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

Percentage Accurate: 88.5% → 97.0%

Time: 10.1s

Alternatives: 17

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \frac{1}{y - z} \cdot \frac{x}{t - z} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (* (/ 1.0 (- y z)) (/ x (- t z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	return (1.0 / (y - z)) * (x / (t - z));
}

Fortran

NOTE: y 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 = (1.0d0 / (y - z)) * (x / (t - z))
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	return (1.0 / (y - z)) * (x / (t - z));
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	return (1.0 / (y - z)) * (x / (t - z))

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	return Float64(Float64(1.0 / Float64(y - z)) * Float64(x / Float64(t - z)))
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp = code(x, y, z, t)
	tmp = (1.0 / (y - z)) * (x / (t - z));
end

Wolfram

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

Derivation

1. Initial program 88.9%

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

   1. *-un-lft-identity 88.9%

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

   2. times-frac 97.3%

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

3. Applied egg-rr 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{y \cdot \left(t - z\right)}\\ t_2 := \frac{1}{\frac{z}{\frac{x}{z}}}\\ t_3 := \frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-176}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* y (- t z))))
        (t_2 (/ 1.0 (/ z (/ x z))))
        (t_3 (/ x (* (- y z) t))))
   (if (<= z -6.5e+87)
     t_2
     (if (<= z -6.6e-33)
       t_1
       (if (<= z 2.7e-176)
         t_3
         (if (<= z 1.4e-97) t_1 (if (<= z 1.5e+58) t_3 t_2)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double t_2 = 1.0 / (z / (x / z));
	double t_3 = x / ((y - z) * t);
	double tmp;
	if (z <= -6.5e+87) {
		tmp = t_2;
	} else if (z <= -6.6e-33) {
		tmp = t_1;
	} else if (z <= 2.7e-176) {
		tmp = t_3;
	} else if (z <= 1.4e-97) {
		tmp = t_1;
	} else if (z <= 1.5e+58) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (y * (t - z))
    t_2 = 1.0d0 / (z / (x / z))
    t_3 = x / ((y - z) * t)
    if (z <= (-6.5d+87)) then
        tmp = t_2
    else if (z <= (-6.6d-33)) then
        tmp = t_1
    else if (z <= 2.7d-176) then
        tmp = t_3
    else if (z <= 1.4d-97) then
        tmp = t_1
    else if (z <= 1.5d+58) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (y * (t - z));
	double t_2 = 1.0 / (z / (x / z));
	double t_3 = x / ((y - z) * t);
	double tmp;
	if (z <= -6.5e+87) {
		tmp = t_2;
	} else if (z <= -6.6e-33) {
		tmp = t_1;
	} else if (z <= 2.7e-176) {
		tmp = t_3;
	} else if (z <= 1.4e-97) {
		tmp = t_1;
	} else if (z <= 1.5e+58) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (y * (t - z))
	t_2 = 1.0 / (z / (x / z))
	t_3 = x / ((y - z) * t)
	tmp = 0
	if z <= -6.5e+87:
		tmp = t_2
	elif z <= -6.6e-33:
		tmp = t_1
	elif z <= 2.7e-176:
		tmp = t_3
	elif z <= 1.4e-97:
		tmp = t_1
	elif z <= 1.5e+58:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(y * Float64(t - z)))
	t_2 = Float64(1.0 / Float64(z / Float64(x / z)))
	t_3 = Float64(x / Float64(Float64(y - z) * t))
	tmp = 0.0
	if (z <= -6.5e+87)
		tmp = t_2;
	elseif (z <= -6.6e-33)
		tmp = t_1;
	elseif (z <= 2.7e-176)
		tmp = t_3;
	elseif (z <= 1.4e-97)
		tmp = t_1;
	elseif (z <= 1.5e+58)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (y * (t - z));
	t_2 = 1.0 / (z / (x / z));
	t_3 = x / ((y - z) * t);
	tmp = 0.0;
	if (z <= -6.5e+87)
		tmp = t_2;
	elseif (z <= -6.6e-33)
		tmp = t_1;
	elseif (z <= 2.7e-176)
		tmp = t_3;
	elseif (z <= 1.4e-97)
		tmp = t_1;
	elseif (z <= 1.5e+58)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.5e+87], t$95$2, If[LessEqual[z, -6.6e-33], t$95$1, If[LessEqual[z, 2.7e-176], t$95$3, If[LessEqual[z, 1.4e-97], t$95$1, If[LessEqual[z, 1.5e+58], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5000000000000002e87 or 1.5000000000000001e58 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 82.7%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.7%

