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

Percentage Accurate: 88.5% → 96.9%

Time: 13.1s

Alternatives: 20

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: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.4%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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. Final simplification 97.7%

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

Alternative 2: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-156}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+270} \lor \neg \left(t \leq 4.1 \cdot 10^{+304}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)))
   (if (<= t -2.1e-168)
     t_1
     (if (<= t 2.15e-156)
       (/ (- x) (* z y))
       (if (<= t 1.6e-8)
         (/ (/ x y) t)
         (if (or (<= t 3.35e+270) (not (<= t 4.1e+304)))
           (/ (/ x t) (- z))
           t_1))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -2.1e-168) {
		tmp = t_1;
	} else if (t <= 2.15e-156) {
		tmp = -x / (z * y);
	} else if (t <= 1.6e-8) {
		tmp = (x / y) / t;
	} else if ((t <= 3.35e+270) || !(t <= 4.1e+304)) {
		tmp = (x / t) / -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / y
    if (t <= (-2.1d-168)) then
        tmp = t_1
    else if (t <= 2.15d-156) then
        tmp = -x / (z * y)
    else if (t <= 1.6d-8) then
        tmp = (x / y) / t
    else if ((t <= 3.35d+270) .or. (.not. (t <= 4.1d+304))) then
        tmp = (x / t) / -z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -2.1e-168) {
		tmp = t_1;
	} else if (t <= 2.15e-156) {
		tmp = -x / (z * y);
	} else if (t <= 1.6e-8) {
		tmp = (x / y) / t;
	} else if ((t <= 3.35e+270) || !(t <= 4.1e+304)) {
		tmp = (x / t) / -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	tmp = 0
	if t <= -2.1e-168:
		tmp = t_1
	elif t <= 2.15e-156:
		tmp = -x / (z * y)
	elif t <= 1.6e-8:
		tmp = (x / y) / t
	elif (t <= 3.35e+270) or not (t <= 4.1e+304):
		tmp = (x / t) / -z
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (t <= -2.1e-168)
		tmp = t_1;
	elseif (t <= 2.15e-156)
		tmp = Float64(Float64(-x) / Float64(z * y));
	elseif (t <= 1.6e-8)
		tmp = Float64(Float64(x / y) / t);
	elseif ((t <= 3.35e+270) || !(t <= 4.1e+304))
		tmp = Float64(Float64(x / t) / Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	tmp = 0.0;
	if (t <= -2.1e-168)
		tmp = t_1;
	elseif (t <= 2.15e-156)
		tmp = -x / (z * y);
	elseif (t <= 1.6e-8)
		tmp = (x / y) / t;
	elseif ((t <= 3.35e+270) || ~((t <= 4.1e+304)))
		tmp = (x / t) / -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.1e-168], t$95$1, If[LessEqual[t, 2.15e-156], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.6e-8], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[t, 3.35e+270], N[Not[LessEqual[t, 4.1e+304]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.09999999999999994e-168 or 3.35e270 < t < 4.09999999999999985e304

   1. Initial program 84.8%

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

   3. Taylor expanded in z around 0 49.8%

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

      1. associate-/r* 56.2%

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

      2. div-inv 56.2%

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

   5. Applied egg-rr 56.2%

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

      1. un-div-inv 56.2%

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

   7. Applied egg-rr 56.2%

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

   if -2.09999999999999994e-168 < t < 2.14999999999999989e-156

   1. Initial program 90.3%

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

      1. associate-/r* 97.1%

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

      2. div-inv 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in t around 0 91.3%

