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

Percentage Accurate: 89.1% → 97.8%

Time: 9.5s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.5× speedup

Math

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

FPCore

NOTE: y 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 0.0) (/ (/ x (- y z)) (- t z)) t_1)))

C

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

Fortran

NOTE: y 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 <= 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < 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 <= 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y 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, 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -0.0

   1. Initial program 90.0%

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

      1. associate-/r* 98.3%

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

   3. Simplified 98.3%

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

   if -0.0 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 98.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 2: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{if}\;z \leq -0.00047:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z (- t z)))))
   (if (<= z -0.00047)
     t_1
     (if (<= z 1.35e-9)
       (/ x (* (- y z) t))
       (if (<= z 1.4e+154) t_1 (/ 1.0 (/ z (/ x z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (t - z));
	double tmp;
	if (z <= -0.00047) {
		tmp = t_1;
	} else if (z <= 1.35e-9) {
		tmp = x / ((y - z) * t);
	} else if (z <= 1.4e+154) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Fortran

NOTE: y 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 * (t - z))
    if (z <= (-0.00047d0)) then
        tmp = t_1
    else if (z <= 1.35d-9) then
        tmp = x / ((y - z) * t)
    else if (z <= 1.4d+154) then
        tmp = t_1
    else
        tmp = 1.0d0 / (z / (x / z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (t - z));
	double tmp;
	if (z <= -0.00047) {
		tmp = t_1;
	} else if (z <= 1.35e-9) {
		tmp = x / ((y - z) * t);
	} else if (z <= 1.4e+154) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -x / (z * (t - z))
	tmp = 0
	if z <= -0.00047:
		tmp = t_1
	elif z <= 1.35e-9:
		tmp = x / ((y - z) * t)
	elif z <= 1.4e+154:
		tmp = t_1
	else:
		tmp = 1.0 / (z / (x / z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * Float64(t - z)))
	tmp = 0.0
	if (z <= -0.00047)
		tmp = t_1;
	elseif (z <= 1.35e-9)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	elseif (z <= 1.4e+154)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * (t - z));
	tmp = 0.0;
	if (z <= -0.00047)
		tmp = t_1;
	elseif (z <= 1.35e-9)
		tmp = x / ((y - z) * t);
	elseif (z <= 1.4e+154)
		tmp = t_1;
	else
		tmp = 1.0 / (z / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.00047], t$95$1, If[LessEqual[z, 1.35e-9], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+154], t$95$1, N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.69999999999999986e-4 or 1.3500000000000001e-9 < z < 1.4e154

   1. Initial program 93.1%

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

   2. Taylor expanded in y around 0 87.4%

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

      1. associate-*r/ 87.4%

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

      2. neg-mul-1 87.4%

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

   4. Simplified 87.4%

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

   if -4.69999999999999986e-4 < z < 1.3500000000000001e-9

   1. Initial program 94.2%

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

   2. Taylor expanded in t around inf 77.8%

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

   if 1.4e154 < z

   1. Initial program 84.3%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. clear-num 99.9%

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

      2. frac-times 99.9%

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

      3. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in z around inf 84.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 84.3%

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

      2. associate-/l* 98.9%

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

   8. Simplified 98.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{x}{z}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00047:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 3: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00017 \lor \neg \left(z \leq 3.8 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00017) (not (<= z 3.8e-11)))
   (/ (/ (- x) z) (- t z))
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00017) || !(z <= 3.8e-11)) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.00017d0)) .or. (.not. (z <= 3.8d-11))) then
        tmp = (-x / z) / (t - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00017) || !(z <= 3.8e-11)) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00017) or not (z <= 3.8e-11):
		tmp = (-x / z) / (t - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00017) || !(z <= 3.8e-11))
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00017) || ~((z <= 3.8e-11)))
		tmp = (-x / z) / (t - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00017], N[Not[LessEqual[z, 3.8e-11]], $MachinePrecision]], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-4 or 3.7999999999999998e-11 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in y around 0 86.3%

