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

Percentage Accurate: 88.7% → 96.9%

Time: 11.9s

Alternatives: 15

Speedup: 0.8×

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: 88.7% 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: 96.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \frac{x}{y - z} \cdot \frac{1}{t - z} \end{array} \]

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 (- y z)) (/ 1.0 (- t z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (y - z)) * (1.0 / (t - 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 / (y - z)) * (1.0d0 / (t - 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 / (y - z)) * (1.0 / (t - z));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (x / (y - z)) * (1.0 / (t - z))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(x / Float64(y - z)) * Float64(1.0 / Float64(t - z)))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (x / (y - z)) * (1.0 / (t - 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[(y - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 88.8%

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

   1. associate-/r* 98.7%

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

   2. div-inv 98.7%

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

4. Applied egg-rr 98.7%

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

Alternative 2: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+140}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-108} \lor \neg \left(z \leq 3.6 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= z -1.65e+140)
   (/ (/ x z) z)
   (if (or (<= z -1.4e-108) (not (<= z 3.6e-87)))
     (/ x (* z (- z t)))
     (/ (/ 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 <= -1.65e+140) {
		tmp = (x / z) / z;
	} else if ((z <= -1.4e-108) || !(z <= 3.6e-87)) {
		tmp = x / (z * (z - t));
	} 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 <= (-1.65d+140)) then
        tmp = (x / z) / z
    else if ((z <= (-1.4d-108)) .or. (.not. (z <= 3.6d-87))) then
        tmp = x / (z * (z - t))
    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 <= -1.65e+140) {
		tmp = (x / z) / z;
	} else if ((z <= -1.4e-108) || !(z <= 3.6e-87)) {
		tmp = x / (z * (z - t));
	} 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 <= -1.65e+140:
		tmp = (x / z) / z
	elif (z <= -1.4e-108) or not (z <= 3.6e-87):
		tmp = x / (z * (z - t))
	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 <= -1.65e+140)
		tmp = Float64(Float64(x / z) / z);
	elseif ((z <= -1.4e-108) || !(z <= 3.6e-87))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	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 <= -1.65e+140)
		tmp = (x / z) / z;
	elseif ((z <= -1.4e-108) || ~((z <= 3.6e-87)))
		tmp = x / (z * (z - t));
	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[z, -1.65e+140], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, -1.4e-108], N[Not[LessEqual[z, 3.6e-87]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6500000000000001e140

   1. Initial program 72.8%

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

   3. Taylor expanded in y around 0 72.8%

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

      1. mul-1-neg 72.8%

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

      2. associate-/r* 94.4%

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

      3. distribute-neg-frac2 94.4%

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

      4. sub-neg 94.4%

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

      5. +-commutative 94.4%

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

      6. distribute-neg-in 94.4%

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

      7. remove-double-neg 94.4%

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

      8. unsub-neg 94.4%

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

   5. Simplified 94.4%

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

   6. Taylor expanded in z around inf 94.4%

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

   if -1.6500000000000001e140 < z < -1.4e-108 or 3.59999999999999993e-87 < z

   1. Initial program 90.8%

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

   3. Taylor expanded in y around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. distribute-rgt-neg-in 66.7%

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

      3. sub-neg 66.7%

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

      4. +-commutative 66.7%

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

      5. distribute-neg-in 66.7%

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

      6. remove-double-neg 66.7%

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

      7. unsub-neg 66.7%

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

   5. Simplified 66.7%

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

   if -1.4e-108 < z < 3.59999999999999993e-87

   1. Initial program 92.7%

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

      1. associate-/l/ 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in t around inf 83.9%

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

   6. Taylor expanded in y around inf 70.8%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+140}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-108} \lor \neg \left(z \leq 3.6 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-299}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -2e-299) t_1 (/ (/ x (- t z)) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2e-299) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-2d-299)) then
        tmp = t_1
    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 t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -2e-299) {
		tmp = t_1;
	} 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):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -2e-299:
		tmp = t_1
	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)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -2e-299)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / 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)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -2e-299)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-299], t$95$1, N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -1.99999999999999998e-299

