Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B

Percentage Accurate: 89.1% → 96.6%

Time: 10.8s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{\frac{x}{t - z}}{y - z} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (/ x (- t z)) (- y z)))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 / (t - z)) / (y - z)
end function

Java

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (t - z)) / (y - z)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(t - z)) / Float64(y - z))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (t - z)) / (y - z);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.7%

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

   1. associate-/l/ 96.8%

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

3. Simplified 96.8%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
4. Add Preprocessing

5. Final simplification 96.8%

   \[\leadsto \frac{\frac{x}{t - z}}{y - z} \]
6. Add Preprocessing

Alternative 2: 77.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z t))))
   (if (<= z -1.25e-9)
     t_1
     (if (<= z 1.05e-91)
       (/ (/ x t) (- y z))
       (if (<= z 1.5e+67) (/ (/ x y) (- t z)) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (z <= -1.25e-9) {
		tmp = t_1;
	} else if (z <= 1.05e-91) {
		tmp = (x / t) / (y - z);
	} else if (z <= 1.5e+67) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 / z) / (z - t)
    if (z <= (-1.25d-9)) then
        tmp = t_1
    else if (z <= 1.05d-91) then
        tmp = (x / t) / (y - z)
    else if (z <= 1.5d+67) then
        tmp = (x / y) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (z <= -1.25e-9) {
		tmp = t_1;
	} else if (z <= 1.05e-91) {
		tmp = (x / t) / (y - z);
	} else if (z <= 1.5e+67) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (z - t)
	tmp = 0
	if z <= -1.25e-9:
		tmp = t_1
	elif z <= 1.05e-91:
		tmp = (x / t) / (y - z)
	elif z <= 1.5e+67:
		tmp = (x / y) / (t - z)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - t))
	tmp = 0.0
	if (z <= -1.25e-9)
		tmp = t_1;
	elseif (z <= 1.05e-91)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 1.5e+67)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (z - t);
	tmp = 0.0;
	if (z <= -1.25e-9)
		tmp = t_1;
	elseif (z <= 1.05e-91)
		tmp = (x / t) / (y - z);
	elseif (z <= 1.5e+67)
		tmp = (x / y) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e-9], t$95$1, If[LessEqual[z, 1.05e-91], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+67], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.25e-9 or 1.50000000000000005e67 < z

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. neg-mul-1 85.1%

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

   5. Simplified 85.1%

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

      1. frac-2neg 85.1%

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

      2. div-inv 85.1%

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

      3. remove-double-neg 85.1%

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

      4. distribute-rgt-neg-in 85.1%

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

   7. Applied egg-rr 85.1%

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

      1. associate-/r* 85.1%

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

   9. Simplified 85.1%

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

   10. Taylor expanded in x around 0 85.1%

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

       1. associate-/r* 92.0%

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

   12. Simplified 92.0%

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

   if -1.25e-9 < z < 1.05e-91

   1. Initial program 93.6%

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

      1. associate-/l/ 94.4%

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

   3. Simplified 94.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.2%

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

   if 1.05e-91 < z < 1.50000000000000005e67

   1. Initial program 94.3%

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

   3. Taylor expanded in x around 0 94.3%

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

      1. associate-/l/ 99.5%

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

   5. Simplified 99.5%

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

   6. Taylor expanded in y around inf 55.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-9}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-9} \lor \neg \left(z \leq 1.15 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.05e-9) (not (<= z 1.15e+22)))
   (/ x (* z (- z t)))
   (/ x (* t (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-9) || !(z <= 1.15e+22)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.05d-9)) .or. (.not. (z <= 1.15d+22))) then
        tmp = x / (z * (z - t))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.05e-9) || !(z <= 1.15e+22)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.05e-9) or not (z <= 1.15e+22):
		tmp = x / (z * (z - t))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.05e-9) || !(z <= 1.15e+22))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.05e-9) || ~((z <= 1.15e+22)))
		tmp = x / (z * (z - t));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.05e-9], N[Not[LessEqual[z, 1.15e+22]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.0500000000000001e-9 or 1.1500000000000001e22 < z

