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

Percentage Accurate: 88.4% → 96.7%

Time: 10.8s

Alternatives: 18

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: 88.4% 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: 96.7% 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 88.6%

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

   1. associate-/l/ 97.4%

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

3. Simplified 97.4%

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

Alternative 2: 92.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{\frac{z}{x}}}{y - z}\\ \end{array} \end{array} \]

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 (* (- t z) (- y z))))
   (if (<= t_1 (- INFINITY))
     (/ 1.0 (* t (/ (- y z) x)))
     (if (<= t_1 5e+278) (/ x t_1) (/ (/ -1.0 (/ z x)) (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 1.0 / (t * ((y - z) / x));
	} else if (t_1 <= 5e+278) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / (z / x)) / (y - z);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 / (t * ((y - z) / x));
	} else if (t_1 <= 5e+278) {
		tmp = x / t_1;
	} else {
		tmp = (-1.0 / (z / x)) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = 1.0 / (t * ((y - z) / x))
	elif t_1 <= 5e+278:
		tmp = x / t_1
	else:
		tmp = (-1.0 / (z / x)) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(1.0 / Float64(t * Float64(Float64(y - z) / x)));
	elseif (t_1 <= 5e+278)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(-1.0 / Float64(z / x)) / 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 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = 1.0 / (t * ((y - z) / x));
	elseif (t_1 <= 5e+278)
		tmp = x / t_1;
	else
		tmp = (-1.0 / (z / x)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(1.0 / N[(t * N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+278], N[(x / t$95$1), $MachinePrecision], N[(N[(-1.0 / N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 51.3%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. 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 95.0%

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

      3. metadata-eval 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in t around inf 40.7%

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

      1. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5.00000000000000029e278

   1. Initial program 99.4%

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

   if 5.00000000000000029e278 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 79.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in t around 0 89.2%

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

      1. associate-*l/ 89.2%

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

      2. associate-*r/ 89.2%

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

      3. clear-num 89.2%

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

      4. un-div-inv 89.2%

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

   9. Applied egg-rr 89.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq -\infty:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-1}{\frac{z}{x}}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t z) (- y z))))
   (if (<= t_1 (- INFINITY))
     (/ 1.0 (* t (/ (- y z) x)))
     (if (<= t_1 5e+278) (/ x t_1) (/ (/ x z) (- z y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = 1.0 / (t * ((y - z) / x));
	} else if (t_1 <= 5e+278) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = 1.0 / (t * ((y - z) / x));
	} else if (t_1 <= 5e+278) {
		tmp = x / t_1;
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = 1.0 / (t * ((y - z) / x))
	elif t_1 <= 5e+278:
		tmp = x / t_1
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(1.0 / Float64(t * Float64(Float64(y - z) / x)));
	elseif (t_1 <= 5e+278)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = 1.0 / (t * ((y - z) / x));
	elseif (t_1 <= 5e+278)
		tmp = x / t_1;
	else
		tmp = (x / z) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(1.0 / N[(t * N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+278], N[(x / t$95$1), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 51.3%

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

      1. associate-/l/ 100.0%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\frac{x}{t - z} \cdot \frac{1}{y - z}} \]
   5. 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 95.0%

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

      3. metadata-eval 95.0%

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

   6. Applied egg-rr 95.0%

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

   7. Taylor expanded in t around inf 40.7%

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

      1. associate-/l* 81.1%

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

   9. Simplified 81.1%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 5.00000000000000029e278

   1. Initial program 99.4%

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

   if 5.00000000000000029e278 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 79.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 89.2%