   1. Initial program 96.1%

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

   if -1.99999999999999998e-299 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 86.9%

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

      1. associate-/l/ 98.0%

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

   3. Simplified 98.0%

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

Alternative 4: 66.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)))
   (if (<= z -5.2e+19)
     t_1
     (if (<= z -1.3e-98)
       (/ x (* y (- z)))
       (if (<= z 3.5e+52) (/ (/ x t) y) 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;
	double tmp;
	if (z <= -5.2e+19) {
		tmp = t_1;
	} else if (z <= -1.3e-98) {
		tmp = x / (y * -z);
	} else if (z <= 3.5e+52) {
		tmp = (x / t) / y;
	} 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
    if (z <= (-5.2d+19)) then
        tmp = t_1
    else if (z <= (-1.3d-98)) then
        tmp = x / (y * -z)
    else if (z <= 3.5d+52) then
        tmp = (x / t) / y
    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;
	double tmp;
	if (z <= -5.2e+19) {
		tmp = t_1;
	} else if (z <= -1.3e-98) {
		tmp = x / (y * -z);
	} else if (z <= 3.5e+52) {
		tmp = (x / t) / y;
	} 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
	tmp = 0
	if z <= -5.2e+19:
		tmp = t_1
	elif z <= -1.3e-98:
		tmp = x / (y * -z)
	elif z <= 3.5e+52:
		tmp = (x / t) / y
	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) / z)
	tmp = 0.0
	if (z <= -5.2e+19)
		tmp = t_1;
	elseif (z <= -1.3e-98)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (z <= 3.5e+52)
		tmp = Float64(Float64(x / t) / y);
	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;
	tmp = 0.0;
	if (z <= -5.2e+19)
		tmp = t_1;
	elseif (z <= -1.3e-98)
		tmp = x / (y * -z);
	elseif (z <= 3.5e+52)
		tmp = (x / t) / y;
	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] / z), $MachinePrecision]}, If[LessEqual[z, -5.2e+19], t$95$1, If[LessEqual[z, -1.3e-98], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+52], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e19 or 3.5e52 < z

   1. Initial program 81.5%

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

   3. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/r* 88.6%

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

      3. distribute-neg-frac2 88.6%

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

      4. sub-neg 88.6%

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

      5. +-commutative 88.6%

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

      6. distribute-neg-in 88.6%

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

      7. remove-double-neg 88.6%

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

      8. unsub-neg 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in z around inf 81.5%

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

   if -5.2e19 < z < -1.30000000000000007e-98

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around 0 48.7%

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

      1. associate-*r/ 48.7%

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

      2. neg-mul-1 48.7%

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

      3. *-commutative 48.7%

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

   8. Simplified 48.7%

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

   if -1.30000000000000007e-98 < z < 3.5e52

   1. Initial program 93.5%

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

      1. associate-/l/ 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 77.7%

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

   6. Taylor expanded in y around inf 64.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 91.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 5e+285) (/ x t_1) (* (/ x (- y z)) (/ -1.0 z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+285) {
		tmp = x / t_1;
	} else {
		tmp = (x / (y - z)) * (-1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if (t_1 <= 5d+285) then
        tmp = x / t_1
    else
        tmp = (x / (y - z)) * ((-1.0d0) / 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 t_1 = (y - z) * (t - z);
	double tmp;
	if (t_1 <= 5e+285) {
		tmp = x / t_1;
	} else {
		tmp = (x / (y - z)) * (-1.0 / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if t_1 <= 5e+285:
		tmp = x / t_1
	else:
		tmp = (x / (y - z)) * (-1.0 / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (t_1 <= 5e+285)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(y - z)) * Float64(-1.0 / z));
	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 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= 5e+285)
		tmp = x / t_1;
	else
		tmp = (x / (y - z)) * (-1.0 / 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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+285], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 5.00000000000000016e285