   1. Initial program 89.2%

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

   3. Taylor expanded in y around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

   5. Simplified 83.7%

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

      1. frac-2neg 83.7%

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

      2. div-inv 83.8%

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

      3. remove-double-neg 83.8%

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

      4. distribute-rgt-neg-in 83.8%

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

   7. Applied egg-rr 83.8%

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

      1. associate-/r* 83.8%

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

   9. Simplified 83.8%

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

   10. Taylor expanded in x around 0 83.7%

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

   if -1.0500000000000001e-9 < z < 1.1500000000000001e22

   1. Initial program 94.0%

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

   3. Taylor expanded in t around inf 74.9%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-9} \lor \neg \left(z \leq 1.15 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3500:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3500.0)
   (/ x (* (- t z) y))
   (if (<= y 1.3e-163) (/ x (* z (- z t))) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3500.0) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.3e-163) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-3500.0d0)) then
        tmp = x / ((t - z) * y)
    else if (y <= 1.3d-163) then
        tmp = x / (z * (z - t))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3500.0) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.3e-163) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3500.0:
		tmp = x / ((t - z) * y)
	elif y <= 1.3e-163:
		tmp = x / (z * (z - t))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3500.0)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 1.3e-163)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3500.0)
		tmp = x / ((t - z) * y);
	elseif (y <= 1.3e-163)
		tmp = x / (z * (z - t));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3500.0], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-163], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3500

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   if -3500 < y < 1.30000000000000001e-163

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

      1. frac-2neg 75.0%

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

      2. div-inv 74.9%

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

      3. remove-double-neg 74.9%

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

      4. distribute-rgt-neg-in 74.9%

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

   7. Applied egg-rr 74.9%

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

      1. associate-/r* 74.9%

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

   9. Simplified 74.9%

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

   10. Taylor expanded in x around 0 75.0%

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

   if 1.30000000000000001e-163 < y

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 54.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3500:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3900:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3900.0)
   (/ x (* (- t z) y))
   (if (<= y 9.6e-164) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3900.0) {
		tmp = x / ((t - z) * y);
	} else if (y <= 9.6e-164) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-3900.0d0)) then
        tmp = x / ((t - z) * y)
    else if (y <= 9.6d-164) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3900.0) {
		tmp = x / ((t - z) * y);
	} else if (y <= 9.6e-164) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3900.0:
		tmp = x / ((t - z) * y)
	elif y <= 9.6e-164:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3900.0)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 9.6e-164)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3900.0)
		tmp = x / ((t - z) * y);
	elseif (y <= 9.6e-164)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3900.0], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.6e-164], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3900

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 81.0%

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

      1. *-commutative 81.0%

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

   5. Simplified 81.0%

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

   if -3900 < y < 9.59999999999999932e-164

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 75.0%

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

      1. associate-*r/ 75.0%

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

      2. neg-mul-1 75.0%

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

   5. Simplified 75.0%

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

      1. frac-2neg 75.0%

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

      2. div-inv 74.9%

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

      3. remove-double-neg 74.9%

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

      4. distribute-rgt-neg-in 74.9%

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

   7. Applied egg-rr 74.9%

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

      1. associate-/r* 74.9%

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

   9. Simplified 74.9%

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

   10. Taylor expanded in x around 0 75.0%

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

   if 9.59999999999999932e-164 < y

   1. Initial program 91.3%

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

      1. associate-/l/ 96.1%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 54.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3900:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-164}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3500:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3500.0)
   (/ (/ x y) (- t z))
   (if (<= y 1.45e-162) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3500.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.45e-162) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-3500.0d0)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.45d-162) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3500.0) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.45e-162) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3500.0:
		tmp = (x / y) / (t - z)
	elif y <= 1.45e-162:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3500.0)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.45e-162)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3500.0)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.45e-162)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3500.0], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e-162], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3500