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

      1. associate-*r/ 89.2%

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

      2. neg-mul-1 89.2%

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

   7. Simplified 89.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq -\infty:\\ \;\;\;\;\frac{1}{t \cdot \frac{y - z}{x}}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \leq 5 \cdot 10^{+278}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e-116)
   (/ (/ x y) (- t z))
   (if (<= t 4.5e-82)
     (/ (/ x z) (- z y))
     (if (<= t 3.5e+95) (/ x (* t (- 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 <= -3.7e-116) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.5e-82) {
		tmp = (x / z) / (z - y);
	} else if (t <= 3.5e+95) {
		tmp = x / (t * (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 <= (-3.7d-116)) then
        tmp = (x / y) / (t - z)
    else if (t <= 4.5d-82) then
        tmp = (x / z) / (z - y)
    else if (t <= 3.5d+95) then
        tmp = x / (t * (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 <= -3.7e-116) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.5e-82) {
		tmp = (x / z) / (z - y);
	} else if (t <= 3.5e+95) {
		tmp = x / (t * (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 <= -3.7e-116:
		tmp = (x / y) / (t - z)
	elif t <= 4.5e-82:
		tmp = (x / z) / (z - y)
	elif t <= 3.5e+95:
		tmp = x / (t * (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 <= -3.7e-116)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 4.5e-82)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	elseif (t <= 3.5e+95)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.7e-116)
		tmp = (x / y) / (t - z);
	elseif (t <= 4.5e-82)
		tmp = (x / z) / (z - y);
	elseif (t <= 3.5e+95)
		tmp = x / (t * (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, -3.7e-116], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-82], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+95], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.7000000000000002e-116

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 86.0%

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

      1. associate-/l/ 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in y around inf 67.7%

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

   if -3.7000000000000002e-116 < t < 4.4999999999999998e-82

   1. Initial program 96.1%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in t around 0 83.2%

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

      1. associate-*r/ 83.2%

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

      2. neg-mul-1 83.2%

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

   7. Simplified 83.2%

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

   if 4.4999999999999998e-82 < t < 3.5e95

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 65.0%

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

   if 3.5e95 < t

   1. Initial program 80.2%

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

      1. associate-/l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 96.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.75e-115)
   (/ (/ x y) (- t z))
   (if (<= t 2.3e-82)
     (/ x (* z (- z y)))
     (if (<= t 2.95e+94) (/ x (* t (- 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 <= -1.75e-115) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2.3e-82) {
		tmp = x / (z * (z - y));
	} else if (t <= 2.95e+94) {
		tmp = x / (t * (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 <= (-1.75d-115)) then
        tmp = (x / y) / (t - z)
    else if (t <= 2.3d-82) then
        tmp = x / (z * (z - y))
    else if (t <= 2.95d+94) then
        tmp = x / (t * (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 <= -1.75e-115) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2.3e-82) {
		tmp = x / (z * (z - y));
	} else if (t <= 2.95e+94) {
		tmp = x / (t * (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 <= -1.75e-115:
		tmp = (x / y) / (t - z)
	elif t <= 2.3e-82:
		tmp = x / (z * (z - y))
	elif t <= 2.95e+94:
		tmp = x / (t * (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 <= -1.75e-115)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 2.3e-82)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (t <= 2.95e+94)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.75e-115)
		tmp = (x / y) / (t - z);
	elseif (t <= 2.3e-82)
		tmp = x / (z * (z - y));
	elseif (t <= 2.95e+94)
		tmp = x / (t * (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, -1.75e-115], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-82], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.95e+94], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.7500000000000001e-115

   1. Initial program 86.0%

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

   3. Taylor expanded in x around 0 86.0%

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

      1. associate-/l/ 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in y around inf 67.7%

