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

Percentage Accurate: 89.1% → 97.0%

Time: 15.8s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

   1. associate-/r* 96.2%

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

   2. div-inv 96.2%

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

4. Applied egg-rr 96.2%

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

   1. un-div-inv 96.2%

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

6. Applied egg-rr 96.2%

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

7. Final simplification 96.2%

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

Alternative 2: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y} \cdot \frac{1}{t}\\ t_2 := -\frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+187}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 10^{+208}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 y) (/ 1.0 t))) (t_2 (- (/ x (* z t)))))
   (if (<= t -1.05e-41)
     t_1
     (if (<= t 5e-15)
       (/ (- x) (* y z))
       (if (<= t 2.9e+147)
         t_2
         (if (<= t 1.6e+187) (/ (/ x y) t) (if (<= t 1e+208) t_2 t_1)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / y) * (1.0 / t);
	double t_2 = -(x / (z * t));
	double tmp;
	if (t <= -1.05e-41) {
		tmp = t_1;
	} else if (t <= 5e-15) {
		tmp = -x / (y * z);
	} else if (t <= 2.9e+147) {
		tmp = t_2;
	} else if (t <= 1.6e+187) {
		tmp = (x / y) / t;
	} else if (t <= 1e+208) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / y) * (1.0d0 / t)
    t_2 = -(x / (z * t))
    if (t <= (-1.05d-41)) then
        tmp = t_1
    else if (t <= 5d-15) then
        tmp = -x / (y * z)
    else if (t <= 2.9d+147) then
        tmp = t_2
    else if (t <= 1.6d+187) then
        tmp = (x / y) / t
    else if (t <= 1d+208) then
        tmp = t_2
    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 / y) * (1.0 / t);
	double t_2 = -(x / (z * t));
	double tmp;
	if (t <= -1.05e-41) {
		tmp = t_1;
	} else if (t <= 5e-15) {
		tmp = -x / (y * z);
	} else if (t <= 2.9e+147) {
		tmp = t_2;
	} else if (t <= 1.6e+187) {
		tmp = (x / y) / t;
	} else if (t <= 1e+208) {
		tmp = t_2;
	} 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 / y) * (1.0 / t)
	t_2 = -(x / (z * t))
	tmp = 0
	if t <= -1.05e-41:
		tmp = t_1
	elif t <= 5e-15:
		tmp = -x / (y * z)
	elif t <= 2.9e+147:
		tmp = t_2
	elif t <= 1.6e+187:
		tmp = (x / y) / t
	elif t <= 1e+208:
		tmp = t_2
	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 / y) * Float64(1.0 / t))
	t_2 = Float64(-Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.05e-41)
		tmp = t_1;
	elseif (t <= 5e-15)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 2.9e+147)
		tmp = t_2;
	elseif (t <= 1.6e+187)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 1e+208)
		tmp = t_2;
	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 / y) * (1.0 / t);
	t_2 = -(x / (z * t));
	tmp = 0.0;
	if (t <= -1.05e-41)
		tmp = t_1;
	elseif (t <= 5e-15)
		tmp = -x / (y * z);
	elseif (t <= 2.9e+147)
		tmp = t_2;
	elseif (t <= 1.6e+187)
		tmp = (x / y) / t;
	elseif (t <= 1e+208)
		tmp = t_2;
	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 / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[t, -1.05e-41], t$95$1, If[LessEqual[t, 5e-15], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.9e+147], t$95$2, If[LessEqual[t, 1.6e+187], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1e+208], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.05000000000000006e-41 or 9.9999999999999998e207 < t

   1. Initial program 84.0%

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

   3. Taylor expanded in z around 0 51.4%

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

      1. *-un-lft-identity 51.4%

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

      2. times-frac 59.0%

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

   5. Applied egg-rr 59.0%

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

   if -1.05000000000000006e-41 < t < 4.99999999999999999e-15

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-/r* 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around 0 42.1%

