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

Percentage Accurate: 89.3% → 96.8%

Time: 12.5s

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: 89.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% 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 87.9%

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

   1. associate-/l/ 96.5%

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

3. Simplified 96.5%

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

Alternative 2: 74.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.75e+19)
   (/ (/ x z) z)
   (if (<= z 3.6e-67)
     (/ x (* (- t z) y))
     (if (<= z 1.14e+164) (/ x (* z (- z y))) (/ 1.0 (* z (/ z x)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+19) {
		tmp = (x / z) / z;
	} else if (z <= 3.6e-67) {
		tmp = x / ((t - z) * y);
	} else if (z <= 1.14e+164) {
		tmp = x / (z * (z - y));
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.75d+19)) then
        tmp = (x / z) / z
    else if (z <= 3.6d-67) then
        tmp = x / ((t - z) * y)
    else if (z <= 1.14d+164) then
        tmp = x / (z * (z - y))
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.75e+19) {
		tmp = (x / z) / z;
	} else if (z <= 3.6e-67) {
		tmp = x / ((t - z) * y);
	} else if (z <= 1.14e+164) {
		tmp = x / (z * (z - y));
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.75e+19:
		tmp = (x / z) / z
	elif z <= 3.6e-67:
		tmp = x / ((t - z) * y)
	elif z <= 1.14e+164:
		tmp = x / (z * (z - y))
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.75e+19)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 3.6e-67)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (z <= 1.14e+164)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.75e+19)
		tmp = (x / z) / z;
	elseif (z <= 3.6e-67)
		tmp = x / ((t - z) * y);
	elseif (z <= 1.14e+164)
		tmp = x / (z * (z - y));
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.75e+19], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.6e-67], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.14e+164], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.75e19

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-/r* 88.3%

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

      3. distribute-neg-frac2 88.3%

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

      4. neg-sub0 88.3%

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

      5. sub-neg 88.3%

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

      6. +-commutative 88.3%

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

      7. associate--r+ 88.3%

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

      8. neg-sub0 88.3%

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

      9. remove-double-neg 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around inf 81.3%