   1. Initial program 96.0%

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

   if 5.00000000000000016e285 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 73.0%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 87.9%

      \[\leadsto \frac{x}{y - z} \cdot \color{blue}{\frac{-1}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 79.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+17} \lor \neg \left(z \leq 1.45 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \end{array} \end{array} \]

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 (or (<= z -8.8e+17) (not (<= z 1.45e-19)))
   (/ (/ x z) (- z t))
   (/ (/ x y) (- t z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e+17) || !(z <= 1.45e-19)) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / y) / (t - 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 <= (-8.8d+17)) .or. (.not. (z <= 1.45d-19))) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / y) / (t - 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 <= -8.8e+17) || !(z <= 1.45e-19)) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / y) / (t - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e+17) or not (z <= 1.45e-19):
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / y) / (t - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e+17) || !(z <= 1.45e-19))
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / y) / Float64(t - 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 <= -8.8e+17) || ~((z <= 1.45e-19)))
		tmp = (x / z) / (z - t);
	else
		tmp = (x / y) / (t - 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, -8.8e+17], N[Not[LessEqual[z, 1.45e-19]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8e17 or 1.45e-19 < z

   1. Initial program 83.2%

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

   3. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-/r* 84.7%

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

      3. distribute-neg-frac2 84.7%

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

      4. sub-neg 84.7%

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

      5. +-commutative 84.7%

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

      6. distribute-neg-in 84.7%

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

      7. remove-double-neg 84.7%

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

      8. unsub-neg 84.7%

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

   5. Simplified 84.7%

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

   if -8.8e17 < z < 1.45e-19

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. associate-/r* 76.8%

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

   5. Simplified 76.8%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+17} \lor \neg \left(z \leq 1.45 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-36}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 0.205:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= t -4e-36)
   (/ (/ x y) (- t z))
   (if (<= t 0.205) (/ (/ x z) (- z y)) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4e-36) {
		tmp = (x / y) / (t - z);
	} else if (t <= 0.205) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = x / ((y - z) * 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 (t <= (-4d-36)) then
        tmp = (x / y) / (t - z)
    else if (t <= 0.205d0) then
        tmp = (x / z) / (z - y)
    else
        tmp = x / ((y - z) * 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 (t <= -4e-36) {
		tmp = (x / y) / (t - z);
	} else if (t <= 0.205) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4e-36:
		tmp = (x / y) / (t - z)
	elif t <= 0.205:
		tmp = (x / z) / (z - y)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4e-36)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 0.205)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(x / Float64(Float64(y - z) * 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 (t <= -4e-36)
		tmp = (x / y) / (t - z);
	elseif (t <= 0.205)
		tmp = (x / z) / (z - y);
	else
		tmp = x / ((y - z) * 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[LessEqual[t, -4e-36], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.205], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9999999999999998e-36

   1. Initial program 86.4%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. associate-/r* 59.2%

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

   5. Simplified 59.2%

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

   if -3.9999999999999998e-36 < t < 0.204999999999999988

   1. Initial program 88.1%

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

   3. Taylor expanded in t around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-/r* 80.4%

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

      3. distribute-neg-frac2 80.4%

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

      4. neg-sub0 80.4%

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

      5. sub-neg 80.4%

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

      6. +-commutative 80.4%

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

      7. associate--r+ 80.4%

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

      8. neg-sub0 80.4%

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

      9. remove-double-neg 80.4%

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

   5. Simplified 80.4%

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

   if 0.204999999999999988 < t

   1. Initial program 91.7%

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

   3. Taylor expanded in t around inf 86.8%

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

Alternative 8: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-104}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -7.5e-104)
   (/ (/ x y) (- t z))
   (if (<= y 1.35e-64) (/ 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 <= -7.5e-104) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.35e-64) {
		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 <= (-7.5d-104)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.35d-64) 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 <= -7.5e-104) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.35e-64) {
		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 <= -7.5e-104:
		tmp = (x / y) / (t - z)
	elif y <= 1.35e-64:
		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 <= -7.5e-104)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.35e-64)
		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 <= -7.5e-104)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.35e-64)
		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, -7.5e-104], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-64], 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 < -7.5e-104

