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

Percentage Accurate: 88.7% → 96.9%

Time: 16.3s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 1.0× speedup

Math

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

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 91.2%

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

3. Taylor expanded in x around 0 91.2%

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

   1. associate-/l/ 97.2%

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

5. Simplified 97.2%

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

6. Final simplification 97.2%

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

Alternative 2: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{x}{z \cdot \left(-t\right)}\\ t_3 := \frac{x}{z \cdot \left(-y\right)}\\ \mathbf{if}\;y \leq -5.6 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -18:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-85}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) t)) (t_2 (/ x (* z (- t)))) (t_3 (/ x (* z (- y)))))
   (if (<= y -5.6e+192)
     t_1
     (if (<= y -2e+34)
       t_3
       (if (<= y -18.0)
         t_1
         (if (<= y -1.9e-63)
           t_2
           (if (<= y -9.8e-85) t_3 (if (<= y 7e+20) 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) / t;
	double t_2 = x / (z * -t);
	double t_3 = x / (z * -y);
	double tmp;
	if (y <= -5.6e+192) {
		tmp = t_1;
	} else if (y <= -2e+34) {
		tmp = t_3;
	} else if (y <= -18.0) {
		tmp = t_1;
	} else if (y <= -1.9e-63) {
		tmp = t_2;
	} else if (y <= -9.8e-85) {
		tmp = t_3;
	} else if (y <= 7e+20) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (x / y) / t
    t_2 = x / (z * -t)
    t_3 = x / (z * -y)
    if (y <= (-5.6d+192)) then
        tmp = t_1
    else if (y <= (-2d+34)) then
        tmp = t_3
    else if (y <= (-18.0d0)) then
        tmp = t_1
    else if (y <= (-1.9d-63)) then
        tmp = t_2
    else if (y <= (-9.8d-85)) then
        tmp = t_3
    else if (y <= 7d+20) 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) / t;
	double t_2 = x / (z * -t);
	double t_3 = x / (z * -y);
	double tmp;
	if (y <= -5.6e+192) {
		tmp = t_1;
	} else if (y <= -2e+34) {
		tmp = t_3;
	} else if (y <= -18.0) {
		tmp = t_1;
	} else if (y <= -1.9e-63) {
		tmp = t_2;
	} else if (y <= -9.8e-85) {
		tmp = t_3;
	} else if (y <= 7e+20) {
		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) / t
	t_2 = x / (z * -t)
	t_3 = x / (z * -y)
	tmp = 0
	if y <= -5.6e+192:
		tmp = t_1
	elif y <= -2e+34:
		tmp = t_3
	elif y <= -18.0:
		tmp = t_1
	elif y <= -1.9e-63:
		tmp = t_2
	elif y <= -9.8e-85:
		tmp = t_3
	elif y <= 7e+20:
		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) / t)
	t_2 = Float64(x / Float64(z * Float64(-t)))
	t_3 = Float64(x / Float64(z * Float64(-y)))
	tmp = 0.0
	if (y <= -5.6e+192)
		tmp = t_1;
	elseif (y <= -2e+34)
		tmp = t_3;
	elseif (y <= -18.0)
		tmp = t_1;
	elseif (y <= -1.9e-63)
		tmp = t_2;
	elseif (y <= -9.8e-85)
		tmp = t_3;
	elseif (y <= 7e+20)
		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) / t;
	t_2 = x / (z * -t);
	t_3 = x / (z * -y);
	tmp = 0.0;
	if (y <= -5.6e+192)
		tmp = t_1;
	elseif (y <= -2e+34)
		tmp = t_3;
	elseif (y <= -18.0)
		tmp = t_1;
	elseif (y <= -1.9e-63)
		tmp = t_2;
	elseif (y <= -9.8e-85)
		tmp = t_3;
	elseif (y <= 7e+20)
		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] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.6e+192], t$95$1, If[LessEqual[y, -2e+34], t$95$3, If[LessEqual[y, -18.0], t$95$1, If[LessEqual[y, -1.9e-63], t$95$2, If[LessEqual[y, -9.8e-85], t$95$3, If[LessEqual[y, 7e+20], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.59999999999999952e192 or -1.99999999999999989e34 < y < -18 or 7e20 < y

   1. Initial program 89.9%

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

   3. Taylor expanded in x around 0 89.9%

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

      1. associate-/l/ 97.4%

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

   5. Simplified 97.4%

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

   6. Taylor expanded in z around 0 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/r* 64.5%

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

   8. Simplified 64.5%

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

   if -5.59999999999999952e192 < y < -1.99999999999999989e34 or -1.90000000000000009e-63 < y < -9.80000000000000029e-85

   1. Initial program 91.7%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around 0 73.8%

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

      1. associate-*r/ 73.8%

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

      2. neg-mul-1 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac2 60.4%

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

      3. *-commutative 60.4%

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

      4. distribute-rgt-neg-out 60.4%

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

   10. Simplified 60.4%

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

   if -18 < y < -1.90000000000000009e-63 or -9.80000000000000029e-85 < y < 7e20

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf 59.7%

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

      1. associate-/r* 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in y around 0 43.9%