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

   if -1.7500000000000001e-115 < t < 2.29999999999999997e-82

   1. Initial program 96.1%

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

   3. Taylor expanded in t around 0 80.7%

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

      1. associate-*r/ 80.7%

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

      2. neg-mul-1 80.7%

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

   5. Simplified 80.7%

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

   if 2.29999999999999997e-82 < t < 2.94999999999999995e94

   1. Initial program 93.4%

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

   3. Taylor expanded in t around inf 65.0%

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

   if 2.94999999999999995e94 < t

   1. Initial program 80.2%

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

      1. associate-/l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 96.0%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.043:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -0.043)
   (/ x (* z (- y)))
   (if (<= z 3.35e-19)
     (/ (/ x t) y)
     (if (<= z 5.4e+147) (/ (/ x y) (- z)) (/ x (* z (- t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.043) {
		tmp = x / (z * -y);
	} else if (z <= 3.35e-19) {
		tmp = (x / t) / y;
	} else if (z <= 5.4e+147) {
		tmp = (x / y) / -z;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-0.043d0)) then
        tmp = x / (z * -y)
    else if (z <= 3.35d-19) then
        tmp = (x / t) / y
    else if (z <= 5.4d+147) then
        tmp = (x / y) / -z
    else
        tmp = x / (z * -t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -0.043) {
		tmp = x / (z * -y);
	} else if (z <= 3.35e-19) {
		tmp = (x / t) / y;
	} else if (z <= 5.4e+147) {
		tmp = (x / y) / -z;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -0.043:
		tmp = x / (z * -y)
	elif z <= 3.35e-19:
		tmp = (x / t) / y
	elif z <= 5.4e+147:
		tmp = (x / y) / -z
	else:
		tmp = x / (z * -t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -0.043)
		tmp = Float64(x / Float64(z * Float64(-y)));
	elseif (z <= 3.35e-19)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 5.4e+147)
		tmp = Float64(Float64(x / y) / Float64(-z));
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -0.043)
		tmp = x / (z * -y);
	elseif (z <= 3.35e-19)
		tmp = (x / t) / y;
	elseif (z <= 5.4e+147)
		tmp = (x / y) / -z;
	else
		tmp = x / (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -0.043], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.35e-19], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 5.4e+147], N[(N[(x / y), $MachinePrecision] / (-z)), $MachinePrecision], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.042999999999999997

   1. Initial program 86.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in z around 0 39.0%

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

      1. associate-*r/ 39.0%

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

      2. mul-1-neg 39.0%

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

      3. *-commutative 39.0%

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

   10. Simplified 39.0%

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

   if -0.042999999999999997 < z < 3.34999999999999999e-19

   1. Initial program 94.2%

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

      1. associate-/l/ 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 93.0%

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

      2. associate-/r/ 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around 0 67.9%

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

      1. associate-/r* 69.9%

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

   9. Simplified 69.9%

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

   if 3.34999999999999999e-19 < z < 5.39999999999999995e147

   1. Initial program 86.6%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 73.2%

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

      1. associate-*r/ 73.2%

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

      2. neg-mul-1 73.2%

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

   7. Simplified 73.2%

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

   8. Taylor expanded in z around 0 46.2%

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

      1. associate-*r/ 46.2%

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

      2. mul-1-neg 46.2%

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

      3. *-commutative 46.2%

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

   10. Simplified 46.2%

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

       1. neg-mul-1 46.2%

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

       2. *-commutative 46.2%

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

       3. times-frac 54.9%

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

   12. Applied egg-rr 54.9%

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

       1. associate-*r/ 50.4%

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

       2. frac-2neg 50.4%

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

       3. metadata-eval 50.4%

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

       4. associate-*l/ 50.5%

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

       5. *-un-lft-identity 50.5%

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

   14. Applied egg-rr 50.5%

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

   if 5.39999999999999995e147 < z

   1. Initial program 74.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 58.9%

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

   6. Taylor expanded in y around 0 56.0%

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

      1. associate-*r/ 56.0%

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

      2. mul-1-neg 56.0%

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

      3. *-commutative 56.0%

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

   8. Simplified 56.0%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.043:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq 3.35 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+147}:\\ \;\;\;\;\frac{\frac{x}{y}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-y\right)}\\ \mathbf{if}\;z \leq -0.043:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z (- y)))))
   (if (<= z -0.043)
     t_1
     (if (<= z 2.5e-18)
       (/ (/ x t) y)
       (if (<= z 8.5e+147) t_1 (/ x (* z (- t))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * -y);
	double tmp;
	if (z <= -0.043) {
		tmp = t_1;
	} else if (z <= 2.5e-18) {
		tmp = (x / t) / y;
	} else if (z <= 8.5e+147) {
		tmp = t_1;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * -y)
    if (z <= (-0.043d0)) then
        tmp = t_1
    else if (z <= 2.5d-18) then
        tmp = (x / t) / y
    else if (z <= 8.5d+147) then
        tmp = t_1
    else
        tmp = x / (z * -t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * -y);
	double tmp;
	if (z <= -0.043) {
		tmp = t_1;
	} else if (z <= 2.5e-18) {
		tmp = (x / t) / y;
	} else if (z <= 8.5e+147) {
		tmp = t_1;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * -y)
	tmp = 0
	if z <= -0.043:
		tmp = t_1
	elif z <= 2.5e-18:
		tmp = (x / t) / y
	elif z <= 8.5e+147:
		tmp = t_1
	else:
		tmp = x / (z * -t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * Float64(-y)))
	tmp = 0.0
	if (z <= -0.043)
		tmp = t_1;
	elseif (z <= 2.5e-18)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 8.5e+147)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	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 * -y);
	tmp = 0.0;
	if (z <= -0.043)
		tmp = t_1;
	elseif (z <= 2.5e-18)
		tmp = (x / t) / y;
	elseif (z <= 8.5e+147)
		tmp = t_1;
	else
		tmp = x / (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.043], t$95$1, If[LessEqual[z, 2.5e-18], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 8.5e+147], t$95$1, N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.042999999999999997 or 2.50000000000000018e-18 < z < 8.5000000000000007e147