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

   6. Taylor expanded in y around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. neg-mul-1 57.4%

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

   8. Simplified 57.4%

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

   if 2.14999999999999989e-156 < t < 1.6000000000000001e-8

   1. Initial program 78.6%

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

   3. Taylor expanded in z around 0 32.3%

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

      1. associate-/r* 32.3%

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

      2. div-inv 32.2%

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

   5. Applied egg-rr 32.2%

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

      1. associate-*l/ 42.2%

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

      2. un-div-inv 42.3%

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

   7. Applied egg-rr 42.3%

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

   if 1.6000000000000001e-8 < t < 3.35e270 or 4.09999999999999985e304 < t

   1. Initial program 69.9%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in t around inf 83.9%

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

   6. Taylor expanded in y around 0 45.9%

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

      1. mul-1-neg 45.9%

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

      2. associate-/r* 56.7%

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

      3. distribute-neg-frac2 56.7%

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

   8. Simplified 56.7%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-156}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 3.35 \cdot 10^{+270} \lor \neg \left(t \leq 4.1 \cdot 10^{+304}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{t \cdot \left(z + y\right)}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+270} \lor \neg \left(t \leq 1.85 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 (<= t -6e-168)
   (* (/ x t) (/ 1.0 y))
   (if (<= t 1.2e-160)
     (/ (- x) (* z y))
     (if (<= t 9.8e+125)
       (/ x (* t (+ z y)))
       (if (or (<= t 1.95e+270) (not (<= t 1.85e+301)))
         (/ (/ 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 (t <= -6e-168) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 1.2e-160) {
		tmp = -x / (z * y);
	} else if (t <= 9.8e+125) {
		tmp = x / (t * (z + y));
	} else if ((t <= 1.95e+270) || !(t <= 1.85e+301)) {
		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 (t <= (-6d-168)) then
        tmp = (x / t) * (1.0d0 / y)
    else if (t <= 1.2d-160) then
        tmp = -x / (z * y)
    else if (t <= 9.8d+125) then
        tmp = x / (t * (z + y))
    else if ((t <= 1.95d+270) .or. (.not. (t <= 1.85d+301))) 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 (t <= -6e-168) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 1.2e-160) {
		tmp = -x / (z * y);
	} else if (t <= 9.8e+125) {
		tmp = x / (t * (z + y));
	} else if ((t <= 1.95e+270) || !(t <= 1.85e+301)) {
		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 t <= -6e-168:
		tmp = (x / t) * (1.0 / y)
	elif t <= 1.2e-160:
		tmp = -x / (z * y)
	elif t <= 9.8e+125:
		tmp = x / (t * (z + y))
	elif (t <= 1.95e+270) or not (t <= 1.85e+301):
		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 (t <= -6e-168)
		tmp = Float64(Float64(x / t) * Float64(1.0 / y));
	elseif (t <= 1.2e-160)
		tmp = Float64(Float64(-x) / Float64(z * y));
	elseif (t <= 9.8e+125)
		tmp = Float64(x / Float64(t * Float64(z + y)));
	elseif ((t <= 1.95e+270) || !(t <= 1.85e+301))
		tmp = Float64(Float64(x / t) / Float64(-z));
	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 (t <= -6e-168)
		tmp = (x / t) * (1.0 / y);
	elseif (t <= 1.2e-160)
		tmp = -x / (z * y);
	elseif (t <= 9.8e+125)
		tmp = x / (t * (z + y));
	elseif ((t <= 1.95e+270) || ~((t <= 1.85e+301)))
		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[LessEqual[t, -6e-168], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-160], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.8e+125], N[(x / N[(t * N[(z + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.95e+270], N[Not[LessEqual[t, 1.85e+301]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.99999999999999983e-168

   1. Initial program 84.4%

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

   3. Taylor expanded in z around 0 46.4%

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

      1. associate-/r* 52.5%

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

      2. div-inv 52.5%

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

   5. Applied egg-rr 52.5%

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

   if -5.99999999999999983e-168 < t < 1.19999999999999995e-160

   1. Initial program 90.3%

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

      1. associate-/r* 97.1%

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

      2. div-inv 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in t around 0 91.3%

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

   6. Taylor expanded in y around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. neg-mul-1 57.4%

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

   8. Simplified 57.4%

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

   if 1.19999999999999995e-160 < t < 9.80000000000000032e125

   1. Initial program 80.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 57.0%

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

      1. div-inv 56.8%

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

      2. associate-/l* 55.1%

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

      3. sub-neg 55.1%

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

      4. add-sqr-sqrt 29.9%

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

      5. sqrt-unprod 57.9%

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

      6. sqr-neg 57.9%

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

      7. sqrt-unprod 20.3%

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

      8. add-sqr-sqrt 46.2%

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

   7. Applied egg-rr 46.2%

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

      1. associate-/r* 44.3%

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

      2. associate-*r/ 44.3%

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

      3. associate-*l/ 44.3%

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

      4. *-rgt-identity 44.3%

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

      5. +-commutative 44.3%

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

   9. Simplified 44.3%

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

   if 9.80000000000000032e125 < t < 1.95e270 or 1.85e301 < t

   1. Initial program 60.7%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in t around inf 85.1%

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

   6. Taylor expanded in y around 0 45.0%

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

      1. mul-1-neg 45.0%

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

      2. associate-/r* 63.4%

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

      3. distribute-neg-frac2 63.4%

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

   8. Simplified 63.4%

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

   if 1.95e270 < t < 1.85e301

   1. Initial program 89.4%

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

   3. Taylor expanded in z around 0 89.4%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. un-div-inv 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+125}:\\ \;\;\;\;\frac{x}{t \cdot \left(z + y\right)}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+270} \lor \neg \left(t \leq 1.85 \cdot 10^{+301}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t}\\ \mathbf{elif}\;t\_1 \leq 10^{+297}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

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))
     (* (/ x (- y z)) (/ 1.0 t))
     (if (<= t_1 1e+297) (/ x t_1) (* (/ x (- t z)) (/ -1.0 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 = (x / (y - z)) * (1.0 / t);
	} else if (t_1 <= 1e+297) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) * (-1.0 / 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 = (x / (y - z)) * (1.0 / t);
	} else if (t_1 <= 1e+297) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) * (-1.0 / 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 = (x / (y - z)) * (1.0 / t)
	elif t_1 <= 1e+297:
		tmp = x / t_1
	else:
		tmp = (x / (t - z)) * (-1.0 / 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(Float64(x / Float64(y - z)) * Float64(1.0 / t));
	elseif (t_1 <= 1e+297)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(-1.0 / 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 = (x / (y - z)) * (1.0 / t);
	elseif (t_1 <= 1e+297)
		tmp = x / t_1;
	else
		tmp = (x / (t - z)) * (-1.0 / 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[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+297], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 55.8%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in t around inf 77.8%