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0 87.4%

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

      1. associate-/l/ 93.5%

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

   5. Simplified 93.5%

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

   6. Taylor expanded in y around inf 87.2%

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

   if -3500 < y < 1.4500000000000001e-162

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 75.3%

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

      1. associate-*r/ 75.3%

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

      2. neg-mul-1 75.3%

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

   5. Simplified 75.3%

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

      1. frac-2neg 75.3%

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

      2. div-inv 75.2%

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

      3. remove-double-neg 75.2%

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

      4. distribute-rgt-neg-in 75.2%

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

   7. Applied egg-rr 75.2%

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

      1. associate-/r* 75.2%

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

   9. Simplified 75.2%

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

   10. Taylor expanded in x around 0 75.3%

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

   if 1.4500000000000001e-162 < y

   1. Initial program 91.2%

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

      1. associate-/l/ 96.1%

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

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 55.4%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3500:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -9e-10)
   (/ (/ x z) (- z t))
   (if (<= z 3.6e-45) (/ (/ x t) (- y z)) (/ (/ x z) (- z y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e-10) {
		tmp = (x / z) / (z - t);
	} else if (z <= 3.6e-45) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-9d-10)) then
        tmp = (x / z) / (z - t)
    else if (z <= 3.6d-45) then
        tmp = (x / t) / (y - z)
    else
        tmp = (x / z) / (z - y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9e-10) {
		tmp = (x / z) / (z - t);
	} else if (z <= 3.6e-45) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -9e-10:
		tmp = (x / z) / (z - t)
	elif z <= 3.6e-45:
		tmp = (x / t) / (y - z)
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9e-10)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	elseif (z <= 3.6e-45)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9e-10)
		tmp = (x / z) / (z - t);
	elseif (z <= 3.6e-45)
		tmp = (x / t) / (y - z);
	else
		tmp = (x / z) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -9e-10], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e-45], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.9999999999999999e-10

   1. Initial program 88.0%

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

   3. Taylor expanded in y around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

   5. Simplified 83.9%

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

      1. frac-2neg 83.9%

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

      2. div-inv 83.9%

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

      3. remove-double-neg 83.9%

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

      4. distribute-rgt-neg-in 83.9%

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

   7. Applied egg-rr 83.9%

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

      1. associate-/r* 83.9%

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

   9. Simplified 83.9%

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

   10. Taylor expanded in x around 0 83.9%

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

       1. associate-/r* 91.9%

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

   12. Simplified 91.9%

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

   if -8.9999999999999999e-10 < z < 3.60000000000000001e-45

   1. Initial program 94.1%

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

      1. associate-/l/ 94.1%

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

   3. Simplified 94.1%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 77.6%

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

   if 3.60000000000000001e-45 < z

   1. Initial program 91.3%

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

      1. associate-/l/ 98.4%

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

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. neg-mul-1 75.5%

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

   7. Simplified 75.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{-10}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-123}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.35e-123)
   (/ (/ x y) t)
   (if (<= y 2.5e-88) (/ x (* t (- z))) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-123) {
		tmp = (x / y) / t;
	} else if (y <= 2.5e-88) {
		tmp = x / (t * -z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.35d-123)) then
        tmp = (x / y) / t
    else if (y <= 2.5d-88) then
        tmp = x / (t * -z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.35e-123) {
		tmp = (x / y) / t;
	} else if (y <= 2.5e-88) {
		tmp = x / (t * -z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.35e-123:
		tmp = (x / y) / t
	elif y <= 2.5e-88:
		tmp = x / (t * -z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.35e-123)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 2.5e-88)
		tmp = Float64(x / Float64(t * Float64(-z)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.35e-123)
		tmp = (x / y) / t;
	elseif (y <= 2.5e-88)
		tmp = x / (t * -z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.35e-123], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 2.5e-88], N[(x / N[(t * (-z)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e-123