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

      1. associate-*r/ 42.1%

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

      2. neg-mul-1 42.1%

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

      3. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 4.99999999999999999e-15 < t < 2.8999999999999998e147 or 1.59999999999999997e187 < t < 9.9999999999999998e207

   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 65.1%

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

      1. associate-*r/ 65.1%

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

      2. neg-mul-1 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in z around 0 54.8%

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

      1. associate-*r/ 54.8%

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

      2. neg-mul-1 54.8%

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

   8. Simplified 54.8%

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

   if 2.8999999999999998e147 < t < 1.59999999999999997e187

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/r* 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-un-lft-identity 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-15}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+147}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+187}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 10^{+208}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := -\frac{x}{z \cdot t}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-16}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+187}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+207}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x (* z t)))))
   (if (<= t -1.05e-41)
     (* (/ x y) (/ 1.0 t))
     (if (<= t 3.9e-16)
       (/ (- x) (* y z))
       (if (<= t 6.5e+147)
         t_1
         (if (<= t 4.1e+187)
           (/ (/ x y) t)
           (if (<= t 4.5e+207) t_1 (/ 1.0 (* t (/ y x))))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -(x / (z * t));
	double tmp;
	if (t <= -1.05e-41) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 3.9e-16) {
		tmp = -x / (y * z);
	} else if (t <= 6.5e+147) {
		tmp = t_1;
	} else if (t <= 4.1e+187) {
		tmp = (x / y) / t;
	} else if (t <= 4.5e+207) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (t * (y / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -(x / (z * t))
    if (t <= (-1.05d-41)) then
        tmp = (x / y) * (1.0d0 / t)
    else if (t <= 3.9d-16) then
        tmp = -x / (y * z)
    else if (t <= 6.5d+147) then
        tmp = t_1
    else if (t <= 4.1d+187) then
        tmp = (x / y) / t
    else if (t <= 4.5d+207) then
        tmp = t_1
    else
        tmp = 1.0d0 / (t * (y / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -(x / (z * t));
	double tmp;
	if (t <= -1.05e-41) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 3.9e-16) {
		tmp = -x / (y * z);
	} else if (t <= 6.5e+147) {
		tmp = t_1;
	} else if (t <= 4.1e+187) {
		tmp = (x / y) / t;
	} else if (t <= 4.5e+207) {
		tmp = t_1;
	} else {
		tmp = 1.0 / (t * (y / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = -(x / (z * t))
	tmp = 0
	if t <= -1.05e-41:
		tmp = (x / y) * (1.0 / t)
	elif t <= 3.9e-16:
		tmp = -x / (y * z)
	elif t <= 6.5e+147:
		tmp = t_1
	elif t <= 4.1e+187:
		tmp = (x / y) / t
	elif t <= 4.5e+207:
		tmp = t_1
	else:
		tmp = 1.0 / (t * (y / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(-Float64(x / Float64(z * t)))
	tmp = 0.0
	if (t <= -1.05e-41)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	elseif (t <= 3.9e-16)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (t <= 6.5e+147)
		tmp = t_1;
	elseif (t <= 4.1e+187)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 4.5e+207)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -(x / (z * t));
	tmp = 0.0;
	if (t <= -1.05e-41)
		tmp = (x / y) * (1.0 / t);
	elseif (t <= 3.9e-16)
		tmp = -x / (y * z);
	elseif (t <= 6.5e+147)
		tmp = t_1;
	elseif (t <= 4.1e+187)
		tmp = (x / y) / t;
	elseif (t <= 4.5e+207)
		tmp = t_1;
	else
		tmp = 1.0 / (t * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[t, -1.05e-41], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.9e-16], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.5e+147], t$95$1, If[LessEqual[t, 4.1e+187], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 4.5e+207], t$95$1, N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.05000000000000006e-41

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 50.5%

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

      1. *-un-lft-identity 50.5%

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

      2. times-frac 56.5%

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

   5. Applied egg-rr 56.5%

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

   if -1.05000000000000006e-41 < t < 3.89999999999999977e-16

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-/r* 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around 0 42.1%