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

      1. mul-1-neg 43.9%

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

      2. distribute-neg-frac2 43.9%

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

   8. Simplified 43.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+192}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -18:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t}\\ t_2 := \frac{x}{z \cdot \left(-t\right)}\\ t_3 := \frac{x}{z \cdot \left(-y\right)}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -780:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-83}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+20}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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) t)) (t_2 (/ x (* z (- t)))) (t_3 (/ x (* z (- y)))))
   (if (<= y -1.2e+192)
     t_1
     (if (<= y -3.2e+34)
       t_3
       (if (<= y -780.0)
         (* x (/ (/ 1.0 t) y))
         (if (<= y -5e-63)
           t_2
           (if (<= y -2.3e-83) t_3 (if (<= y 8.2e+20) 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) / t;
	double t_2 = x / (z * -t);
	double t_3 = x / (z * -y);
	double tmp;
	if (y <= -1.2e+192) {
		tmp = t_1;
	} else if (y <= -3.2e+34) {
		tmp = t_3;
	} else if (y <= -780.0) {
		tmp = x * ((1.0 / t) / y);
	} else if (y <= -5e-63) {
		tmp = t_2;
	} else if (y <= -2.3e-83) {
		tmp = t_3;
	} else if (y <= 8.2e+20) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (x / y) / t
    t_2 = x / (z * -t)
    t_3 = x / (z * -y)
    if (y <= (-1.2d+192)) then
        tmp = t_1
    else if (y <= (-3.2d+34)) then
        tmp = t_3
    else if (y <= (-780.0d0)) then
        tmp = x * ((1.0d0 / t) / y)
    else if (y <= (-5d-63)) then
        tmp = t_2
    else if (y <= (-2.3d-83)) then
        tmp = t_3
    else if (y <= 8.2d+20) 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) / t;
	double t_2 = x / (z * -t);
	double t_3 = x / (z * -y);
	double tmp;
	if (y <= -1.2e+192) {
		tmp = t_1;
	} else if (y <= -3.2e+34) {
		tmp = t_3;
	} else if (y <= -780.0) {
		tmp = x * ((1.0 / t) / y);
	} else if (y <= -5e-63) {
		tmp = t_2;
	} else if (y <= -2.3e-83) {
		tmp = t_3;
	} else if (y <= 8.2e+20) {
		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) / t
	t_2 = x / (z * -t)
	t_3 = x / (z * -y)
	tmp = 0
	if y <= -1.2e+192:
		tmp = t_1
	elif y <= -3.2e+34:
		tmp = t_3
	elif y <= -780.0:
		tmp = x * ((1.0 / t) / y)
	elif y <= -5e-63:
		tmp = t_2
	elif y <= -2.3e-83:
		tmp = t_3
	elif y <= 8.2e+20:
		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) / t)
	t_2 = Float64(x / Float64(z * Float64(-t)))
	t_3 = Float64(x / Float64(z * Float64(-y)))
	tmp = 0.0
	if (y <= -1.2e+192)
		tmp = t_1;
	elseif (y <= -3.2e+34)
		tmp = t_3;
	elseif (y <= -780.0)
		tmp = Float64(x * Float64(Float64(1.0 / t) / y));
	elseif (y <= -5e-63)
		tmp = t_2;
	elseif (y <= -2.3e-83)
		tmp = t_3;
	elseif (y <= 8.2e+20)
		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) / t;
	t_2 = x / (z * -t);
	t_3 = x / (z * -y);
	tmp = 0.0;
	if (y <= -1.2e+192)
		tmp = t_1;
	elseif (y <= -3.2e+34)
		tmp = t_3;
	elseif (y <= -780.0)
		tmp = x * ((1.0 / t) / y);
	elseif (y <= -5e-63)
		tmp = t_2;
	elseif (y <= -2.3e-83)
		tmp = t_3;
	elseif (y <= 8.2e+20)
		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] / t), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e+192], t$95$1, If[LessEqual[y, -3.2e+34], t$95$3, If[LessEqual[y, -780.0], N[(x * N[(N[(1.0 / t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-63], t$95$2, If[LessEqual[y, -2.3e-83], t$95$3, If[LessEqual[y, 8.2e+20], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1999999999999999e192 or 8.2e20 < y

   1. Initial program 89.0%

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

   3. Taylor expanded in x around 0 89.0%

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

      1. associate-/l/ 97.2%

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

   5. Simplified 97.2%

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

   6. Taylor expanded in z around 0 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/r* 65.6%

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

   8. Simplified 65.6%

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

   if -1.1999999999999999e192 < y < -3.1999999999999998e34 or -5.0000000000000002e-63 < y < -2.2999999999999999e-83

   1. Initial program 91.7%

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

      1. associate-/l/ 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in t around 0 73.8%

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

      1. associate-*r/ 73.8%

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

      2. neg-mul-1 73.8%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in z around 0 60.4%

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

      1. mul-1-neg 60.4%

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

      2. distribute-neg-frac2 60.4%

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

      3. *-commutative 60.4%

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

      4. distribute-rgt-neg-out 60.4%

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

   10. Simplified 60.4%

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

   if -3.1999999999999998e34 < y < -780

   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 61.9%

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

      1. clear-num 61.9%

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

      2. associate-/r/ 61.9%

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

      3. associate-/r* 61.9%

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

   5. Applied egg-rr 61.9%

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

   if -780 < y < -5.0000000000000002e-63 or -2.2999999999999999e-83 < y < 8.2e20

   1. Initial program 91.8%

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

   3. Taylor expanded in t around inf 59.3%

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

      1. associate-/r* 60.3%

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

   5. Simplified 60.3%

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

   6. Taylor expanded in y around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. distribute-neg-frac2 43.6%

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

   8. Simplified 43.6%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+192}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq -780:\\ \;\;\;\;x \cdot \frac{\frac{1}{t}}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \end{array} \]