   1. Initial program 91.0%

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

   3. Taylor expanded in z around 0 48.8%

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

      1. *-un-lft-identity 48.8%

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

      2. times-frac 52.9%

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

   5. Applied egg-rr 52.9%

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

      1. associate-*l/ 52.9%

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

      2. *-lft-identity 52.9%

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

   7. Simplified 52.9%

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

   if -1.35e-123 < y < 2.50000000000000004e-88

   1. Initial program 91.7%

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

      1. associate-/l/ 97.2%

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

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 55.0%

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

   6. Taylor expanded in y around 0 41.4%

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

      1. associate-*r/ 41.4%

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

      2. neg-mul-1 41.4%

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

   8. Simplified 41.4%

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

   if 2.50000000000000004e-88 < y

   1. Initial program 92.4%

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

   3. Taylor expanded in z around 0 44.7%

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

      1. associate-/r* 43.6%

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

      2. div-inv 43.6%

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

   5. Applied egg-rr 43.6%

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

      1. un-div-inv 43.6%

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

   7. Applied egg-rr 43.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-123}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{x}{t \cdot \left(-z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 45.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{-7} \lor \neg \left(z \leq 8.8 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.92e-7) (not (<= z 8.8e+61))) (/ x (* t z)) (/ x (* t y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.92e-7) || !(z <= 8.8e+61)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.92d-7)) .or. (.not. (z <= 8.8d+61))) then
        tmp = x / (t * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.92e-7) || !(z <= 8.8e+61)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.92e-7) or not (z <= 8.8e+61):
		tmp = x / (t * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.92e-7) || !(z <= 8.8e+61))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.92e-7) || ~((z <= 8.8e+61)))
		tmp = x / (t * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.92e-7], N[Not[LessEqual[z, 8.8e+61]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.91999999999999999e-7 or 8.8000000000000001e61 < z

   1. Initial program 88.6%

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

   3. Taylor expanded in y around 0 83.6%

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

      1. associate-*r/ 83.6%

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

      2. neg-mul-1 83.6%

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

   5. Simplified 83.6%

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

      1. div-inv 83.6%

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

      2. add-sqr-sqrt 45.3%

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

      3. sqrt-unprod 62.1%

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

      4. sqr-neg 62.1%

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

      5. sqrt-unprod 25.5%

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

      6. add-sqr-sqrt 58.7%

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

      7. *-commutative 58.7%

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

      8. associate-/r* 58.7%

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

   7. Applied egg-rr 58.7%

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

      1. associate-*r/ 58.3%

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

      2. associate-*l/ 58.3%

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

      3. associate-*r/ 58.3%

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

      4. *-rgt-identity 58.3%

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

   9. Simplified 58.3%

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

   10. Taylor expanded in z around 0 30.8%

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

       1. *-commutative 30.8%

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

   12. Simplified 30.8%

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

   if -1.91999999999999999e-7 < z < 8.8000000000000001e61

   1. Initial program 94.3%

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

   3. Taylor expanded in z around 0 57.6%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{-7} \lor \neg \left(z \leq 8.8 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{-7} \lor \neg \left(z \leq 1.8 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.92e-7) (not (<= z 1.8e+67))) (/ x (* t z)) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.92e-7) || !(z <= 1.8e+67)) {
		tmp = x / (t * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.92d-7)) .or. (.not. (z <= 1.8d+67))) then
        tmp = x / (t * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.92e-7) || !(z <= 1.8e+67)) {
		tmp = x / (t * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.92e-7) or not (z <= 1.8e+67):
		tmp = x / (t * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.92e-7) || !(z <= 1.8e+67))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.92e-7) || ~((z <= 1.8e+67)))
		tmp = x / (t * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.92e-7], N[Not[LessEqual[z, 1.8e+67]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.91999999999999999e-7 or 1.7999999999999999e67 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. associate-*r/ 84.8%

