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

Percentage Accurate: 88.8% → 97.0%

Time: 11.4s

Alternatives: 11

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: 88.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

   1. associate-/l/ 98.0%

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

3. Simplified 98.0%

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

Alternative 2: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-41}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z) z)) (t_2 (/ x (* z (- z y)))))
   (if (<= z -5.6e+159)
     t_1
     (if (<= z -1.95e-59)
       t_2
       (if (<= z 1.95e-41) (/ (/ x t) (- y z)) (if (<= z 8e+143) 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 / z) / z;
	double t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -5.6e+159) {
		tmp = t_1;
	} else if (z <= -1.95e-59) {
		tmp = t_2;
	} else if (z <= 1.95e-41) {
		tmp = (x / t) / (y - z);
	} else if (z <= 8e+143) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (z * (z - y))
    if (z <= (-5.6d+159)) then
        tmp = t_1
    else if (z <= (-1.95d-59)) then
        tmp = t_2
    else if (z <= 1.95d-41) then
        tmp = (x / t) / (y - z)
    else if (z <= 8d+143) 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 / z) / z;
	double t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -5.6e+159) {
		tmp = t_1;
	} else if (z <= -1.95e-59) {
		tmp = t_2;
	} else if (z <= 1.95e-41) {
		tmp = (x / t) / (y - z);
	} else if (z <= 8e+143) {
		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 / z) / z
	t_2 = x / (z * (z - y))
	tmp = 0
	if z <= -5.6e+159:
		tmp = t_1
	elif z <= -1.95e-59:
		tmp = t_2
	elif z <= 1.95e-41:
		tmp = (x / t) / (y - z)
	elif z <= 8e+143:
		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 / z) / z)
	t_2 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (z <= -5.6e+159)
		tmp = t_1;
	elseif (z <= -1.95e-59)
		tmp = t_2;
	elseif (z <= 1.95e-41)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 8e+143)
		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 / z) / z;
	t_2 = x / (z * (z - y));
	tmp = 0.0;
	if (z <= -5.6e+159)
		tmp = t_1;
	elseif (z <= -1.95e-59)
		tmp = t_2;
	elseif (z <= 1.95e-41)
		tmp = (x / t) / (y - z);
	elseif (z <= 8e+143)
		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 / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e+159], t$95$1, If[LessEqual[z, -1.95e-59], t$95$2, If[LessEqual[z, 1.95e-41], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+143], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6000000000000002e159 or 8.0000000000000002e143 < z

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. associate-/r* 97.3%

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

      3. distribute-neg-frac2 97.3%

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

      4. neg-sub0 97.3%

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

      5. sub-neg 97.3%

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

      6. +-commutative 97.3%

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

      7. associate--r+ 97.3%

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

      8. neg-sub0 97.3%

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

      9. remove-double-neg 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in z around inf 91.7%

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

   if -5.6000000000000002e159 < z < -1.95000000000000009e-59 or 1.94999999999999995e-41 < z < 8.0000000000000002e143

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-rgt-neg-in 76.5%

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

      3. neg-sub0 76.5%

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

      4. sub-neg 76.5%

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

      5. +-commutative 76.5%

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

      6. associate--r+ 76.5%

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

      7. neg-sub0 76.5%

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

      8. remove-double-neg 76.5%

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

   5. Simplified 76.5%

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

   if -1.95000000000000009e-59 < z < 1.94999999999999995e-41

   1. Initial program 92.5%

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

      1. associate-/l/ 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around inf 80.8%