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

   if -inf.0 < (*.f64 (-.f64 y z) (-.f64 t z)) < 1e297

   1. Initial program 99.7%

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

   if 1e297 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 63.6%

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

      1. associate-/l/ 99.8%

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

      2. 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. Taylor expanded in y around 0 83.5%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq -\infty:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{1}{t}\\ \mathbf{elif}\;\left(t - z\right) \cdot \left(y - z\right) \leq 10^{+297}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{-1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{if}\;z \leq -4400000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -1.34 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ -1.0 t))))
   (if (<= z -4400000000.0)
     t_1
     (if (<= z -1.05e-40)
       (/ (/ x y) t)
       (if (<= z -1.34e-79)
         (/ (/ x t) (- z))
         (if (<= z 7.8e-8) (/ (/ x t) y) t_1))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (-1.0 / t);
	double tmp;
	if (z <= -4400000000.0) {
		tmp = t_1;
	} else if (z <= -1.05e-40) {
		tmp = (x / y) / t;
	} else if (z <= -1.34e-79) {
		tmp = (x / t) / -z;
	} else if (z <= 7.8e-8) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * ((-1.0d0) / t)
    if (z <= (-4400000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.05d-40)) then
        tmp = (x / y) / t
    else if (z <= (-1.34d-79)) then
        tmp = (x / t) / -z
    else if (z <= 7.8d-8) then
        tmp = (x / t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (-1.0 / t);
	double tmp;
	if (z <= -4400000000.0) {
		tmp = t_1;
	} else if (z <= -1.05e-40) {
		tmp = (x / y) / t;
	} else if (z <= -1.34e-79) {
		tmp = (x / t) / -z;
	} else if (z <= 7.8e-8) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) * (-1.0 / t)
	tmp = 0
	if z <= -4400000000.0:
		tmp = t_1
	elif z <= -1.05e-40:
		tmp = (x / y) / t
	elif z <= -1.34e-79:
		tmp = (x / t) / -z
	elif z <= 7.8e-8:
		tmp = (x / t) / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(-1.0 / t))
	tmp = 0.0
	if (z <= -4400000000.0)
		tmp = t_1;
	elseif (z <= -1.05e-40)
		tmp = Float64(Float64(x / y) / t);
	elseif (z <= -1.34e-79)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (z <= 7.8e-8)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (-1.0 / t);
	tmp = 0.0;
	if (z <= -4400000000.0)
		tmp = t_1;
	elseif (z <= -1.05e-40)
		tmp = (x / y) / t;
	elseif (z <= -1.34e-79)
		tmp = (x / t) / -z;
	elseif (z <= 7.8e-8)
		tmp = (x / t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4400000000.0], t$95$1, If[LessEqual[z, -1.05e-40], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -1.34e-79], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 7.8e-8], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.4e9 or 7.7999999999999997e-8 < z

   1. Initial program 72.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 38.7%

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

   6. Taylor expanded in y around 0 31.5%

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

      1. associate-*r/ 31.5%

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

      2. neg-mul-1 31.5%

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

   8. Simplified 31.5%

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

      1. neg-mul-1 31.5%

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

      2. times-frac 40.7%

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

   10. Applied egg-rr 40.7%

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

   if -4.4e9 < z < -1.05000000000000009e-40

   1. Initial program 71.7%

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

   3. Taylor expanded in z around 0 24.4%

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

      1. associate-/r* 62.0%

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

      2. div-inv 62.1%

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

   5. Applied egg-rr 62.1%

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

      1. associate-*l/ 52.5%

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

      2. un-div-inv 52.7%

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

   7. Applied egg-rr 52.7%

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

   if -1.05000000000000009e-40 < z < -1.34e-79

   1. Initial program 99.5%

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

      1. associate-/r* 100.0%

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

      2. div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in t around inf 33.9%

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

   6. Taylor expanded in y around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/r* 36.3%

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

      3. distribute-neg-frac2 36.3%

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

   8. Simplified 36.3%

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

   if -1.34e-79 < z < 7.7999999999999997e-8

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 63.9%

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

      1. associate-/r* 67.4%

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

      2. div-inv 67.3%

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

   5. Applied egg-rr 67.3%

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

      1. un-div-inv 67.4%

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

   7. Applied egg-rr 67.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4400000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-40}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;z \leq -1.34 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{if}\;z \leq -900000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{t} \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 2.76 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ -1.0 t))))
   (if (<= z -900000000.0)
     t_1
     (if (<= z -7.5e-38)
       (* (/ 1.0 t) (/ x y))
       (if (<= z -1.2e-75)
         (/ (/ x t) (- z))
         (if (<= z 2.76e-5) (/ (/ x t) y) t_1))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (-1.0 / t);
	double tmp;
	if (z <= -900000000.0) {
		tmp = t_1;
	} else if (z <= -7.5e-38) {
		tmp = (1.0 / t) * (x / y);
	} else if (z <= -1.2e-75) {
		tmp = (x / t) / -z;
	} else if (z <= 2.76e-5) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * ((-1.0d0) / t)
    if (z <= (-900000000.0d0)) then
        tmp = t_1
    else if (z <= (-7.5d-38)) then
        tmp = (1.0d0 / t) * (x / y)
    else if (z <= (-1.2d-75)) then
        tmp = (x / t) / -z
    else if (z <= 2.76d-5) then
        tmp = (x / t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (-1.0 / t);
	double tmp;
	if (z <= -900000000.0) {
		tmp = t_1;
	} else if (z <= -7.5e-38) {
		tmp = (1.0 / t) * (x / y);
	} else if (z <= -1.2e-75) {
		tmp = (x / t) / -z;
	} else if (z <= 2.76e-5) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) * (-1.0 / t)
	tmp = 0
	if z <= -900000000.0:
		tmp = t_1
	elif z <= -7.5e-38:
		tmp = (1.0 / t) * (x / y)
	elif z <= -1.2e-75:
		tmp = (x / t) / -z
	elif z <= 2.76e-5:
		tmp = (x / t) / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(-1.0 / t))
	tmp = 0.0
	if (z <= -900000000.0)
		tmp = t_1;
	elseif (z <= -7.5e-38)
		tmp = Float64(Float64(1.0 / t) * Float64(x / y));
	elseif (z <= -1.2e-75)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (z <= 2.76e-5)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (-1.0 / t);
	tmp = 0.0;
	if (z <= -900000000.0)
		tmp = t_1;
	elseif (z <= -7.5e-38)
		tmp = (1.0 / t) * (x / y);
	elseif (z <= -1.2e-75)
		tmp = (x / t) / -z;
	elseif (z <= 2.76e-5)
		tmp = (x / t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -900000000.0], t$95$1, If[LessEqual[z, -7.5e-38], N[(N[(1.0 / t), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.2e-75], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, 2.76e-5], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9e8 or 2.76e-5 < z