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

      1. mul-1-neg 86.3%

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

      2. distribute-frac-neg 86.3%

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

      3. associate-/r* 93.5%

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

   4. Simplified 93.5%

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

   if -1.7e-4 < z < 3.7999999999999998e-11

   1. Initial program 94.2%

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

   2. Taylor expanded in t around inf 77.8%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00017 \lor \neg \left(z \leq 3.8 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 4: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.009:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.009)
   (/ (/ x z) z)
   (if (<= z 3.5e-9) (/ (/ x t) y) (/ 1.0 (/ z (/ x z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.009) {
		tmp = (x / z) / z;
	} else if (z <= 3.5e-9) {
		tmp = (x / t) / y;
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.009d0)) then
        tmp = (x / z) / z
    else if (z <= 3.5d-9) then
        tmp = (x / t) / y
    else
        tmp = 1.0d0 / (z / (x / z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.009) {
		tmp = (x / z) / z;
	} else if (z <= 3.5e-9) {
		tmp = (x / t) / y;
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -0.009:
		tmp = (x / z) / z
	elif z <= 3.5e-9:
		tmp = (x / t) / y
	else:
		tmp = 1.0 / (z / (x / z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.009)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 3.5e-9)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.009)
		tmp = (x / z) / z;
	elseif (z <= 3.5e-9)
		tmp = (x / t) / y;
	else
		tmp = 1.0 / (z / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -0.009], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.5e-9], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00899999999999999932

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 84.9%

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

      1. unpow2 84.9%

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

      2. associate-/r* 86.9%

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

   4. Simplified 86.9%

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

   if -0.00899999999999999932 < z < 3.4999999999999999e-9

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 68.2%

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

      1. *-un-lft-identity 68.2%

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

      2. times-frac 70.2%

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

   4. Applied egg-rr 70.2%

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

      1. associate-*l/ 70.3%

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

      2. *-lft-identity 70.3%

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

   6. Simplified 70.3%

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

   if 3.4999999999999999e-9 < z

   1. Initial program 87.4%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. clear-num 99.6%

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

      2. frac-times 99.7%

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

      3. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 75.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 75.8%

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

      2. associate-/l* 83.9%

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

   8. Simplified 83.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{x}{z}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.009:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 5: 72.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0026:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.0026)
   (/ (/ x z) z)
   (if (<= z 4.2e+49) (/ x (* (- y z) t)) (/ 1.0 (/ z (/ x z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.0026) {
		tmp = (x / z) / z;
	} else if (z <= 4.2e+49) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.0026d0)) then
        tmp = (x / z) / z
    else if (z <= 4.2d+49) then
        tmp = x / ((y - z) * t)
    else
        tmp = 1.0d0 / (z / (x / z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.0026) {
		tmp = (x / z) / z;
	} else if (z <= 4.2e+49) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -0.0026:
		tmp = (x / z) / z
	elif z <= 4.2e+49:
		tmp = x / ((y - z) * t)
	else:
		tmp = 1.0 / (z / (x / z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.0026)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 4.2e+49)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.0026)
		tmp = (x / z) / z;
	elseif (z <= 4.2e+49)
		tmp = x / ((y - z) * t);
	else
		tmp = 1.0 / (z / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -0.0026], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.2e+49], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0025999999999999999

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 84.9%

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

      1. unpow2 84.9%

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

      2. associate-/r* 86.9%

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

   4. Simplified 86.9%

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

   if -0.0025999999999999999 < z < 4.20000000000000022e49

   1. Initial program 93.9%

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

   2. Taylor expanded in t around inf 75.8%

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

   if 4.20000000000000022e49 < z

   1. Initial program 87.2%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. frac-times 99.7%

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

      3. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 81.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 81.3%

