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

Percentage Accurate: 89.0% → 96.9%

Time: 14.7s

Alternatives: 16

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: 89.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / (t - z)) / (y - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

   1. *-un-lft-identity 88.5%

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

   2. times-frac 96.5%

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

4. Applied egg-rr 96.5%

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

   1. associate-*l/ 96.5%

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

   2. *-un-lft-identity 96.5%

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

6. Applied egg-rr 96.5%

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

7. Final simplification 96.5%

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

Alternative 2: 52.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 0.032:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+162}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -5.5e-84)
   (/ (/ x y) t)
   (if (<= t 3.6e-163)
     (/ (/ (- x) z) y)
     (if (<= t 0.032)
       (/ x (* t y))
       (if (<= t 5.8e+85)
         (/ (- x) (* t z))
         (if (<= t 2.85e+162) (/ 1.0 (* y (/ t x))) (/ (/ (- x) t) z)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -5.5e-84) {
		tmp = (x / y) / t;
	} else if (t <= 3.6e-163) {
		tmp = (-x / z) / y;
	} else if (t <= 0.032) {
		tmp = x / (t * y);
	} else if (t <= 5.8e+85) {
		tmp = -x / (t * z);
	} else if (t <= 2.85e+162) {
		tmp = 1.0 / (y * (t / x));
	} else {
		tmp = (-x / 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 (t <= (-5.5d-84)) then
        tmp = (x / y) / t
    else if (t <= 3.6d-163) then
        tmp = (-x / z) / y
    else if (t <= 0.032d0) then
        tmp = x / (t * y)
    else if (t <= 5.8d+85) then
        tmp = -x / (t * z)
    else if (t <= 2.85d+162) then
        tmp = 1.0d0 / (y * (t / x))
    else
        tmp = (-x / 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 (t <= -5.5e-84) {
		tmp = (x / y) / t;
	} else if (t <= 3.6e-163) {
		tmp = (-x / z) / y;
	} else if (t <= 0.032) {
		tmp = x / (t * y);
	} else if (t <= 5.8e+85) {
		tmp = -x / (t * z);
	} else if (t <= 2.85e+162) {
		tmp = 1.0 / (y * (t / x));
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -5.5e-84:
		tmp = (x / y) / t
	elif t <= 3.6e-163:
		tmp = (-x / z) / y
	elif t <= 0.032:
		tmp = x / (t * y)
	elif t <= 5.8e+85:
		tmp = -x / (t * z)
	elif t <= 2.85e+162:
		tmp = 1.0 / (y * (t / x))
	else:
		tmp = (-x / t) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -5.5e-84)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 3.6e-163)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 0.032)
		tmp = Float64(x / Float64(t * y));
	elseif (t <= 5.8e+85)
		tmp = Float64(Float64(-x) / Float64(t * z));
	elseif (t <= 2.85e+162)
		tmp = Float64(1.0 / Float64(y * Float64(t / x)));
	else
		tmp = Float64(Float64(Float64(-x) / 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 (t <= -5.5e-84)
		tmp = (x / y) / t;
	elseif (t <= 3.6e-163)
		tmp = (-x / z) / y;
	elseif (t <= 0.032)
		tmp = x / (t * y);
	elseif (t <= 5.8e+85)
		tmp = -x / (t * z);
	elseif (t <= 2.85e+162)
		tmp = 1.0 / (y * (t / x));
	else
		tmp = (-x / 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[t, -5.5e-84], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 3.6e-163], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 0.032], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+85], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.85e+162], N[(1.0 / N[(y * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -5.50000000000000019e-84

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 52.7%

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

      1. associate-/r* 57.0%

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

      2. div-inv 57.0%

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

   5. Applied egg-rr 57.0%

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

      1. associate-*l/ 57.4%

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

      2. un-div-inv 57.5%

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

   7. Applied egg-rr 57.5%

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

   if -5.50000000000000019e-84 < t < 3.5999999999999998e-163

   1. Initial program 90.5%

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

   3. Taylor expanded in y around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-/r* 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in t around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. neg-mul-1 45.3%

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

   8. Simplified 45.3%

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

   if 3.5999999999999998e-163 < t < 0.032000000000000001

   1. Initial program 93.7%

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

   3. Taylor expanded in z around 0 59.3%

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

   if 0.032000000000000001 < t < 5.79999999999999995e85

   1. Initial program 89.9%

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

      1. clear-num 89.9%

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

      2. associate-/r/ 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. associate-/r* 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in z around 0 59.5%