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

      1. associate-*r/ 42.1%

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

      2. neg-mul-1 42.1%

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

      3. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 3.89999999999999977e-16 < t < 6.5e147 or 4.1e187 < t < 4.50000000000000003e207

   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 65.1%

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

      1. associate-*r/ 65.1%

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

      2. neg-mul-1 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in z around 0 54.8%

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

      1. associate-*r/ 54.8%

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

      2. neg-mul-1 54.8%

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

   8. Simplified 54.8%

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

   if 6.5e147 < t < 4.1e187

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/r* 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. associate-*l/ 100.0%

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

      2. associate-*l/ 100.0%

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

      3. *-un-lft-identity 100.0%

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

   7. Applied egg-rr 100.0%

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

   if 4.50000000000000003e207 < t

   1. Initial program 70.5%

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

   3. Taylor expanded in z around 0 55.0%

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

      1. clear-num 54.9%

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

      2. associate-/r/ 55.0%

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

      3. *-commutative 55.0%

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

      4. associate-/r* 49.9%

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

   5. Applied egg-rr 49.9%

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

      1. associate-/l/ 55.0%

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

      2. associate-*l/ 55.0%

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

      3. *-commutative 55.0%

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

      4. times-frac 64.5%

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

      5. associate-/r/ 64.6%

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

      6. associate-/r/ 69.4%

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

   7. Applied egg-rr 69.4%

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x} \cdot t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-16}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{+147}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+187}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+207}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+147} \lor \neg \left(t \leq 6.3 \cdot 10^{+187}\right) \land t \leq 8.8 \cdot 10^{+207}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.3e-41)
   (/ (/ x t) y)
   (if (<= t 2.7e-15)
     (/ (- x) (* y z))
     (if (or (<= t 2.3e+147) (and (not (<= t 6.3e+187)) (<= t 8.8e+207)))
       (- (/ x (* z t)))
       (/ (/ x y) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-41) {
		tmp = (x / t) / y;
	} else if (t <= 2.7e-15) {
		tmp = -x / (y * z);
	} else if ((t <= 2.3e+147) || (!(t <= 6.3e+187) && (t <= 8.8e+207))) {
		tmp = -(x / (z * t));
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.3d-41)) then
        tmp = (x / t) / y
    else if (t <= 2.7d-15) then
        tmp = -x / (y * z)
    else if ((t <= 2.3d+147) .or. (.not. (t <= 6.3d+187)) .and. (t <= 8.8d+207)) then
        tmp = -(x / (z * t))
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.3e-41) {
		tmp = (x / t) / y;
	} else if (t <= 2.7e-15) {
		tmp = -x / (y * z);
	} else if ((t <= 2.3e+147) || (!(t <= 6.3e+187) && (t <= 8.8e+207))) {
		tmp = -(x / (z * t));
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.3e-41:
		tmp = (x / t) / y
	elif t <= 2.7e-15:
		tmp = -x / (y * z)
	elif (t <= 2.3e+147) or (not (t <= 6.3e+187) and (t <= 8.8e+207)):
		tmp = -(x / (z * t))
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.3e-41)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 2.7e-15)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif ((t <= 2.3e+147) || (!(t <= 6.3e+187) && (t <= 8.8e+207)))
		tmp = Float64(-Float64(x / Float64(z * t)));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.3e-41)
		tmp = (x / t) / y;
	elseif (t <= 2.7e-15)
		tmp = -x / (y * z);
	elseif ((t <= 2.3e+147) || (~((t <= 6.3e+187)) && (t <= 8.8e+207)))
		tmp = -(x / (z * t));
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.3e-41], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.7e-15], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.3e+147], And[N[Not[LessEqual[t, 6.3e+187]], $MachinePrecision], LessEqual[t, 8.8e+207]]], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.3000000000000001e-41

   1. Initial program 87.3%

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

   3. Taylor expanded in y around inf 51.2%

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

      1. *-commutative 51.2%

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

      2. associate-/r* 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in t around inf 55.2%

