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

Percentage Accurate: 88.8% → 97.0%

Time: 7.5s

Alternatives: 12

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: 88.8% 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: 97.0% accurate, 0.8× 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 86.6%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/r* N/A

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

   5. lower-/.f64 N/A

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

   6. lower-/.f64 97.8

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

4. Applied rewrites 97.8%

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

Alternative 2: 92.5% accurate, 0.4× speedup

Math

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

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 (- INFINITY))
     (/ (/ x (- y z)) t)
     (if (<= t_1 2e+299) (/ x t_1) (/ (/ x z) (+ (- y) 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 <= -((double) INFINITY)) {
		tmp = (x / (y - z)) / t;
	} else if (t_1 <= 2e+299) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (-y + z);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (y - z)) / t;
	} else if (t_1 <= 2e+299) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (-y + 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 <= -math.inf:
		tmp = (x / (y - z)) / t
	elif t_1 <= 2e+299:
		tmp = x / t_1
	else:
		tmp = (x / z) / (-y + 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 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (t_1 <= 2e+299)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / z) / Float64(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 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (y - z)) / t;
	elseif (t_1 <= 2e+299)
		tmp = x / t_1;
	else
		tmp = (x / 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[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 2e+299], N[(x / t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[((-y) + z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 57.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 92.3

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

   5. Applied rewrites 92.3%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 2.0000000000000001e299

   1. Initial program 99.0%

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

   if 2.0000000000000001e299 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 74.7%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 87.1

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

   5. Applied rewrites 87.1%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;\left(y - z\right) \cdot \left(t - z\right) \leq 2 \cdot 10^{+299}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\left(-y\right) + z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+304}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (<= t_1 (- INFINITY))
     (/ (/ x (- y z)) t)
     (if (<= t_1 1e+304) (/ x t_1) (/ (/ (- x) z) (- t 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 <= -((double) INFINITY)) {
		tmp = (x / (y - z)) / t;
	} else if (t_1 <= 1e+304) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = (x / (y - z)) / t;
	} else if (t_1 <= 1e+304) {
		tmp = x / t_1;
	} else {
		tmp = (-x / z) / (t - 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 <= -math.inf:
		tmp = (x / (y - z)) / t
	elif t_1 <= 1e+304:
		tmp = x / t_1
	else:
		tmp = (-x / z) / (t - 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 <= Float64(-Inf))
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	elseif (t_1 <= 1e+304)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(Float64(-x) / z) / 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)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (x / (y - z)) / t;
	elseif (t_1 <= 1e+304)
		tmp = x / t_1;
	else
		tmp = (-x / z) / (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_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t$95$1, 1e+304], N[(x / t$95$1), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -inf.0

   1. Initial program 57.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 92.3

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

   5. Applied rewrites 92.3%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 9.9999999999999994e303

   1. Initial program 99.0%

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

   if 9.9999999999999994e303 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 74.1%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. distribute-neg-frac N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower-neg.f64 N/A

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

      7. lower--.f64 80.8

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

   5. Applied rewrites 80.8%

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

Alternative 4: 92.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+157} \lor \neg \left(z \leq 1.32 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

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 -3e+157) (not (<= z 1.32e+154)))
   (/ (/ x z) z)
   (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3e+157) || !(z <= 1.32e+154)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * (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 <= (-3d+157)) .or. (.not. (z <= 1.32d+154))) then
        tmp = (x / z) / z
    else
        tmp = x / ((y - z) * (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 <= -3e+157) || !(z <= 1.32e+154)) {
		tmp = (x / z) / z;
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3e+157) or not (z <= 1.32e+154):
		tmp = (x / z) / z
	else:
		tmp = x / ((y - z) * (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 <= -3e+157) || !(z <= 1.32e+154))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(x / Float64(Float64(y - z) * 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 <= -3e+157) || ~((z <= 1.32e+154)))
		tmp = (x / z) / z;
	else
		tmp = x / ((y - z) * (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, -3e+157], N[Not[LessEqual[z, 1.32e+154]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0000000000000001e157 or 1.31999999999999998e154 < z

   1. Initial program 76.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. *-commutative N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 99.9

