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

Percentage Accurate: 89.3% → 96.7%

Time: 12.4s

Alternatives: 15

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.3% 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, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (/ (* (/ 1.0 (- y z)) x) (- t z)))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((1.0d0 / (y - z)) * x) / (t - z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

   1. associate-/l/ 98.3%

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

   2. clear-num 97.9%

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

   3. inv-pow 97.9%

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

   4. div-inv 97.8%

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

   5. clear-num 98.2%

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

4. Applied egg-rr 98.2%

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

   1. unpow-1 98.2%

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

6. Simplified 98.2%

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

   1. clear-num 97.8%

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

   2. associate-/r/ 98.1%

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

8. Applied egg-rr 98.1%

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

   1. *-un-lft-identity 98.1%

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

   2. associate-/r* 98.5%

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

   3. associate-*l/ 98.5%

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

   4. *-un-lft-identity 98.5%

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

   5. associate-/r/ 90.8%

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

10. Applied egg-rr 90.8%

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

    1. *-lft-identity 90.8%

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

    2. associate-*l/ 96.8%

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

12. Simplified 96.8%

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

Alternative 2: 97.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-210}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -1e-210) t_1 (/ (/ x (- t z)) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -1e-210) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-1d-210)) then
        tmp = t_1
    else
        tmp = (x / (t - z)) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -1e-210) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -1e-210:
		tmp = t_1
	else:
		tmp = (x / (t - z)) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -1e-210)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -1e-210)
		tmp = t_1;
	else
		tmp = (x / (t - z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-210], t$95$1, N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -1e-210

   1. Initial program 97.3%

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

   if -1e-210 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 88.7%

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

      1. associate-/l/ 98.4%

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

   3. Simplified 98.4%

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

Alternative 3: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-110} \lor \neg \left(z \leq 5.1 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-110) (not (<= z 5.1e-70)))
   (/ x (* z (- z t)))
   (/ (/ x y) t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-110) || !(z <= 5.1e-70)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.65d-110)) .or. (.not. (z <= 5.1d-70))) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-110) || !(z <= 5.1e-70)) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e-110) or not (z <= 5.1e-70):
		tmp = x / (z * (z - t))
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-110) || !(z <= 5.1e-70))
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e-110) || ~((z <= 5.1e-70)))
		tmp = x / (z * (z - t));
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-110], N[Not[LessEqual[z, 5.1e-70]], $MachinePrecision]], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e-110 or 5.10000000000000025e-70 < z

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-rgt-neg-in 72.3%

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

      3. sub-neg 72.3%

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

      4. +-commutative 72.3%

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

      5. distribute-neg-in 72.3%

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

      6. remove-double-neg 72.3%

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

      7. unsub-neg 72.3%

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

   5. Simplified 72.3%

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

   if -1.65e-110 < z < 5.10000000000000025e-70

   1. Initial program 92.4%

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

   3. Taylor expanded in y around inf 83.1%

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

      1. associate-/r* 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in t around inf 74.6%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-110} \lor \neg \left(z \leq 5.1 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-132}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -2.7e-132)
   (/ (/ x y) (- t z))
   (if (<= t 1.45e-64) (/ (/ x z) (- 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 <= -2.7e-132) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.45e-64) {
		tmp = (x / z) / (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 <= (-2.7d-132)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.45d-64) then
        tmp = (x / z) / (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 <= -2.7e-132) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.45e-64) {
		tmp = (x / z) / (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 <= -2.7e-132:
		tmp = (x / y) / (t - z)
	elif t <= 1.45e-64:
		tmp = (x / z) / (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 <= -2.7e-132)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.45e-64)
		tmp = Float64(Float64(x / z) / Float64(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 <= -2.7e-132)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.45e-64)
		tmp = (x / z) / (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, -2.7e-132], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.45e-64], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999999e-132

   1. Initial program 86.0%

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

   3. Taylor expanded in y around inf 64.8%

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

      1. associate-/r* 68.8%

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

   5. Simplified 68.8%

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

   if -2.6999999999999999e-132 < t < 1.4499999999999999e-64

   1. Initial program 91.9%

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

   3. Taylor expanded in t around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. associate-/r* 84.3%

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

      3. distribute-neg-frac2 84.3%

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

      4. neg-sub0 84.3%

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

      5. sub-neg 84.3%

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

      6. +-commutative 84.3%

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

      7. associate--r+ 84.3%

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

      8. neg-sub0 84.3%

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

      9. remove-double-neg 84.3%

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

   5. Simplified 84.3%

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

   if 1.4499999999999999e-64 < t

   1. Initial program 92.6%

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

      1. associate-/l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around inf 87.7%