   1. Initial program 86.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. neg-mul-1 80.9%

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

   7. Simplified 80.9%

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

   8. Taylor expanded in z around 0 42.0%

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

      1. associate-*r/ 42.0%

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

      2. mul-1-neg 42.0%

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

      3. *-commutative 42.0%

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

   10. Simplified 42.0%

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

   if -0.042999999999999997 < z < 2.50000000000000018e-18

   1. Initial program 94.2%

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

      1. associate-/l/ 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 93.0%

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

      2. associate-/r/ 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around 0 67.9%

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

      1. associate-/r* 69.9%

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

   9. Simplified 69.9%

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

   if 8.5000000000000007e147 < z

   1. Initial program 74.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 58.9%

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

   6. Taylor expanded in y around 0 56.0%

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

      1. associate-*r/ 56.0%

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

      2. mul-1-neg 56.0%

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

      3. *-commutative 56.0%

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

   8. Simplified 56.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.043:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+147}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 45.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot y}\\ \mathbf{if}\;z \leq -21:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+148}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z y))))
   (if (<= z -21.0)
     t_1
     (if (<= z 6e+45) (/ x (* t y)) (if (<= z 1.15e+148) 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 / (z * y);
	double tmp;
	if (z <= -21.0) {
		tmp = t_1;
	} else if (z <= 6e+45) {
		tmp = x / (t * y);
	} else if (z <= 1.15e+148) {
		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 / (z * y)
    if (z <= (-21.0d0)) then
        tmp = t_1
    else if (z <= 6d+45) then
        tmp = x / (t * y)
    else if (z <= 1.15d+148) 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 / (z * y);
	double tmp;
	if (z <= -21.0) {
		tmp = t_1;
	} else if (z <= 6e+45) {
		tmp = x / (t * y);
	} else if (z <= 1.15e+148) {
		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 / (z * y)
	tmp = 0
	if z <= -21.0:
		tmp = t_1
	elif z <= 6e+45:
		tmp = x / (t * y)
	elif z <= 1.15e+148:
		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(z * y))
	tmp = 0.0
	if (z <= -21.0)
		tmp = t_1;
	elseif (z <= 6e+45)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 1.15e+148)
		tmp = t_1;
	else
		tmp = 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)
	t_1 = x / (z * y);
	tmp = 0.0;
	if (z <= -21.0)
		tmp = t_1;
	elseif (z <= 6e+45)
		tmp = x / (t * y);
	elseif (z <= 1.15e+148)
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -21.0], t$95$1, If[LessEqual[z, 6e+45], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+148], t$95$1, N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -21 or 6.00000000000000021e45 < z < 1.15e148