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

   if -2.75e19 < z < 3.59999999999999999e-67

   1. Initial program 96.1%

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

      1. associate-/l/ 92.5%

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

   3. Simplified 92.5%

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

      1. clear-num 92.0%

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

      2. associate-/r/ 92.4%

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

   6. Applied egg-rr 92.4%

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

   7. Taylor expanded in y around inf 75.8%

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

   if 3.59999999999999999e-67 < z < 1.14e164

   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 0 68.0%

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

      1. mul-1-neg 68.0%

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

      2. distribute-rgt-neg-in 68.0%

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

      3. neg-sub0 68.0%

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

      4. sub-neg 68.0%

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

      5. +-commutative 68.0%

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

      6. associate--r+ 68.0%

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

      7. neg-sub0 68.0%

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

      8. remove-double-neg 68.0%

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

   5. Simplified 68.0%

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

   if 1.14e164 < z

   1. Initial program 73.5%

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

   3. Taylor expanded in t around 0 73.5%

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

      1. mul-1-neg 73.5%

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

      2. associate-/r* 97.5%

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

      3. distribute-neg-frac2 97.5%

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

      4. neg-sub0 97.5%

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

      5. sub-neg 97.5%

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

      6. +-commutative 97.5%

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

      7. associate--r+ 97.5%

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

      8. neg-sub0 97.5%

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

      9. remove-double-neg 97.5%

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

   5. Simplified 97.5%

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

      1. clear-num 97.4%

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

      2. inv-pow 97.4%

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

      3. div-inv 97.5%

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

      4. clear-num 97.5%

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

   7. Applied egg-rr 97.5%

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

      1. unpow-1 97.5%

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

   9. Simplified 97.5%

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

   10. Taylor expanded in z around inf 90.8%

       \[\leadsto \frac{1}{\color{blue}{z} \cdot \frac{z}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{+164}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -430000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-166}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)))
   (if (<= z -430000000.0)
     t_1
     (if (<= z 6.5e-166)
       (/ (/ x t) y)
       (if (<= z 2.5e-5) (/ x (* 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;
	double tmp;
	if (z <= -430000000.0) {
		tmp = t_1;
	} else if (z <= 6.5e-166) {
		tmp = (x / t) / y;
	} else if (z <= 2.5e-5) {
		tmp = x / (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
    if (z <= (-430000000.0d0)) then
        tmp = t_1
    else if (z <= 6.5d-166) then
        tmp = (x / t) / y
    else if (z <= 2.5d-5) then
        tmp = x / (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;
	double tmp;
	if (z <= -430000000.0) {
		tmp = t_1;
	} else if (z <= 6.5e-166) {
		tmp = (x / t) / y;
	} else if (z <= 2.5e-5) {
		tmp = x / (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
	tmp = 0
	if z <= -430000000.0:
		tmp = t_1
	elif z <= 6.5e-166:
		tmp = (x / t) / y
	elif z <= 2.5e-5:
		tmp = x / (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) / z)
	tmp = 0.0
	if (z <= -430000000.0)
		tmp = t_1;
	elseif (z <= 6.5e-166)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 2.5e-5)
		tmp = Float64(x / Float64(z * Float64(-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;
	tmp = 0.0;
	if (z <= -430000000.0)
		tmp = t_1;
	elseif (z <= 6.5e-166)
		tmp = (x / t) / y;
	elseif (z <= 2.5e-5)
		tmp = x / (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] / z), $MachinePrecision]}, If[LessEqual[z, -430000000.0], t$95$1, If[LessEqual[z, 6.5e-166], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 2.5e-5], N[(x / N[(z * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.3e8 or 2.50000000000000012e-5 < z

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. associate-/r* 85.0%

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

      3. distribute-neg-frac2 85.0%

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

      4. neg-sub0 85.0%

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

      5. sub-neg 85.0%

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

      6. +-commutative 85.0%

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

      7. associate--r+ 85.0%

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

      8. neg-sub0 85.0%

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

      9. remove-double-neg 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around inf 76.0%

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

   if -4.3e8 < z < 6.50000000000000019e-166

   1. Initial program 95.3%

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

      1. associate-/l/ 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around inf 77.6%

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

   6. Taylor expanded in y around inf 67.3%

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

   if 6.50000000000000019e-166 < z < 2.50000000000000012e-5

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/r* 48.2%

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

      3. distribute-neg-frac2 48.2%

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

      4. neg-sub0 48.2%

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

      5. sub-neg 48.2%

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

      6. +-commutative 48.2%

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

      7. associate--r+ 48.2%

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

      8. neg-sub0 48.2%

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

      9. remove-double-neg 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in z around 0 42.0%

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

      1. associate-*r/ 42.0%

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

      2. neg-mul-1 42.0%

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

      3. *-commutative 42.0%

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

   8. Simplified 42.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -430000000:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-166}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{z \cdot \left(-y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+105} \lor \neg \left(z \leq 1.6 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.5e+105) (not (<= z 1.6e+130)))
   (/ (/ x z) (- z y))
   (/ x (* (- t z) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+105) || !(z <= 1.6e+130)) {
		tmp = (x / z) / (z - y);
	} 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) :: tmp
    if ((z <= (-3.5d+105)) .or. (.not. (z <= 1.6d+130))) then
        tmp = (x / z) / (z - y)
    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 tmp;
	if ((z <= -3.5e+105) || !(z <= 1.6e+130)) {
		tmp = (x / z) / (z - y);
	} 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):
	tmp = 0
	if (z <= -3.5e+105) or not (z <= 1.6e+130):
		tmp = (x / z) / (z - y)
	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)
	tmp = 0.0
	if ((z <= -3.5e+105) || !(z <= 1.6e+130))
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(x / Float64(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)
	tmp = 0.0;
	if ((z <= -3.5e+105) || ~((z <= 1.6e+130)))
		tmp = (x / z) / (z - y);
	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_] := If[Or[LessEqual[z, -3.5e+105], N[Not[LessEqual[z, 1.6e+130]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.49999999999999991e105 or 1.6e130 < 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 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/r* 91.7%

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

      3. distribute-neg-frac2 91.7%

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

      4. neg-sub0 91.7%

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

      5. sub-neg 91.7%

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

      6. +-commutative 91.7%

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

      7. associate--r+ 91.7%

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

      8. neg-sub0 91.7%

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

      9. remove-double-neg 91.7%

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

   5. Simplified 91.7%

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

   if -3.49999999999999991e105 < z < 1.6e130

   1. Initial program 96.5%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+105} \lor \neg \left(z \leq 1.6 \cdot 10^{+130}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot \frac{1}{z}}{z - y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

