inf 61.3%

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

Alternative 12: 34.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. associate-*l/ 81.8%

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

   2. associate-/l* 85.5%

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

3. Simplified 85.5%

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

5. Taylor expanded in y around inf 37.5%

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

Developer target: 96.9% 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 2024110 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :alt
  (/ t (/ (- z y) (- x y)))

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