   1. Initial program 85.1%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. neg-mul-1 85.1%

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

   7. Simplified 85.1%

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

   8. Taylor expanded in z around 0 44.6%

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

      1. associate-*r/ 44.6%

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

      2. mul-1-neg 44.6%

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

      3. *-commutative 44.6%

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

   10. Simplified 44.6%

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

       1. div-inv 44.6%

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

       2. add-sqr-sqrt 26.3%

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

       3. sqrt-unprod 44.8%

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

       4. sqr-neg 44.8%

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

       5. sqrt-unprod 13.7%

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

       6. add-sqr-sqrt 35.6%

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

       7. *-commutative 35.6%

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

   12. Applied egg-rr 35.6%

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

       1. associate-*r/ 35.6%

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

       2. *-commutative 35.6%

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

       3. *-rgt-identity 35.6%

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

   14. Simplified 35.6%

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

   if -21 < z < 6.00000000000000021e45

   1. Initial program 94.1%

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

   3. Taylor expanded in z around 0 63.2%

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

   if 1.15e148 < z

   1. Initial program 74.4%

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

   3. Taylor expanded in y around 0 71.5%

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

      1. associate-*r/ 71.5%

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

      2. neg-mul-1 71.5%

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

   5. Simplified 71.5%

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

      1. div-inv 71.5%

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

      2. add-sqr-sqrt 36.7%

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

      3. sqrt-unprod 64.3%

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

      4. sqr-neg 64.3%

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

      5. sqrt-unprod 34.8%

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

      6. add-sqr-sqrt 71.5%

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

   7. Applied egg-rr 71.5%

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

      1. associate-*r/ 71.5%

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

      2. *-rgt-identity 71.5%

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

   9. Simplified 71.5%

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

   10. Taylor expanded in z around 0 55.9%

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

Alternative 9: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-72)
   (/ (/ x y) (- t z))
   (if (<= y 2.1e-204) (/ x (* z (- z t))) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-72) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.1e-204) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9d-72)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.1d-204) then
        tmp = x / (z * (z - t))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-72) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.1e-204) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -9e-72:
		tmp = (x / y) / (t - z)
	elif y <= 2.1e-204:
		tmp = x / (z * (z - t))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-72)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.1e-204)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e-72)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.1e-204)
		tmp = x / (z * (z - t));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -9e-72], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-204], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e-72

   1. Initial program 86.7%

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

   3. Taylor expanded in x around 0 86.7%

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

      1. associate-/l/ 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in y around inf 84.3%

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

   if -9e-72 < y < 2.10000000000000009e-204

   1. Initial program 92.5%

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

   3. Taylor expanded in y around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. neg-mul-1 82.8%

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

   5. Simplified 82.8%

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

   if 2.10000000000000009e-204 < y

   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 62.6%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-204}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 -5.1e-79)
   (/ (/ x y) t)
   (if (<= t 7e-86) (/ (/ (- 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 <= -5.1e-79) {
		tmp = (x / y) / t;
	} else if (t <= 7e-86) {
		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 <= (-5.1d-79)) then
        tmp = (x / y) / t
    else if (t <= 7d-86) 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 <= -5.1e-79) {
		tmp = (x / y) / t;
	} else if (t <= 7e-86) {
		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 <= -5.1e-79:
		tmp = (x / y) / t
	elif t <= 7e-86:
		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 <= -5.1e-79)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 7e-86)
		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 <= -5.1e-79)
		tmp = (x / y) / t;
	elseif (t <= 7e-86)
		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, -5.1e-79], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 7e-86], 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 < -5.0999999999999999e-79

   1. Initial program 86.7%

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

   3. Taylor expanded in z around 0 58.7%

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

      1. div-inv 58.7%

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

      2. associate-/r* 57.7%

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

   5. Applied egg-rr 57.7%

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

      1. *-commutative 57.7%

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

      2. associate-*l/ 60.7%

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

      3. associate-*r/ 60.6%

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

      4. associate-*l/ 60.6%

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

      5. *-lft-identity 60.6%

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

   7. Simplified 60.6%

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

   if -5.0999999999999999e-79 < t < 7.00000000000000041e-86

   1. Initial program 93.9%

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

      1. associate-/l/ 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in t around 0 80.4%

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

      1. associate-*r/ 80.4%

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

      2. neg-mul-1 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in z around 0 51.7%

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

      1. associate-*r/ 51.7%

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

      2. mul-1-neg 51.7%

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

      3. *-commutative 51.7%

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

   10. Simplified 51.7%

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

       1. neg-mul-1 51.7%

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

       2. *-commutative 51.7%

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

       3. times-frac 55.8%

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

   12. Applied egg-rr 55.8%

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

       1. associate-*l/ 55.9%

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

       2. associate-*r/ 55.9%

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

       3. associate-*l/ 55.9%

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

       4. *-commutative 55.9%

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

       5. frac-2neg 55.9%

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

       6. metadata-eval 55.9%

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

       7. un-div-inv 55.9%

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

   14. Applied egg-rr 55.9%

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

   if 7.00000000000000041e-86 < t

   1. Initial program 84.8%

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

   3. Taylor expanded in t around inf 74.9%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.029 \lor \neg \left(z \leq 5.2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -0.029) (not (<= z 5.2e-19))) (/ (/ (- 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 <= -0.029) || !(z <= 5.2e-19)) {
		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 <= (-0.029d0)) .or. (.not. (z <= 5.2d-19))) 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 <= -0.029) || !(z <= 5.2e-19)) {
		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 <= -0.029) or not (z <= 5.2e-19):
		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 <= -0.029) || !(z <= 5.2e-19))
		tmp = Float64(Float64(Float64(-x) / 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 <= -0.029) || ~((z <= 5.2e-19)))
		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, -0.029], N[Not[LessEqual[z, 5.2e-19]], $MachinePrecision]], N[(N[((-x) / z), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0290000000000000015 or 5.20000000000000026e-19 < z