   1. Initial program 72.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 38.7%

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

   6. Taylor expanded in y around 0 31.5%

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

      1. associate-*r/ 31.5%

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

      2. neg-mul-1 31.5%

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

   8. Simplified 31.5%

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

      1. neg-mul-1 31.5%

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

      2. times-frac 40.7%

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

   10. Applied egg-rr 40.7%

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

   if -9e8 < z < -7.5e-38

   1. Initial program 71.7%

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

   3. Taylor expanded in z around 0 24.4%

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

      1. *-un-lft-identity 24.4%

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

      2. times-frac 52.3%

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

   5. Applied egg-rr 52.3%

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

   if -7.5e-38 < z < -1.2000000000000001e-75

   1. Initial program 99.5%

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

      1. associate-/r* 100.0%

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

      2. div-inv 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in t around inf 33.9%

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

   6. Taylor expanded in y around 0 35.8%

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

      1. mul-1-neg 35.8%

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

      2. associate-/r* 36.3%

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

      3. distribute-neg-frac2 36.3%

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

   8. Simplified 36.3%

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

   if -1.2000000000000001e-75 < z < 2.76e-5

   1. Initial program 94.7%

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

   3. Taylor expanded in z around 0 63.9%

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

      1. associate-/r* 67.4%

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

      2. div-inv 67.3%

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

   5. Applied egg-rr 67.3%

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

      1. un-div-inv 67.4%

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

   7. Applied egg-rr 67.4%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -900000000:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{t} \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \leq 2.76 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z t))))
   (if (<= y -8.8e+14)
     (/ (/ x y) (- t z))
     (if (<= y -5000.0)
       t_1
       (if (<= y -1.02e-16)
         (/ x (* (- t z) y))
         (if (<= y 2.8e-235) t_1 (/ (/ x t) (- y z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (y <= -8.8e+14) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5000.0) {
		tmp = t_1;
	} else if (y <= -1.02e-16) {
		tmp = x / ((t - z) * y);
	} else if (y <= 2.8e-235) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (z - t)
    if (y <= (-8.8d+14)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-5000.0d0)) then
        tmp = t_1
    else if (y <= (-1.02d-16)) then
        tmp = x / ((t - z) * y)
    else if (y <= 2.8d-235) then
        tmp = t_1
    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 t_1 = (x / z) / (z - t);
	double tmp;
	if (y <= -8.8e+14) {
		tmp = (x / y) / (t - z);
	} else if (y <= -5000.0) {
		tmp = t_1;
	} else if (y <= -1.02e-16) {
		tmp = x / ((t - z) * y);
	} else if (y <= 2.8e-235) {
		tmp = t_1;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (z - t)
	tmp = 0
	if y <= -8.8e+14:
		tmp = (x / y) / (t - z)
	elif y <= -5000.0:
		tmp = t_1
	elif y <= -1.02e-16:
		tmp = x / ((t - z) * y)
	elif y <= 2.8e-235:
		tmp = t_1
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - t))
	tmp = 0.0
	if (y <= -8.8e+14)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -5000.0)
		tmp = t_1;
	elseif (y <= -1.02e-16)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 2.8e-235)
		tmp = t_1;
	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)
	t_1 = (x / z) / (z - t);
	tmp = 0.0;
	if (y <= -8.8e+14)
		tmp = (x / y) / (t - z);
	elseif (y <= -5000.0)
		tmp = t_1;
	elseif (y <= -1.02e-16)
		tmp = x / ((t - z) * y);
	elseif (y <= 2.8e-235)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.8e+14], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5000.0], t$95$1, If[LessEqual[y, -1.02e-16], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e-235], t$95$1, N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.8e14

   1. Initial program 77.6%

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

   3. Taylor expanded in x around 0 77.6%

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

      1. associate-/l/ 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in y around inf 91.9%

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

   if -8.8e14 < y < -5e3 or -1.0200000000000001e-16 < y < 2.79999999999999995e-235

   1. Initial program 81.2%

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

   3. Taylor expanded in x around 0 81.2%

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

      1. associate-/l/ 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

   8. Simplified 86.5%

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

   if -5e3 < y < -1.0200000000000001e-16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   5. Simplified 81.3%