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

      1. mul-1-neg 59.5%

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

   10. Simplified 59.5%

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

   if 5.79999999999999995e85 < t < 2.84999999999999998e162

   1. Initial program 85.3%

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

   3. Taylor expanded in z around 0 77.8%

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

      1. associate-/r* 68.8%

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

      2. div-inv 68.8%

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

   5. Applied egg-rr 68.8%

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

      1. clear-num 68.7%

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

      2. frac-times 70.7%

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

      3. metadata-eval 70.7%

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

   7. Applied egg-rr 70.7%

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

   if 2.84999999999999998e162 < t

   1. Initial program 84.5%

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

      1. clear-num 83.9%

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

      2. associate-/r/ 84.3%

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

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. associate-/r* 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in z around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/r* 71.4%

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

      3. distribute-neg-frac 71.4%

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

   10. Simplified 71.4%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 0.032:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{+162}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{t \cdot y}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 0.032:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

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 (/ x (* t y))))
   (if (<= t -1.2e-82)
     (/ (/ x y) t)
     (if (<= t 4.2e-163)
       (/ (/ (- x) z) y)
       (if (<= t 0.032)
         t_1
         (if (<= t 4.9e+85)
           (/ (- x) (* t z))
           (if (<= t 6.6e+160) t_1 (/ (/ (- x) t) z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (t * y);
	double tmp;
	if (t <= -1.2e-82) {
		tmp = (x / y) / t;
	} else if (t <= 4.2e-163) {
		tmp = (-x / z) / y;
	} else if (t <= 0.032) {
		tmp = t_1;
	} else if (t <= 4.9e+85) {
		tmp = -x / (t * z);
	} else if (t <= 6.6e+160) {
		tmp = t_1;
	} else {
		tmp = (-x / 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) :: t_1
    real(8) :: tmp
    t_1 = x / (t * y)
    if (t <= (-1.2d-82)) then
        tmp = (x / y) / t
    else if (t <= 4.2d-163) then
        tmp = (-x / z) / y
    else if (t <= 0.032d0) then
        tmp = t_1
    else if (t <= 4.9d+85) then
        tmp = -x / (t * z)
    else if (t <= 6.6d+160) then
        tmp = t_1
    else
        tmp = (-x / 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 t_1 = x / (t * y);
	double tmp;
	if (t <= -1.2e-82) {
		tmp = (x / y) / t;
	} else if (t <= 4.2e-163) {
		tmp = (-x / z) / y;
	} else if (t <= 0.032) {
		tmp = t_1;
	} else if (t <= 4.9e+85) {
		tmp = -x / (t * z);
	} else if (t <= 6.6e+160) {
		tmp = t_1;
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (t * y)
	tmp = 0
	if t <= -1.2e-82:
		tmp = (x / y) / t
	elif t <= 4.2e-163:
		tmp = (-x / z) / y
	elif t <= 0.032:
		tmp = t_1
	elif t <= 4.9e+85:
		tmp = -x / (t * z)
	elif t <= 6.6e+160:
		tmp = t_1
	else:
		tmp = (-x / t) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(t * y))
	tmp = 0.0
	if (t <= -1.2e-82)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 4.2e-163)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	elseif (t <= 0.032)
		tmp = t_1;
	elseif (t <= 4.9e+85)
		tmp = Float64(Float64(-x) / Float64(t * z));
	elseif (t <= 6.6e+160)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-x) / 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 = x / (t * y);
	tmp = 0.0;
	if (t <= -1.2e-82)
		tmp = (x / y) / t;
	elseif (t <= 4.2e-163)
		tmp = (-x / z) / y;
	elseif (t <= 0.032)
		tmp = t_1;
	elseif (t <= 4.9e+85)
		tmp = -x / (t * z);
	elseif (t <= 6.6e+160)
		tmp = t_1;
	else
		tmp = (-x / 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[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e-82], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 4.2e-163], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 0.032], t$95$1, If[LessEqual[t, 4.9e+85], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.6e+160], t$95$1, N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.20000000000000004e-82