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

   if -2.3000000000000001e-41 < t < 2.70000000000000009e-15

   1. Initial program 87.2%

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

   3. Taylor expanded in y around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-/r* 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in t around 0 42.1%

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

      1. associate-*r/ 42.1%

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

      2. neg-mul-1 42.1%

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

      3. *-commutative 42.1%

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

   8. Simplified 42.1%

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

   if 2.70000000000000009e-15 < t < 2.2999999999999999e147 or 6.30000000000000005e187 < t < 8.80000000000000034e207

   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 65.1%

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

      1. associate-*r/ 65.1%

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

      2. neg-mul-1 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in z around 0 54.8%

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

      1. associate-*r/ 54.8%

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

      2. neg-mul-1 54.8%

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

   8. Simplified 54.8%

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

   if 2.2999999999999999e147 < t < 6.30000000000000005e187 or 8.80000000000000034e207 < t

   1. Initial program 80.7%

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

   3. Taylor expanded in z around 0 70.5%

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

      1. clear-num 70.4%

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

      2. associate-/r/ 70.4%

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

      3. *-commutative 70.4%

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

      4. associate-/r* 67.2%

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

   5. Applied egg-rr 67.2%

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

      1. associate-*l/ 79.8%

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

      2. associate-*l/ 79.9%

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

      3. *-un-lft-identity 79.9%

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

   7. Applied egg-rr 79.9%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-15}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+147} \lor \neg \left(t \leq 6.3 \cdot 10^{+187}\right) \land t \leq 8.8 \cdot 10^{+207}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y - z}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;t_1 \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- y z))))
   (if (<= t -3.3e-186)
     (* (/ x (- t z)) (/ 1.0 y))
     (if (<= t 3.5e+19) (* t_1 (/ -1.0 z)) (/ t_1 t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (t <= -3.3e-186) {
		tmp = (x / (t - z)) * (1.0 / y);
	} else if (t <= 3.5e+19) {
		tmp = t_1 * (-1.0 / z);
	} else {
		tmp = t_1 / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y - z)
    if (t <= (-3.3d-186)) then
        tmp = (x / (t - z)) * (1.0d0 / y)
    else if (t <= 3.5d+19) then
        tmp = t_1 * ((-1.0d0) / z)
    else
        tmp = t_1 / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (t <= -3.3e-186) {
		tmp = (x / (t - z)) * (1.0 / y);
	} else if (t <= 3.5e+19) {
		tmp = t_1 * (-1.0 / z);
	} else {
		tmp = t_1 / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (y - z)
	tmp = 0
	if t <= -3.3e-186:
		tmp = (x / (t - z)) * (1.0 / y)
	elif t <= 3.5e+19:
		tmp = t_1 * (-1.0 / z)
	else:
		tmp = t_1 / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y - z))
	tmp = 0.0
	if (t <= -3.3e-186)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(1.0 / y));
	elseif (t <= 3.5e+19)
		tmp = Float64(t_1 * Float64(-1.0 / z));
	else
		tmp = Float64(t_1 / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y - z);
	tmp = 0.0;
	if (t <= -3.3e-186)
		tmp = (x / (t - z)) * (1.0 / y);
	elseif (t <= 3.5e+19)
		tmp = t_1 * (-1.0 / z);
	else
		tmp = t_1 / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-186], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e+19], N[(t$95$1 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.29999999999999999e-186

   1. Initial program 85.2%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. *-commutative 53.3%

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

      2. associate-/r* 60.1%

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

   5. Simplified 60.1%

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

      1. div-inv 60.1%

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

   7. Applied egg-rr 60.1%

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

   if -3.29999999999999999e-186 < t < 3.5e19

   1. Initial program 88.7%

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

      1. associate-/r* 93.0%

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

      2. div-inv 93.0%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in t around 0 79.2%