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

      2. associate-/l* 90.6%

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

   8. Simplified 90.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{x}{z}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0026:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 6: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.007)
   (/ (/ x z) z)
   (if (<= z 2.85e+48) (/ (/ x t) (- y z)) (/ 1.0 (/ z (/ x z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.007) {
		tmp = (x / z) / z;
	} else if (z <= 2.85e+48) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.007d0)) then
        tmp = (x / z) / z
    else if (z <= 2.85d+48) then
        tmp = (x / t) / (y - z)
    else
        tmp = 1.0d0 / (z / (x / z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.007) {
		tmp = (x / z) / z;
	} else if (z <= 2.85e+48) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -0.007:
		tmp = (x / z) / z
	elif z <= 2.85e+48:
		tmp = (x / t) / (y - z)
	else:
		tmp = 1.0 / (z / (x / z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.007)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 2.85e+48)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.007)
		tmp = (x / z) / z;
	elseif (z <= 2.85e+48)
		tmp = (x / t) / (y - z);
	else
		tmp = 1.0 / (z / (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -0.007], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.85e+48], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00700000000000000015

   1. Initial program 94.3%

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

   2. Taylor expanded in z around inf 84.9%

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

      1. unpow2 84.9%

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

      2. associate-/r* 86.9%

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

   4. Simplified 86.9%

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

   if -0.00700000000000000015 < z < 2.84999999999999984e48

   1. Initial program 93.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. Taylor expanded in t around inf 77.3%

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

   if 2.84999999999999984e48 < z

   1. Initial program 87.2%

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

      1. associate-/l/ 99.9%

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

      2. div-inv 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. frac-times 99.7%

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

      3. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 81.3%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 81.3%

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

      2. associate-/l* 90.6%

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

   8. Simplified 90.6%

      \[\leadsto \frac{1}{\color{blue}{\frac{z}{\frac{x}{z}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+48}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 7: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 5e+106) (/ x (* (- y z) (- t z))) (/ (/ (- x) z) (- t z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5e+106) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Fortran

NOTE: y 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+106) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (-x / z) / (t - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5e+106) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (-x / z) / (t - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 5e+106:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (-x / z) / (t - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5e+106)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5e+106)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (-x / z) / (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, 5e+106], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.9999999999999998e106

   1. Initial program 94.3%

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

   if 4.9999999999999998e106 < z

   1. Initial program 84.6%

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

   2. Taylor expanded in y around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-frac-neg 84.5%

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

      3. associate-/r* 95.8%

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

   4. Simplified 95.8%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \]

Alternative 8: 46.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0052 \lor \neg \left(z \leq 3.2 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.0052) (not (<= z 3.2e+93))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0052) || !(z <= 3.2e+93)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.0052d0)) .or. (.not. (z <= 3.2d+93))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0052) || !(z <= 3.2e+93)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.0052) or not (z <= 3.2e+93):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.0052) || !(z <= 3.2e+93))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.0052) || ~((z <= 3.2e+93)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.0052], N[Not[LessEqual[z, 3.2e+93]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0051999999999999998 or 3.2000000000000001e93 < z

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 43.8%

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

      1. *-commutative 43.8%

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

      2. associate-/r* 49.0%

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

   4. Simplified 49.0%

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

   5. Taylor expanded in t around 0 43.7%

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

      1. associate-*r/ 43.7%

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

      2. neg-mul-1 43.7%

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

   7. Simplified 43.7%

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

      1. expm1-log1p-u 43.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-x}{y \cdot z}\right)\right)} \]

      2. expm1-udef 71.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-x}{y \cdot z}\right)} - 1} \]

      3. add-sqr-sqrt 34.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y \cdot z}\right)} - 1 \]

      4. sqrt-unprod 69.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y \cdot z}\right)} - 1 \]

      5. sqr-neg 69.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\sqrt{\color{blue}{x \cdot x}}}{y \cdot z}\right)} - 1 \]