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

   if 2.79999999999999995e-235 < y

   1. Initial program 84.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. Taylor expanded in t around inf 52.4%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -5000:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;t \leq -6 \cdot 10^{-168}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-157}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)))
   (if (<= t -6e-168)
     t_1
     (if (<= t 6e-157)
       (/ (- x) (* z y))
       (if (<= t 2.4e-8)
         (/ (/ x y) t)
         (if (<= t 2.1e+192) (/ x (* z (- t))) t_1))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -6e-168) {
		tmp = t_1;
	} else if (t <= 6e-157) {
		tmp = -x / (z * y);
	} else if (t <= 2.4e-8) {
		tmp = (x / y) / t;
	} else if (t <= 2.1e+192) {
		tmp = x / (z * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / y
    if (t <= (-6d-168)) then
        tmp = t_1
    else if (t <= 6d-157) then
        tmp = -x / (z * y)
    else if (t <= 2.4d-8) then
        tmp = (x / y) / t
    else if (t <= 2.1d+192) then
        tmp = x / (z * -t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (t <= -6e-168) {
		tmp = t_1;
	} else if (t <= 6e-157) {
		tmp = -x / (z * y);
	} else if (t <= 2.4e-8) {
		tmp = (x / y) / t;
	} else if (t <= 2.1e+192) {
		tmp = x / (z * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	tmp = 0
	if t <= -6e-168:
		tmp = t_1
	elif t <= 6e-157:
		tmp = -x / (z * y)
	elif t <= 2.4e-8:
		tmp = (x / y) / t
	elif t <= 2.1e+192:
		tmp = x / (z * -t)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (t <= -6e-168)
		tmp = t_1;
	elseif (t <= 6e-157)
		tmp = Float64(Float64(-x) / Float64(z * y));
	elseif (t <= 2.4e-8)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 2.1e+192)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	tmp = 0.0;
	if (t <= -6e-168)
		tmp = t_1;
	elseif (t <= 6e-157)
		tmp = -x / (z * y);
	elseif (t <= 2.4e-8)
		tmp = (x / y) / t;
	elseif (t <= 2.1e+192)
		tmp = x / (z * -t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -6e-168], t$95$1, If[LessEqual[t, 6e-157], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-8], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.1e+192], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.99999999999999983e-168 or 2.09999999999999995e192 < t

   1. Initial program 79.9%

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

   3. Taylor expanded in z around 0 46.3%

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

      1. associate-/r* 56.7%

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

      2. div-inv 56.7%

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

   5. Applied egg-rr 56.7%

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

      1. un-div-inv 56.7%

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

   7. Applied egg-rr 56.7%

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

   if -5.99999999999999983e-168 < t < 6e-157

   1. Initial program 90.3%

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

      1. associate-/r* 97.1%

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

      2. div-inv 97.0%

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

   4. Applied egg-rr 97.0%

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

   5. Taylor expanded in t around 0 91.3%

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

   6. Taylor expanded in y around inf 57.4%

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

      1. associate-*r/ 57.4%

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

      2. neg-mul-1 57.4%

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

   8. Simplified 57.4%

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

   if 6e-157 < t < 2.39999999999999998e-8

   1. Initial program 78.6%

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

   3. Taylor expanded in z around 0 32.3%

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

      1. associate-/r* 32.3%

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

      2. div-inv 32.2%

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

   5. Applied egg-rr 32.2%

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

      1. associate-*l/ 42.2%

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

      2. un-div-inv 42.3%

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

   7. Applied egg-rr 42.3%

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

   if 2.39999999999999998e-8 < t < 2.09999999999999995e192

   1. Initial program 80.7%

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

      1. associate-/l/ 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 80.5%

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

   6. Taylor expanded in y around 0 52.2%

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

      1. associate-*r/ 52.2%

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

      2. neg-mul-1 52.2%

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

   8. Simplified 52.2%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-168}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-157}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{t + z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (+ t z))))
   (if (<= z -4.8e+31)
     t_1
     (if (<= z 1.95e-57)
       (/ (/ x y) (- t z))
       (if (<= z 2.4e+39) (/ x (* t (- y z))) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (t + z);
	double tmp;
	if (z <= -4.8e+31) {
		tmp = t_1;
	} else if (z <= 1.95e-57) {
		tmp = (x / y) / (t - z);
	} else if (z <= 2.4e+39) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (t + z)
    if (z <= (-4.8d+31)) then
        tmp = t_1
    else if (z <= 1.95d-57) then
        tmp = (x / y) / (t - z)
    else if (z <= 2.4d+39) then
        tmp = x / (t * (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (t + z);
	double tmp;
	if (z <= -4.8e+31) {
		tmp = t_1;
	} else if (z <= 1.95e-57) {
		tmp = (x / y) / (t - z);
	} else if (z <= 2.4e+39) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (t + z)
	tmp = 0
	if z <= -4.8e+31:
		tmp = t_1
	elif z <= 1.95e-57:
		tmp = (x / y) / (t - z)
	elif z <= 2.4e+39:
		tmp = x / (t * (y - z))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(t + z))
	tmp = 0.0
	if (z <= -4.8e+31)
		tmp = t_1;
	elseif (z <= 1.95e-57)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 2.4e+39)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (t + z);
	tmp = 0.0;
	if (z <= -4.8e+31)
		tmp = t_1;
	elseif (z <= 1.95e-57)
		tmp = (x / y) / (t - z);
	elseif (z <= 2.4e+39)
		tmp = x / (t * (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(t + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+31], t$95$1, If[LessEqual[z, 1.95e-57], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+39], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999965e31 or 2.4000000000000001e39 < z