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

   if 3.5e19 < t

   1. Initial program 82.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 90.0%

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

      1. un-div-inv 90.1%

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

   7. Applied egg-rr 90.1%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y - z}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{-185}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t - z}{x}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+19}:\\ \;\;\;\;t_1 \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (- y z))))
   (if (<= t -1.26e-185)
     (/ 1.0 (* y (/ (- t z) x)))
     (if (<= t 7e+19) (* t_1 (/ -1.0 z)) (/ t_1 t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (t <= -1.26e-185) {
		tmp = 1.0 / (y * ((t - z) / x));
	} else if (t <= 7e+19) {
		tmp = t_1 * (-1.0 / z);
	} else {
		tmp = t_1 / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y - z)
    if (t <= (-1.26d-185)) then
        tmp = 1.0d0 / (y * ((t - z) / x))
    else if (t <= 7d+19) then
        tmp = t_1 * ((-1.0d0) / z)
    else
        tmp = t_1 / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y - z);
	double tmp;
	if (t <= -1.26e-185) {
		tmp = 1.0 / (y * ((t - z) / x));
	} else if (t <= 7e+19) {
		tmp = t_1 * (-1.0 / z);
	} else {
		tmp = t_1 / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (y - z)
	tmp = 0
	if t <= -1.26e-185:
		tmp = 1.0 / (y * ((t - z) / x))
	elif t <= 7e+19:
		tmp = t_1 * (-1.0 / z)
	else:
		tmp = t_1 / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y - z))
	tmp = 0.0
	if (t <= -1.26e-185)
		tmp = Float64(1.0 / Float64(y * Float64(Float64(t - z) / x)));
	elseif (t <= 7e+19)
		tmp = Float64(t_1 * Float64(-1.0 / z));
	else
		tmp = Float64(t_1 / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y - z);
	tmp = 0.0;
	if (t <= -1.26e-185)
		tmp = 1.0 / (y * ((t - z) / x));
	elseif (t <= 7e+19)
		tmp = t_1 * (-1.0 / z);
	else
		tmp = t_1 / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e-185], N[(1.0 / N[(y * N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e+19], N[(t$95$1 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.2599999999999999e-185

   1. Initial program 85.2%

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

   3. Taylor expanded in y around inf 53.3%

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

      1. *-commutative 53.3%

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

      2. associate-/r* 60.1%

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

   5. Simplified 60.1%

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

      1. clear-num 60.1%

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

      2. inv-pow 60.1%

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

      3. div-inv 60.1%

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

      4. clear-num 60.2%

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

   7. Applied egg-rr 60.2%

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

      1. unpow-1 60.2%

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

   9. Simplified 60.2%

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

   if -1.2599999999999999e-185 < t < 7e19

   1. Initial program 88.7%

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

      1. associate-/r* 93.0%

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

      2. div-inv 93.0%

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

   4. Applied egg-rr 93.0%

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

   5. Taylor expanded in t around 0 79.2%

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

   if 7e19 < t

   1. Initial program 82.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 90.0%

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

      1. un-div-inv 90.1%

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

   7. Applied egg-rr 90.1%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-185}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t - z}{x}}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e-61)
   (/ (/ x (- t z)) y)
   (if (<= y 7.6e-187) (/ (- x) (* z (- t z))) (/ (/ x (- y z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-61) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 7.6e-187) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.2d-61)) then
        tmp = (x / (t - z)) / y
    else if (y <= 7.6d-187) then
        tmp = -x / (z * (t - z))
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-61) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 7.6e-187) {
		tmp = -x / (z * (t - z));
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e-61:
		tmp = (x / (t - z)) / y
	elif y <= 7.6e-187:
		tmp = -x / (z * (t - z))
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e-61)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 7.6e-187)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e-61)
		tmp = (x / (t - z)) / y;
	elseif (y <= 7.6e-187)
		tmp = -x / (z * (t - z));
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e-61], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7.6e-187], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e-61