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 72.7%

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

      1. associate-/r* 79.3%

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

   5. Simplified 79.3%

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

   if -7.5e-104 < y < 1.34999999999999993e-64

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-rgt-neg-in 85.6%

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

      3. sub-neg 85.6%

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

      4. +-commutative 85.6%

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

      5. distribute-neg-in 85.6%

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

      6. remove-double-neg 85.6%

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

      7. unsub-neg 85.6%

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

   5. Simplified 85.6%

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

   if 1.34999999999999993e-64 < y

   1. Initial program 86.8%

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

      1. associate-/l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 63.7%

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

Alternative 9: 77.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -7e-104)
   (/ x (* y (- t z)))
   (if (<= y 1.8e-61) (/ 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 <= -7e-104) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.8e-61) {
		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 <= (-7d-104)) then
        tmp = x / (y * (t - z))
    else if (y <= 1.8d-61) 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 <= -7e-104) {
		tmp = x / (y * (t - z));
	} else if (y <= 1.8e-61) {
		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 <= -7e-104:
		tmp = x / (y * (t - z))
	elif y <= 1.8e-61:
		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 <= -7e-104)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 1.8e-61)
		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 <= -7e-104)
		tmp = x / (y * (t - z));
	elseif (y <= 1.8e-61)
		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, -7e-104], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-61], 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 < -7.00000000000000057e-104

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -7.00000000000000057e-104 < y < 1.80000000000000007e-61

   1. Initial program 94.1%

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

   3. Taylor expanded in y around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-in 84.5%

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

      3. sub-neg 84.5%

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

      4. +-commutative 84.5%

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

      5. distribute-neg-in 84.5%

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

      6. remove-double-neg 84.5%

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

      7. unsub-neg 84.5%

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

   5. Simplified 84.5%

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

   if 1.80000000000000007e-61 < y

   1. Initial program 86.6%

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

      1. associate-/l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 63.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \end{array} \]

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 (<= z -1.18e+21)
   (/ (/ x z) z)
   (if (<= z 1.25e-19) (/ x (* y (- t z))) (/ x (* z (- z t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.18e+21) {
		tmp = (x / z) / z;
	} else if (z <= 1.25e-19) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / (z * (z - 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 <= (-1.18d+21)) then
        tmp = (x / z) / z
    else if (z <= 1.25d-19) then
        tmp = x / (y * (t - z))
    else
        tmp = x / (z * (z - 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 <= -1.18e+21) {
		tmp = (x / z) / z;
	} else if (z <= 1.25e-19) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / (z * (z - t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.18e+21:
		tmp = (x / z) / z
	elif z <= 1.25e-19:
		tmp = x / (y * (t - z))
	else:
		tmp = x / (z * (z - t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.18e+21)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 1.25e-19)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(z * Float64(z - 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 <= -1.18e+21)
		tmp = (x / z) / z;
	elseif (z <= 1.25e-19)
		tmp = x / (y * (t - z));
	else
		tmp = x / (z * (z - 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[LessEqual[z, -1.18e+21], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.25e-19], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.18e21