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

   4. Simplified 82.7%

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

      1. clear-num 82.2%

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

      2. inv-pow 82.2%

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

   6. Applied egg-rr 82.2%

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

      1. unpow-1 82.2%

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

      2. associate-/l* 93.8%

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

   8. Simplified 93.8%

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

   if -6.5000000000000002e87 < z < -6.6000000000000005e-33 or 2.6999999999999998e-176 < z < 1.4000000000000001e-97

   1. Initial program 88.1%

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

   2. Taylor expanded in y around inf 60.2%

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

      1. *-commutative 60.2%

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

   4. Simplified 60.2%

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

   if -6.6000000000000005e-33 < z < 2.6999999999999998e-176 or 1.4000000000000001e-97 < z < 1.5000000000000001e58

   1. Initial program 92.0%

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

   2. Taylor expanded in t around inf 70.3%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+87}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-176}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 3: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ z x)))))
   (if (<= z -9.5e+33)
     t_1
     (if (<= z 1.8e-43)
       (/ (/ x t) y)
       (if (<= z 7.2e+57) (/ (- x) (* z t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -9.5e+33) {
		tmp = t_1;
	} else if (z <= 1.8e-43) {
		tmp = (x / t) / y;
	} else if (z <= 7.2e+57) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y 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 = 1.0d0 / (z * (z / x))
    if (z <= (-9.5d+33)) then
        tmp = t_1
    else if (z <= 1.8d-43) then
        tmp = (x / t) / y
    else if (z <= 7.2d+57) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -9.5e+33) {
		tmp = t_1;
	} else if (z <= 1.8e-43) {
		tmp = (x / t) / y;
	} else if (z <= 7.2e+57) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (z * (z / x))
	tmp = 0
	if z <= -9.5e+33:
		tmp = t_1
	elif z <= 1.8e-43:
		tmp = (x / t) / y
	elif z <= 7.2e+57:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(z * Float64(z / x)))
	tmp = 0.0
	if (z <= -9.5e+33)
		tmp = t_1;
	elseif (z <= 1.8e-43)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 7.2e+57)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (z * (z / x));
	tmp = 0.0;
	if (z <= -9.5e+33)
		tmp = t_1;
	elseif (z <= 1.8e-43)
		tmp = (x / t) / y;
	elseif (z <= 7.2e+57)
		tmp = -x / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+33], t$95$1, If[LessEqual[z, 1.8e-43], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 7.2e+57], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000003e33 or 7.2000000000000005e57 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 79.0%

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

   4. Simplified 79.0%

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

      1. clear-num 78.6%

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

      2. inv-pow 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. unpow-1 78.6%

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

      2. associate-/l* 89.5%

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

   8. Simplified 89.5%

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

      1. associate-/r/ 89.4%

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

   10. Applied egg-rr 89.4%

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

   if -9.5000000000000003e33 < z < 1.7999999999999999e-43

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 71.0%

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

      1. *-commutative 71.0%

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

   4. Simplified 71.0%

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

      1. associate-/r* 76.6%

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

      2. div-inv 76.6%

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

   6. Applied egg-rr 76.6%

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

      1. associate-*r/ 76.6%

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

      2. *-rgt-identity 76.6%

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

   8. Simplified 76.6%

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

   9. Taylor expanded in t around inf 58.4%

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

       1. associate-/r* 64.4%

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

   11. Simplified 64.4%

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

   if 1.7999999999999999e-43 < z < 7.2000000000000005e57

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. associate-*r/ 60.8%

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

      2. neg-mul-1 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in z around 0 42.2%