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 52.7%

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

      1. associate-/r* 57.0%

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

      2. div-inv 57.0%

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

   5. Applied egg-rr 57.0%

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

      1. associate-*l/ 57.4%

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

      2. un-div-inv 57.5%

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

   7. Applied egg-rr 57.5%

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

   if -1.20000000000000004e-82 < t < 4.19999999999999996e-163

   1. Initial program 90.5%

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

   3. Taylor expanded in y around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. associate-/r* 50.8%

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

   5. Simplified 50.8%

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

   6. Taylor expanded in t around 0 45.3%

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

      1. associate-*r/ 45.3%

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

      2. neg-mul-1 45.3%

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

   8. Simplified 45.3%

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

   if 4.19999999999999996e-163 < t < 0.032000000000000001 or 4.8999999999999997e85 < t < 6.5999999999999994e160

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 64.8%

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

   if 0.032000000000000001 < t < 4.8999999999999997e85

   1. Initial program 89.9%

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

      1. clear-num 89.9%

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

      2. associate-/r/ 89.9%

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

   4. Applied egg-rr 89.9%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. associate-/r* 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in z around 0 59.5%

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

      1. mul-1-neg 59.5%

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

   10. Simplified 59.5%

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

   if 6.5999999999999994e160 < t

   1. Initial program 84.5%

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

      1. clear-num 83.9%

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

      2. associate-/r/ 84.3%

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

   4. Applied egg-rr 84.3%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. associate-/r* 63.6%

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

   7. Simplified 63.6%

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

   8. Taylor expanded in z around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. associate-/r* 71.4%

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

      3. distribute-neg-frac 71.4%

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

   10. Simplified 71.4%

       \[\leadsto \color{blue}{\frac{-\frac{x}{t}}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{elif}\;t \leq 0.032:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+85}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+160}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z (- t z)))))
   (if (<= z -2.2e-22)
     t_1
     (if (<= z 2.1e-154)
       (/ x (* t (- y z)))
       (if (<= z 3.1e+64) (/ (/ x (- t z)) y) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (t - z));
	double tmp;
	if (z <= -2.2e-22) {
		tmp = t_1;
	} else if (z <= 2.1e-154) {
		tmp = x / (t * (y - z));
	} else if (z <= 3.1e+64) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / (z * (t - z))
    if (z <= (-2.2d-22)) then
        tmp = t_1
    else if (z <= 2.1d-154) then
        tmp = x / (t * (y - z))
    else if (z <= 3.1d+64) then
        tmp = (x / (t - z)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * (t - z));
	double tmp;
	if (z <= -2.2e-22) {
		tmp = t_1;
	} else if (z <= 2.1e-154) {
		tmp = x / (t * (y - z));
	} else if (z <= 3.1e+64) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -x / (z * (t - z))
	tmp = 0
	if z <= -2.2e-22:
		tmp = t_1
	elif z <= 2.1e-154:
		tmp = x / (t * (y - z))
	elif z <= 3.1e+64:
		tmp = (x / (t - z)) / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * Float64(t - z)))
	tmp = 0.0
	if (z <= -2.2e-22)
		tmp = t_1;
	elseif (z <= 2.1e-154)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 3.1e+64)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * (t - z));
	tmp = 0.0;
	if (z <= -2.2e-22)
		tmp = t_1;
	elseif (z <= 2.1e-154)
		tmp = x / (t * (y - z));
	elseif (z <= 3.1e+64)
		tmp = (x / (t - z)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e-22], t$95$1, If[LessEqual[z, 2.1e-154], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+64], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e-22 or 3.0999999999999999e64 < z