   1. Initial program 70.8%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 99.7%

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

      2. div-inv 99.8%

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

      3. div-inv 99.7%

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

      4. clear-num 99.6%

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

      5. frac-times 98.0%

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

      6. metadata-eval 98.0%

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

      7. sub-neg 98.0%

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

      8. add-sqr-sqrt 45.9%

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

      9. sqrt-unprod 69.0%

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

      10. sqr-neg 69.0%

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

      11. sqrt-unprod 34.2%

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

      12. add-sqr-sqrt 68.6%

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

      13. sub-neg 68.6%

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

      14. add-sqr-sqrt 34.3%

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

      15. sqrt-unprod 67.9%

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

      16. sqr-neg 67.9%

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

      17. sqrt-unprod 42.2%

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

      18. add-sqr-sqrt 84.4%

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

   6. Applied egg-rr 84.4%

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

   7. Taylor expanded in y around 0 64.8%

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

      1. associate-/r* 80.6%

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

   9. Simplified 80.6%

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

   if -4.79999999999999965e31 < z < 1.95000000000000003e-57

   1. Initial program 91.5%

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

   3. Taylor expanded in x around 0 91.5%

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

      1. associate-/l/ 95.7%

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

   5. Simplified 95.7%

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

   6. Taylor expanded in y around inf 75.7%

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

   if 1.95000000000000003e-57 < z < 2.4000000000000001e39

   1. Initial program 99.7%

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

   3. Taylor expanded in t around inf 63.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{z}}{t + z}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t + z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{t + z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (+ t z))))
   (if (<= z -4.6e+31)
     t_1
     (if (<= z 1.7e-7)
       (/ (/ x y) (- t z))
       (if (<= z 3e+137) (/ x (* z (- z t))) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (t + z);
	double tmp;
	if (z <= -4.6e+31) {
		tmp = t_1;
	} else if (z <= 1.7e-7) {
		tmp = (x / y) / (t - z);
	} else if (z <= 3e+137) {
		tmp = x / (z * (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (t + z)
    if (z <= (-4.6d+31)) then
        tmp = t_1
    else if (z <= 1.7d-7) then
        tmp = (x / y) / (t - z)
    else if (z <= 3d+137) then
        tmp = x / (z * (z - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (t + z);
	double tmp;
	if (z <= -4.6e+31) {
		tmp = t_1;
	} else if (z <= 1.7e-7) {
		tmp = (x / y) / (t - z);
	} else if (z <= 3e+137) {
		tmp = x / (z * (z - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (t + z)
	tmp = 0
	if z <= -4.6e+31:
		tmp = t_1
	elif z <= 1.7e-7:
		tmp = (x / y) / (t - z)
	elif z <= 3e+137:
		tmp = x / (z * (z - t))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(t + z))
	tmp = 0.0
	if (z <= -4.6e+31)
		tmp = t_1;
	elseif (z <= 1.7e-7)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 3e+137)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (t + z);
	tmp = 0.0;
	if (z <= -4.6e+31)
		tmp = t_1;
	elseif (z <= 1.7e-7)
		tmp = (x / y) / (t - z);
	elseif (z <= 3e+137)
		tmp = x / (z * (z - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(t + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+31], t$95$1, If[LessEqual[z, 1.7e-7], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e+137], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5999999999999999e31 or 3.0000000000000001e137 < z

   1. Initial program 70.5%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.7%

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

   4. Applied egg-rr 99.7%

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

      1. associate-*l/ 99.7%

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

      2. div-inv 99.8%

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

      3. div-inv 99.8%

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

      4. clear-num 99.6%

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

      5. frac-times 97.7%

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

      6. metadata-eval 97.7%

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

      7. sub-neg 97.7%

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

      8. add-sqr-sqrt 54.9%

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

      9. sqrt-unprod 71.5%

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

      10. sqr-neg 71.5%

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

      11. sqrt-unprod 29.9%

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

      12. add-sqr-sqrt 71.0%

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

      13. sub-neg 71.0%

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

      14. add-sqr-sqrt 41.1%

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

      15. sqrt-unprod 67.8%

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

      16. sqr-neg 67.8%

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

      17. sqrt-unprod 37.1%

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

      18. add-sqr-sqrt 87.5%

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

   6. Applied egg-rr 87.5%

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

   7. Taylor expanded in y around 0 65.0%

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

      1. associate-/r* 84.0%

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

   9. Simplified 84.0%

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

   if -4.5999999999999999e31 < z < 1.69999999999999987e-7

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 92.4%

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

      1. associate-/l/ 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in y around inf 75.4%

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

   if 1.69999999999999987e-7 < z < 3.0000000000000001e137

   1. Initial program 82.1%

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

   3. Taylor expanded in y around 0 64.2%

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

      1. associate-*r/ 64.2%

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

      2. neg-mul-1 64.2%

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

   5. Simplified 64.2%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+31}:\\ \;\;\;\;\frac{\frac{x}{z}}{t + z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+137}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{t + z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-204}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -2e-204)
   (/ (/ x y) (- t z))
   (if (<= t 1.1e-16) (* (/ x (- y z)) (/ -1.0 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 <= -2e-204) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.1e-16) {
		tmp = (x / (y - z)) * (-1.0 / 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 <= (-2d-204)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.1d-16) then
        tmp = (x / (y - z)) * ((-1.0d0) / 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 <= -2e-204) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.1e-16) {
		tmp = (x / (y - z)) * (-1.0 / 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 <= -2e-204:
		tmp = (x / y) / (t - z)
	elif t <= 1.1e-16:
		tmp = (x / (y - z)) * (-1.0 / 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 <= -2e-204)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.1e-16)
		tmp = Float64(Float64(x / Float64(y - z)) * Float64(-1.0 / 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 <= -2e-204)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.1e-16)
		tmp = (x / (y - z)) * (-1.0 / 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, -2e-204], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-16], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e-204

   1. Initial program 85.2%

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

   3. Taylor expanded in x around 0 85.2%

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

      1. associate-/l/ 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in y around inf 61.4%