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 -3.7e+105)
   (/ (* x (/ 1.0 z)) (- z y))
   (if (<= z 2.4e+129) (/ 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 <= -3.7e+105) {
		tmp = (x * (1.0 / z)) / (z - y);
	} else if (z <= 2.4e+129) {
		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 <= (-3.7d+105)) then
        tmp = (x * (1.0d0 / z)) / (z - y)
    else if (z <= 2.4d+129) 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 <= -3.7e+105) {
		tmp = (x * (1.0 / z)) / (z - y);
	} else if (z <= 2.4e+129) {
		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 <= -3.7e+105:
		tmp = (x * (1.0 / z)) / (z - y)
	elif z <= 2.4e+129:
		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 <= -3.7e+105)
		tmp = Float64(Float64(x * Float64(1.0 / z)) / Float64(z - y));
	elseif (z <= 2.4e+129)
		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 <= -3.7e+105)
		tmp = (x * (1.0 / z)) / (z - y);
	elseif (z <= 2.4e+129)
		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, -3.7e+105], N[(N[(x * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e+129], 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 < -3.69999999999999985e105

   1. Initial program 72.3%

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

   3. Taylor expanded in t around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/r* 91.6%

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

      3. distribute-neg-frac2 91.6%

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

      4. neg-sub0 91.6%

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

      5. sub-neg 91.6%

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

      6. +-commutative 91.6%

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

      7. associate--r+ 91.6%

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

      8. neg-sub0 91.6%

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

      9. remove-double-neg 91.6%

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

   5. Simplified 91.6%

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

      1. clear-num 91.6%

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

      2. associate-/r/ 91.6%

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

   7. Applied egg-rr 91.6%

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

   if -3.69999999999999985e105 < z < 2.3999999999999999e129

   1. Initial program 96.5%

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

   if 2.3999999999999999e129 < z

   1. Initial program 70.1%

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

   3. Taylor expanded in t around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. associate-/r* 91.9%

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

      3. distribute-neg-frac2 91.9%

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

      4. neg-sub0 91.9%

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

      5. sub-neg 91.9%

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

      6. +-commutative 91.9%

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

      7. associate--r+ 91.9%

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

      8. neg-sub0 91.9%

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

      9. remove-double-neg 91.9%

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

   5. Simplified 91.9%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{x \cdot \frac{1}{z}}{z - y}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 480:\\ \;\;\;\;\frac{1}{\left(z - y\right) \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -5e-45)
   (/ (/ x (- t z)) y)
   (if (<= t 480.0) (/ 1.0 (* (- z y) (/ z x))) (/ (/ 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 <= -5e-45) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 480.0) {
		tmp = 1.0 / ((z - y) * (z / x));
	} 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 <= (-5d-45)) then
        tmp = (x / (t - z)) / y
    else if (t <= 480.0d0) then
        tmp = 1.0d0 / ((z - y) * (z / x))
    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 <= -5e-45) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 480.0) {
		tmp = 1.0 / ((z - y) * (z / x));
	} 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 <= -5e-45:
		tmp = (x / (t - z)) / y
	elif t <= 480.0:
		tmp = 1.0 / ((z - y) * (z / x))
	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 <= -5e-45)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 480.0)
		tmp = Float64(1.0 / Float64(Float64(z - y) * Float64(z / x)));
	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 <= -5e-45)
		tmp = (x / (t - z)) / y;
	elseif (t <= 480.0)
		tmp = 1.0 / ((z - y) * (z / x));
	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, -5e-45], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 480.0], N[(1.0 / N[(N[(z - y), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.99999999999999976e-45

   1. Initial program 84.5%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf 65.8%

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

   if -4.99999999999999976e-45 < t < 480

   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 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/r* 78.8%

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

      3. distribute-neg-frac2 78.8%

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

      4. neg-sub0 78.8%

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

      5. sub-neg 78.8%

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

      6. +-commutative 78.8%

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

      7. associate--r+ 78.8%

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

      8. neg-sub0 78.8%

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

      9. remove-double-neg 78.8%

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

   5. Simplified 78.8%

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

      1. clear-num 78.6%

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

      2. inv-pow 78.6%

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

      3. div-inv 78.6%

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

      4. clear-num 79.6%

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

   7. Applied egg-rr 79.6%

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

      1. unpow-1 79.6%

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

   9. Simplified 79.6%

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

   if 480 < t

   1. Initial program 84.9%

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

      1. associate-/l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around inf 86.9%