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

Alternative 5: 77.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.2e-129)
   (/ (/ x y) (- t z))
   (if (<= y 7.8e-186) (/ 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 <= -6.2e-129) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7.8e-186) {
		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 <= (-6.2d-129)) then
        tmp = (x / y) / (t - z)
    else if (y <= 7.8d-186) 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 <= -6.2e-129) {
		tmp = (x / y) / (t - z);
	} else if (y <= 7.8e-186) {
		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 <= -6.2e-129:
		tmp = (x / y) / (t - z)
	elif y <= 7.8e-186:
		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 <= -6.2e-129)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 7.8e-186)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.2e-129)
		tmp = (x / y) / (t - z);
	elseif (y <= 7.8e-186)
		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, -6.2e-129], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-186], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2000000000000001e-129

   1. Initial program 85.6%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. associate-/r* 74.2%

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

   5. Simplified 74.2%

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

   if -6.2000000000000001e-129 < y < 7.8000000000000002e-186

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-rgt-neg-in 80.5%

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

      3. sub-neg 80.5%

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

      4. +-commutative 80.5%

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

      5. distribute-neg-in 80.5%

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

      6. remove-double-neg 80.5%

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

      7. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   if 7.8000000000000002e-186 < y

   1. Initial program 94.8%

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

      1. associate-/l/ 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around inf 66.0%

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

Alternative 6: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e-130)
   (/ x (* y (- t z)))
   (if (<= y 8e-186) (/ 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 <= -9.5e-130) {
		tmp = x / (y * (t - z));
	} else if (y <= 8e-186) {
		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 <= (-9.5d-130)) then
        tmp = x / (y * (t - z))
    else if (y <= 8d-186) 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 <= -9.5e-130) {
		tmp = x / (y * (t - z));
	} else if (y <= 8e-186) {
		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 <= -9.5e-130:
		tmp = x / (y * (t - z))
	elif y <= 8e-186:
		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 <= -9.5e-130)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 8e-186)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.5e-130)
		tmp = x / (y * (t - z));
	elseif (y <= 8e-186)
		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, -9.5e-130], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-186], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999962e-130

   1. Initial program 85.6%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   if -9.49999999999999962e-130 < y < 7.9999999999999993e-186

   1. Initial program 91.2%

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

   3. Taylor expanded in y around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. distribute-rgt-neg-in 80.5%

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

      3. sub-neg 80.5%

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

      4. +-commutative 80.5%

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

      5. distribute-neg-in 80.5%

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

      6. remove-double-neg 80.5%

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

      7. unsub-neg 80.5%

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

   5. Simplified 80.5%

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

   if 7.9999999999999993e-186 < y

   1. Initial program 94.8%

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

      1. associate-/l/ 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around inf 66.0%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{t}}{\frac{y}{x}}\\ \end{array} \end{array} \]

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 -6.2e-129)
   (/ x (* y (- t z)))
   (if (<= y 2.9e-41) (/ x (* z (- z t))) (/ (/ 1.0 t) (/ y x)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.2e-129) {
		tmp = x / (y * (t - z));
	} else if (y <= 2.9e-41) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (1.0 / t) / (y / x);
	}
	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 <= (-6.2d-129)) then
        tmp = x / (y * (t - z))
    else if (y <= 2.9d-41) then
        tmp = x / (z * (z - t))
    else
        tmp = (1.0d0 / t) / (y / x)
    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 <= -6.2e-129) {
		tmp = x / (y * (t - z));
	} else if (y <= 2.9e-41) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (1.0 / t) / (y / x);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -6.2e-129:
		tmp = x / (y * (t - z))
	elif y <= 2.9e-41:
		tmp = x / (z * (z - t))
	else:
		tmp = (1.0 / t) / (y / x)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.2e-129)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 2.9e-41)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(1.0 / t) / Float64(y / x));
	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 <= -6.2e-129)
		tmp = x / (y * (t - z));
	elseif (y <= 2.9e-41)
		tmp = x / (z * (z - t));
	else
		tmp = (1.0 / t) / (y / x);
	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, -6.2e-129], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-41], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / t), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.2000000000000001e-129