      6. sqrt-unprod 36.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y \cdot z}\right)} - 1 \]

      7. add-sqr-sqrt 71.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{x}}{y \cdot z}\right)} - 1 \]

   9. Applied egg-rr 71.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)} - 1} \]
   10. Step-by-step derivation

       1. expm1-def 43.0%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{y \cdot z}\right)\right)} \]

       2. expm1-log1p 43.3%

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

       3. *-commutative 43.3%

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

   11. Simplified 43.3%

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

   if -0.0051999999999999998 < z < 3.2000000000000001e93

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 62.7%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0052 \lor \neg \left(z \leq 3.2 \cdot 10^{+93}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 9: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0064 \lor \neg \left(z \leq 1.9 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.0064) (not (<= z 1.9e-9))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0064) || !(z <= 1.9e-9)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.0064d0)) .or. (.not. (z <= 1.9d-9))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.0064) || !(z <= 1.9e-9)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.0064) or not (z <= 1.9e-9):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.0064) || !(z <= 1.9e-9))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.0064) || ~((z <= 1.9e-9)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.0064], N[Not[LessEqual[z, 1.9e-9]], $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 < -0.00640000000000000031 or 1.90000000000000006e-9 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. unpow2 79.4%

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

   4. Simplified 79.4%

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

   if -0.00640000000000000031 < z < 1.90000000000000006e-9

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 68.2%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0064 \lor \neg \left(z \leq 1.9 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 10: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00066 \lor \neg \left(z \leq 5.5 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00066) (not (<= z 5.5e-10))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00066) || !(z <= 5.5e-10)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.00066d0)) .or. (.not. (z <= 5.5d-10))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00066) || !(z <= 5.5e-10)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00066) or not (z <= 5.5e-10):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00066) || !(z <= 5.5e-10))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00066) || ~((z <= 5.5e-10)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00066], N[Not[LessEqual[z, 5.5e-10]], $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 < -6.6e-4 or 5.4999999999999996e-10 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. unpow2 79.4%

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

   4. Simplified 79.4%

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

   if -6.6e-4 < z < 5.4999999999999996e-10

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 68.2%

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

      1. *-un-lft-identity 68.2%

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

      2. times-frac 70.2%

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

   4. Applied egg-rr 70.2%

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

      1. associate-*l/ 70.3%

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

      2. *-lft-identity 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00066 \lor \neg \left(z \leq 5.5 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 11: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00155 \lor \neg \left(z \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00155) (not (<= z 3.2e-10))) (/ (/ x z) z) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00155) || !(z <= 3.2e-10)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-0.00155d0)) .or. (.not. (z <= 3.2d-10))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -0.00155) || !(z <= 3.2e-10)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -0.00155) or not (z <= 3.2e-10):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -0.00155) || !(z <= 3.2e-10))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -0.00155) || ~((z <= 3.2e-10)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -0.00155], N[Not[LessEqual[z, 3.2e-10]], $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 < -0.00154999999999999995 or 3.19999999999999981e-10 < z

   1. Initial program 90.2%

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

   2. Taylor expanded in z around inf 79.4%

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

      1. unpow2 79.4%

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

      2. associate-/r* 85.1%

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

   4. Simplified 85.1%

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

   if -0.00154999999999999995 < z < 3.19999999999999981e-10

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0 68.2%

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

      1. *-un-lft-identity 68.2%

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

      2. times-frac 70.2%

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

   4. Applied egg-rr 70.2%

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

      1. associate-*l/ 70.3%

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

      2. *-lft-identity 70.3%

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

   6. Simplified 70.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00155 \lor \neg \left(z \leq 3.2 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 12: 96.6% accurate, 1.0× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y 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 92.2%

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

   1. associate-/l/ 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 13: 39.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y 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 92.2%

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

2. Taylor expanded in z around 0 46.1%

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

3. Final simplification 46.1%

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

Developer target: 88.0% 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 2023221 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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