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

Alternative 7: 77.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-47} \lor \neg \left(t \leq 1.4 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \end{array} \end{array} \]

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 (<= t -8.2e-47) (not (<= t 1.4e-82)))
   (/ (/ x t) (- 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 ((t <= -8.2e-47) || !(t <= 1.4e-82)) {
		tmp = (x / t) / (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 ((t <= (-8.2d-47)) .or. (.not. (t <= 1.4d-82))) then
        tmp = (x / t) / (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 ((t <= -8.2e-47) || !(t <= 1.4e-82)) {
		tmp = (x / t) / (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 (t <= -8.2e-47) or not (t <= 1.4e-82):
		tmp = (x / t) / (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 ((t <= -8.2e-47) || !(t <= 1.4e-82))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(x / Float64(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 ((t <= -8.2e-47) || ~((t <= 1.4e-82)))
		tmp = (x / t) / (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[Or[LessEqual[t, -8.2e-47], N[Not[LessEqual[t, 1.4e-82]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.20000000000000003e-47 or 1.40000000000000012e-82 < t

   1. Initial program 83.5%

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

      1. associate-/l/ 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 81.7%

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

   if -8.20000000000000003e-47 < t < 1.40000000000000012e-82

   1. Initial program 93.7%

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

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-47} \lor \neg \left(t \leq 1.4 \cdot 10^{-82}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -5.4 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 445:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -5.4e-45)
   (/ (/ x (- t z)) y)
   (if (<= t 445.0) (/ (/ 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 <= -5.4e-45) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 445.0) {
		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 <= (-5.4d-45)) then
        tmp = (x / (t - z)) / y
    else if (t <= 445.0d0) 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 <= -5.4e-45) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 445.0) {
		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 <= -5.4e-45:
		tmp = (x / (t - z)) / y
	elif t <= 445.0:
		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 <= -5.4e-45)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 445.0)
		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 <= -5.4e-45)
		tmp = (x / (t - z)) / y;
	elseif (t <= 445.0)
		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, -5.4e-45], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 445.0], 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 < -5.3999999999999997e-45

   1. Initial program 84.5%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf 65.8%

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

   if -5.3999999999999997e-45 < t < 445

   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 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/r* 78.8%

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

      3. distribute-neg-frac2 78.8%

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

      4. neg-sub0 78.8%

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

      5. sub-neg 78.8%

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

      6. +-commutative 78.8%

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

      7. associate--r+ 78.8%

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

      8. neg-sub0 78.8%

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

      9. remove-double-neg 78.8%

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

   5. Simplified 78.8%

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

   if 445 < t

   1. Initial program 84.9%

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

      1. associate-/l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around inf 86.9%

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

Alternative 9: 81.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.05 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 250:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.05e-44)
   (/ (/ x y) (- t z))
   (if (<= t 250.0) (/ (/ x z) (- z y)) (/ (/ x t) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e-44) {
		tmp = (x / y) / (t - z);
	} else if (t <= 250.0) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.05d-44)) then
        tmp = (x / y) / (t - z)
    else if (t <= 250.0d0) then
        tmp = (x / z) / (z - y)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.05e-44) {
		tmp = (x / y) / (t - z);
	} else if (t <= 250.0) {
		tmp = (x / z) / (z - y);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.05e-44:
		tmp = (x / y) / (t - z)
	elif t <= 250.0:
		tmp = (x / z) / (z - y)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.05e-44)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 250.0)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.05e-44)
		tmp = (x / y) / (t - z);
	elseif (t <= 250.0)
		tmp = (x / z) / (z - y);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.05e-44], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 250.0], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.04999999999999996e-44

   1. Initial program 84.5%

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

   3. Taylor expanded in y around inf 55.5%

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

      1. associate-/r* 59.4%

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

   5. Simplified 59.4%

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

   if -2.04999999999999996e-44 < t < 250

   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 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/r* 78.8%

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

      3. distribute-neg-frac2 78.8%

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

      4. neg-sub0 78.8%

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

      5. sub-neg 78.8%

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

      6. +-commutative 78.8%

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

      7. associate--r+ 78.8%

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

      8. neg-sub0 78.8%

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

      9. remove-double-neg 78.8%

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

   5. Simplified 78.8%

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

   if 250 < t

   1. Initial program 84.9%

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

      1. associate-/l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in t around inf 86.9%