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

   if -2e-204 < t < 1.1e-16

   1. Initial program 85.7%

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

      1. associate-/r* 98.9%

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

      2. div-inv 98.8%

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

   4. Applied egg-rr 98.8%

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

   5. Taylor expanded in t around 0 89.9%

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

   if 1.1e-16 < t

   1. Initial program 73.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 86.5%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-204}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-161}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 -3.4e-186)
   (* (/ x t) (/ 1.0 y))
   (if (<= t 5.5e-161) (/ (- 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 <= -3.4e-186) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 5.5e-161) {
		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 <= (-3.4d-186)) then
        tmp = (x / t) * (1.0d0 / y)
    else if (t <= 5.5d-161) 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 <= -3.4e-186) {
		tmp = (x / t) * (1.0 / y);
	} else if (t <= 5.5e-161) {
		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 <= -3.4e-186:
		tmp = (x / t) * (1.0 / y)
	elif t <= 5.5e-161:
		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 <= -3.4e-186)
		tmp = Float64(Float64(x / t) * Float64(1.0 / y));
	elseif (t <= 5.5e-161)
		tmp = Float64(Float64(-x) / Float64(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 <= -3.4e-186)
		tmp = (x / t) * (1.0 / y);
	elseif (t <= 5.5e-161)
		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, -3.4e-186], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e-161], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.3999999999999999e-186

   1. Initial program 85.1%

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

   3. Taylor expanded in z around 0 46.3%

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

      1. associate-/r* 52.1%

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

      2. div-inv 52.1%

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

   5. Applied egg-rr 52.1%

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

   if -3.3999999999999999e-186 < t < 5.5e-161

   1. Initial program 89.5%

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

      1. associate-/r* 98.5%

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

      2. div-inv 98.4%

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

   4. Applied egg-rr 98.4%

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

   5. Taylor expanded in t around 0 93.9%

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

   6. Taylor expanded in y around inf 60.3%

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

      1. associate-*r/ 60.3%

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

      2. neg-mul-1 60.3%

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

   8. Simplified 60.3%

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

   if 5.5e-161 < t

   1. Initial program 74.5%

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

   3. Taylor expanded in t around inf 59.5%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-161}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -3e-235)
   (/ (/ x y) (- t z))
   (if (<= t 1.3e-16) (/ (/ 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 <= -3e-235) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.3e-16) {
		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 <= (-3d-235)) then
        tmp = (x / y) / (t - z)
    else if (t <= 1.3d-16) 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 <= -3e-235) {
		tmp = (x / y) / (t - z);
	} else if (t <= 1.3e-16) {
		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 <= -3e-235:
		tmp = (x / y) / (t - z)
	elif t <= 1.3e-16:
		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 <= -3e-235)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 1.3e-16)
		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 <= -3e-235)
		tmp = (x / y) / (t - z);
	elseif (t <= 1.3e-16)
		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, -3e-235], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-16], 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 < -2.9999999999999999e-235

   1. Initial program 85.9%

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

   3. Taylor expanded in x around 0 85.9%

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

      1. associate-/l/ 96.5%

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

   5. Simplified 96.5%

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

   6. Taylor expanded in y around inf 62.3%

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

   if -2.9999999999999999e-235 < t < 1.2999999999999999e-16

   1. Initial program 84.8%

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

      1. associate-/l/ 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around 0 88.9%

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

      1. associate-*r/ 88.9%

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

      2. neg-mul-1 88.9%

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

   7. Simplified 88.9%

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

   if 1.2999999999999999e-16 < t

   1. Initial program 73.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 86.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 100:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -4.5e-54)
   (/ (/ x y) t)
   (if (<= y 100.0) (/ 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 <= -4.5e-54) {
		tmp = (x / y) / t;
	} else if (y <= 100.0) {
		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 <= (-4.5d-54)) then
        tmp = (x / y) / t
    else if (y <= 100.0d0) 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 <= -4.5e-54) {
		tmp = (x / y) / t;
	} else if (y <= 100.0) {
		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 <= -4.5e-54:
		tmp = (x / y) / t
	elif y <= 100.0:
		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 <= -4.5e-54)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 100.0)
		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 <= -4.5e-54)
		tmp = (x / y) / t;
	elseif (y <= 100.0)
		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, -4.5e-54], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 100.0], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.4999999999999998e-54

   1. Initial program 78.3%

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

   3. Taylor expanded in z around 0 51.3%

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

      1. associate-/r* 58.5%

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

      2. div-inv 58.4%

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

   5. Applied egg-rr 58.4%

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

      1. associate-*l/ 59.7%

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

      2. un-div-inv 59.8%

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

   7. Applied egg-rr 59.8%

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

   if -4.4999999999999998e-54 < y < 100

   1. Initial program 85.6%

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

   5. Taylor expanded in t around inf 60.7%

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

   6. Taylor expanded in y around 0 44.6%

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

      1. associate-*r/ 44.6%

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

      2. neg-mul-1 44.6%

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

   8. Simplified 44.6%

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

   if 100 < y

   1. Initial program 81.9%

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

   3. Taylor expanded in z around 0 39.1%

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

      1. associate-/r* 45.1%

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

      2. div-inv 45.1%

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

   5. Applied egg-rr 45.1%

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

      1. un-div-inv 45.1%

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

   7. Applied egg-rr 45.1%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 100:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+31} \lor \neg \left(z \leq 17000000\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -4.6e+31) (not (<= z 17000000.0))) (/ 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 <= -4.6e+31) || !(z <= 17000000.0)) {
		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 <= (-4.6d+31)) .or. (.not. (z <= 17000000.0d0))) 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 <= -4.6e+31) || !(z <= 17000000.0)) {
		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 <= -4.6e+31) or not (z <= 17000000.0):
		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 <= -4.6e+31) || !(z <= 17000000.0))
		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 <= -4.6e+31) || ~((z <= 17000000.0)))
		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, -4.6e+31], N[Not[LessEqual[z, 17000000.0]], $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 < -4.5999999999999999e31 or 1.7e7 < z