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

      1. associate-*r/ 42.2%

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

      2. neg-mul-1 42.2%

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

      3. *-commutative 42.2%

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

   7. Simplified 42.2%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 4: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ z (/ x z)))))
   (if (<= z -3.3e+33)
     t_1
     (if (<= z 1.15e-43)
       (/ (/ x t) y)
       (if (<= z 1.35e+59) (/ (- x) (* z t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z / (x / z));
	double tmp;
	if (z <= -3.3e+33) {
		tmp = t_1;
	} else if (z <= 1.15e-43) {
		tmp = (x / t) / y;
	} else if (z <= 1.35e+59) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y 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 = 1.0d0 / (z / (x / z))
    if (z <= (-3.3d+33)) then
        tmp = t_1
    else if (z <= 1.15d-43) then
        tmp = (x / t) / y
    else if (z <= 1.35d+59) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z / (x / z));
	double tmp;
	if (z <= -3.3e+33) {
		tmp = t_1;
	} else if (z <= 1.15e-43) {
		tmp = (x / t) / y;
	} else if (z <= 1.35e+59) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (z / (x / z))
	tmp = 0
	if z <= -3.3e+33:
		tmp = t_1
	elif z <= 1.15e-43:
		tmp = (x / t) / y
	elif z <= 1.35e+59:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(z / Float64(x / z)))
	tmp = 0.0
	if (z <= -3.3e+33)
		tmp = t_1;
	elseif (z <= 1.15e-43)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 1.35e+59)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (z / (x / z));
	tmp = 0.0;
	if (z <= -3.3e+33)
		tmp = t_1;
	elseif (z <= 1.15e-43)
		tmp = (x / t) / y;
	elseif (z <= 1.35e+59)
		tmp = -x / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+33], t$95$1, If[LessEqual[z, 1.15e-43], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.35e+59], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999976e33 or 1.3500000000000001e59 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 79.0%

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

   4. Simplified 79.0%

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

      1. clear-num 78.6%

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

      2. inv-pow 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. unpow-1 78.6%

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

      2. associate-/l* 89.5%

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

   8. Simplified 89.5%

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

   if -3.29999999999999976e33 < z < 1.1499999999999999e-43

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 71.0%

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

      1. *-commutative 71.0%

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

   4. Simplified 71.0%

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

      1. associate-/r* 76.6%

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

      2. div-inv 76.6%

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

   6. Applied egg-rr 76.6%

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

      1. associate-*r/ 76.6%

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

      2. *-rgt-identity 76.6%

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

   8. Simplified 76.6%

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

   9. Taylor expanded in t around inf 58.4%

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

       1. associate-/r* 64.4%

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

   11. Simplified 64.4%

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

   if 1.1499999999999999e-43 < z < 1.3500000000000001e59

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. associate-*r/ 60.8%

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

      2. neg-mul-1 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in z around 0 42.2%