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

Alternative 3: 76.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z) z)) (t_2 (/ x (* z (- z y)))))
   (if (<= z -5.5e+159)
     t_1
     (if (<= z -2.45e-59)
       t_2
       (if (<= z 8e-44) (/ x (* t (- y z))) (if (<= z 8e+143) 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 / z) / z;
	double t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -5.5e+159) {
		tmp = t_1;
	} else if (z <= -2.45e-59) {
		tmp = t_2;
	} else if (z <= 8e-44) {
		tmp = x / (t * (y - z));
	} else if (z <= 8e+143) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (z * (z - y))
    if (z <= (-5.5d+159)) then
        tmp = t_1
    else if (z <= (-2.45d-59)) then
        tmp = t_2
    else if (z <= 8d-44) then
        tmp = x / (t * (y - z))
    else if (z <= 8d+143) 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 / z) / z;
	double t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -5.5e+159) {
		tmp = t_1;
	} else if (z <= -2.45e-59) {
		tmp = t_2;
	} else if (z <= 8e-44) {
		tmp = x / (t * (y - z));
	} else if (z <= 8e+143) {
		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 / z) / z
	t_2 = x / (z * (z - y))
	tmp = 0
	if z <= -5.5e+159:
		tmp = t_1
	elif z <= -2.45e-59:
		tmp = t_2
	elif z <= 8e-44:
		tmp = x / (t * (y - z))
	elif z <= 8e+143:
		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 / z) / z)
	t_2 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (z <= -5.5e+159)
		tmp = t_1;
	elseif (z <= -2.45e-59)
		tmp = t_2;
	elseif (z <= 8e-44)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 8e+143)
		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 / z) / z;
	t_2 = x / (z * (z - y));
	tmp = 0.0;
	if (z <= -5.5e+159)
		tmp = t_1;
	elseif (z <= -2.45e-59)
		tmp = t_2;
	elseif (z <= 8e-44)
		tmp = x / (t * (y - z));
	elseif (z <= 8e+143)
		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 / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+159], t$95$1, If[LessEqual[z, -2.45e-59], t$95$2, If[LessEqual[z, 8e-44], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+143], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999998e159 or 8.0000000000000002e143 < z

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. associate-/r* 97.3%

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

      3. distribute-neg-frac2 97.3%

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

      4. neg-sub0 97.3%

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

      5. sub-neg 97.3%

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

      6. +-commutative 97.3%

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

      7. associate--r+ 97.3%

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

      8. neg-sub0 97.3%

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

      9. remove-double-neg 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in z around inf 91.7%

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

   if -5.4999999999999998e159 < z < -2.44999999999999989e-59 or 7.99999999999999962e-44 < z < 8.0000000000000002e143

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-rgt-neg-in 76.5%

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

      3. neg-sub0 76.5%

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

      4. sub-neg 76.5%

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

      5. +-commutative 76.5%

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

      6. associate--r+ 76.5%

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

      7. neg-sub0 76.5%

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

      8. remove-double-neg 76.5%

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

   5. Simplified 76.5%

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

   if -2.44999999999999989e-59 < z < 7.99999999999999962e-44

   1. Initial program 92.5%

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

   3. Taylor expanded in t around inf 78.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-59}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+143}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 z) z)) (t_2 (/ x (* z (- z y)))))
   (if (<= z -5.5e+159)
     t_1
     (if (<= z -1.5e-65)
       t_2
       (if (<= z 1.9e-44) (/ (/ x t) y) (if (<= z 3.9e+143) 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 / z) / z;
	double t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -5.5e+159) {
		tmp = t_1;
	} else if (z <= -1.5e-65) {
		tmp = t_2;
	} else if (z <= 1.9e-44) {
		tmp = (x / t) / y;
	} else if (z <= 3.9e+143) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (z * (z - y))
    if (z <= (-5.5d+159)) then
        tmp = t_1
    else if (z <= (-1.5d-65)) then
        tmp = t_2
    else if (z <= 1.9d-44) then
        tmp = (x / t) / y
    else if (z <= 3.9d+143) 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 / z) / z;
	double t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -5.5e+159) {
		tmp = t_1;
	} else if (z <= -1.5e-65) {
		tmp = t_2;
	} else if (z <= 1.9e-44) {
		tmp = (x / t) / y;
	} else if (z <= 3.9e+143) {
		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 / z) / z
	t_2 = x / (z * (z - y))
	tmp = 0
	if z <= -5.5e+159:
		tmp = t_1
	elif z <= -1.5e-65:
		tmp = t_2
	elif z <= 1.9e-44:
		tmp = (x / t) / y
	elif z <= 3.9e+143:
		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 / z) / z)
	t_2 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (z <= -5.5e+159)
		tmp = t_1;
	elseif (z <= -1.5e-65)
		tmp = t_2;
	elseif (z <= 1.9e-44)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 3.9e+143)
		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 / z) / z;
	t_2 = x / (z * (z - y));
	tmp = 0.0;
	if (z <= -5.5e+159)
		tmp = t_1;
	elseif (z <= -1.5e-65)
		tmp = t_2;
	elseif (z <= 1.9e-44)
		tmp = (x / t) / y;
	elseif (z <= 3.9e+143)
		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 / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.5e+159], t$95$1, If[LessEqual[z, -1.5e-65], t$95$2, If[LessEqual[z, 1.9e-44], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.9e+143], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.4999999999999998e159 or 3.8999999999999998e143 < z