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-71)
   (/ (/ x t) y)
   (if (<= t 1.46e-158)
     (/ x (* z (- y)))
     (if (<= t 1.4e+18)
       (/ (/ x y) t)
       (if (<= t 7.8e+174) (/ x (* z (- t))) (/ 1.0 (/ y (/ x 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-71) {
		tmp = (x / t) / y;
	} else if (t <= 1.46e-158) {
		tmp = x / (z * -y);
	} else if (t <= 1.4e+18) {
		tmp = (x / y) / t;
	} else if (t <= 7.8e+174) {
		tmp = x / (z * -t);
	} else {
		tmp = 1.0 / (y / (x / 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-71)) then
        tmp = (x / t) / y
    else if (t <= 1.46d-158) then
        tmp = x / (z * -y)
    else if (t <= 1.4d+18) then
        tmp = (x / y) / t
    else if (t <= 7.8d+174) then
        tmp = x / (z * -t)
    else
        tmp = 1.0d0 / (y / (x / 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-71) {
		tmp = (x / t) / y;
	} else if (t <= 1.46e-158) {
		tmp = x / (z * -y);
	} else if (t <= 1.4e+18) {
		tmp = (x / y) / t;
	} else if (t <= 7.8e+174) {
		tmp = x / (z * -t);
	} else {
		tmp = 1.0 / (y / (x / 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-71:
		tmp = (x / t) / y
	elif t <= 1.46e-158:
		tmp = x / (z * -y)
	elif t <= 1.4e+18:
		tmp = (x / y) / t
	elif t <= 7.8e+174:
		tmp = x / (z * -t)
	else:
		tmp = 1.0 / (y / (x / 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-71)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 1.46e-158)
		tmp = Float64(x / Float64(z * Float64(-y)));
	elseif (t <= 1.4e+18)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 7.8e+174)
		tmp = Float64(x / Float64(z * Float64(-t)));
	else
		tmp = Float64(1.0 / Float64(y / Float64(x / 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-71)
		tmp = (x / t) / y;
	elseif (t <= 1.46e-158)
		tmp = x / (z * -y);
	elseif (t <= 1.4e+18)
		tmp = (x / y) / t;
	elseif (t <= 7.8e+174)
		tmp = x / (z * -t);
	else
		tmp = 1.0 / (y / (x / 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-71], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.46e-158], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+18], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 7.8e+174], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.0500000000000001e-71

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 51.7%

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

      1. clear-num 53.0%

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

      2. associate-/r/ 51.6%

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

      3. associate-/r* 51.7%

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

   5. Applied egg-rr 51.7%

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

      1. associate-*l/ 58.5%

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

      2. associate-*l/ 58.6%

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

      3. *-un-lft-identity 58.6%

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

   7. Applied egg-rr 58.6%

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

   if -1.0500000000000001e-71 < t < 1.4599999999999999e-158

   1. Initial program 91.2%

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

      1. associate-/l/ 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in t around 0 86.5%

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

      1. associate-*r/ 86.5%

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

      2. neg-mul-1 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in z around 0 40.1%

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

      1. mul-1-neg 40.1%

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

      2. distribute-neg-frac2 40.1%

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

      3. *-commutative 40.1%

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

      4. distribute-rgt-neg-out 40.1%

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

   10. Simplified 40.1%

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

   if 1.4599999999999999e-158 < t < 1.4e18

   1. Initial program 91.8%

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

   3. Taylor expanded in x around 0 91.8%

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

      1. associate-/l/ 99.8%

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

   5. Simplified 99.8%

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

   6. Taylor expanded in z around 0 37.7%

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

      1. *-commutative 37.7%

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

      2. associate-/r* 42.9%

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

   8. Simplified 42.9%

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

   if 1.4e18 < t < 7.79999999999999962e174

   1. Initial program 92.6%

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

   3. Taylor expanded in t around inf 85.4%

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

      1. associate-/r* 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in y around 0 61.1%

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

      1. mul-1-neg 61.1%

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

      2. distribute-neg-frac2 61.1%

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

   8. Simplified 61.1%

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

   if 7.79999999999999962e174 < t

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0 59.7%

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

      1. clear-num 59.7%

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

      2. associate-/r/ 59.7%

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

      3. associate-/r* 59.7%

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

   5. Applied egg-rr 59.7%

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

      1. associate-*l/ 66.5%

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

      2. clear-num 66.6%

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

      3. associate-*l/ 66.6%

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

      4. *-un-lft-identity 66.6%

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

   7. Applied egg-rr 66.6%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.46 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+174}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{y}}{t - z}\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{+93}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -14:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x y) (- t z))))
   (if (<= y -1.4e+93)
     t_1
     (if (<= y -4.6e+32)
       (/ x (* z (- z y)))
       (if (<= y -14.0)
         t_1
         (if (<= y 7e-8) (/ (/ x z) (- z t)) (/ (/ x t) (- y z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / (t - z);
	double tmp;
	if (y <= -1.4e+93) {
		tmp = t_1;
	} else if (y <= -4.6e+32) {
		tmp = x / (z * (z - y));
	} else if (y <= -14.0) {
		tmp = t_1;
	} else if (y <= 7e-8) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) / (t - z)
    if (y <= (-1.4d+93)) then
        tmp = t_1
    else if (y <= (-4.6d+32)) then
        tmp = x / (z * (z - y))
    else if (y <= (-14.0d0)) then
        tmp = t_1
    else if (y <= 7d-8) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) / (t - z);
	double tmp;
	if (y <= -1.4e+93) {
		tmp = t_1;
	} else if (y <= -4.6e+32) {
		tmp = x / (z * (z - y));
	} else if (y <= -14.0) {
		tmp = t_1;
	} else if (y <= 7e-8) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / y) / (t - z)
	tmp = 0
	if y <= -1.4e+93:
		tmp = t_1
	elif y <= -4.6e+32:
		tmp = x / (z * (z - y))
	elif y <= -14.0:
		tmp = t_1
	elif y <= 7e-8:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) / Float64(t - z))
	tmp = 0.0
	if (y <= -1.4e+93)
		tmp = t_1;
	elseif (y <= -4.6e+32)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (y <= -14.0)
		tmp = t_1;
	elseif (y <= 7e-8)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) / (t - z);
	tmp = 0.0;
	if (y <= -1.4e+93)
		tmp = t_1;
	elseif (y <= -4.6e+32)
		tmp = x / (z * (z - y));
	elseif (y <= -14.0)
		tmp = t_1;
	elseif (y <= 7e-8)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.4e+93], t$95$1, If[LessEqual[y, -4.6e+32], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -14.0], t$95$1, If[LessEqual[y, 7e-8], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.39999999999999994e93 or -4.5999999999999999e32 < y < -14