   1. Initial program 72.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 38.0%

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

   6. Taylor expanded in y around 0 31.2%

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

      1. associate-*r/ 31.2%

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

      2. neg-mul-1 31.2%

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

   8. Simplified 31.2%

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

      1. add-sqr-sqrt 16.0%

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

      2. sqrt-unprod 39.2%

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

      3. sqr-neg 39.2%

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

      4. sqrt-unprod 15.1%

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

      5. add-sqr-sqrt 31.3%

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

      6. div-inv 31.3%

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

      7. *-commutative 31.3%

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

   10. Applied egg-rr 31.3%

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

       1. associate-*r/ 31.3%

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

       2. *-commutative 31.3%

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

       3. *-rgt-identity 31.3%

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

   12. Simplified 31.3%

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

   if -4.5999999999999999e31 < z < 1.7e7

   1. Initial program 92.6%

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

   3. Taylor expanded in z around 0 55.5%

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

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+31} \lor \neg \left(z \leq 17000000\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+79} \lor \neg \left(z \leq 1.9 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -3.2e+79) (not (<= z 1.9e+162))) (/ 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 <= -3.2e+79) || !(z <= 1.9e+162)) {
		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 <= (-3.2d+79)) .or. (.not. (z <= 1.9d+162))) 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 <= -3.2e+79) || !(z <= 1.9e+162)) {
		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 <= -3.2e+79) or not (z <= 1.9e+162):
		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 <= -3.2e+79) || !(z <= 1.9e+162))
		tmp = Float64(x / Float64(t * z));
	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 <= -3.2e+79) || ~((z <= 1.9e+162)))
		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, -3.2e+79], N[Not[LessEqual[z, 1.9e+162]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000003e79 or 1.90000000000000012e162 < z

   1. Initial program 69.4%

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

      1. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 36.3%

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

   6. Taylor expanded in y around 0 35.1%

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

      1. associate-*r/ 35.1%

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

      2. neg-mul-1 35.1%

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

   8. Simplified 35.1%

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

      1. add-sqr-sqrt 20.0%

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

      2. sqrt-unprod 39.7%

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

      3. sqr-neg 39.7%

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

      4. sqrt-unprod 15.0%

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

      5. add-sqr-sqrt 35.1%

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

      6. div-inv 35.1%

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

      7. *-commutative 35.1%

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

   10. Applied egg-rr 35.1%

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

       1. associate-*r/ 35.1%

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

       2. *-commutative 35.1%

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

       3. *-rgt-identity 35.1%

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

   12. Simplified 35.1%

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

   if -3.20000000000000003e79 < z < 1.90000000000000012e162

   1. Initial program 89.0%

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

   3. Taylor expanded in z around 0 47.2%

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

      1. associate-/r* 54.3%

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

      2. div-inv 54.3%

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

   5. Applied egg-rr 54.3%

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

      1. un-div-inv 54.3%

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

   7. Applied egg-rr 54.3%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+79} \lor \neg \left(z \leq 1.9 \cdot 10^{+162}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 3.1e-55) (/ 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 <= 3.1e-55) {
		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 <= 3.1d-55) 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 <= 3.1e-55) {
		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 <= 3.1e-55:
		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 <= 3.1e-55)
		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 <= 3.1e-55)
		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, 3.1e-55], 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 < 3.09999999999999997e-55

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   if 3.09999999999999997e-55 < t

   1. Initial program 74.7%

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

   3. Taylor expanded in t around inf 67.9%

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

4. Final simplification 61.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 3.1 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 72.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 1.45e-55) (/ 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 <= 1.45e-55) {
		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 <= 1.45d-55) 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 <= 1.45e-55) {
		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 <= 1.45e-55:
		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 <= 1.45e-55)
		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 <= 1.45e-55)
		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, 1.45e-55], 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 < 1.45e-55

   1. Initial program 85.1%

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

   3. Taylor expanded in y around inf 58.9%

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

      1. *-commutative 58.9%

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

   5. Simplified 58.9%

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

   if 1.45e-55 < t

   1. Initial program 74.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 72.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 2.95 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 2.95e-55) (/ (/ x y) (- t z)) (/ (/ x t) (- y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.95e-55) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 2.95d-55) then
        tmp = (x / y) / (t - z)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.95e-55) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 2.95e-55:
		tmp = (x / y) / (t - z)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.95e-55)
		tmp = Float64(Float64(x / y) / Float64(t - 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 <= 2.95e-55)
		tmp = (x / y) / (t - z);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, 2.95e-55], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.9499999999999999e-55

   1. Initial program 85.1%

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

   3. Taylor expanded in x around 0 85.1%

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

      1. associate-/l/ 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around inf 63.2%

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

   if 2.9499999999999999e-55 < t

   1. Initial program 74.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.95 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.8% 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 82.4%

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

3. Taylor expanded in z around 0 35.6%

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

4. Final simplification 35.6%

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

Developer target: 87.5% 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 2024071 
(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))))