   1. Initial program 83.7%

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

   3. Taylor expanded in y around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   5. Simplified 76.8%

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

   if -2.2000000000000001e-22 < z < 2.09999999999999984e-154

   1. Initial program 94.6%

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

   3. Taylor expanded in t around inf 75.5%

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

   if 2.09999999999999984e-154 < z < 3.0999999999999999e64

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/r* 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{-x}{z}}{t - z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-152}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) z) (- t z))))
   (if (<= z -1.4e-21)
     t_1
     (if (<= z 1.82e-152)
       (/ x (* t (- y z)))
       (if (<= z 3.1e+64) (/ (/ x (- t z)) y) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / (t - z);
	double tmp;
	if (z <= -1.4e-21) {
		tmp = t_1;
	} else if (z <= 1.82e-152) {
		tmp = x / (t * (y - z));
	} else if (z <= 3.1e+64) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-x / z) / (t - z)
    if (z <= (-1.4d-21)) then
        tmp = t_1
    else if (z <= 1.82d-152) then
        tmp = x / (t * (y - z))
    else if (z <= 3.1d+64) then
        tmp = (x / (t - z)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (-x / z) / (t - z);
	double tmp;
	if (z <= -1.4e-21) {
		tmp = t_1;
	} else if (z <= 1.82e-152) {
		tmp = x / (t * (y - z));
	} else if (z <= 3.1e+64) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (-x / z) / (t - z)
	tmp = 0
	if z <= -1.4e-21:
		tmp = t_1
	elif z <= 1.82e-152:
		tmp = x / (t * (y - z))
	elif z <= 3.1e+64:
		tmp = (x / (t - z)) / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(-x) / z) / Float64(t - z))
	tmp = 0.0
	if (z <= -1.4e-21)
		tmp = t_1;
	elseif (z <= 1.82e-152)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 3.1e+64)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (-x / z) / (t - z);
	tmp = 0.0;
	if (z <= -1.4e-21)
		tmp = t_1;
	elseif (z <= 1.82e-152)
		tmp = x / (t * (y - z));
	elseif (z <= 3.1e+64)
		tmp = (x / (t - z)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e-21], t$95$1, If[LessEqual[z, 1.82e-152], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+64], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000002e-21 or 3.0999999999999999e64 < z

   1. Initial program 83.7%

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

      1. *-un-lft-identity 83.7%

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

      2. times-frac 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0 76.8%

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

      1. mul-1-neg 76.8%

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

      2. associate-/r* 87.5%

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

      3. distribute-neg-frac 87.5%

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

      4. distribute-frac-neg 87.5%

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

   7. Simplified 87.5%

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

   if -1.40000000000000002e-21 < z < 1.82000000000000009e-152

   1. Initial program 94.6%

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

   3. Taylor expanded in t around inf 75.5%

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

   if 1.82000000000000009e-152 < z < 3.0999999999999999e64

   1. Initial program 89.3%

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

   3. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-/r* 70.9%

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

   5. Simplified 70.9%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-21}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-152}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+64}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 93.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) z)))
   (if (<= z -1.4e+157)
     (/ t_1 (- t z))
     (if (<= z 7.4e+110) (/ x (* (- t z) (- y z))) (/ t_1 (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (z <= -1.4e+157) {
		tmp = t_1 / (t - z);
	} else if (z <= 7.4e+110) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = t_1 / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -x / z
    if (z <= (-1.4d+157)) then
        tmp = t_1 / (t - z)
    else if (z <= 7.4d+110) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = t_1 / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (z <= -1.4e+157) {
		tmp = t_1 / (t - z);
	} else if (z <= 7.4e+110) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = t_1 / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -x / z
	tmp = 0
	if z <= -1.4e+157:
		tmp = t_1 / (t - z)
	elif z <= 7.4e+110:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = t_1 / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -1.4e+157)
		tmp = Float64(t_1 / Float64(t - z));
	elseif (z <= 7.4e+110)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(t_1 / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / z;
	tmp = 0.0;
	if (z <= -1.4e+157)
		tmp = t_1 / (t - z);
	elseif (z <= 7.4e+110)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = t_1 / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -1.4e+157], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e+110], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4000000000000001e157

   1. Initial program 77.6%

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

      1. *-un-lft-identity 77.6%

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

      2. times-frac 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. associate-/r* 100.0%

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

      3. distribute-neg-frac 100.0%

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

      4. distribute-frac-neg 100.0%

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

   7. Simplified 100.0%

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

   if -1.4000000000000001e157 < z < 7.40000000000000024e110

   1. Initial program 92.7%

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

   if 7.40000000000000024e110 < z

   1. Initial program 77.2%

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

      1. *-un-lft-identity 77.2%

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

      2. times-frac 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in t around 0 77.0%

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

      1. mul-1-neg 77.0%

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

      2. associate-/r* 92.1%

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

      3. distribute-neg-frac 92.1%

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

      4. distribute-frac-neg 92.1%

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

   7. Simplified 92.1%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-105}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.9e-105)
   (/ (/ x (- t z)) y)
   (if (<= t 1.4e-113) (/ (- x) (* z (- y z))) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.9e-105) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.4e-113) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.9d-105)) then
        tmp = (x / (t - z)) / y
    else if (t <= 1.4d-113) then
        tmp = -x / (z * (y - z))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.9e-105) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.4e-113) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.9e-105:
		tmp = (x / (t - z)) / y
	elif t <= 1.4e-113:
		tmp = -x / (z * (y - z))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.9e-105)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 1.4e-113)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.9e-105)
		tmp = (x / (t - z)) / y;
	elseif (t <= 1.4e-113)
		tmp = -x / (z * (y - z));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.9e-105], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.4e-113], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.9e-105