   1. Initial program 93.9%

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

   3. Taylor expanded in y around inf 91.9%

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

      1. associate-/r* 93.9%

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

   5. Simplified 93.9%

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

   if -1.39999999999999994e93 < y < -4.5999999999999999e32

   1. Initial program 89.3%

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

      1. associate-/l/ 99.8%

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

      2. div-inv 99.5%

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

      3. div-inv 99.3%

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

      4. associate-*l* 88.5%

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

   4. Applied egg-rr 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-*r* 99.5%

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

      3. div-inv 99.8%

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

      4. clear-num 99.7%

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

      5. frac-times 99.8%

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

      6. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 89.2%

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

      1. mul-1-neg 89.2%

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

      2. associate-/l* 89.0%

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

      3. distribute-lft-neg-out 89.0%

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

      4. *-commutative 89.0%

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

   9. Simplified 89.0%

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

       1. associate-/r* 88.8%

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

       2. add-sqr-sqrt 44.1%

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

       3. clear-num 44.1%

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

       4. sqrt-unprod 56.0%

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

       5. sqr-neg 56.0%

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

       6. sqrt-unprod 11.5%

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

       7. add-sqr-sqrt 12.6%

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

       8. associate-/r* 12.6%

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

       9. associate-/l/ 12.6%

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

       10. frac-2neg 12.6%

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

       11. div-inv 12.6%

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

       12. distribute-neg-frac2 12.6%

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

       13. add-sqr-sqrt 1.1%

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

       14. sqrt-unprod 45.6%

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

       15. sqr-neg 45.6%

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

       16. sqrt-unprod 44.1%

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

       17. add-sqr-sqrt 88.6%

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

       18. sub-neg 88.6%

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

       19. distribute-neg-in 88.6%

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

       20. add-sqr-sqrt 44.1%

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

       21. sqrt-unprod 66.6%

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

       22. sqr-neg 66.6%

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

       23. sqrt-unprod 22.5%

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

       24. add-sqr-sqrt 55.8%

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

   11. Applied egg-rr 88.6%

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

       1. associate-*r/ 89.0%

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

       2. *-rgt-identity 89.0%

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

       3. associate-/r* 89.2%

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

       4. +-commutative 89.2%

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

       5. unsub-neg 89.2%

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

   13. Simplified 89.2%

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

   if -14 < y < 7.00000000000000048e-8

   1. Initial program 92.0%

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

   3. Taylor expanded in x around 0 92.0%

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

      1. associate-/l/ 96.4%

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

   5. Simplified 96.4%

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

   6. Taylor expanded in y around 0 79.6%

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

      1. mul-1-neg 79.6%

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

      2. distribute-neg-frac2 79.6%

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

   8. Simplified 79.6%

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

   if 7.00000000000000048e-8 < y

   1. Initial program 87.5%

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

   3. Taylor expanded in t around inf 57.7%

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

      1. associate-/r* 61.3%

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

   5. Simplified 61.3%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+93}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;y \leq -14:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-8}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))))
   (if (<= t_1 -5e-261) t_1 (/ (/ x (- t z)) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-261) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    if (t_1 <= (-5d-261)) then
        tmp = t_1
    else
        tmp = (x / (t - z)) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double tmp;
	if (t_1 <= -5e-261) {
		tmp = t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	tmp = 0
	if t_1 <= -5e-261:
		tmp = t_1
	else:
		tmp = (x / (t - z)) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	tmp = 0.0
	if (t_1 <= -5e-261)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	tmp = 0.0;
	if (t_1 <= -5e-261)
		tmp = t_1;
	else
		tmp = (x / (t - z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-261], t$95$1, N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z))) < -4.99999999999999981e-261

   1. Initial program 97.8%

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

   if -4.99999999999999981e-261 < (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

   1. Initial program 88.8%

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

      1. associate-/l/ 99.3%

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

   3. Simplified 99.3%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \leq -5 \cdot 10^{-261}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= t -8.8e-52)
   (/ (/ x t) y)
   (if (<= t 1.65e-158) (/ x (* 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 (t <= -8.8e-52) {
		tmp = (x / t) / y;
	} else if (t <= 1.65e-158) {
		tmp = x / (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 (t <= (-8.8d-52)) then
        tmp = (x / t) / y
    else if (t <= 1.65d-158) then
        tmp = x / (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 (t <= -8.8e-52) {
		tmp = (x / t) / y;
	} else if (t <= 1.65e-158) {
		tmp = x / (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 t <= -8.8e-52:
		tmp = (x / t) / y
	elif t <= 1.65e-158:
		tmp = x / (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 (t <= -8.8e-52)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 1.65e-158)
		tmp = Float64(x / Float64(z * Float64(-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 (t <= -8.8e-52)
		tmp = (x / t) / y;
	elseif (t <= 1.65e-158)
		tmp = x / (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[t, -8.8e-52], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.65e-158], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.80000000000000036e-52

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 53.4%

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

      1. clear-num 54.9%

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

      2. associate-/r/ 53.4%

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

      3. associate-/r* 53.4%

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

   5. Applied egg-rr 53.4%

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

      1. associate-*l/ 60.9%

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

      2. associate-*l/ 61.0%

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

      3. *-un-lft-identity 61.0%

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

   7. Applied egg-rr 61.0%

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

   if -8.80000000000000036e-52 < t < 1.6500000000000001e-158

   1. Initial program 91.8%

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

      1. associate-/l/ 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around 0 87.6%