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

      1. associate-*r/ 42.2%

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

      2. neg-mul-1 42.2%

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

      3. *-commutative 42.2%

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

   7. Simplified 42.2%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+59}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 5: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ z (/ x z)))))
   (if (<= z -1.75e+82)
     t_1
     (if (<= z -6.5e-32)
       (/ x (* y (- t z)))
       (if (<= z 5e+67) (/ (/ x t) (- y z)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z / (x / z));
	double tmp;
	if (z <= -1.75e+82) {
		tmp = t_1;
	} else if (z <= -6.5e-32) {
		tmp = x / (y * (t - z));
	} else if (z <= 5e+67) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y 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 = 1.0d0 / (z / (x / z))
    if (z <= (-1.75d+82)) then
        tmp = t_1
    else if (z <= (-6.5d-32)) then
        tmp = x / (y * (t - z))
    else if (z <= 5d+67) then
        tmp = (x / t) / (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z / (x / z));
	double tmp;
	if (z <= -1.75e+82) {
		tmp = t_1;
	} else if (z <= -6.5e-32) {
		tmp = x / (y * (t - z));
	} else if (z <= 5e+67) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (z / (x / z))
	tmp = 0
	if z <= -1.75e+82:
		tmp = t_1
	elif z <= -6.5e-32:
		tmp = x / (y * (t - z))
	elif z <= 5e+67:
		tmp = (x / t) / (y - z)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(z / Float64(x / z)))
	tmp = 0.0
	if (z <= -1.75e+82)
		tmp = t_1;
	elseif (z <= -6.5e-32)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 5e+67)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (z / (x / z));
	tmp = 0.0;
	if (z <= -1.75e+82)
		tmp = t_1;
	elseif (z <= -6.5e-32)
		tmp = x / (y * (t - z));
	elseif (z <= 5e+67)
		tmp = (x / t) / (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+82], t$95$1, If[LessEqual[z, -6.5e-32], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+67], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.75e82 or 4.99999999999999976e67 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 82.7%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.7%

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

   4. Simplified 82.7%

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

      1. clear-num 82.2%

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

      2. inv-pow 82.2%

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

   6. Applied egg-rr 82.2%

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

      1. unpow-1 82.2%

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

      2. associate-/l* 93.8%

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

   8. Simplified 93.8%

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

   if -1.75e82 < z < -6.49999999999999988e-32

   1. Initial program 87.5%

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

   2. Taylor expanded in y around inf 58.7%

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

      1. *-commutative 58.7%

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

   4. Simplified 58.7%

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

   if -6.49999999999999988e-32 < z < 4.99999999999999976e67

   1. Initial program 91.6%

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

   2. Taylor expanded in t around inf 68.3%

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

      1. associate-/r* 70.8%

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

   4. Simplified 70.8%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+67}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 6: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (/ z (/ x z)))))
   (if (<= z -2.3e+81)
     t_1
     (if (<= z -8e-33)
       (/ (/ x y) (- t z))
       (if (<= z 4.9e+61) (/ (/ x t) (- y z)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z / (x / z));
	double tmp;
	if (z <= -2.3e+81) {
		tmp = t_1;
	} else if (z <= -8e-33) {
		tmp = (x / y) / (t - z);
	} else if (z <= 4.9e+61) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y 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 = 1.0d0 / (z / (x / z))
    if (z <= (-2.3d+81)) then
        tmp = t_1
    else if (z <= (-8d-33)) then
        tmp = (x / y) / (t - z)
    else if (z <= 4.9d+61) then
        tmp = (x / t) / (y - z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z / (x / z));
	double tmp;
	if (z <= -2.3e+81) {
		tmp = t_1;
	} else if (z <= -8e-33) {
		tmp = (x / y) / (t - z);
	} else if (z <= 4.9e+61) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (z / (x / z))
	tmp = 0
	if z <= -2.3e+81:
		tmp = t_1
	elif z <= -8e-33:
		tmp = (x / y) / (t - z)
	elif z <= 4.9e+61:
		tmp = (x / t) / (y - z)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(z / Float64(x / z)))
	tmp = 0.0
	if (z <= -2.3e+81)
		tmp = t_1;
	elseif (z <= -8e-33)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 4.9e+61)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (z / (x / z));
	tmp = 0.0;
	if (z <= -2.3e+81)
		tmp = t_1;
	elseif (z <= -8e-33)
		tmp = (x / y) / (t - z);
	elseif (z <= 4.9e+61)
		tmp = (x / t) / (y - z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e+81], t$95$1, If[LessEqual[z, -8e-33], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e+61], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2999999999999999e81 or 4.90000000000000025e61 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 82.7%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 82.7%

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

   4. Simplified 82.7%

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

      1. clear-num 82.2%

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

      2. inv-pow 82.2%

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

   6. Applied egg-rr 82.2%

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

      1. unpow-1 82.2%

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

      2. associate-/l* 93.8%

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

   8. Simplified 93.8%

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

   if -2.2999999999999999e81 < z < -8.0000000000000004e-33

   1. Initial program 87.5%

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

      1. *-un-lft-identity 87.5%

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

      2. times-frac 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. clear-num 99.5%