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

   4. Applied rewrites 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   6. Step-by-step derivation

      1. unpow2 N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 93.7

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

   7. Applied rewrites 93.7%

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

   if -3.0000000000000001e157 < z < 1.31999999999999998e154

   1. Initial program 90.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+157} \lor \neg \left(z \leq 1.32 \cdot 10^{+154}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{-221}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= y -1.36e-22)
   (/ x (* (- t z) y))
   (if (<= y 3.65e-221) (/ x (* (- z) (- t z))) (/ 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 (y <= -1.36e-22) {
		tmp = x / ((t - z) * y);
	} else if (y <= 3.65e-221) {
		tmp = x / (-z * (t - z));
	} 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 (y <= (-1.36d-22)) then
        tmp = x / ((t - z) * y)
    else if (y <= 3.65d-221) then
        tmp = x / (-z * (t - z))
    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 (y <= -1.36e-22) {
		tmp = x / ((t - z) * y);
	} else if (y <= 3.65e-221) {
		tmp = x / (-z * (t - z));
	} 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 y <= -1.36e-22:
		tmp = x / ((t - z) * y)
	elif y <= 3.65e-221:
		tmp = x / (-z * (t - z))
	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 (y <= -1.36e-22)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 3.65e-221)
		tmp = Float64(x / Float64(Float64(-z) * Float64(t - z)));
	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 (y <= -1.36e-22)
		tmp = x / ((t - z) * y);
	elseif (y <= 3.65e-221)
		tmp = x / (-z * (t - z));
	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[y, -1.36e-22], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.65e-221], N[(x / N[((-z) * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.36e-22

   1. Initial program 83.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 76.3

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

   5. Applied rewrites 76.3%

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

   if -1.36e-22 < y < 3.65e-221

   1. Initial program 94.5%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if 3.65e-221 < y

   1. Initial program 83.4%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 58.7

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

   5. Applied rewrites 58.7%

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

Alternative 6: 71.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-23} \lor \neg \left(z \leq 4.5 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \end{array} \end{array} \]

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 -8.5e-23) (not (<= z 4.5e+77)))
   (/ x (* (- z y) z))
   (/ x (* (- t z) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e-23) || !(z <= 4.5e+77)) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / ((t - 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 <= (-8.5d-23)) .or. (.not. (z <= 4.5d+77))) then
        tmp = x / ((z - y) * z)
    else
        tmp = x / ((t - 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 <= -8.5e-23) || !(z <= 4.5e+77)) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / ((t - z) * y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e-23) or not (z <= 4.5e+77):
		tmp = x / ((z - y) * z)
	else:
		tmp = x / ((t - 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 <= -8.5e-23) || !(z <= 4.5e+77))
		tmp = Float64(x / Float64(Float64(z - y) * z));
	else
		tmp = Float64(x / Float64(Float64(t - 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 <= -8.5e-23) || ~((z <= 4.5e+77)))
		tmp = x / ((z - y) * z);
	else
		tmp = x / ((t - 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[Or[LessEqual[z, -8.5e-23], N[Not[LessEqual[z, 4.5e+77]], $MachinePrecision]], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999996e-23 or 4.50000000000000024e77 < z

   1. Initial program 77.9%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 70.0

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

   5. Applied rewrites 70.0%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x}{-1 \cdot \left(y \cdot z\right) + \color{blue}{{z}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 70.0%

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

   if -8.4999999999999996e-23 < z < 4.50000000000000024e77

   1. Initial program 93.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 71.0

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

   5. Applied rewrites 71.0%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-23} \lor \neg \left(z \leq 4.5 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-148} \lor \neg \left(z \leq 1.15 \cdot 10^{-127}\right):\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -6.2e-148) (not (<= z 1.15e-127)))
   (/ x (* (- z y) 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 <= -6.2e-148) || !(z <= 1.15e-127)) {
		tmp = x / ((z - y) * 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 <= (-6.2d-148)) .or. (.not. (z <= 1.15d-127))) then
        tmp = x / ((z - y) * 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 <= -6.2e-148) || !(z <= 1.15e-127)) {
		tmp = x / ((z - y) * 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 <= -6.2e-148) or not (z <= 1.15e-127):
		tmp = x / ((z - y) * 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 <= -6.2e-148) || !(z <= 1.15e-127))
		tmp = Float64(x / Float64(Float64(z - y) * 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 <= -6.2e-148) || ~((z <= 1.15e-127)))
		tmp = x / ((z - y) * 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, -6.2e-148], N[Not[LessEqual[z, 1.15e-127]], $MachinePrecision]], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.2000000000000003e-148 or 1.15000000000000009e-127 < z

   1. Initial program 84.2%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 61.2

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

   5. Applied rewrites 61.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x}{-1 \cdot \left(y \cdot z\right) + \color{blue}{{z}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.2%

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

   if -6.2000000000000003e-148 < z < 1.15000000000000009e-127

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-148} \lor \neg \left(z \leq 1.15 \cdot 10^{-127}\right):\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 -8e-117)
   (/ x (* (- t z) y))
   (if (<= t 1.46e-52) (/ x (* (- z y) z)) (/ 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 <= -8e-117) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.46e-52) {
		tmp = x / ((z - y) * z);
	} 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 <= (-8d-117)) then
        tmp = x / ((t - z) * y)
    else if (t <= 1.46d-52) then
        tmp = x / ((z - y) * z)
    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 <= -8e-117) {
		tmp = x / ((t - z) * y);
	} else if (t <= 1.46e-52) {
		tmp = x / ((z - y) * z);
	} 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 <= -8e-117:
		tmp = x / ((t - z) * y)
	elif t <= 1.46e-52:
		tmp = x / ((z - y) * z)
	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 <= -8e-117)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 1.46e-52)
		tmp = Float64(x / Float64(Float64(z - y) * z));
	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 <= -8e-117)
		tmp = x / ((t - z) * y);
	elseif (t <= 1.46e-52)
		tmp = x / ((z - y) * z);
	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, -8e-117], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.46e-52], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.00000000000000024e-117