   1. Initial program 80.7%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/r* 83.3%

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

   5. Simplified 83.3%

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

   if -1.2e-61 < y < 7.60000000000000051e-187

   1. Initial program 90.8%

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

   3. Taylor expanded in y around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   5. Simplified 83.3%

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

   if 7.60000000000000051e-187 < y

   1. Initial program 86.4%

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

      1. associate-/r* 95.2%

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

      2. div-inv 95.2%

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

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in t around inf 65.4%

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

      1. un-div-inv 65.4%

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

   7. Applied egg-rr 65.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-187}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-173}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.6e-61)
   (/ (/ x (- t z)) y)
   (if (<= y 8.4e-173) (/ (- (/ x z)) (- t z)) (/ (/ x (- y z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e-61) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 8.4e-173) {
		tmp = -(x / z) / (t - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.6d-61)) then
        tmp = (x / (t - z)) / y
    else if (y <= 8.4d-173) then
        tmp = -(x / z) / (t - z)
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.6e-61) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 8.4e-173) {
		tmp = -(x / z) / (t - z);
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.6e-61:
		tmp = (x / (t - z)) / y
	elif y <= 8.4e-173:
		tmp = -(x / z) / (t - z)
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.6e-61)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 8.4e-173)
		tmp = Float64(Float64(-Float64(x / z)) / Float64(t - z));
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.6e-61)
		tmp = (x / (t - z)) / y;
	elseif (y <= 8.4e-173)
		tmp = -(x / z) / (t - z);
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.6e-61], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 8.4e-173], N[((-N[(x / z), $MachinePrecision]) / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000014e-61

   1. Initial program 80.7%

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

   3. Taylor expanded in y around inf 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-/r* 83.3%

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

   5. Simplified 83.3%

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

   if -3.60000000000000014e-61 < y < 8.40000000000000006e-173

   1. Initial program 90.1%

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

      1. associate-/r* 95.8%

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

      2. div-inv 95.8%

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

   4. Applied egg-rr 95.8%

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

      1. un-div-inv 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in y around 0 86.1%

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

      1. associate-*r/ 86.1%

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

      2. neg-mul-1 86.1%

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

   9. Simplified 86.1%

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

   if 8.40000000000000006e-173 < y

   1. Initial program 86.9%

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

      1. associate-/r* 95.1%

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

      2. div-inv 95.1%

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

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in t around inf 66.6%

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

      1. un-div-inv 66.6%

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

   7. Applied egg-rr 66.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-173}:\\ \;\;\;\;\frac{-\frac{x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+84} \lor \neg \left(z \leq 1.6 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.7e+84) (not (<= z 1.6e+60)))
   (/ x (* z (- t z)))
   (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e+84) || !(z <= 1.6e+60)) {
		tmp = x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2.7d+84)) .or. (.not. (z <= 1.6d+60))) then
        tmp = x / (z * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.7e+84) || !(z <= 1.6e+60)) {
		tmp = x / (z * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2.7e+84) or not (z <= 1.6e+60):
		tmp = x / (z * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.7e+84) || !(z <= 1.6e+60))
		tmp = Float64(x / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.7e+84) || ~((z <= 1.6e+60)))
		tmp = x / (z * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.7e+84], N[Not[LessEqual[z, 1.6e+60]], $MachinePrecision]], N[(x / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e84 or 1.59999999999999995e60 < z