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

      2. un-div-inv 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 58.7%

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

      1. associate-/r* 66.8%

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

   8. Simplified 66.8%

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

   if -8.0000000000000004e-33 < z < 4.90000000000000025e61

   1. Initial program 91.6%

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

   2. Taylor expanded in t around inf 68.3%

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

      1. associate-/r* 70.8%

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

   4. Simplified 70.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-33}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 7: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.8e+161)
   (/ (/ (- x) z) (- y z))
   (if (<= z 4.2e+102) (/ x (* (- y z) (- t z))) (/ (/ x z) (- z t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+161) {
		tmp = (-x / z) / (y - z);
	} else if (z <= 4.2e+102) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-6.8d+161)) then
        tmp = (-x / z) / (y - z)
    else if (z <= 4.2d+102) then
        tmp = x / ((y - z) * (t - z))
    else
        tmp = (x / z) / (z - t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.8e+161) {
		tmp = (-x / z) / (y - z);
	} else if (z <= 4.2e+102) {
		tmp = x / ((y - z) * (t - z));
	} else {
		tmp = (x / z) / (z - t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -6.8e+161:
		tmp = (-x / z) / (y - z)
	elif z <= 4.2e+102:
		tmp = x / ((y - z) * (t - z))
	else:
		tmp = (x / z) / (z - t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.8e+161)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	elseif (z <= 4.2e+102)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.8e+161)
		tmp = (-x / z) / (y - z);
	elseif (z <= 4.2e+102)
		tmp = x / ((y - z) * (t - z));
	else
		tmp = (x / z) / (z - t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+161], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+102], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999986e161

   1. Initial program 71.4%

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

   2. Taylor expanded in t around 0 71.4%

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

      1. associate-*r/ 71.4%

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

      2. neg-mul-1 71.4%

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

      3. associate-/r* 95.6%

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

   4. Simplified 95.6%

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

   if -6.79999999999999986e161 < z < 4.20000000000000003e102

   1. Initial program 92.3%

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

   if 4.20000000000000003e102 < z

   1. Initial program 83.5%

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

      1. frac-2neg 83.5%

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

      2. div-inv 83.4%

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

      3. distribute-rgt-neg-in 83.4%

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

   3. Applied egg-rr 83.4%

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

      1. associate-/r* 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in y around 0 82.5%

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

      1. associate-/r* 94.8%

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

   8. Simplified 94.8%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \end{array} \]

Alternative 8: 62.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y 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 -1.65e+34)
     t_1
     (if (<= z 3.5e-42)
       (/ (/ x t) y)
       (if (<= z 7.5e+57) (/ (- x) (* z t)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -1.65e+34) {
		tmp = t_1;
	} else if (z <= 3.5e-42) {
		tmp = (x / t) / y;
	} else if (z <= 7.5e+57) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-1.65d+34)) then
        tmp = t_1
    else if (z <= 3.5d-42) then
        tmp = (x / t) / y
    else if (z <= 7.5d+57) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -1.65e+34) {
		tmp = t_1;
	} else if (z <= 3.5e-42) {
		tmp = (x / t) / y;
	} else if (z <= 7.5e+57) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -1.65e+34:
		tmp = t_1
	elif z <= 3.5e-42:
		tmp = (x / t) / y
	elif z <= 7.5e+57:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -1.65e+34)
		tmp = t_1;
	elseif (z <= 3.5e-42)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 7.5e+57)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -1.65e+34)
		tmp = t_1;
	elseif (z <= 3.5e-42)
		tmp = (x / t) / y;
	elseif (z <= 7.5e+57)
		tmp = -x / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+34], t$95$1, If[LessEqual[z, 3.5e-42], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 7.5e+57], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.64999999999999994e34 or 7.5000000000000006e57 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 79.0%