   1. Initial program 71.2%

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

   3. Taylor expanded in t around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. associate-/r* 97.3%

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

      3. distribute-neg-frac2 97.3%

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

      4. neg-sub0 97.3%

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

      5. sub-neg 97.3%

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

      6. +-commutative 97.3%

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

      7. associate--r+ 97.3%

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

      8. neg-sub0 97.3%

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

      9. remove-double-neg 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in z around inf 91.7%

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

   if -5.4999999999999998e159 < z < -1.49999999999999999e-65 or 1.9e-44 < z < 3.8999999999999998e143

   1. Initial program 94.3%

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

   3. Taylor expanded in t around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-rgt-neg-in 76.7%

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

      3. neg-sub0 76.7%

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

      4. sub-neg 76.7%

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

      5. +-commutative 76.7%

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

      6. associate--r+ 76.7%

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

      7. neg-sub0 76.7%

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

      8. remove-double-neg 76.7%

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

   5. Simplified 76.7%

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

   if -1.49999999999999999e-65 < z < 1.9e-44

   1. Initial program 92.4%

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

      1. associate-/l/ 95.3%

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

   3. Simplified 95.3%

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

      1. clear-num 95.2%

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

      2. inv-pow 95.2%

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

   6. Applied egg-rr 95.2%

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

      1. unpow-1 95.2%

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

   8. Simplified 95.2%

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

   9. Taylor expanded in z around 0 74.6%

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

       1. associate-/r* 78.0%

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

   11. Simplified 78.0%

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

Alternative 5: 78.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - t}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z t))))
   (if (<= z -3.3e-21)
     t_1
     (if (<= z 1.8e-42)
       (/ (/ x t) (- y z))
       (if (<= z 6.5e+104) (/ x (* z (- z y))) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (z <= -3.3e-21) {
		tmp = t_1;
	} else if (z <= 1.8e-42) {
		tmp = (x / t) / (y - z);
	} else if (z <= 6.5e+104) {
		tmp = x / (z * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (z - t)
    if (z <= (-3.3d-21)) then
        tmp = t_1
    else if (z <= 1.8d-42) then
        tmp = (x / t) / (y - z)
    else if (z <= 6.5d+104) then
        tmp = x / (z * (z - y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - t);
	double tmp;
	if (z <= -3.3e-21) {
		tmp = t_1;
	} else if (z <= 1.8e-42) {
		tmp = (x / t) / (y - z);
	} else if (z <= 6.5e+104) {
		tmp = x / (z * (z - y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (z - t)
	tmp = 0
	if z <= -3.3e-21:
		tmp = t_1
	elif z <= 1.8e-42:
		tmp = (x / t) / (y - z)
	elif z <= 6.5e+104:
		tmp = x / (z * (z - y))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - t))
	tmp = 0.0
	if (z <= -3.3e-21)
		tmp = t_1;
	elseif (z <= 1.8e-42)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 6.5e+104)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (z - t);
	tmp = 0.0;
	if (z <= -3.3e-21)
		tmp = t_1;
	elseif (z <= 1.8e-42)
		tmp = (x / t) / (y - z);
	elseif (z <= 6.5e+104)
		tmp = x / (z * (z - y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e-21], t$95$1, If[LessEqual[z, 1.8e-42], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+104], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.30000000000000009e-21 or 6.5000000000000005e104 < z

   1. Initial program 79.8%

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

   3. Taylor expanded in y around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-/r* 85.5%

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

      3. distribute-neg-frac2 85.5%

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

      4. sub-neg 85.5%

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

      5. +-commutative 85.5%

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

      6. distribute-neg-in 85.5%

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

      7. remove-double-neg 85.5%

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

      8. unsub-neg 85.5%

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

   5. Simplified 85.5%

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

   if -3.30000000000000009e-21 < z < 1.8000000000000001e-42

   1. Initial program 92.9%

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

      1. associate-/l/ 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in t around inf 78.4%