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

      1. associate-*r/ 87.6%

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

      2. neg-mul-1 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in z around 0 40.6%

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

      1. mul-1-neg 40.6%

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

      2. distribute-neg-frac2 40.6%

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

      3. *-commutative 40.6%

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

      4. distribute-rgt-neg-out 40.6%

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

   10. Simplified 40.6%

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

   if 1.6500000000000001e-158 < t

   1. Initial program 91.3%

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

   3. Taylor expanded in t around inf 71.3%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= t -1.38e-45)
   (/ (/ x t) y)
   (if (<= t 5.1e+17) (/ x (* z (- 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 (t <= -1.38e-45) {
		tmp = (x / t) / y;
	} else if (t <= 5.1e+17) {
		tmp = x / (z * (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 (t <= (-1.38d-45)) then
        tmp = (x / t) / y
    else if (t <= 5.1d+17) then
        tmp = x / (z * (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 (t <= -1.38e-45) {
		tmp = (x / t) / y;
	} else if (t <= 5.1e+17) {
		tmp = x / (z * (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 t <= -1.38e-45:
		tmp = (x / t) / y
	elif t <= 5.1e+17:
		tmp = x / (z * (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 (t <= -1.38e-45)
		tmp = Float64(Float64(x / t) / y);
	elseif (t <= 5.1e+17)
		tmp = Float64(x / Float64(z * Float64(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 (t <= -1.38e-45)
		tmp = (x / t) / y;
	elseif (t <= 5.1e+17)
		tmp = x / (z * (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[t, -1.38e-45], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 5.1e+17], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.38e-45

   1. Initial program 90.5%

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

   3. Taylor expanded in z around 0 53.4%

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

      1. clear-num 54.9%

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

      2. associate-/r/ 53.4%

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

      3. associate-/r* 53.4%

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

   5. Applied egg-rr 53.4%

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

      1. associate-*l/ 60.9%

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

      2. associate-*l/ 61.0%

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

      3. *-un-lft-identity 61.0%

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

   7. Applied egg-rr 61.0%

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

   if -1.38e-45 < t < 5.1e17

   1. Initial program 91.8%

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

      1. associate-/l/ 99.1%

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

      2. div-inv 99.0%

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

      3. div-inv 98.8%

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

      4. associate-*l* 91.8%

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

   4. Applied egg-rr 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*r* 98.1%

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

      3. div-inv 98.2%

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

      4. clear-num 98.2%

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

      5. frac-times 97.6%

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

      6. metadata-eval 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in t around 0 77.2%

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

      1. mul-1-neg 77.2%

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

      2. associate-/l* 84.4%

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

      3. distribute-lft-neg-out 84.4%

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

      4. *-commutative 84.4%

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

   9. Simplified 84.4%

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

       1. associate-/r* 85.1%

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

       2. add-sqr-sqrt 50.8%

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

       3. clear-num 50.8%

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

       4. sqrt-unprod 56.9%

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

       5. sqr-neg 56.9%

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

       6. sqrt-unprod 17.7%

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

       7. add-sqr-sqrt 37.4%

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

       8. associate-/r* 36.7%

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

       9. associate-/l/ 36.6%

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

       10. frac-2neg 36.6%

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

       11. div-inv 36.6%

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

       12. distribute-neg-frac2 36.6%

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

       13. add-sqr-sqrt 18.9%

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

       14. sqrt-unprod 52.0%

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

       15. sqr-neg 52.0%

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

       16. sqrt-unprod 34.0%

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

       17. add-sqr-sqrt 84.3%

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

       18. sub-neg 84.3%

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

       19. distribute-neg-in 84.3%

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

       20. add-sqr-sqrt 50.1%

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

       21. sqrt-unprod 67.6%

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

       22. sqr-neg 67.6%

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

       23. sqrt-unprod 25.4%

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

       24. add-sqr-sqrt 56.7%

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

   11. Applied egg-rr 84.3%

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

       1. associate-*r/ 84.3%

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

       2. *-rgt-identity 84.3%

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

       3. associate-/r* 77.8%

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

       4. +-commutative 77.8%

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

       5. unsub-neg 77.8%

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

   13. Simplified 77.8%

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

   if 5.1e17 < t

   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 87.5%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

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 (<= t -5.2e-141)
   (/ x (* y (- t z)))
   (if (<= t 4.6e+17) (/ x (* z (- 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 (t <= -5.2e-141) {
		tmp = x / (y * (t - z));
	} else if (t <= 4.6e+17) {
		tmp = x / (z * (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 (t <= (-5.2d-141)) then
        tmp = x / (y * (t - z))
    else if (t <= 4.6d+17) then
        tmp = x / (z * (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 (t <= -5.2e-141) {
		tmp = x / (y * (t - z));
	} else if (t <= 4.6e+17) {
		tmp = x / (z * (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 t <= -5.2e-141:
		tmp = x / (y * (t - z))
	elif t <= 4.6e+17:
		tmp = x / (z * (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 (t <= -5.2e-141)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 4.6e+17)
		tmp = Float64(x / Float64(z * Float64(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 (t <= -5.2e-141)
		tmp = x / (y * (t - z));
	elseif (t <= 4.6e+17)
		tmp = x / (z * (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[t, -5.2e-141], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+17], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.20000000000000022e-141

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   if -5.20000000000000022e-141 < t < 4.6e17