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

   4. Simplified 79.0%

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

   if -1.64999999999999994e34 < z < 3.5000000000000002e-42

   1. Initial program 89.5%

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

   2. Taylor expanded in y around inf 71.0%

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

      1. *-commutative 71.0%

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

   4. Simplified 71.0%

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

      1. associate-/r* 76.6%

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

      2. div-inv 76.6%

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

   6. Applied egg-rr 76.6%

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

      1. associate-*r/ 76.6%

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

      2. *-rgt-identity 76.6%

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

   8. Simplified 76.6%

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

   9. Taylor expanded in t around inf 58.4%

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

       1. associate-/r* 64.4%

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

   11. Simplified 64.4%

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

   if 3.5000000000000002e-42 < z < 7.5000000000000006e57

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 60.8%

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

      1. associate-*r/ 60.8%

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

      2. neg-mul-1 60.8%

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

   4. Simplified 60.8%

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

   5. Taylor expanded in z around 0 42.2%

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

      1. associate-*r/ 42.2%

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

      2. neg-mul-1 42.2%

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

      3. *-commutative 42.2%

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

   7. Simplified 42.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-42}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 9: 73.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+33} \lor \neg \left(z \leq 3.8 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.5e+33) (not (<= z 3.8e+63)))
   (/ 1.0 (/ z (/ x z)))
   (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+33) || !(z <= 3.8e+63)) {
		tmp = 1.0 / (z / (x / z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.5d+33)) .or. (.not. (z <= 3.8d+63))) then
        tmp = 1.0d0 / (z / (x / z))
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.5e+33) || !(z <= 3.8e+63)) {
		tmp = 1.0 / (z / (x / z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -5.5e+33) or not (z <= 3.8e+63):
		tmp = 1.0 / (z / (x / z))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.5e+33) || !(z <= 3.8e+63))
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.5e+33) || ~((z <= 3.8e+63)))
		tmp = 1.0 / (z / (x / z));
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.5e+33], N[Not[LessEqual[z, 3.8e+63]], $MachinePrecision]], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.5000000000000006e33 or 3.8000000000000001e63 < z

   1. Initial program 85.3%

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

   2. Taylor expanded in z around inf 79.0%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 79.0%

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

   4. Simplified 79.0%

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

      1. clear-num 78.6%

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

      2. inv-pow 78.6%

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

   6. Applied egg-rr 78.6%

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

      1. unpow-1 78.6%

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

      2. associate-/l* 89.5%

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

   8. Simplified 89.5%

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

   if -5.5000000000000006e33 < z < 3.8000000000000001e63

   1. Initial program 91.3%

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

   2. Taylor expanded in t around inf 66.8%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+33} \lor \neg \left(z \leq 3.8 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 10: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.2e+32)
   (/ (/ x y) (- t z))
   (if (<= y 2.6e-107) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.2e+32) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.6e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.2d+32)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.6d-107) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.2e+32) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.6e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -9.2e+32:
		tmp = (x / y) / (t - z)
	elif y <= 2.6e-107:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.2e+32)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.6e-107)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.2e+32)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.6e-107)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -9.2e+32], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e-107], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.1999999999999998e32

   1. Initial program 89.1%

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

      1. *-un-lft-identity 89.1%

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

      2. times-frac 98.4%

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

   3. Applied egg-rr 98.4%

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

      1. clear-num 98.3%

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

      2. un-div-inv 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in y around inf 87.5%

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

      1. associate-/r* 90.8%

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

   8. Simplified 90.8%

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

   if -9.1999999999999998e32 < y < 2.6000000000000001e-107

   1. Initial program 87.3%

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

      1. frac-2neg 87.3%

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

      2. div-inv 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

   3. Applied egg-rr 87.2%

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

      1. associate-/r* 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in y around 0 72.4%