   1. Initial program 79.8%

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

   3. Taylor expanded in y around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-/r* 91.0%

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

      3. distribute-neg-frac2 91.0%

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

      4. sub-neg 91.0%

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

      5. +-commutative 91.0%

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

      6. distribute-neg-in 91.0%

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

      7. remove-double-neg 91.0%

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

      8. unsub-neg 91.0%

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

   5. Simplified 91.0%

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

   6. Taylor expanded in z around inf 86.0%

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

   if -1.18e21 < z < 1.2500000000000001e-19

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 73.8%

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

      1. *-commutative 73.8%

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

   5. Simplified 73.8%

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

   if 1.2500000000000001e-19 < z

   1. Initial program 86.0%

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

   3. Taylor expanded in y around 0 72.5%

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

      1. mul-1-neg 72.5%

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

      2. distribute-rgt-neg-in 72.5%

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

      3. sub-neg 72.5%

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

      4. +-commutative 72.5%

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

      5. distribute-neg-in 72.5%

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

      6. remove-double-neg 72.5%

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

      7. unsub-neg 72.5%

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

   5. Simplified 72.5%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 67.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+23} \lor \neg \left(z \leq 6.8 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -5e+23) (not (<= z 6.8e+50))) (/ (/ x z) 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 <= -5e+23) || !(z <= 6.8e+50)) {
		tmp = (x / z) / 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 <= (-5d+23)) .or. (.not. (z <= 6.8d+50))) then
        tmp = (x / z) / 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 <= -5e+23) || !(z <= 6.8e+50)) {
		tmp = (x / z) / 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 <= -5e+23) or not (z <= 6.8e+50):
		tmp = (x / z) / 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 <= -5e+23) || !(z <= 6.8e+50))
		tmp = Float64(Float64(x / z) / 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 <= -5e+23) || ~((z <= 6.8e+50)))
		tmp = (x / z) / 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, -5e+23], N[Not[LessEqual[z, 6.8e+50]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e23 or 6.7999999999999997e50 < z

   1. Initial program 81.5%

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

   3. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. associate-/r* 88.6%

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

      3. distribute-neg-frac2 88.6%

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

      4. sub-neg 88.6%

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

      5. +-commutative 88.6%

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

      6. distribute-neg-in 88.6%

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

      7. remove-double-neg 88.6%

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

      8. unsub-neg 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in z around inf 81.5%

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

   if -4.9999999999999999e23 < z < 6.7999999999999997e50

   1. Initial program 94.5%

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

      1. associate-/l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around inf 73.1%

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

   6. Taylor expanded in y around inf 58.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+23} \lor \neg \left(z \leq 6.8 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+19} \lor \neg \left(z \leq 6.6 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -1.1e+19) (not (<= z 6.6e+50))) (/ x (* z 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 <= -1.1e+19) || !(z <= 6.6e+50)) {
		tmp = x / (z * 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 <= (-1.1d+19)) .or. (.not. (z <= 6.6d+50))) then
        tmp = x / (z * 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 <= -1.1e+19) || !(z <= 6.6e+50)) {
		tmp = x / (z * 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 <= -1.1e+19) or not (z <= 6.6e+50):
		tmp = x / (z * 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 <= -1.1e+19) || !(z <= 6.6e+50))
		tmp = Float64(x / Float64(z * 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 <= -1.1e+19) || ~((z <= 6.6e+50)))
		tmp = x / (z * 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, -1.1e+19], N[Not[LessEqual[z, 6.6e+50]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e19 or 6.6000000000000001e50 < z

   1. Initial program 81.5%

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

   3. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. distribute-rgt-neg-in 77.1%

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

      3. sub-neg 77.1%

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

      4. +-commutative 77.1%

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

      5. distribute-neg-in 77.1%

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

      6. remove-double-neg 77.1%

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

      7. unsub-neg 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around inf 73.0%

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

   if -1.1e19 < z < 6.6000000000000001e50

   1. Initial program 94.5%

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

      1. associate-/l/ 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in t around inf 73.1%