   1. Initial program 91.0%

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

      1. associate-/l/ 98.9%

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

      2. div-inv 98.8%

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

      3. div-inv 98.6%

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

      4. associate-*l* 91.1%

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

   4. Applied egg-rr 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*r* 97.7%

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

      3. div-inv 97.9%

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

      4. clear-num 97.8%

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

      5. frac-times 97.2%

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

      6. metadata-eval 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in t around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 86.7%

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

      3. distribute-lft-neg-out 86.7%

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

      4. *-commutative 86.7%

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

   9. Simplified 86.7%

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

       1. associate-/r* 87.5%

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

       2. add-sqr-sqrt 53.5%

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

       3. clear-num 53.5%

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

       4. sqrt-unprod 59.0%

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

       5. sqr-neg 59.0%

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

       6. sqrt-unprod 17.8%

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

       7. add-sqr-sqrt 34.8%

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

       8. associate-/r* 34.0%

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

       9. associate-/l/ 33.9%

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

       10. frac-2neg 33.9%

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

       11. div-inv 33.9%

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

       12. distribute-neg-frac2 33.9%

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

       13. add-sqr-sqrt 16.1%

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

       14. sqrt-unprod 49.6%

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

       15. sqr-neg 49.6%

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

       16. sqrt-unprod 33.7%

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

       17. add-sqr-sqrt 86.5%

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

       18. sub-neg 86.5%

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

       19. distribute-neg-in 86.5%

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

       20. add-sqr-sqrt 52.6%

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

       21. sqrt-unprod 70.1%

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

       22. sqr-neg 70.1%

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

       23. sqrt-unprod 26.2%

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

       24. add-sqr-sqrt 57.6%

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

   11. Applied egg-rr 86.5%

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

       1. associate-*r/ 86.5%

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

       2. *-rgt-identity 86.5%

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

       3. associate-/r* 79.6%

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

       4. +-commutative 79.6%

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

       5. unsub-neg 79.6%

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

   13. Simplified 79.6%

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

   if 4.6e17 < t

   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 87.5%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.5e-140)
   (/ x (* y (- t z)))
   (if (<= t 4.6e+17) (/ x (* z (- z y))) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-140) {
		tmp = x / (y * (t - z));
	} else if (t <= 4.6e+17) {
		tmp = x / (z * (z - y));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.5d-140)) then
        tmp = x / (y * (t - z))
    else if (t <= 4.6d+17) then
        tmp = x / (z * (z - y))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.5e-140) {
		tmp = x / (y * (t - z));
	} else if (t <= 4.6e+17) {
		tmp = x / (z * (z - y));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.5e-140:
		tmp = x / (y * (t - z))
	elif t <= 4.6e+17:
		tmp = x / (z * (z - y))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.5e-140)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 4.6e+17)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.5e-140)
		tmp = x / (y * (t - z));
	elseif (t <= 4.6e+17)
		tmp = x / (z * (z - y));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.5e-140], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+17], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.50000000000000009e-140

   1. Initial program 91.5%

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

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

   5. Simplified 53.3%

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

   if -1.50000000000000009e-140 < t < 4.6e17

   1. Initial program 91.1%

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

      1. associate-/l/ 98.9%

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

      2. div-inv 98.8%

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

      3. div-inv 98.6%

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

      4. associate-*l* 91.2%

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

   4. Applied egg-rr 91.2%

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

      1. *-commutative 91.2%

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

      2. associate-*r* 97.8%

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

      3. div-inv 97.9%

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

      4. clear-num 97.8%

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

      5. frac-times 97.2%

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

      6. metadata-eval 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in t around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-/l* 86.8%

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

      3. distribute-lft-neg-out 86.8%

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

      4. *-commutative 86.8%

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

   9. Simplified 86.8%

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

       1. associate-/r* 87.6%

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

       2. add-sqr-sqrt 52.9%

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

       3. clear-num 53.0%

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

       4. sqrt-unprod 59.4%

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

       5. sqr-neg 59.4%

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

       6. sqrt-unprod 18.6%

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

       7. add-sqr-sqrt 35.5%

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

       8. associate-/r* 34.6%

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

       9. associate-/l/ 34.5%

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

       10. frac-2neg 34.5%

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

       11. div-inv 34.5%

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

       12. distribute-neg-frac2 34.5%

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

       13. add-sqr-sqrt 15.9%

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

       14. sqrt-unprod 50.1%

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

       15. sqr-neg 50.1%

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

       16. sqrt-unprod 34.4%

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

       17. add-sqr-sqrt 86.6%

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

       18. sub-neg 86.6%

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

       19. distribute-neg-in 86.6%

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

       20. add-sqr-sqrt 52.0%

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

       21. sqrt-unprod 70.4%

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

       22. sqr-neg 70.4%

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

       23. sqrt-unprod 27.0%

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

       24. add-sqr-sqrt 58.0%

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

   11. Applied egg-rr 86.6%

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

       1. associate-*r/ 86.7%

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

       2. *-rgt-identity 86.7%

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

       3. associate-/r* 79.8%

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

       4. +-commutative 79.8%

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

       5. unsub-neg 79.8%

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

   13. Simplified 79.8%

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

   if 4.6e17 < t

   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 87.5%

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

      1. associate-/r* 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-140}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.5e-141)
   (/ (/ x y) (- t z))
   (if (<= t 4.6e+17) (/ x (* z (- z y))) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e-141) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.6e+17) {
		tmp = x / (z * (z - y));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.5d-141)) then
        tmp = (x / y) / (t - z)
    else if (t <= 4.6d+17) then
        tmp = x / (z * (z - y))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e-141) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.6e+17) {
		tmp = x / (z * (z - y));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.5e-141:
		tmp = (x / y) / (t - z)
	elif t <= 4.6e+17:
		tmp = x / (z * (z - y))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.5e-141)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 4.6e+17)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.5e-141)
		tmp = (x / y) / (t - z);
	elseif (t <= 4.6e+17)
		tmp = x / (z * (z - y));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.5e-141], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+17], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.5e-141