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

Alternative 10: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -3.6e-71)
   (/ (/ x y) (- t z))
   (if (<= t 4e-82) (/ 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 <= -3.6e-71) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4e-82) {
		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 <= (-3.6d-71)) then
        tmp = (x / y) / (t - z)
    else if (t <= 4d-82) 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 <= -3.6e-71) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4e-82) {
		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 <= -3.6e-71:
		tmp = (x / y) / (t - z)
	elif t <= 4e-82:
		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 <= -3.6e-71)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 4e-82)
		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 <= -3.6e-71)
		tmp = (x / y) / (t - z);
	elseif (t <= 4e-82)
		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, -3.6e-71], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-82], 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 < -3.6e-71

   1. Initial program 84.0%

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

   3. Taylor expanded in y around inf 55.3%

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

      1. associate-/r* 59.0%

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

   5. Simplified 59.0%

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

   if -3.6e-71 < t < 4e-82

   1. Initial program 93.5%

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

   3. Taylor expanded in t around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

      3. neg-sub0 76.9%

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

      4. sub-neg 76.9%

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

      5. +-commutative 76.9%

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

      6. associate--r+ 76.9%

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

      7. neg-sub0 76.9%

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

      8. remove-double-neg 76.9%

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

   5. Simplified 76.9%

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

   if 4e-82 < t

   1. Initial program 83.7%

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

      1. associate-/l/ 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in t around inf 81.2%

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

Alternative 11: 76.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2e-57)
   (/ x (* (- t z) y))
   (if (<= t 4.4e-82) (/ 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 <= -2e-57) {
		tmp = x / ((t - z) * y);
	} else if (t <= 4.4e-82) {
		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 <= (-2d-57)) then
        tmp = x / ((t - z) * y)
    else if (t <= 4.4d-82) 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 <= -2e-57) {
		tmp = x / ((t - z) * y);
	} else if (t <= 4.4e-82) {
		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 <= -2e-57:
		tmp = x / ((t - z) * y)
	elif t <= 4.4e-82:
		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 <= -2e-57)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 4.4e-82)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2e-57)
		tmp = x / ((t - z) * y);
	elseif (t <= 4.4e-82)
		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, -2e-57], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e-82], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999991e-57

   1. Initial program 83.8%

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

      1. associate-/l/ 98.6%

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

   3. Simplified 98.6%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.5%

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

   6. Applied egg-rr 98.5%

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

   7. Taylor expanded in y around inf 54.7%

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

   if -1.99999999999999991e-57 < t < 4.39999999999999971e-82

   1. Initial program 93.5%

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

   3. Taylor expanded in t around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. distribute-rgt-neg-in 76.2%

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

      3. neg-sub0 76.2%

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

      4. sub-neg 76.2%

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

      5. +-commutative 76.2%

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

      6. associate--r+ 76.2%

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

      7. neg-sub0 76.2%

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

      8. remove-double-neg 76.2%

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

   5. Simplified 76.2%

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

   if 4.39999999999999971e-82 < t

   1. Initial program 83.7%

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

   3. Taylor expanded in t around inf 79.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3e+18)
   (/ (/ x z) z)
   (if (<= z 2.5e+87) (/ x (* (- t z) y)) (/ 1.0 (* z (/ z x))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3e+18) {
		tmp = (x / z) / z;
	} else if (z <= 2.5e+87) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-3d+18)) then
        tmp = (x / z) / z
    else if (z <= 2.5d+87) then
        tmp = x / ((t - z) * y)
    else
        tmp = 1.0d0 / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3e+18) {
		tmp = (x / z) / z;
	} else if (z <= 2.5e+87) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3e+18:
		tmp = (x / z) / z
	elif z <= 2.5e+87:
		tmp = x / ((t - z) * y)
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3e+18)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 2.5e+87)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3e+18)
		tmp = (x / z) / z;
	elseif (z <= 2.5e+87)
		tmp = x / ((t - z) * y);
	else
		tmp = 1.0 / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3e+18], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.5e+87], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e18