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

   if 1.8000000000000001e-42 < z < 6.5000000000000005e104

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. distribute-rgt-neg-in 77.9%

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

      3. neg-sub0 77.9%

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

      4. sub-neg 77.9%

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

      5. +-commutative 77.9%

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

      6. associate--r+ 77.9%

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

      7. neg-sub0 77.9%

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

      8. remove-double-neg 77.9%

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

   5. Simplified 77.9%

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

Alternative 6: 93.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2e+91)
   (/ (/ x z) (- z t))
   (if (<= z 1.15e+143) (/ x (* (- t z) (- y z))) (/ (/ x z) (- z y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e+91) {
		tmp = (x / z) / (z - t);
	} else if (z <= 1.15e+143) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2d+91)) then
        tmp = (x / z) / (z - t)
    else if (z <= 1.15d+143) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = (x / z) / (z - y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2e+91) {
		tmp = (x / z) / (z - t);
	} else if (z <= 1.15e+143) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2e+91:
		tmp = (x / z) / (z - t)
	elif z <= 1.15e+143:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2e+91)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	elseif (z <= 1.15e+143)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2e+91)
		tmp = (x / z) / (z - t);
	elseif (z <= 1.15e+143)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (x / z) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2e+91], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+143], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000016e91

   1. Initial program 77.0%

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

   3. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. associate-/r* 90.1%

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

      3. distribute-neg-frac2 90.1%

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

      4. sub-neg 90.1%

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

      5. +-commutative 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. unsub-neg 90.1%

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

   5. Simplified 90.1%

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

   if -2.00000000000000016e91 < z < 1.15e143

   1. Initial program 94.2%

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

   if 1.15e143 < z

   1. Initial program 69.7%

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

   3. Taylor expanded in t around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. associate-/r* 97.3%

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

      3. distribute-neg-frac2 97.3%

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

      4. neg-sub0 97.3%

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

      5. sub-neg 97.3%

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

      6. +-commutative 97.3%

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

      7. associate--r+ 97.3%

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

      8. neg-sub0 97.3%

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

      9. remove-double-neg 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+91}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-60} \lor \neg \left(z \leq 1.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 (or (<= z -1.05e-60) (not (<= z 1.5e-41)))
   (/ (/ 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 ((z <= -1.05e-60) || !(z <= 1.5e-41)) {
		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 ((z <= (-1.05d-60)) .or. (.not. (z <= 1.5d-41))) 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 ((z <= -1.05e-60) || !(z <= 1.5e-41)) {
		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 (z <= -1.05e-60) or not (z <= 1.5e-41):
		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 ((z <= -1.05e-60) || !(z <= 1.5e-41))
		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 ((z <= -1.05e-60) || ~((z <= 1.5e-41)))
		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[Or[LessEqual[z, -1.05e-60], N[Not[LessEqual[z, 1.5e-41]], $MachinePrecision]], 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 2 regimes

2. if z < -1.04999999999999996e-60 or 1.49999999999999994e-41 < z

   1. Initial program 84.2%

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

   3. Taylor expanded in t around 0 74.2%

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

      1. mul-1-neg 74.2%

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

      2. associate-/r* 86.2%

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

      3. distribute-neg-frac2 86.2%

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

      4. neg-sub0 86.2%

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

      5. sub-neg 86.2%

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

      6. +-commutative 86.2%

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

      7. associate--r+ 86.2%

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

      8. neg-sub0 86.2%

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

      9. remove-double-neg 86.2%

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

   5. Simplified 86.2%

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

   if -1.04999999999999996e-60 < z < 1.49999999999999994e-41

   1. Initial program 92.5%

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

      1. associate-/l/ 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around inf 80.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-60} \lor \neg \left(z \leq 1.5 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -155000000000 \lor \neg \left(z \leq 1.2 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -155000000000.0) (not (<= z 1.2e+17)))
   (/ (/ x z) z)
   (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -155000000000.0) || !(z <= 1.2e+17)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-155000000000.0d0)) .or. (.not. (z <= 1.2d+17))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -155000000000.0) || !(z <= 1.2e+17)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -155000000000.0) or not (z <= 1.2e+17):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -155000000000.0) || !(z <= 1.2e+17))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -155000000000.0) || ~((z <= 1.2e+17)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -155000000000.0], N[Not[LessEqual[z, 1.2e+17]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.55e11 or 1.2e17 < z