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 52.8%

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

      1. associate-/r* 53.2%

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

   5. Simplified 53.2%

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

   if -4.5e-141 < t < 4.6e17

   1. Initial program 91.0%

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

      1. associate-/l/ 98.9%

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

      2. div-inv 98.8%

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

      3. div-inv 98.6%

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

      4. associate-*l* 91.1%

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

   4. Applied egg-rr 91.1%

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

      1. *-commutative 91.1%

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

      2. associate-*r* 97.7%

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

      3. div-inv 97.9%

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

      4. clear-num 97.8%

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

      5. frac-times 97.2%

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

      6. metadata-eval 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in t around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 86.7%

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

      3. distribute-lft-neg-out 86.7%

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

      4. *-commutative 86.7%

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

   9. Simplified 86.7%

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

       1. associate-/r* 87.5%

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

       2. add-sqr-sqrt 53.5%

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

       3. clear-num 53.5%

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

       4. sqrt-unprod 59.0%

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

       5. sqr-neg 59.0%

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

       6. sqrt-unprod 17.8%

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

       7. add-sqr-sqrt 34.8%

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

       8. associate-/r* 34.0%

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

       9. associate-/l/ 33.9%

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

       10. frac-2neg 33.9%

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

       11. div-inv 33.9%

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

       12. distribute-neg-frac2 33.9%

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

       13. add-sqr-sqrt 16.1%

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

       14. sqrt-unprod 49.6%

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

       15. sqr-neg 49.6%

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

       16. sqrt-unprod 33.7%

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

       17. add-sqr-sqrt 86.5%

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

       18. sub-neg 86.5%

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

       19. distribute-neg-in 86.5%

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

       20. add-sqr-sqrt 52.6%

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

       21. sqrt-unprod 70.1%

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

       22. sqr-neg 70.1%

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

       23. sqrt-unprod 26.2%

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

       24. add-sqr-sqrt 57.6%

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

   11. Applied egg-rr 86.5%

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

       1. associate-*r/ 86.5%

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

       2. *-rgt-identity 86.5%

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

       3. associate-/r* 79.6%

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

       4. +-commutative 79.6%

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

       5. unsub-neg 79.6%

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

   13. Simplified 79.6%

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

   if 4.6e17 < t

   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 87.5%

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

      1. associate-/r* 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.6e-140)
   (/ (/ x y) (- t z))
   (if (<= t 3.7e+18) (/ (/ x z) (- z y)) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-140) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.7e+18) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.6d-140)) then
        tmp = (x / y) / (t - z)
    else if (t <= 3.7d+18) then
        tmp = (x / z) / (z - y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.6e-140) {
		tmp = (x / y) / (t - z);
	} else if (t <= 3.7e+18) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.6e-140:
		tmp = (x / y) / (t - z)
	elif t <= 3.7e+18:
		tmp = (x / z) / (z - y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.6e-140)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 3.7e+18)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.6e-140)
		tmp = (x / y) / (t - z);
	elseif (t <= 3.7e+18)
		tmp = (x / z) / (z - y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -1.6e-140], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+18], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6000000000000001e-140

   1. Initial program 91.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. associate-/r* 53.6%

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

   5. Simplified 53.6%

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

   if -1.6000000000000001e-140 < t < 3.7e18

   1. Initial program 91.1%

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

      1. associate-/l/ 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around 0 86.7%

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

      1. associate-*r/ 86.7%

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

      2. neg-mul-1 86.7%

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

   7. Simplified 86.7%

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

   if 3.7e18 < t

   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 87.5%

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

      1. associate-/r* 91.7%

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

   5. Simplified 91.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-140}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -12.5 \lor \neg \left(y \leq 6.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -12.5) (not (<= y 6.8e+20))) (/ (/ x y) t) (/ x (* z (- t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -12.5) || !(y <= 6.8e+20)) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-12.5d0)) .or. (.not. (y <= 6.8d+20))) then
        tmp = (x / y) / t
    else
        tmp = x / (z * -t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -12.5) || !(y <= 6.8e+20)) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (z * -t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (y <= -12.5) or not (y <= 6.8e+20):
		tmp = (x / y) / t
	else:
		tmp = x / (z * -t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -12.5) || !(y <= 6.8e+20))
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(x / Float64(z * Float64(-t)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -12.5) || ~((y <= 6.8e+20)))
		tmp = (x / y) / t;
	else
		tmp = x / (z * -t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[y, -12.5], N[Not[LessEqual[y, 6.8e+20]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(z * (-t)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -12.5 or 6.8e20 < y

   1. Initial program 90.0%

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

   3. Taylor expanded in x around 0 90.0%

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

      1. associate-/l/ 98.1%

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

   5. Simplified 98.1%

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

   6. Taylor expanded in z around 0 52.4%

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

      1. *-commutative 52.4%

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

      2. associate-/r* 59.8%

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

   8. Simplified 59.8%

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

   if -12.5 < y < 6.8e20

   1. Initial program 92.0%

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

   3. Taylor expanded in t around inf 58.5%

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

      1. associate-/r* 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in y around 0 43.2%

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

      1. mul-1-neg 43.2%

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

      2. distribute-neg-frac2 43.2%

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

   8. Simplified 43.2%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12.5 \lor \neg \left(y \leq 6.8 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(-t\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 91.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