   1. Initial program 85.6%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   if -6.2000000000000001e-129 < y < 2.89999999999999977e-41

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. distribute-rgt-neg-in 80.2%

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

      3. sub-neg 80.2%

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

      4. +-commutative 80.2%

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

      5. distribute-neg-in 80.2%

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

      6. remove-double-neg 80.2%

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

      7. unsub-neg 80.2%

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

   5. Simplified 80.2%

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

   if 2.89999999999999977e-41 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 56.2%

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

      1. associate-/r* 58.7%

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

      2. div-inv 58.6%

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

   5. Applied egg-rr 58.6%

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

      1. associate-*l/ 60.6%

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

      2. div-inv 60.7%

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

      3. div-inv 60.6%

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

      4. clear-num 60.6%

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

      5. associate-*l/ 60.6%

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

      6. *-un-lft-identity 60.6%

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

   7. Applied egg-rr 60.6%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{t}}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5e-129)
   (/ x (* y (- t z)))
   (if (<= y 6.5e-47) (/ x (* z (- z t))) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-129) {
		tmp = x / (y * (t - z));
	} else if (y <= 6.5e-47) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5d-129)) then
        tmp = x / (y * (t - z))
    else if (y <= 6.5d-47) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5e-129) {
		tmp = x / (y * (t - z));
	} else if (y <= 6.5e-47) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5e-129:
		tmp = x / (y * (t - z))
	elif y <= 6.5e-47:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5e-129)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 6.5e-47)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5e-129)
		tmp = x / (y * (t - z));
	elseif (y <= 6.5e-47)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -5e-129], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-47], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.00000000000000027e-129

   1. Initial program 85.6%

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

   3. Taylor expanded in y around inf 72.2%

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

      1. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   if -5.00000000000000027e-129 < y < 6.5000000000000004e-47

   1. Initial program 93.6%

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

   3. Taylor expanded in y around 0 80.2%

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

      1. mul-1-neg 80.2%

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

      2. distribute-rgt-neg-in 80.2%

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

      3. sub-neg 80.2%

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

      4. +-commutative 80.2%

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

      5. distribute-neg-in 80.2%

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

      6. remove-double-neg 80.2%

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

      7. unsub-neg 80.2%

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

   5. Simplified 80.2%

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

   if 6.5000000000000004e-47 < y

   1. Initial program 93.1%

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

   3. Taylor expanded in z around 0 56.2%

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

      1. associate-/r* 58.7%

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

      2. div-inv 58.6%

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

   5. Applied egg-rr 58.6%

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

      1. un-div-inv 58.7%

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

   7. Applied egg-rr 58.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.15e-157)
   (/ (/ x y) t)
   (if (<= y 9e-75) (/ x (* z (- t))) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e-157) {
		tmp = (x / y) / t;
	} else if (y <= 9e-75) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.15d-157)) then
        tmp = (x / y) / t
    else if (y <= 9d-75) then
        tmp = x / (z * -t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e-157) {
		tmp = (x / y) / t;
	} else if (y <= 9e-75) {
		tmp = x / (z * -t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.15e-157:
		tmp = (x / y) / t
	elif y <= 9e-75:
		tmp = x / (z * -t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.15e-157)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 9e-75)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.15e-157)
		tmp = (x / y) / t;
	elseif (y <= 9e-75)
		tmp = x / (z * -t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.15e-157], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 9e-75], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1499999999999999e-157