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.1

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

   5. Applied rewrites 56.1%

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

   if -8.00000000000000024e-117 < t < 1.46000000000000003e-52

   1. Initial program 89.8%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 76.9

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \frac{x}{-1 \cdot \left(y \cdot z\right) + \color{blue}{{z}^{2}}} \]
   7. Step-by-step derivation

   8. Applied rewrites 76.9%

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

   if 1.46000000000000003e-52 < t

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.6

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

   5. Applied rewrites 73.6%

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

Alternative 9: 91.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+195}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

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 -5e+195) (/ (/ x (- t z)) y) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e+195) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * (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 (y <= (-5d+195)) then
        tmp = (x / (t - z)) / y
    else
        tmp = x / ((y - z) * (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 (y <= -5e+195) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5e+195:
		tmp = (x / (t - z)) / y
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e+195)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(x / Float64(Float64(y - z) * 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 (y <= -5e+195)
		tmp = (x / (t - z)) / y;
	else
		tmp = x / ((y - z) * (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[LessEqual[y, -5e+195], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999998e195

   1. Initial program 73.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower--.f64 94.5

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

   5. Applied rewrites 94.5%

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

   if -4.9999999999999998e195 < y

   1. Initial program 87.6%

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

Alternative 10: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3500000 \lor \neg \left(z \leq 1.95 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -3500000.0) (not (<= z 1.95e+29))) (/ 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 <= -3500000.0) || !(z <= 1.95e+29)) {
		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 <= (-3500000.0d0)) .or. (.not. (z <= 1.95d+29))) 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 <= -3500000.0) || !(z <= 1.95e+29)) {
		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 <= -3500000.0) or not (z <= 1.95e+29):
		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 <= -3500000.0) || !(z <= 1.95e+29))
		tmp = Float64(x / Float64(z * 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 <= -3500000.0) || ~((z <= 1.95e+29)))
		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, -3500000.0], N[Not[LessEqual[z, 1.95e+29]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e6 or 1.94999999999999984e29 < z

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf

      \[\leadsto \frac{x}{\color{blue}{{z}^{2}}} \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. lower-*.f64 66.6

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

   5. Applied rewrites 66.6%

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

   if -3.5e6 < z < 1.94999999999999984e29

   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

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

      1. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3500000 \lor \neg \left(z \leq 1.95 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 45.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+96} \lor \neg \left(z \leq 6.5 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -8.2e+96) (not (<= z 6.5e+150))) (/ x (* z y)) (/ 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 <= -8.2e+96) || !(z <= 6.5e+150)) {
		tmp = x / (z * y);
	} 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 <= (-8.2d+96)) .or. (.not. (z <= 6.5d+150))) then
        tmp = x / (z * y)
    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 <= -8.2e+96) || !(z <= 6.5e+150)) {
		tmp = x / (z * y);
	} 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 <= -8.2e+96) or not (z <= 6.5e+150):
		tmp = x / (z * y)
	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 <= -8.2e+96) || !(z <= 6.5e+150))
		tmp = Float64(x / Float64(z * y));
	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 <= -8.2e+96) || ~((z <= 6.5e+150)))
		tmp = x / (z * y);
	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, -8.2e+96], N[Not[LessEqual[z, 6.5e+150]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.19999999999999996e96 or 6.50000000000000033e150 < z

   1. Initial program 78.3%

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

   3. Taylor expanded in t around 0

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. lower--.f64 78.3

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

   5. Applied rewrites 78.3%

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

   7. Applied rewrites 75.9%

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

   8. Taylor expanded in y around inf

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

   10. Applied rewrites 41.4%

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

   if -8.19999999999999996e96 < z < 6.50000000000000033e150

   1. Initial program 90.3%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 50.3

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

   5. Applied rewrites 50.3%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+96} \lor \neg \left(z \leq 6.5 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 21.7% accurate, 1.4× speedup

Math

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

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 (* z y)))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 86.6%

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

3. Taylor expanded in t around 0

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

   1. associate-*r* N/A

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

   2. lower-*.f64 N/A

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

   3. mul-1-neg N/A

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

   4. lower-neg.f64 N/A

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

   5. lower--.f64 50.6

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

5. Applied rewrites 50.6%

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

7. Applied rewrites 34.6%

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

8. Taylor expanded in y around inf

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

10. Applied rewrites 22.8%

    \[\leadsto \frac{x}{z \cdot \color{blue}{y}} \]
11. Add Preprocessing

Developer Target 1: 87.6% 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 2024339 
(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))))