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/r* 59.0%

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

   5. Simplified 59.0%

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

   if -4.9e-105 < t < 1.4e-113

   1. Initial program 91.2%

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

   3. Taylor expanded in t around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. neg-mul-1 78.6%

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

   5. Simplified 78.6%

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

   if 1.4e-113 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 80.5%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.9 \cdot 10^{-105}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.8e-108)
   (/ (/ x (- t z)) y)
   (if (<= t 1.5e-113) (/ (/ (- x) z) (- y z)) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e-108) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.5e-113) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.8d-108)) then
        tmp = (x / (t - z)) / y
    else if (t <= 1.5d-113) then
        tmp = (-x / z) / (y - z)
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e-108) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.5e-113) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.8e-108:
		tmp = (x / (t - z)) / y
	elif t <= 1.5e-113:
		tmp = (-x / z) / (y - z)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.8e-108)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 1.5e-113)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.8e-108)
		tmp = (x / (t - z)) / y;
	elseif (t <= 1.5e-113)
		tmp = (-x / z) / (y - z);
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.8e-108], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.5e-113], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e-108

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 56.1%

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

      1. *-commutative 56.1%

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

      2. associate-/r* 59.0%

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

   5. Simplified 59.0%

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

   if -2.8e-108 < t < 1.5e-113

   1. Initial program 91.2%

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

      1. *-un-lft-identity 91.2%

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

      2. times-frac 93.0%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in t around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. associate-/r* 82.7%

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

      3. distribute-neg-frac 82.7%

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

      4. distribute-frac-neg 82.7%

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

   7. Simplified 82.7%

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

   if 1.5e-113 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 80.5%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-108}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.5e-85)
   (/ (/ x y) t)
   (if (<= t 9e-168) (/ (/ (- x) z) y) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.5e-85) {
		tmp = (x / y) / t;
	} else if (t <= 9e-168) {
		tmp = (-x / z) / y;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-8.5d-85)) then
        tmp = (x / y) / t
    else if (t <= 9d-168) then
        tmp = (-x / z) / y
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.5e-85) {
		tmp = (x / y) / t;
	} else if (t <= 9e-168) {
		tmp = (-x / z) / y;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -8.5e-85:
		tmp = (x / y) / t
	elif t <= 9e-168:
		tmp = (-x / z) / y
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.5e-85)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 9e-168)
		tmp = Float64(Float64(Float64(-x) / z) / y);
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -8.5e-85)
		tmp = (x / y) / t;
	elseif (t <= 9e-168)
		tmp = (-x / z) / y;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -8.5e-85], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 9e-168], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.50000000000000052e-85

   1. Initial program 86.5%

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

   3. Taylor expanded in z around 0 52.7%

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

      1. associate-/r* 57.0%

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

      2. div-inv 57.0%

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

   5. Applied egg-rr 57.0%

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

      1. associate-*l/ 57.4%

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

      2. un-div-inv 57.5%

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

   7. Applied egg-rr 57.5%

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

   if -8.50000000000000052e-85 < t < 9.0000000000000002e-168

   1. Initial program 90.3%

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

   3. Taylor expanded in y around inf 54.3%

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

      1. *-commutative 54.3%

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

      2. associate-/r* 52.0%

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

   5. Simplified 52.0%

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

   6. Taylor expanded in t around 0 46.4%

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

      1. associate-*r/ 46.4%

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

      2. neg-mul-1 46.4%

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

   8. Simplified 46.4%

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

   if 9.0000000000000002e-168 < t

   1. Initial program 88.7%

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

   3. Taylor expanded in t around inf 75.6%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-132} \lor \neg \left(y \leq 1.15 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5.2e-132) (not (<= y 1.15e-82)))
   (/ (/ x y) t)
   (/ (- x) (* t z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5.2e-132) || !(y <= 1.15e-82)) {
		tmp = (x / y) / t;
	} else {
		tmp = -x / (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 <= (-5.2d-132)) .or. (.not. (y <= 1.15d-82))) then
        tmp = (x / y) / t
    else
        tmp = -x / (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 <= -5.2e-132) || !(y <= 1.15e-82)) {
		tmp = (x / y) / t;
	} else {
		tmp = -x / (t * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -5.2e-132) or not (y <= 1.15e-82):
		tmp = (x / y) / t
	else:
		tmp = -x / (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 <= -5.2e-132) || !(y <= 1.15e-82))
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(-x) / 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 <= -5.2e-132) || ~((y <= 1.15e-82)))
		tmp = (x / y) / t;
	else
		tmp = -x / (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[y, -5.2e-132], N[Not[LessEqual[y, 1.15e-82]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[((-x) / N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000002e-132 or 1.14999999999999998e-82 < y