   1. Initial program 83.6%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 82.7%

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

      1. associate-*r/ 82.7%

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

      2. neg-mul-1 82.7%

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

   7. Simplified 82.7%

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

   8. Taylor expanded in z around 0 41.7%

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

      1. associate-*r/ 41.7%

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

      2. mul-1-neg 41.7%

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

      3. *-commutative 41.7%

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

   10. Simplified 41.7%

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

       1. neg-mul-1 41.7%

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

       2. *-commutative 41.7%

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

       3. times-frac 49.3%

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

   12. Applied egg-rr 49.3%

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

       1. associate-*l/ 49.3%

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

       2. associate-*r/ 49.3%

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

       3. associate-*l/ 49.3%

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

       4. *-commutative 49.3%

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

       5. frac-2neg 49.3%

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

       6. metadata-eval 49.3%

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

       7. un-div-inv 49.3%

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

   14. Applied egg-rr 49.3%

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

   if -0.0290000000000000015 < z < 5.20000000000000026e-19

   1. Initial program 94.2%

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

      1. associate-/l/ 94.6%

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

   3. Simplified 94.6%

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

      1. clear-num 93.0%

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

      2. associate-/r/ 94.5%

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

   6. Applied egg-rr 94.5%

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

   7. Taylor expanded in z around 0 67.9%

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

      1. associate-/r* 69.9%

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

   9. Simplified 69.9%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.029 \lor \neg \left(z \leq 5.2 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.56e+31)
   (/ x (* z y))
   (if (<= z 2.2e+87) (/ (/ x y) t) (/ x (* z (- t))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.56e+31) {
		tmp = x / (z * y);
	} else if (z <= 2.2e+87) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.56d+31)) then
        tmp = x / (z * y)
    else if (z <= 2.2d+87) then
        tmp = (x / y) / t
    else
        tmp = x / (z * -t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.56e+31) {
		tmp = x / (z * y);
	} else if (z <= 2.2e+87) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.56e+31:
		tmp = x / (z * y)
	elif z <= 2.2e+87:
		tmp = (x / y) / t
	else:
		tmp = x / (z * -t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.56e+31)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 2.2e+87)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.56e+31)
		tmp = x / (z * y);
	elseif (z <= 2.2e+87)
		tmp = (x / y) / t;
	else
		tmp = x / (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -1.56e+31], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+87], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.56000000000000004e31

   1. Initial program 86.1%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 88.1%

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

      1. associate-*r/ 88.1%

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

      2. neg-mul-1 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in z around 0 38.9%

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

      1. associate-*r/ 38.9%

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

      2. mul-1-neg 38.9%

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

      3. *-commutative 38.9%

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

   10. Simplified 38.9%

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

       1. div-inv 38.9%

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

       2. add-sqr-sqrt 30.0%

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

       3. sqrt-unprod 43.4%

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

       4. sqr-neg 43.4%

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

       5. sqrt-unprod 6.7%

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

       6. add-sqr-sqrt 35.1%

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

       7. *-commutative 35.1%

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

   12. Applied egg-rr 35.1%

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

       1. associate-*r/ 35.1%

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

       2. *-commutative 35.1%

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

       3. *-rgt-identity 35.1%

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

   14. Simplified 35.1%

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

   if -1.56000000000000004e31 < z < 2.2000000000000001e87

   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 57.7%

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

      1. div-inv 57.6%

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

      2. associate-/r* 57.9%

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

   5. Applied egg-rr 57.9%

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

      1. *-commutative 57.9%

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

      2. associate-*l/ 62.2%

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

      3. associate-*r/ 63.0%

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

      4. associate-*l/ 63.1%

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

      5. *-lft-identity 63.1%

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

   7. Simplified 63.1%

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

   if 2.2000000000000001e87 < z

   1. Initial program 78.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 52.7%

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

   6. Taylor expanded in y around 0 46.2%

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

      1. associate-*r/ 46.2%

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

      2. mul-1-neg 46.2%

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

      3. *-commutative 46.2%

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

   8. Simplified 46.2%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+35} \lor \neg \left(z \leq 3.8 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e+35) (not (<= z 3.8e+135))) (/ x (* t z)) (/ x (* t y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e+35) || !(z <= 3.8e+135)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.4d+35)) .or. (.not. (z <= 3.8d+135))) then
        tmp = x / (t * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e+35) || !(z <= 3.8e+135)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e+35) or not (z <= 3.8e+135):
		tmp = x / (t * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e+35) || !(z <= 3.8e+135))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.4e+35) || ~((z <= 3.8e+135)))
		tmp = x / (t * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e+35], N[Not[LessEqual[z, 3.8e+135]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000015e35 or 3.8000000000000001e135 < z