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

   6. Taylor expanded in y around inf 58.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+19} \lor \neg \left(z \leq 6.6 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 60.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+18} \lor \neg \left(z \leq 6.6 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1.1e+18) (not (<= z 6.6e+50))) (/ x (* z 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 <= -1.1e+18) || !(z <= 6.6e+50)) {
		tmp = x / (z * 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 <= (-1.1d+18)) .or. (.not. (z <= 6.6d+50))) then
        tmp = x / (z * 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 <= -1.1e+18) || !(z <= 6.6e+50)) {
		tmp = x / (z * 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 <= -1.1e+18) or not (z <= 6.6e+50):
		tmp = x / (z * 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 <= -1.1e+18) || !(z <= 6.6e+50))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(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 <= -1.1e+18) || ~((z <= 6.6e+50)))
		tmp = x / (z * 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, -1.1e+18], N[Not[LessEqual[z, 6.6e+50]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e18 or 6.6000000000000001e50 < z

   1. Initial program 81.5%

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

   3. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. distribute-rgt-neg-in 77.1%

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

      3. sub-neg 77.1%

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

      4. +-commutative 77.1%

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

      5. distribute-neg-in 77.1%

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

      6. remove-double-neg 77.1%

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

      7. unsub-neg 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around inf 73.0%

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

   if -1.1e18 < z < 6.6000000000000001e50

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 55.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+18} \lor \neg \left(z \leq 6.6 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+24} \lor \neg \left(z \leq 3.7 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -1.7e+24) (not (<= z 3.7e+51))) (/ x (* z t)) (/ 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 <= -1.7e+24) || !(z <= 3.7e+51)) {
		tmp = x / (z * t);
	} 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 <= (-1.7d+24)) .or. (.not. (z <= 3.7d+51))) then
        tmp = x / (z * t)
    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 <= -1.7e+24) || !(z <= 3.7e+51)) {
		tmp = x / (z * t);
	} 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 <= -1.7e+24) or not (z <= 3.7e+51):
		tmp = x / (z * t)
	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 <= -1.7e+24) || !(z <= 3.7e+51))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(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 <= -1.7e+24) || ~((z <= 3.7e+51)))
		tmp = x / (z * t);
	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, -1.7e+24], N[Not[LessEqual[z, 3.7e+51]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e24 or 3.7000000000000002e51 < z

   1. Initial program 81.5%

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

   3. Taylor expanded in y around 0 77.1%

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

      1. mul-1-neg 77.1%

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

      2. distribute-rgt-neg-in 77.1%

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

      3. sub-neg 77.1%

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

      4. +-commutative 77.1%

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

      5. distribute-neg-in 77.1%

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

      6. remove-double-neg 77.1%

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

      7. unsub-neg 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in z around 0 43.6%

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

      1. associate-*r/ 43.6%

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

      2. mul-1-neg 43.6%

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

      3. *-commutative 43.6%

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

   8. Simplified 43.6%

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

      1. distribute-frac-neg 43.6%

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

      2. associate-/r* 50.3%

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

      3. distribute-frac-neg2 50.3%

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

      4. *-un-lft-identity 50.3%

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

      5. *-commutative 50.3%

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

      6. add-sqr-sqrt 17.9%

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

      7. sqrt-unprod 40.1%

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

      8. sqr-neg 40.1%

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

      9. sqrt-unprod 31.6%

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

      10. add-sqr-sqrt 46.2%

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

   10. Applied egg-rr 46.2%

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

       1. *-rgt-identity 46.2%

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

       2. associate-/r* 41.2%

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

   12. Simplified 41.2%

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

   if -1.7e24 < z < 3.7000000000000002e51

   1. Initial program 94.5%

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

   3. Taylor expanded in z around 0 55.4%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+24} \lor \neg \left(z \leq 3.7 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.9% accurate, 1.8× speedup

Math

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

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 (* y t)))

C

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

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 / (y * t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 88.8%

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

3. Taylor expanded in z around 0 39.0%

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

4. Final simplification 39.0%

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

Developer Target 1: 87.5% 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 2024165 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

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