   1. Initial program 77.1%

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

   3. Taylor expanded in y around 0 74.2%

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

      1. associate-*r/ 74.2%

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

      2. neg-mul-1 74.2%

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

   5. Simplified 74.2%

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

      1. expm1-log1p-u 74.0%

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

      2. expm1-udef 67.4%

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

      3. add-sqr-sqrt 29.3%

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

      4. sqrt-unprod 61.0%

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

      5. sqr-neg 61.0%

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

      6. sqrt-unprod 35.2%

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

      7. add-sqr-sqrt 64.5%

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

   7. Applied egg-rr 64.5%

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

      1. expm1-def 63.5%

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

      2. expm1-log1p 63.5%

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

   9. Simplified 63.5%

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

   if -2.7e84 < z < 1.59999999999999995e60

   1. Initial program 91.0%

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

   3. Taylor expanded in t around inf 66.8%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+84} \lor \neg \left(z \leq 1.6 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-127}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.05e-41)
   (* (/ x y) (/ 1.0 t))
   (if (<= t 1.36e-127) (/ (- x) (* y z)) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e-41) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 1.36e-127) {
		tmp = -x / (y * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.05d-41)) then
        tmp = (x / y) * (1.0d0 / t)
    else if (t <= 1.36d-127) then
        tmp = -x / (y * z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.05e-41) {
		tmp = (x / y) * (1.0 / t);
	} else if (t <= 1.36e-127) {
		tmp = -x / (y * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.05e-41:
		tmp = (x / y) * (1.0 / t)
	elif t <= 1.36e-127:
		tmp = -x / (y * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.05e-41)
		tmp = Float64(Float64(x / y) * Float64(1.0 / t));
	elseif (t <= 1.36e-127)
		tmp = Float64(Float64(-x) / Float64(y * z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.05e-41)
		tmp = (x / y) * (1.0 / t);
	elseif (t <= 1.36e-127)
		tmp = -x / (y * z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.05e-41], N[(N[(x / y), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.36e-127], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000006e-41

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0 50.5%

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

      1. *-un-lft-identity 50.5%

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

      2. times-frac 56.5%

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

   5. Applied egg-rr 56.5%

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

   if -1.05000000000000006e-41 < t < 1.3599999999999999e-127

   1. Initial program 85.9%

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

   3. Taylor expanded in y around inf 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 62.7%

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

   5. Simplified 62.7%

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

   6. Taylor expanded in t around 0 41.7%

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

      1. associate-*r/ 41.7%

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

      2. neg-mul-1 41.7%

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

      3. *-commutative 41.7%

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

   8. Simplified 41.7%

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

   if 1.3599999999999999e-127 < t

   1. Initial program 84.1%

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

   3. Taylor expanded in t around inf 70.6%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{t}\\ \mathbf{elif}\;t \leq 1.36 \cdot 10^{-127}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+18}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e-175)
   (/ (/ x y) t)
   (if (<= y 4e+18) (- (/ 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 <= -3.2e-175) {
		tmp = (x / y) / t;
	} else if (y <= 4e+18) {
		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 <= (-3.2d-175)) then
        tmp = (x / y) / t
    else if (y <= 4d+18) 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 <= -3.2e-175) {
		tmp = (x / y) / t;
	} else if (y <= 4e+18) {
		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 <= -3.2e-175:
		tmp = (x / y) / t
	elif y <= 4e+18:
		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 <= -3.2e-175)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 4e+18)
		tmp = Float64(-Float64(x / Float64(z * t)));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e-175)
		tmp = (x / y) / t;
	elseif (y <= 4e+18)
		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, -3.2e-175], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 4e+18], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e-175

   1. Initial program 83.9%

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

   3. Taylor expanded in z around 0 48.4%

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

      1. clear-num 49.7%

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

      2. associate-/r/ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-/r* 48.4%

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

   5. Applied egg-rr 48.4%

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

      1. associate-*l/ 53.8%

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

      2. associate-*l/ 53.8%

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

      3. *-un-lft-identity 53.8%

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

   7. Applied egg-rr 53.8%

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

   if -3.2e-175 < y < 4e18

   1. Initial program 88.5%

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

   3. Taylor expanded in y around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in z around 0 45.0%

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

      1. associate-*r/ 45.0%

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

      2. neg-mul-1 45.0%

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

   8. Simplified 45.0%

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

   if 4e18 < y

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-/r* 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in t around inf 63.2%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+18}:\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 91.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.4e+150) (* (/ x (- y z)) (/ -1.0 z)) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+150) {
		tmp = (x / (y - z)) * (-1.0 / z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.4d+150)) then
        tmp = (x / (y - z)) * ((-1.0d0) / z)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+150) {
		tmp = (x / (y - z)) * (-1.0 / z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.4e+150:
		tmp = (x / (y - z)) * (-1.0 / z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.4e+150)
		tmp = Float64(Float64(x / Float64(y - z)) * Float64(-1.0 / z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.4e+150)
		tmp = (x / (y - z)) * (-1.0 / z);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -6.4e+150], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000031e150