   1. Initial program 81.8%

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

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

      1. div-inv 76.8%

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

      2. add-sqr-sqrt 48.6%

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

      3. sqrt-unprod 65.2%

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

      4. sqr-neg 65.2%

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

      5. sqrt-unprod 24.2%

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

      6. add-sqr-sqrt 68.4%

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

   7. Applied egg-rr 68.4%

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

      1. associate-*r/ 68.4%

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

      2. *-rgt-identity 68.4%

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

   9. Simplified 68.4%

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

   10. Taylor expanded in z around 0 46.7%

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

   if -2.40000000000000015e35 < z < 3.8000000000000001e135

   1. Initial program 92.0%

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

   3. Taylor expanded in z around 0 54.5%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+35} \lor \neg \left(z \leq 3.8 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.7 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \end{array} \]

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 (<= z -7.7e+31)
   (/ x (* z y))
   (if (<= z 1.95e+136) (/ (/ 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 (z <= -7.7e+31) {
		tmp = x / (z * y);
	} else if (z <= 1.95e+136) {
		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 (z <= (-7.7d+31)) then
        tmp = x / (z * y)
    else if (z <= 1.95d+136) 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 (z <= -7.7e+31) {
		tmp = x / (z * y);
	} else if (z <= 1.95e+136) {
		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 z <= -7.7e+31:
		tmp = x / (z * y)
	elif z <= 1.95e+136:
		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 (z <= -7.7e+31)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 1.95e+136)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = 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 (z <= -7.7e+31)
		tmp = x / (z * y);
	elseif (z <= 1.95e+136)
		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[LessEqual[z, -7.7e+31], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+136], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.69999999999999967e31

   1. Initial program 86.1%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 88.1%

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

      1. associate-*r/ 88.1%

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

      2. neg-mul-1 88.1%

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

   7. Simplified 88.1%

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

   8. Taylor expanded in z around 0 38.9%

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

      1. associate-*r/ 38.9%

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

      2. mul-1-neg 38.9%

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

      3. *-commutative 38.9%

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

   10. Simplified 38.9%

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

       1. div-inv 38.9%

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

       2. add-sqr-sqrt 30.0%

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

       3. sqrt-unprod 43.4%

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

       4. sqr-neg 43.4%

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

       5. sqrt-unprod 6.7%

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

       6. add-sqr-sqrt 35.1%

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

       7. *-commutative 35.1%

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

   12. Applied egg-rr 35.1%

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

       1. associate-*r/ 35.1%

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

       2. *-commutative 35.1%

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

       3. *-rgt-identity 35.1%

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

   14. Simplified 35.1%

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

   if -7.69999999999999967e31 < z < 1.9500000000000001e136

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 54.8%

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

      1. div-inv 54.7%

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

      2. associate-/r* 55.0%

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

   5. Applied egg-rr 55.0%

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

      1. *-commutative 55.0%

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

      2. associate-*l/ 59.5%

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

      3. associate-*r/ 61.0%

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

      4. associate-*l/ 61.1%

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

      5. *-lft-identity 61.1%

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

   7. Simplified 61.1%

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

   if 1.9500000000000001e136 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in y around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. neg-mul-1 73.1%

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

   5. Simplified 73.1%

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

      1. div-inv 73.1%

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

      2. add-sqr-sqrt 40.4%

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

      3. sqrt-unprod 66.4%

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

      4. sqr-neg 66.4%

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

      5. sqrt-unprod 32.8%

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

      6. add-sqr-sqrt 73.1%

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

   7. Applied egg-rr 73.1%

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

      1. associate-*r/ 73.1%

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

      2. *-rgt-identity 73.1%

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

   9. Simplified 73.1%

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

   10. Taylor expanded in z around 0 55.7%

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

Alternative 15: 47.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -29:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+136}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \end{array} \end{array} \]