   1. Initial program 85.0%

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

   3. Taylor expanded in y around inf 68.0%

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

      1. associate-/r* 70.7%

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

   5. Simplified 70.7%

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

   6. Taylor expanded in t around inf 54.8%

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

   if -2.1499999999999999e-157 < y < 9.0000000000000006e-75

   1. Initial program 95.1%

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

      1. associate-/l/ 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 52.0%

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

   6. Taylor expanded in y around 0 41.1%

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

      1. associate-*r/ 41.1%

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

      2. neg-mul-1 41.1%

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

      3. *-commutative 41.1%

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

   8. Simplified 41.1%

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

   if 9.0000000000000006e-75 < y

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 54.2%

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

      1. associate-/r* 56.6%

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

      2. div-inv 56.5%

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

   5. Applied egg-rr 56.5%

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

      1. un-div-inv 56.6%

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

   7. Applied egg-rr 56.6%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-75}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+97} \lor \neg \left(z \leq 35000\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.2e+97) (not (<= z 35000.0))) (/ x (* z t)) (/ (/ x y) t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+97) || !(z <= 35000.0)) {
		tmp = x / (z * t);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.2d+97)) .or. (.not. (z <= 35000.0d0))) then
        tmp = x / (z * t)
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.2e+97) || !(z <= 35000.0)) {
		tmp = x / (z * t);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.2e+97) or not (z <= 35000.0):
		tmp = x / (z * t)
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.2e+97) || !(z <= 35000.0))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.2e+97) || ~((z <= 35000.0)))
		tmp = x / (z * t);
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.2e+97], N[Not[LessEqual[z, 35000.0]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000001e97 or 35000 < z

   1. Initial program 85.1%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 39.2%

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

   6. Taylor expanded in y around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. associate-/r* 36.7%

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

      3. distribute-neg-frac2 36.7%

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

   8. Simplified 36.7%

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

      1. add-sqr-sqrt 9.1%

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

      2. sqrt-unprod 50.9%

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

      3. sqr-neg 50.9%

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

      4. sqrt-unprod 25.6%

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

      5. add-sqr-sqrt 34.2%

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

      6. *-un-lft-identity 34.2%

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

      7. associate-/l/ 35.2%

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

      8. *-commutative 35.2%

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

   10. Applied egg-rr 35.2%

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

       1. *-lft-identity 35.2%

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

       2. *-commutative 35.2%

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

   12. Simplified 35.2%

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

   if -2.2000000000000001e97 < z < 35000

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf 72.6%

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

      1. associate-/r* 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in t around inf 61.3%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+97} \lor \neg \left(z \leq 35000\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+98} \lor \neg \left(z \leq 3.8 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+98) (not (<= z 3.8e+85))) (/ x (* z t)) (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+98) || !(z <= 3.8e+85)) {
		tmp = x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.8d+98)) .or. (.not. (z <= 3.8d+85))) then
        tmp = x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+98) || !(z <= 3.8e+85)) {
		tmp = x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+98) or not (z <= 3.8e+85):
		tmp = x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+98) || !(z <= 3.8e+85))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e+98) || ~((z <= 3.8e+85)))
		tmp = x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e+98], N[Not[LessEqual[z, 3.8e+85]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7999999999999999e98 or 3.79999999999999992e85 < z

   1. Initial program 81.9%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 38.5%

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

   6. Taylor expanded in y around 0 37.4%

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

      1. mul-1-neg 37.4%

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

      2. associate-/r* 36.7%

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

      3. distribute-neg-frac2 36.7%

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

   8. Simplified 36.7%

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

      1. add-sqr-sqrt 11.1%

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

      2. sqrt-unprod 56.5%

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

      3. sqr-neg 56.5%

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

      4. sqrt-unprod 25.6%

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

      5. add-sqr-sqrt 36.2%

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

      6. *-un-lft-identity 36.2%

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

      7. associate-/l/ 37.3%

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

      8. *-commutative 37.3%

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

   10. Applied egg-rr 37.3%

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

       1. *-lft-identity 37.3%

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

       2. *-commutative 37.3%

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

   12. Simplified 37.3%

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

   if -1.7999999999999999e98 < z < 3.79999999999999992e85

   1. Initial program 94.6%

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

   3. Taylor expanded in z around 0 51.5%

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

      1. associate-/r* 57.8%

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

      2. div-inv 57.8%

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

   5. Applied egg-rr 57.8%

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

      1. un-div-inv 57.8%

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

   7. Applied egg-rr 57.8%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+98} \lor \neg \left(z \leq 3.8 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 44.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+97} \lor \neg \left(z \leq 1.96 \cdot 10^{-66}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.4e+97) (not (<= z 1.96e-66))) (/ x (* z t)) (/ x (* y t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e+97) || !(z <= 1.96e-66)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.4d+97)) .or. (.not. (z <= 1.96d-66))) then
        tmp = x / (z * t)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.4e+97) || !(z <= 1.96e-66)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.4e+97) or not (z <= 1.96e-66):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.4e+97) || !(z <= 1.96e-66))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.4e+97) || ~((z <= 1.96e-66)))
		tmp = x / (z * t);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.4e+97], N[Not[LessEqual[z, 1.96e-66]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e97 or 1.95999999999999997e-66 < z