   1. Initial program 61.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 0 93.7%

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

   if -6.40000000000000031e150 < z

   1. Initial program 91.0%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y - z} \cdot \frac{-1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e-79) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-79) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.8d-79)) then
        tmp = x / (y * (t - z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e-79) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e-79:
		tmp = x / (y * (t - z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e-79)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e-79)
		tmp = x / (y * (t - z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e-79], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000001e-79

   1. Initial program 81.4%

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

   3. Taylor expanded in y around inf 76.4%

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

      1. *-commutative 76.4%

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

   5. Simplified 76.4%

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

   if -3.8000000000000001e-79 < y

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 57.1%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.22e-79) (/ (/ x y) (- t z)) (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e-79) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.22d-79)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.22e-79) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.22e-79:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.22e-79)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.22e-79)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.22e-79], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22e-79

   1. Initial program 81.4%

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

      1. associate-/r* 98.0%

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

      2. div-inv 98.0%

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

   4. Applied egg-rr 98.0%

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

      1. un-div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in y around inf 76.4%

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

      1. associate-/r* 83.2%

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

   9. Simplified 83.2%

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

   if -1.22e-79 < y

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 57.1%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e-79) (/ (/ x (- t z)) y) (/ x (* (- y z) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-79) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d-79)) then
        tmp = (x / (t - z)) / y
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-79) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-79:
		tmp = (x / (t - z)) / y
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-79)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e-79)
		tmp = (x / (t - z)) / y;
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e-79], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.40000000000000006e-79

   1. Initial program 81.4%

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

   3. Taylor expanded in y around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-/r* 83.8%

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

   5. Simplified 83.8%

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

   if -2.40000000000000006e-79 < y

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf 57.1%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.1e-79) (/ (/ x (- t z)) y) (/ (/ x (- y z)) t)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e-79) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.1d-79)) then
        tmp = (x / (t - z)) / y
    else
        tmp = (x / (y - z)) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.1e-79) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / (y - z)) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.1e-79:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / (y - z)) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.1e-79)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	else
		tmp = Float64(Float64(x / Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.1e-79)
		tmp = (x / (t - z)) / y;
	else
		tmp = (x / (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.1e-79], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999999e-79

   1. Initial program 81.4%

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

   3. Taylor expanded in y around inf 76.4%

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

      1. *-commutative 76.4%

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

      2. associate-/r* 83.8%

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

   5. Simplified 83.8%

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

   if -3.0999999999999999e-79 < y

   1. Initial program 88.0%

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

      1. associate-/r* 95.3%

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

      2. div-inv 95.3%

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

   4. Applied egg-rr 95.3%

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

   5. Taylor expanded in t around inf 61.5%

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

      1. un-div-inv 61.5%

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

   7. Applied egg-rr 61.5%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.6% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in z around 0 38.4%

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

4. Final simplification 38.4%

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

Alternative 18: 43.0% accurate, 1.8× speedup

Math

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

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(Float64(x / 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[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in y around inf 54.8%

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

   1. *-commutative 54.8%

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

   2. associate-/r* 59.5%

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

5. Simplified 59.5%

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

6. Taylor expanded in t around inf 40.2%

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

7. Final simplification 40.2%

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

Alternative 19: 43.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in z around 0 38.4%

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

   1. clear-num 38.9%

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

   2. associate-/r/ 38.4%

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

   3. *-commutative 38.4%

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

   4. associate-/r* 38.5%

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

5. Applied egg-rr 38.5%

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

   1. associate-*l/ 43.1%

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

   2. associate-*l/ 43.1%

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

   3. *-un-lft-identity 43.1%

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

7. Applied egg-rr 43.1%

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

8. Final simplification 43.1%

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

Developer target: 87.8% 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 2024020 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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