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

      1. associate-/r* 81.6%

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

   8. Simplified 81.6%

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

   if 2.6000000000000001e-107 < y

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 61.9%

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

      1. associate-/r* 65.5%

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

   4. Simplified 65.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+32}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.2e+33)
   (/ (/ x (- t z)) y)
   (if (<= y 6.8e-107) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+33) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 6.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.2d+33)) then
        tmp = (x / (t - z)) / y
    else if (y <= 6.8d-107) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.2e+33) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 6.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.2e+33:
		tmp = (x / (t - z)) / y
	elif y <= 6.8e-107:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.2e+33)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 6.8e-107)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.2e+33)
		tmp = (x / (t - z)) / y;
	elseif (y <= 6.8e-107)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.2e+33], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 6.8e-107], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2000000000000001e33

   1. Initial program 89.1%

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

   2. Taylor expanded in y around inf 87.5%

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

      1. *-commutative 87.5%

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

   4. Simplified 87.5%

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

      1. associate-/r* 92.1%

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

      2. div-inv 92.1%

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

   6. Applied egg-rr 92.1%

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

      1. associate-*r/ 92.1%

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

      2. *-rgt-identity 92.1%

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

   8. Simplified 92.1%

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

   if -4.2000000000000001e33 < y < 6.79999999999999989e-107

   1. Initial program 87.3%

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

      1. frac-2neg 87.3%

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

      2. div-inv 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

   3. Applied egg-rr 87.2%

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

      1. associate-/r* 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in y around 0 72.4%

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

      1. associate-/r* 81.6%

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

   8. Simplified 81.6%

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

   if 6.79999999999999989e-107 < y

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 61.9%

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

      1. associate-/r* 65.5%

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

   4. Simplified 65.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 12: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.06e+33)
   (* (/ x (- t z)) (/ 1.0 y))
   (if (<= y 9.8e-107) (/ (/ x z) (- z t)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e+33) {
		tmp = (x / (t - z)) * (1.0 / y);
	} else if (y <= 9.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.06d+33)) then
        tmp = (x / (t - z)) * (1.0d0 / y)
    else if (y <= 9.8d-107) then
        tmp = (x / z) / (z - t)
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.06e+33) {
		tmp = (x / (t - z)) * (1.0 / y);
	} else if (y <= 9.8e-107) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.06e+33:
		tmp = (x / (t - z)) * (1.0 / y)
	elif y <= 9.8e-107:
		tmp = (x / z) / (z - t)
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.06e+33)
		tmp = Float64(Float64(x / Float64(t - z)) * Float64(1.0 / y));
	elseif (y <= 9.8e-107)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.06e+33)
		tmp = (x / (t - z)) * (1.0 / y);
	elseif (y <= 9.8e-107)
		tmp = (x / z) / (z - t);
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.06e+33], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-107], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05999999999999993e33

   1. Initial program 89.1%

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

   2. Taylor expanded in y around inf 87.5%

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

      1. *-commutative 87.5%

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

   4. Simplified 87.5%

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

      1. associate-/r* 92.1%

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

      2. div-inv 92.1%

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

   6. Applied egg-rr 92.1%

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

   if -2.05999999999999993e33 < y < 9.79999999999999959e-107

   1. Initial program 87.3%

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

      1. frac-2neg 87.3%

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

      2. div-inv 87.2%

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

      3. distribute-rgt-neg-in 87.2%

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

   3. Applied egg-rr 87.2%

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

      1. associate-/r* 87.5%

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

   5. Simplified 87.5%

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

   6. Taylor expanded in y around 0 72.4%

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

      1. associate-/r* 81.6%

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

   8. Simplified 81.6%

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

   if 9.79999999999999959e-107 < y

   1. Initial program 91.0%

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

   2. Taylor expanded in t around inf 61.9%

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

      1. associate-/r* 65.5%

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

   4. Simplified 65.5%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.06 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t - z} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 13: 45.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+33} \lor \neg \left(z \leq 1.26 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.1e+33) (not (<= z 1.26e+36))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+33) || !(z <= 1.26e+36)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5.1d+33)) .or. (.not. (z <= 1.26d+36))) then
        tmp = x / (y * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.1e+33) || !(z <= 1.26e+36)) {
		tmp = x / (y * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -5.1e+33) or not (z <= 1.26e+36):
		tmp = x / (y * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.1e+33) || !(z <= 1.26e+36))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.1e+33) || ~((z <= 1.26e+36)))
		tmp = x / (y * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.1e+33], N[Not[LessEqual[z, 1.26e+36]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0999999999999999e33 or 1.25999999999999994e36 < z