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

      2. neg-mul-1 84.8%

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

   5. Simplified 84.8%

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

      1. div-inv 84.8%

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

      2. add-sqr-sqrt 46.9%

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

      3. sqrt-unprod 64.2%

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

      4. sqr-neg 64.2%

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

      5. sqrt-unprod 26.3%

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

      6. add-sqr-sqrt 60.7%

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

      7. *-commutative 60.7%

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

      8. associate-/r* 60.6%

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

   7. Applied egg-rr 60.6%

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

      1. associate-*r/ 60.2%

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

      2. associate-*l/ 60.2%

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

      3. associate-*r/ 60.2%

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

      4. *-rgt-identity 60.2%

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

   9. Simplified 60.2%

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

   10. Taylor expanded in z around 0 31.8%

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

       1. *-commutative 31.8%

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

   12. Simplified 31.8%

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

   if -1.91999999999999999e-7 < z < 1.7999999999999999e67

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 56.1%

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

      1. associate-/r* 60.1%

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

      2. div-inv 60.1%

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

   5. Applied egg-rr 60.1%

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

      1. un-div-inv 60.1%

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

   7. Applied egg-rr 60.1%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.92 \cdot 10^{-7} \lor \neg \left(z \leq 1.8 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-7} \lor \neg \left(z \leq 9.5 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.85e-7) (not (<= z 9.5e+67))) (/ x (* t z)) (/ (/ x y) t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-7) || !(z <= 9.5e+67)) {
		tmp = x / (t * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.85d-7)) .or. (.not. (z <= 9.5d+67))) then
        tmp = x / (t * z)
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.85e-7) || !(z <= 9.5e+67)) {
		tmp = x / (t * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.85e-7) or not (z <= 9.5e+67):
		tmp = x / (t * z)
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.85e-7) || !(z <= 9.5e+67))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.85e-7) || ~((z <= 9.5e+67)))
		tmp = x / (t * z);
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.85e-7], N[Not[LessEqual[z, 9.5e+67]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.85000000000000002e-7 or 9.5000000000000002e67 < z

   1. Initial program 89.0%

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

   3. Taylor expanded in y around 0 84.8%

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

      1. associate-*r/ 84.8%

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

      2. neg-mul-1 84.8%

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

   5. Simplified 84.8%

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

      1. div-inv 84.8%

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

      2. add-sqr-sqrt 46.9%

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

      3. sqrt-unprod 64.2%

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

      4. sqr-neg 64.2%

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

      5. sqrt-unprod 26.3%

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

      6. add-sqr-sqrt 60.7%

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

      7. *-commutative 60.7%

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

      8. associate-/r* 60.6%

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

   7. Applied egg-rr 60.6%

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

      1. associate-*r/ 60.2%

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

      2. associate-*l/ 60.2%

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

      3. associate-*r/ 60.2%

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

      4. *-rgt-identity 60.2%

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

   9. Simplified 60.2%

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

   10. Taylor expanded in z around 0 31.8%

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

       1. *-commutative 31.8%

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

   12. Simplified 31.8%

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

   if -1.85000000000000002e-7 < z < 9.5000000000000002e67

   1. Initial program 93.8%

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

   3. Taylor expanded in z around 0 56.1%

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

      1. *-un-lft-identity 56.1%

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

      2. times-frac 58.8%

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

   5. Applied egg-rr 58.8%

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

      1. associate-*l/ 58.8%

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

      2. *-lft-identity 58.8%

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

   7. Simplified 58.8%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-7} \lor \neg \left(z \leq 9.5 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 90.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+185) (/ (/ x y) (- t z)) (/ x (* (- t z) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+185) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-2.6d+185)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((t - z) * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+185) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e+185:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((t - z) * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+185)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e+185)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((t - z) * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+185], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.60000000000000001e185

   1. Initial program 75.5%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. associate-/l/ 95.1%

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

   5. Simplified 95.1%

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

   6. Taylor expanded in y around inf 95.1%

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

   if -2.60000000000000001e185 < y

   1. Initial program 92.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+185}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.85e+153) (/ (/ x y) t) (/ x (* t (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+153) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 <= (-1.85d+153)) then
        tmp = (x / y) / t
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.85e+153) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.85e+153:
		tmp = (x / y) / t
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.85e+153)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.85e+153)
		tmp = (x / y) / t;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.85e+153], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8500000000000001e153

   1. Initial program 79.0%

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

   3. Taylor expanded in z around 0 45.9%

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

      1. *-un-lft-identity 45.9%

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

      2. times-frac 58.8%

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

   5. Applied egg-rr 58.8%

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

      1. associate-*l/ 58.7%

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

      2. *-lft-identity 58.7%

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

   7. Simplified 58.7%

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

   if -1.8500000000000001e153 < y

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 58.4%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+153}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{t \cdot y} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ x (* t y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return x / (t * y);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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 / (t * y)
end function

Java

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

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return x / (t * y)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(x / Float64(t * y))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = x / (t * y);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.7%

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

3. Taylor expanded in z around 0 38.3%

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

4. Final simplification 38.3%

   \[\leadsto \frac{x}{t \cdot y} \]
5. Add Preprocessing

Developer target: 88.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t\_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024074 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 (* (- y z) (- t z)))))

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