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 52.0%

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

      1. associate-/r* 53.7%

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

      2. div-inv 53.6%

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

   5. Applied egg-rr 53.6%

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

      1. associate-*l/ 57.3%

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

      2. un-div-inv 57.4%

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

   7. Applied egg-rr 57.4%

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

   if -5.2000000000000002e-132 < y < 1.14999999999999998e-82

   1. Initial program 86.5%

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

      1. clear-num 85.8%

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

      2. associate-/r/ 86.3%

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

   4. Applied egg-rr 86.3%

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

   5. Taylor expanded in y around 0 76.0%

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

      1. associate-/r* 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in z around 0 44.2%

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

      1. mul-1-neg 44.2%

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

   10. Simplified 44.2%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-132} \lor \neg \left(y \leq 1.15 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-132} \lor \neg \left(y \leq 7.8 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.45e-132) (not (<= y 7.8e-61)))
   (/ (/ x y) t)
   (/ (/ (- x) t) z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.45e-132) || !(y <= 7.8e-61)) {
		tmp = (x / y) / t;
	} else {
		tmp = (-x / 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 <= (-2.45d-132)) .or. (.not. (y <= 7.8d-61))) then
        tmp = (x / y) / t
    else
        tmp = (-x / 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 <= -2.45e-132) || !(y <= 7.8e-61)) {
		tmp = (x / y) / t;
	} else {
		tmp = (-x / t) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -2.45e-132) or not (y <= 7.8e-61):
		tmp = (x / y) / t
	else:
		tmp = (-x / 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 <= -2.45e-132) || !(y <= 7.8e-61))
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(Float64(-x) / 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 <= -2.45e-132) || ~((y <= 7.8e-61)))
		tmp = (x / y) / t;
	else
		tmp = (-x / 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[y, -2.45e-132], N[Not[LessEqual[y, 7.8e-61]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[((-x) / t), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4499999999999999e-132 or 7.80000000000000065e-61 < y

   1. Initial program 89.2%

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

   3. Taylor expanded in z around 0 53.4%

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

      1. associate-/r* 55.1%

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

      2. div-inv 55.1%

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

   5. Applied egg-rr 55.1%

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

      1. associate-*l/ 58.8%

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

      2. un-div-inv 58.9%

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

   7. Applied egg-rr 58.9%

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

   if -2.4499999999999999e-132 < y < 7.80000000000000065e-61

   1. Initial program 87.2%

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

      1. clear-num 86.5%

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

      2. associate-/r/ 87.0%

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

   4. Applied egg-rr 87.0%

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

   5. Taylor expanded in y around 0 74.1%

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

      1. associate-/r* 74.1%

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

   7. Simplified 74.1%

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

   8. Taylor expanded in z around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. associate-/r* 44.3%

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

      3. distribute-neg-frac 44.3%

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

   10. Simplified 44.3%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{-132} \lor \neg \left(y \leq 7.8 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+43} \lor \neg \left(z \leq 2.9 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -9.5e+43) (not (<= z 2.9e+49))) (/ 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 <= -9.5e+43) || !(z <= 2.9e+49)) {
		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 <= (-9.5d+43)) .or. (.not. (z <= 2.9d+49))) 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 <= -9.5e+43) || !(z <= 2.9e+49)) {
		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 <= -9.5e+43) or not (z <= 2.9e+49):
		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 <= -9.5e+43) || !(z <= 2.9e+49))
		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 <= -9.5e+43) || ~((z <= 2.9e+49)))
		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, -9.5e+43], N[Not[LessEqual[z, 2.9e+49]], $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 < -9.5000000000000004e43 or 2.9e49 < z

   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 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in z around 0 35.7%