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 (<= z -29.0)
   (/ x (* z y))
   (if (<= z 1.95e+136) (/ (/ x t) y) (/ x (* t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -29.0) {
		tmp = x / (z * y);
	} else if (z <= 1.95e+136) {
		tmp = (x / t) / y;
	} 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 (z <= (-29.0d0)) then
        tmp = x / (z * y)
    else if (z <= 1.95d+136) then
        tmp = (x / t) / y
    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 (z <= -29.0) {
		tmp = x / (z * y);
	} else if (z <= 1.95e+136) {
		tmp = (x / t) / y;
	} 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 z <= -29.0:
		tmp = x / (z * y)
	elif z <= 1.95e+136:
		tmp = (x / t) / y
	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 (z <= -29.0)
		tmp = Float64(x / Float64(z * y));
	elseif (z <= 1.95e+136)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = 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 (z <= -29.0)
		tmp = x / (z * y);
	elseif (z <= 1.95e+136)
		tmp = (x / t) / y;
	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[z, -29.0], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+136], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -29

   1. Initial program 86.1%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 86.3%

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

      1. associate-*r/ 86.3%

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

      2. neg-mul-1 86.3%

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

   7. Simplified 86.3%

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

   8. Taylor expanded in z around 0 39.6%

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

      1. associate-*r/ 39.6%

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

      2. mul-1-neg 39.6%

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

      3. *-commutative 39.6%

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

   10. Simplified 39.6%

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

       1. div-inv 39.6%

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

       2. add-sqr-sqrt 28.3%

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

       3. sqrt-unprod 41.8%

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

       4. sqr-neg 41.8%

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

       5. sqrt-unprod 6.0%

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

       6. add-sqr-sqrt 31.3%

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

       7. *-commutative 31.3%

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

   12. Applied egg-rr 31.3%

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

       1. associate-*r/ 31.3%

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

       2. *-commutative 31.3%

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

       3. *-rgt-identity 31.3%

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

   14. Simplified 31.3%

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

   if -29 < z < 1.9500000000000001e136

   1. Initial program 92.1%

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

      1. associate-/l/ 96.0%

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

   3. Simplified 96.0%

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

      1. clear-num 94.8%

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

      2. associate-/r/ 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in z around 0 57.0%

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

      1. associate-/r* 60.8%

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

   9. Simplified 60.8%

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

   if 1.9500000000000001e136 < z

   1. Initial program 75.9%

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

   3. Taylor expanded in y around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. neg-mul-1 73.1%

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

   5. Simplified 73.1%

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

      1. div-inv 73.1%

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

      2. add-sqr-sqrt 40.4%

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

      3. sqrt-unprod 66.4%

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

      4. sqr-neg 66.4%

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

      5. sqrt-unprod 32.8%

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

      6. add-sqr-sqrt 73.1%

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

   7. Applied egg-rr 73.1%

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

      1. associate-*r/ 73.1%

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

      2. *-rgt-identity 73.1%

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

   9. Simplified 73.1%

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

   10. Taylor expanded in z around 0 55.7%

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

Alternative 16: 71.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.72 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.72e+37) (/ 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 <= 1.72e+37) {
		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 <= 1.72d+37) 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 <= 1.72e+37) {
		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 <= 1.72e+37:
		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 <= 1.72e+37)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.72e+37)
		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, 1.72e+37], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.72000000000000002e37

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 66.8%

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

      1. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   if 1.72000000000000002e37 < t

   1. Initial program 81.8%

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

      1. associate-/l/ 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 94.4%

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

Alternative 17: 70.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.28 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 1.28e-23) (/ 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 <= 1.28e-23) {
		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 <= 1.28d-23) 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 <= 1.28e-23) {
		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 <= 1.28e-23:
		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 <= 1.28e-23)
		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 <= 1.28e-23)
		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, 1.28e-23], 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 < 1.28000000000000005e-23

   1. Initial program 90.8%

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

   3. Taylor expanded in y around inf 67.1%

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

      1. *-commutative 67.1%

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

   5. Simplified 67.1%

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

   if 1.28000000000000005e-23 < t

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf 76.4%

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

Alternative 18: 39.2% 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 88.6%

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

3. Taylor expanded in z around 0 44.2%

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

Developer target: 87.1% 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 2024090 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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