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 45.8%

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

      1. *-commutative 45.8%

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

   4. Simplified 45.8%

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

   5. Taylor expanded in t around 0 41.3%

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

      1. associate-*r/ 41.3%

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

      2. neg-mul-1 41.3%

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

      3. *-commutative 41.3%

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

   7. Simplified 41.3%

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

      1. expm1-log1p-u 41.0%

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

      2. expm1-udef 59.0%

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

      3. add-sqr-sqrt 30.7%

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

      4. sqrt-unprod 57.7%

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

      5. sqr-neg 57.7%

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

      6. sqrt-unprod 28.2%

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

      7. add-sqr-sqrt 58.9%

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

      8. *-commutative 58.9%

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

   9. Applied egg-rr 58.9%

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

       1. expm1-def 39.2%

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

       2. expm1-log1p 39.5%

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

       3. *-commutative 39.5%

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

   11. Simplified 39.5%

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

   if -5.0999999999999999e33 < z < 1.25999999999999994e36

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 53.3%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+33} \lor \neg \left(z \leq 1.26 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+33} \lor \neg \left(z \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+33) (not (<= z 6.8e+55))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+33) || !(z <= 6.8e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-3.1d+33)) .or. (.not. (z <= 6.8d+55))) then
        tmp = x / (z * z)
    else
        tmp = x / (y * t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+33) || !(z <= 6.8e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+33) or not (z <= 6.8e+55):
		tmp = x / (z * z)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+33) || !(z <= 6.8e+55))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(y * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e+33) || ~((z <= 6.8e+55)))
		tmp = x / (z * z);
	else
		tmp = x / (y * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+33], N[Not[LessEqual[z, 6.8e+55]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1e33 or 6.7999999999999996e55 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 78.3%

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

   4. Simplified 78.3%

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

   if -3.1e33 < z < 6.7999999999999996e55

   1. Initial program 91.3%

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

   2. Taylor expanded in z around 0 53.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+33} \lor \neg \left(z \leq 6.8 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+33} \lor \neg \left(z \leq 7 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.6e+33) (not (<= z 7e+55))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+33) || !(z <= 7e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y 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 <= (-8.6d+33)) .or. (.not. (z <= 7d+55))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.6e+33) || !(z <= 7e+55)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -8.6e+33) or not (z <= 7e+55):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.6e+33) || !(z <= 7e+55))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.6e+33) || ~((z <= 7e+55)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.6e+33], N[Not[LessEqual[z, 7e+55]], $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 < -8.60000000000000057e33 or 7.00000000000000021e55 < z

   1. Initial program 85.4%

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

   2. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{\frac{x}{{z}^{2}}} \]
   3. Step-by-step derivation

      1. unpow2 78.3%

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

   4. Simplified 78.3%

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

   if -8.60000000000000057e33 < z < 7.00000000000000021e55

   1. Initial program 91.3%

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

   2. Taylor expanded in y around inf 68.6%

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

      1. *-commutative 68.6%

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

   4. Simplified 68.6%

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

      1. associate-/r* 75.1%

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

      2. div-inv 75.0%

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

   6. Applied egg-rr 75.0%

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

      1. associate-*r/ 75.1%

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

      2. *-rgt-identity 75.1%

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

   8. Simplified 75.1%

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

   9. Taylor expanded in t around inf 53.3%

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

       1. associate-/r* 60.1%

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

   11. Simplified 60.1%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+33} \lor \neg \left(z \leq 7 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 16: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

   1. associate-/r* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 17: 38.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

2. Taylor expanded in z around 0 40.7%

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

3. Final simplification 40.7%

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

Developer target: 87.2% 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 2023297 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

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

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