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

      1. mul-1-neg 35.7%

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

      2. associate-/r* 34.1%

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

      3. distribute-neg-frac 34.1%

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

      4. distribute-frac-neg 34.1%

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

   8. Simplified 34.1%

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

      1. expm1-log1p-u 33.7%

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

      2. expm1-udef 54.3%

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

      3. associate-/l/ 54.3%

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

      4. add-sqr-sqrt 26.2%

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

      5. sqrt-unprod 51.4%

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

      6. sqr-neg 51.4%

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

      7. sqrt-unprod 28.0%

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

      8. add-sqr-sqrt 54.3%

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

      9. *-commutative 54.3%

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

   10. Applied egg-rr 54.3%

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

       1. expm1-def 34.2%

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

       2. expm1-log1p 34.5%

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

       3. *-commutative 34.5%

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

   12. Simplified 34.5%

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

   if -9.5000000000000004e43 < z < 2.9e49

   1. Initial program 92.9%

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

   3. Taylor expanded in z around 0 56.1%

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

4. Final simplification 46.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+43} \lor \neg \left(z \leq 2.9 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+212} \lor \neg \left(z \leq 1.35 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.3e+212) (not (<= z 1.35e+111))) (/ 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 <= -2.3e+212) || !(z <= 1.35e+111)) {
		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 <= (-2.3d+212)) .or. (.not. (z <= 1.35d+111))) 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 <= -2.3e+212) || !(z <= 1.35e+111)) {
		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 <= -2.3e+212) or not (z <= 1.35e+111):
		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 <= -2.3e+212) || !(z <= 1.35e+111))
		tmp = Float64(x / Float64(z * y));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.3e+212) || ~((z <= 1.35e+111)))
		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, -2.3e+212], N[Not[LessEqual[z, 1.35e+111]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e212 or 1.3499999999999999e111 < z

   1. Initial program 81.5%

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

   3. Taylor expanded in t around 0 81.4%

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

      1. associate-*r/ 81.4%

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

      2. neg-mul-1 81.4%

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

   5. Simplified 81.4%

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

   6. Taylor expanded in z around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. associate-/r* 40.6%

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

      3. distribute-neg-frac 40.6%

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

      4. distribute-frac-neg 40.6%

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

   8. Simplified 40.6%

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

      1. expm1-log1p-u 40.2%

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

      2. expm1-udef 64.3%

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

      3. associate-/l/ 64.4%

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

      4. add-sqr-sqrt 27.4%

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

      5. sqrt-unprod 60.5%

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

      6. sqr-neg 60.5%

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

      7. sqrt-unprod 36.9%

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

      8. add-sqr-sqrt 64.3%

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

      9. *-commutative 64.3%

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

   10. Applied egg-rr 64.3%

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

       1. expm1-def 45.4%

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

       2. expm1-log1p 45.8%

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

       3. *-commutative 45.8%

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

   12. Simplified 45.8%

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

   if -2.2999999999999998e212 < z < 1.3499999999999999e111

   1. Initial program 90.4%

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

   3. Taylor expanded in y around inf 61.1%

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

      1. *-commutative 61.1%

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

      2. associate-/r* 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in t around inf 49.9%

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

4. Final simplification 49.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+212} \lor \neg \left(z \leq 1.35 \cdot 10^{+111}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.5e-113) (/ x (* (- t z) y)) (/ x (* t (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.5e-113) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.5d-113) then
        tmp = x / ((t - z) * y)
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.5e-113) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.5e-113:
		tmp = x / ((t - z) * y)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.5e-113)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.5e-113)
		tmp = x / ((t - z) * y);
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.5e-113], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.5e-113

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   if 1.5e-113 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 80.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.4e-113) (/ (/ x (- t z)) y) (/ x (* t (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e-113) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.4d-113) then
        tmp = (x / (t - z)) / y
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.4e-113) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.4e-113:
		tmp = (x / (t - z)) / y
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.4e-113)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.4e-113)
		tmp = (x / (t - z)) / y;
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 1.4e-113], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.4e-113

   1. Initial program 88.8%

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

   3. Taylor expanded in y around inf 55.8%

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

      1. *-commutative 55.8%

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

      2. associate-/r* 56.8%

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

   5. Simplified 56.8%

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

   if 1.4e-113 < t

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 80.5%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.4 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (t * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.5%

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

3. Taylor expanded in z around 0 40.5%

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

4. Final simplification 40.5%

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

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 2024021 
(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))))