   1. Initial program 78.2%

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

   3. Taylor expanded in t around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-/r* 88.3%

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

      3. distribute-neg-frac2 88.3%

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

      4. neg-sub0 88.3%

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

      5. sub-neg 88.3%

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

      6. +-commutative 88.3%

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

      7. associate--r+ 88.3%

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

      8. neg-sub0 88.3%

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

      9. remove-double-neg 88.3%

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

   5. Simplified 88.3%

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

   6. Taylor expanded in z around inf 81.3%

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

   if -3e18 < z < 2.4999999999999999e87

   1. Initial program 96.0%

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

      1. associate-/l/ 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 93.4%

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

      2. associate-/r/ 93.8%

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

   6. Applied egg-rr 93.8%

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

   7. Taylor expanded in y around inf 72.9%

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

   if 2.4999999999999999e87 < z

   1. Initial program 76.6%

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

   3. Taylor expanded in t around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/r* 90.2%

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

      3. distribute-neg-frac2 90.2%

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

      4. neg-sub0 90.2%

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

      5. sub-neg 90.2%

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

      6. +-commutative 90.2%

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

      7. associate--r+ 90.2%

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

      8. neg-sub0 90.2%

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

      9. remove-double-neg 90.2%

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

   5. Simplified 90.2%

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

      1. clear-num 90.2%

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

      2. inv-pow 90.2%

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

      3. div-inv 90.2%

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

      4. clear-num 90.2%

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

   7. Applied egg-rr 90.2%

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

      1. unpow-1 90.2%

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

   9. Simplified 90.2%

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

   10. Taylor expanded in z around inf 85.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+18}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+15} \lor \neg \left(z \leq 0.0044\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -2.15e+15) (not (<= z 0.0044))) (/ (/ 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 <= -2.15e+15) || !(z <= 0.0044)) {
		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 <= (-2.15d+15)) .or. (.not. (z <= 0.0044d0))) 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 <= -2.15e+15) || !(z <= 0.0044)) {
		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 <= -2.15e+15) or not (z <= 0.0044):
		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 <= -2.15e+15) || !(z <= 0.0044))
		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 <= -2.15e+15) || ~((z <= 0.0044)))
		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, -2.15e+15], N[Not[LessEqual[z, 0.0044]], $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 < -2.15e15 or 0.00440000000000000027 < z

   1. Initial program 79.8%

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

   3. Taylor expanded in t around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. associate-/r* 85.0%

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

      3. distribute-neg-frac2 85.0%

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

      4. neg-sub0 85.0%

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

      5. sub-neg 85.0%

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

      6. +-commutative 85.0%

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

      7. associate--r+ 85.0%

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

      8. neg-sub0 85.0%

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

      9. remove-double-neg 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in z around inf 76.0%

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

   if -2.15e15 < z < 0.00440000000000000027

   1. Initial program 96.3%

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

      1. associate-/l/ 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 71.5%

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

   6. Taylor expanded in y around inf 58.5%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{+15} \lor \neg \left(z \leq 0.0044\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+15} \lor \neg \left(z \leq 0.009\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -6.5e+15) (not (<= z 0.009))) (/ 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 <= -6.5e+15) || !(z <= 0.009)) {
		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 <= (-6.5d+15)) .or. (.not. (z <= 0.009d0))) 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 <= -6.5e+15) || !(z <= 0.009)) {
		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 <= -6.5e+15) or not (z <= 0.009):
		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 <= -6.5e+15) || !(z <= 0.009))
		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 <= -6.5e+15) || ~((z <= 0.009)))
		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, -6.5e+15], N[Not[LessEqual[z, 0.009]], $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 < -6.5e15 or 0.00899999999999999932 < z