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-/r* 89.3%

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

      3. distribute-neg-frac2 89.3%

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

      4. neg-sub0 89.3%

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

      5. sub-neg 89.3%

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

      6. +-commutative 89.3%

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

      7. associate--r+ 89.3%

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

      8. neg-sub0 89.3%

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

      9. remove-double-neg 89.3%

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

   5. Simplified 89.3%

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

   6. Taylor expanded in z around inf 77.6%

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

   if -1.55e11 < z < 1.2e17

   1. Initial program 93.0%

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

      1. associate-/l/ 96.2%

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

   3. Simplified 96.2%

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

      1. clear-num 96.1%

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

      2. inv-pow 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. unpow-1 96.1%

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

   8. Simplified 96.1%

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

   9. Taylor expanded in z around 0 66.4%

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

       1. associate-/r* 69.9%

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

   11. Simplified 69.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -155000000000 \lor \neg \left(z \leq 1.2 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -160000000000 \lor \neg \left(z \leq 5.2 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -160000000000.0) (not (<= z 5.2e+23)))
   (/ x (* z z))
   (/ (/ x t) y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -160000000000.0) || !(z <= 5.2e+23)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-160000000000.0d0)) .or. (.not. (z <= 5.2d+23))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -160000000000.0) || !(z <= 5.2e+23)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -160000000000.0) or not (z <= 5.2e+23):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -160000000000.0) || !(z <= 5.2e+23))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -160000000000.0) || ~((z <= 5.2e+23)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -160000000000.0], N[Not[LessEqual[z, 5.2e+23]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e11 or 5.19999999999999983e23 < z

   1. Initial program 82.1%

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

   3. Taylor expanded in t around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-rgt-neg-in 75.1%

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

      3. neg-sub0 75.1%

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

      4. sub-neg 75.1%

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

      5. +-commutative 75.1%

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

      6. associate--r+ 75.1%

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

      7. neg-sub0 75.1%

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

      8. remove-double-neg 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in z around inf 67.1%

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

   if -1.6e11 < z < 5.19999999999999983e23

   1. Initial program 93.0%

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

      1. associate-/l/ 96.2%

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

   3. Simplified 96.2%

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

      1. clear-num 96.1%

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

      2. inv-pow 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. unpow-1 96.1%

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

   8. Simplified 96.1%

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

   9. Taylor expanded in z around 0 66.4%

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

       1. associate-/r* 69.9%

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

   11. Simplified 69.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -160000000000 \lor \neg \left(z \leq 5.2 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \lor \neg \left(z \leq 8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.3) (not (<= z 8e+22))) (/ x (* z z)) (/ x (* t y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3) || !(z <= 8e+22)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.3d0)) .or. (.not. (z <= 8d+22))) then
        tmp = x / (z * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.3) || !(z <= 8e+22)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.3) or not (z <= 8e+22):
		tmp = x / (z * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.3) || !(z <= 8e+22))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.3) || ~((z <= 8e+22)))
		tmp = x / (z * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.3], N[Not[LessEqual[z, 8e+22]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999998 or 8e22 < z

   1. Initial program 81.8%

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

   3. Taylor expanded in t around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. distribute-rgt-neg-in 74.9%

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

      3. neg-sub0 74.9%

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

      4. sub-neg 74.9%

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

      5. +-commutative 74.9%

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

      6. associate--r+ 74.9%

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

      7. neg-sub0 74.9%

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

      8. remove-double-neg 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in z around inf 66.4%

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

   if -3.2999999999999998 < z < 8e22

   1. Initial program 93.6%

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

   3. Taylor expanded in z around 0 67.9%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \lor \neg \left(z \leq 8 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.6%

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

3. Taylor expanded in z around 0 42.3%

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

Developer Target 1: 87.7% 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 2024139 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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