   1. Initial program 86.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 41.6%

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

   6. Taylor expanded in y around 0 39.2%

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

      1. mul-1-neg 39.2%

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

      2. associate-/r* 38.7%

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

      3. distribute-neg-frac2 38.7%

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

   8. Simplified 38.7%

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

      1. add-sqr-sqrt 7.6%

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

      2. sqrt-unprod 48.1%

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

      3. sqr-neg 48.1%

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

      4. sqrt-unprod 26.8%

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

      5. add-sqr-sqrt 34.1%

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

      6. *-un-lft-identity 34.1%

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

      7. associate-/l/ 34.9%

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

      8. *-commutative 34.9%

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

   10. Applied egg-rr 34.9%

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

       1. *-lft-identity 34.9%

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

       2. *-commutative 34.9%

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

   12. Simplified 34.9%

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

   if -2.4e97 < z < 1.95999999999999997e-66

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0 59.6%

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

4. Final simplification 48.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+97} \lor \neg \left(z \leq 1.96 \cdot 10^{-66}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 91.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -7.4e+105) (/ (* x (/ -1.0 z)) (- t z)) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.4e+105) {
		tmp = (x * (-1.0 / z)) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-7.4d+105)) then
        tmp = (x * ((-1.0d0) / z)) / (t - z)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -7.4e+105) {
		tmp = (x * (-1.0 / z)) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -7.4e+105:
		tmp = (x * (-1.0 / z)) / (t - z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -7.4e+105)
		tmp = Float64(Float64(x * Float64(-1.0 / z)) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -7.4e+105)
		tmp = (x * (-1.0 / z)) / (t - z);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -7.4e+105], N[(N[(x * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.3999999999999997e105

   1. Initial program 67.4%

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

      1. associate-/l/ 99.8%

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

      2. clear-num 97.7%

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

      3. inv-pow 97.7%

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

      4. div-inv 97.6%

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

      5. clear-num 97.7%

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

   4. Applied egg-rr 97.7%

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

      1. unpow-1 97.7%

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

   6. Simplified 97.7%

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

      1. clear-num 97.6%

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

      2. associate-/r/ 97.6%

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

   8. Applied egg-rr 97.6%

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

      1. *-un-lft-identity 97.6%

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

      2. associate-/r* 99.7%

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

      3. associate-*l/ 99.7%

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

      4. *-un-lft-identity 99.7%

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

      5. associate-/r/ 69.8%

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

   10. Applied egg-rr 69.8%

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

       1. *-lft-identity 69.8%

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

       2. associate-*l/ 99.7%

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

   12. Simplified 99.7%

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

   13. Taylor expanded in y around 0 87.1%

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

   if -7.3999999999999997e105 < z

   1. Initial program 94.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot \frac{-1}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 91.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+143}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -5e+143) (/ (/ x z) (- z y)) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+143) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5d+143)) then
        tmp = (x / z) / (z - y)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5e+143) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -5e+143:
		tmp = (x / z) / (z - y)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5e+143)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5e+143)
		tmp = (x / z) / (z - y);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -5e+143], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.00000000000000012e143

   1. Initial program 65.5%

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

   3. Taylor expanded in t around 0 65.5%

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

      1. mul-1-neg 65.5%

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

      2. associate-/r* 95.3%

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

      3. distribute-neg-frac2 95.3%

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

      4. neg-sub0 95.3%

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

      5. sub-neg 95.3%

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

      6. +-commutative 95.3%

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

      7. associate--r+ 95.3%

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

      8. neg-sub0 95.3%

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

      9. remove-double-neg 95.3%

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

   5. Simplified 95.3%

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

   if -5.00000000000000012e143 < z

   1. Initial program 93.9%

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

Alternative 15: 38.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.6%

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

3. Taylor expanded in z around 0 41.6%

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

4. Final simplification 41.6%

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

Developer Target 1: 88.2% 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 2024181 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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