   1. Initial program 79.8%

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

      1. clear-num 79.6%

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

      2. associate-/r/ 79.7%

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

   4. Applied egg-rr 79.7%

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

   5. Taylor expanded in t around 0 70.5%

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

      1. associate-/r* 70.5%

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

   7. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. frac-2neg 70.5%

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

      3. associate-*r/ 85.0%

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

      4. distribute-neg-frac2 85.0%

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

      5. add-sqr-sqrt 37.9%

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

      6. sqrt-unprod 63.6%

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

      7. sqr-neg 63.6%

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

      8. sqrt-unprod 32.0%

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

      9. add-sqr-sqrt 55.1%

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

      10. *-commutative 55.1%

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

      11. frac-2neg 55.1%

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

      12. metadata-eval 55.1%

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

      13. associate-*l/ 55.1%

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

      14. *-un-lft-identity 55.1%

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

      15. add-sqr-sqrt 23.1%

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

      16. sqrt-unprod 63.0%

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

      17. sqr-neg 63.0%

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

      18. sqrt-unprod 46.9%

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

      19. add-sqr-sqrt 85.0%

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

      20. sub-neg 85.0%

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

      21. distribute-neg-in 85.0%

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

      22. remove-double-neg 85.0%

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

   9. Applied egg-rr 85.0%

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

       1. associate-/l/ 70.5%

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

       2. +-commutative 70.5%

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

       3. unsub-neg 70.5%

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

   11. Simplified 70.5%

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

   12. Taylor expanded in z around inf 65.9%

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

   if -6.5e15 < z < 0.00899999999999999932

   1. Initial program 96.3%

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

      1. associate-/l/ 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 71.5%

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

   6. Taylor expanded in y around inf 58.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+15} \lor \neg \left(z \leq 0.009\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000 \lor \neg \left(z \leq 6.7 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -48000000.0) (not (<= z 6.7e-15))) (/ 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 <= -48000000.0) || !(z <= 6.7e-15)) {
		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 <= (-48000000.0d0)) .or. (.not. (z <= 6.7d-15))) 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 <= -48000000.0) || !(z <= 6.7e-15)) {
		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 <= -48000000.0) or not (z <= 6.7e-15):
		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 <= -48000000.0) || !(z <= 6.7e-15))
		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 <= -48000000.0) || ~((z <= 6.7e-15)))
		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, -48000000.0], N[Not[LessEqual[z, 6.7e-15]], $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 < -4.8e7 or 6.70000000000000001e-15 < z

   1. Initial program 79.8%

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

      1. clear-num 79.6%

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

      2. associate-/r/ 79.7%

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

   4. Applied egg-rr 79.7%

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

   5. Taylor expanded in t around 0 70.5%

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

      1. associate-/r* 70.5%

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

   7. Simplified 70.5%

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

      1. *-commutative 70.5%

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

      2. frac-2neg 70.5%

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

      3. associate-*r/ 85.0%

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

      4. distribute-neg-frac2 85.0%

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

      5. add-sqr-sqrt 37.9%

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

      6. sqrt-unprod 63.6%

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

      7. sqr-neg 63.6%

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

      8. sqrt-unprod 32.0%

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

      9. add-sqr-sqrt 55.1%

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

      10. *-commutative 55.1%

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

      11. frac-2neg 55.1%

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

      12. metadata-eval 55.1%

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

      13. associate-*l/ 55.1%

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

      14. *-un-lft-identity 55.1%

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

      15. add-sqr-sqrt 23.1%

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

      16. sqrt-unprod 63.0%

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

      17. sqr-neg 63.0%

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

      18. sqrt-unprod 46.9%

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

      19. add-sqr-sqrt 85.0%

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

      20. sub-neg 85.0%

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

      21. distribute-neg-in 85.0%

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

      22. remove-double-neg 85.0%

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

   9. Applied egg-rr 85.0%

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

       1. associate-/l/ 70.5%

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

       2. +-commutative 70.5%

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

       3. unsub-neg 70.5%

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

   11. Simplified 70.5%

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

   12. Taylor expanded in z around inf 65.9%

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

   if -4.8e7 < z < 6.70000000000000001e-15

   1. Initial program 96.3%

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

   3. Taylor expanded in z around 0 56.7%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000 \lor \neg \left(z \leq 6.7 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+31} \lor \neg \left(z \leq 1.7 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7e+31) (not (<= z 1.7e+85))) (/ x (* t z)) (/ x (* t y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e+31) || !(z <= 1.7e+85)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7d+31)) .or. (.not. (z <= 1.7d+85))) then
        tmp = x / (t * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e+31) || !(z <= 1.7e+85)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -7e+31) or not (z <= 1.7e+85):
		tmp = x / (t * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7e+31) || !(z <= 1.7e+85))
		tmp = Float64(x / Float64(t * z));
	else
		tmp = Float64(x / Float64(t * y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7e+31) || ~((z <= 1.7e+85)))
		tmp = x / (t * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7e+31], N[Not[LessEqual[z, 1.7e+85]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7e31 or 1.7000000000000002e85 < z