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 -2.5e+151) (/ (/ x z) (- z t)) (/ 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 <= -2.5e+151) {
		tmp = (x / z) / (z - t);
	} 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 <= (-2.5d+151)) then
        tmp = (x / z) / (z - t)
    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 <= -2.5e+151) {
		tmp = (x / z) / (z - t);
	} 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 <= -2.5e+151:
		tmp = (x / z) / (z - t)
	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 <= -2.5e+151)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	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 <= -2.5e+151)
		tmp = (x / z) / (z - t);
	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, -2.5e+151], N[(N[(x / z), $MachinePrecision] / N[(z - t), $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 < -2.5000000000000001e151

   1. Initial program 67.6%

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

   3. Taylor expanded in x around 0 67.6%

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

      1. associate-/l/ 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 95.8%

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

      1. mul-1-neg 95.8%

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

      2. distribute-neg-frac2 95.8%

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

   8. Simplified 95.8%

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

   if -2.5000000000000001e151 < z

   1. Initial program 94.6%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 43.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.2e+113) (/ x (* y t)) (/ x (* y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.2e+113) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 5.2d+113) then
        tmp = x / (y * t)
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.2e+113) {
		tmp = x / (y * t);
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 5.2e+113:
		tmp = x / (y * t)
	else:
		tmp = x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.2e+113)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.2e+113)
		tmp = x / (y * t);
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, 5.2e+113], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.1999999999999998e113

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 41.5%

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

   if 5.1999999999999998e113 < z

   1. Initial program 87.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.4%

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

      1. associate-*r/ 94.4%

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

      2. neg-mul-1 94.4%

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

   7. Simplified 94.4%

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

      1. div-inv 94.4%

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

      2. associate-/l* 88.8%

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

      3. add-sqr-sqrt 56.2%

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

      4. sqrt-unprod 83.3%

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

      5. sqr-neg 83.3%

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

      6. sqrt-unprod 32.6%

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

      7. add-sqr-sqrt 82.3%

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

   9. Applied egg-rr 82.3%

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

       1. associate-/r* 82.8%

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

       2. associate-*r/ 82.8%

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

       3. *-rgt-identity 82.8%

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

       4. associate-/r* 82.3%

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

   11. Simplified 82.3%

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

   12. Taylor expanded in z around 0 31.7%

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

       1. *-commutative 31.7%

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

   14. Simplified 31.7%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 5.1 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 5.1e+113) (/ (/ x t) y) (/ x (* y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.1e+113) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 5.1d+113) then
        tmp = (x / t) / y
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 5.1e+113) {
		tmp = (x / t) / y;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 5.1e+113:
		tmp = (x / t) / y
	else:
		tmp = x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 5.1e+113)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 5.1e+113)
		tmp = (x / t) / y;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, 5.1e+113], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.09999999999999994e113

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 41.5%

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

      1. clear-num 42.0%

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

      2. associate-/r/ 41.5%

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

      3. associate-/r* 41.5%

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

   5. Applied egg-rr 41.5%

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

      1. associate-*l/ 44.7%

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

      2. associate-*l/ 44.8%

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

      3. *-un-lft-identity 44.8%

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

   7. Applied egg-rr 44.8%

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

   if 5.09999999999999994e113 < z

   1. Initial program 87.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.4%

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

      1. associate-*r/ 94.4%

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

      2. neg-mul-1 94.4%

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

   7. Simplified 94.4%

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

      1. div-inv 94.4%

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

      2. associate-/l* 88.8%

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

      3. add-sqr-sqrt 56.2%

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

      4. sqrt-unprod 83.3%

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

      5. sqr-neg 83.3%

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

      6. sqrt-unprod 32.6%

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

      7. add-sqr-sqrt 82.3%

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

   9. Applied egg-rr 82.3%

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

       1. associate-/r* 82.8%

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

       2. associate-*r/ 82.8%

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

       3. *-rgt-identity 82.8%

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

       4. associate-/r* 82.3%

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

   11. Simplified 82.3%

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

   12. Taylor expanded in z around 0 31.7%

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

       1. *-commutative 31.7%

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

   14. Simplified 31.7%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5.1 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 45.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+115}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 1.7e+115) (/ (/ x y) t) (/ x (* y z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.7e+115) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 1.7d+115) then
        tmp = (x / y) / t
    else
        tmp = x / (y * z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 1.7e+115) {
		tmp = (x / y) / t;
	} else {
		tmp = x / (y * z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 1.7e+115:
		tmp = (x / y) / t
	else:
		tmp = x / (y * z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 1.7e+115)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(x / Float64(y * z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 1.7e+115)
		tmp = (x / y) / t;
	else
		tmp = x / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, 1.7e+115], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.7e115

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 91.9%

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

      1. associate-/l/ 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in z around 0 41.5%

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

      1. *-commutative 41.5%

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

      2. associate-/r* 43.6%

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

   8. Simplified 43.6%

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

   if 1.7e115 < z

   1. Initial program 87.3%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.4%

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

      1. associate-*r/ 94.4%

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

      2. neg-mul-1 94.4%

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

   7. Simplified 94.4%

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

      1. div-inv 94.4%

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

      2. associate-/l* 88.8%

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

      3. add-sqr-sqrt 56.2%

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

      4. sqrt-unprod 83.3%

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

      5. sqr-neg 83.3%

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

      6. sqrt-unprod 32.6%

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

      7. add-sqr-sqrt 82.3%

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

   9. Applied egg-rr 82.3%

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

       1. associate-/r* 82.8%

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

       2. associate-*r/ 82.8%

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

       3. *-rgt-identity 82.8%

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

       4. associate-/r* 82.3%

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

   11. Simplified 82.3%

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

   12. Taylor expanded in z around 0 31.7%

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

       1. *-commutative 31.7%

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

   14. Simplified 31.7%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+115}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 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 91.2%

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

3. Taylor expanded in z around 0 38.6%

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

4. Final simplification 38.6%

   \[\leadsto \frac{x}{y \cdot t} \]
5. 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 2024053 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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