   1. Initial program 77.0%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 39.3%

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

   6. Taylor expanded in y around 0 38.0%

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

      1. neg-mul-1 38.0%

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

   8. Simplified 38.0%

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

      1. add-sqr-sqrt 17.8%

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

      2. sqrt-unprod 56.8%

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

      3. sqr-neg 56.8%

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

      4. sqrt-unprod 18.0%

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

      5. add-sqr-sqrt 31.3%

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

      6. *-un-lft-identity 31.3%

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

      7. associate-/l/ 32.4%

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

      8. *-commutative 32.4%

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

   10. Applied egg-rr 32.4%

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

       1. *-lft-identity 32.4%

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

       2. *-commutative 32.4%

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

   12. Simplified 32.4%

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

   if -7e31 < z < 1.7000000000000002e85

   1. Initial program 96.0%

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

   3. Taylor expanded in z around 0 51.6%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+31} \lor \neg \left(z \leq 1.7 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 46.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \end{array} \end{array} \]

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 (<= z -1.65e+31)
   (/ x (* t z))
   (if (<= z 5.7e+87) (/ x (* t y)) (/ x (* z y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+31) {
		tmp = x / (t * z);
	} else if (z <= 5.7e+87) {
		tmp = x / (t * y);
	} else {
		tmp = x / (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 <= (-1.65d+31)) then
        tmp = x / (t * z)
    else if (z <= 5.7d+87) then
        tmp = x / (t * y)
    else
        tmp = x / (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 <= -1.65e+31) {
		tmp = x / (t * z);
	} else if (z <= 5.7e+87) {
		tmp = x / (t * y);
	} else {
		tmp = x / (z * y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+31:
		tmp = x / (t * z)
	elif z <= 5.7e+87:
		tmp = x / (t * y)
	else:
		tmp = x / (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 <= -1.65e+31)
		tmp = Float64(x / Float64(t * z));
	elseif (z <= 5.7e+87)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = Float64(x / 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 <= -1.65e+31)
		tmp = x / (t * z);
	elseif (z <= 5.7e+87)
		tmp = x / (t * y);
	else
		tmp = x / (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, -1.65e+31], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.7e+87], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999996e31

   1. Initial program 76.5%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 37.3%

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

   6. Taylor expanded in y around 0 37.2%

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

      1. neg-mul-1 37.2%

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

   8. Simplified 37.2%

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

      1. add-sqr-sqrt 37.2%

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

      2. sqrt-unprod 53.6%

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

      3. sqr-neg 53.6%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 27.9%

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

      6. *-un-lft-identity 27.9%

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

      7. associate-/l/ 29.9%

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

      8. *-commutative 29.9%

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

   10. Applied egg-rr 29.9%

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

       1. *-lft-identity 29.9%

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

       2. *-commutative 29.9%

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

   12. Simplified 29.9%

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

   if -1.64999999999999996e31 < z < 5.70000000000000039e87

   1. Initial program 96.1%

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

   3. Taylor expanded in z around 0 51.1%

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

   if 5.70000000000000039e87 < z

   1. Initial program 76.6%

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

   3. Taylor expanded in t around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-/r* 90.2%

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

      3. distribute-neg-frac2 90.2%

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

      4. neg-sub0 90.2%

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

      5. sub-neg 90.2%

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

      6. +-commutative 90.2%

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

      7. associate--r+ 90.2%

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

      8. neg-sub0 90.2%

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

      9. remove-double-neg 90.2%

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

   5. Simplified 90.2%

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

   6. Taylor expanded in z around 0 29.2%

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

      1. associate-*r/ 29.2%

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

      2. neg-mul-1 29.2%

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

      3. *-commutative 29.2%

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

   8. Simplified 29.2%

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

      1. neg-sub0 29.2%

         \[\leadsto \frac{\color{blue}{0 - x}}{z \cdot y} \]

      2. sub-neg 29.2%

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

      3. add-sqr-sqrt 17.8%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z \cdot y} \]

      4. sqrt-unprod 38.2%

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

      5. sqr-neg 38.2%

         \[\leadsto \frac{0 + \sqrt{\color{blue}{x \cdot x}}}{z \cdot y} \]

      6. sqrt-unprod 11.4%

         \[\leadsto \frac{0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z \cdot y} \]

      7. add-sqr-sqrt 29.2%

         \[\leadsto \frac{0 + \color{blue}{x}}{z \cdot y} \]

   10. Applied egg-rr 29.2%

       \[\leadsto \frac{\color{blue}{0 + x}}{z \cdot y} \]
   11. Step-by-step derivation

       1. +-lft-identity 29.2%

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

   12. Simplified 29.2%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.7% 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 87.9%

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

3. Taylor expanded in z around 0 36.7%

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

Developer Target 1: 88.1% 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 2024185 
(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))))