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

Percentage Accurate: 88.9% → 98.8%

Time: 12.0s

Alternatives: 18

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.9% 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: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+162} \lor \neg \left(t_1 \leq 10^{+247}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t_1}\\ \end{array} \end{array} \]

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 (* (- y z) (- t z))))
   (if (or (<= t_1 -1e+162) (not (<= t_1 1e+247)))
     (/ (/ x (- t z)) (- y z))
     (/ x t_1))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -1e+162) || !(t_1 <= 1e+247)) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = x / 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 = (y - z) * (t - z)
    if ((t_1 <= (-1d+162)) .or. (.not. (t_1 <= 1d+247))) then
        tmp = (x / (t - z)) / (y - z)
    else
        tmp = x / 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 = (y - z) * (t - z);
	double tmp;
	if ((t_1 <= -1e+162) || !(t_1 <= 1e+247)) {
		tmp = (x / (t - z)) / (y - z);
	} else {
		tmp = x / t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (t_1 <= -1e+162) or not (t_1 <= 1e+247):
		tmp = (x / (t - z)) / (y - z)
	else:
		tmp = x / t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if ((t_1 <= -1e+162) || !(t_1 <= 1e+247))
		tmp = Float64(Float64(x / Float64(t - z)) / Float64(y - z));
	else
		tmp = Float64(x / t_1);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((t_1 <= -1e+162) || ~((t_1 <= 1e+247)))
		tmp = (x / (t - z)) / (y - z);
	else
		tmp = x / 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[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+162], N[Not[LessEqual[t$95$1, 1e+247]], $MachinePrecision]], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < -9.9999999999999994e161 or 9.99999999999999952e246 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 79.4%

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

      1. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

   if -9.9999999999999994e161 < (*.f64 (-.f64 y z) (-.f64 t z)) < 9.99999999999999952e246

   1. Initial program 98.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y - z\right) \cdot \left(t - z\right) \leq -1 \cdot 10^{+162} \lor \neg \left(\left(y - z\right) \cdot \left(t - z\right) \leq 10^{+247}\right):\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 2: 81.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+162}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-145}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.6e+162)
   (/ (/ x y) (- t z))
   (if (<= y -1.45e-23)
     (/ x (* y (- t z)))
     (if (<= y -1.5e-59)
       (/ (- x) (* z (- y z)))
       (if (<= y -5.7e-145)
         (/ (/ x (- t z)) y)
         (if (<= y 1.92e-47) (/ (/ (- x) z) (- t z)) (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.6e+162) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.45e-23) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.5e-59) {
		tmp = -x / (z * (y - z));
	} else if (y <= -5.7e-145) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.92e-47) {
		tmp = (-x / z) / (t - z);
	} 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 <= (-8.6d+162)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-1.45d-23)) then
        tmp = x / (y * (t - z))
    else if (y <= (-1.5d-59)) then
        tmp = -x / (z * (y - z))
    else if (y <= (-5.7d-145)) then
        tmp = (x / (t - z)) / y
    else if (y <= 1.92d-47) then
        tmp = (-x / z) / (t - z)
    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 <= -8.6e+162) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.45e-23) {
		tmp = x / (y * (t - z));
	} else if (y <= -1.5e-59) {
		tmp = -x / (z * (y - z));
	} else if (y <= -5.7e-145) {
		tmp = (x / (t - z)) / y;
	} else if (y <= 1.92e-47) {
		tmp = (-x / z) / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -8.6e+162:
		tmp = (x / y) / (t - z)
	elif y <= -1.45e-23:
		tmp = x / (y * (t - z))
	elif y <= -1.5e-59:
		tmp = -x / (z * (y - z))
	elif y <= -5.7e-145:
		tmp = (x / (t - z)) / y
	elif y <= 1.92e-47:
		tmp = (-x / z) / (t - z)
	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 <= -8.6e+162)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -1.45e-23)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -1.5e-59)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	elseif (y <= -5.7e-145)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= 1.92e-47)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	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 <= -8.6e+162)
		tmp = (x / y) / (t - z);
	elseif (y <= -1.45e-23)
		tmp = x / (y * (t - z));
	elseif (y <= -1.5e-59)
		tmp = -x / (z * (y - z));
	elseif (y <= -5.7e-145)
		tmp = (x / (t - z)) / y;
	elseif (y <= 1.92e-47)
		tmp = (-x / z) / (t - z);
	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, -8.6e+162], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-23], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.5e-59], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.7e-145], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 1.92e-47], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -8.6000000000000004e162

   1. Initial program 77.8%

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

      1. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 92.1%

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

   if -8.6000000000000004e162 < y < -1.4500000000000001e-23

   1. Initial program 83.5%

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

   2. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

   4. Simplified 74.7%

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

   if -1.4500000000000001e-23 < y < -1.5e-59

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   if -1.5e-59 < y < -5.70000000000000032e-145

   1. Initial program 99.8%

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

   2. Taylor expanded in y around inf 61.3%

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

      1. *-commutative 61.3%

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

      2. associate-/r* 67.7%

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

   4. Simplified 67.7%

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

   if -5.70000000000000032e-145 < y < 1.92e-47

   1. Initial program 92.2%

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

   2. Taylor expanded in y around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. distribute-frac-neg 81.2%

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

      3. associate-/r* 86.6%

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

   4. Simplified 86.6%

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

   if 1.92e-47 < y

   1. Initial program 88.8%

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

      1. associate-/l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around inf 57.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{t}}}{y - z} \]
3. Recombined 6 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+162}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq -5.7 \cdot 10^{-145}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{-47}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ t_2 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;z \leq -11:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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))) (t_2 (/ (/ x t) y)))
   (if (<= z -11.0)
     t_1
     (if (<= z -2.7e-201)
       t_2
       (if (<= z 8.8e-197) (/ x (* y t)) (if (<= z 6e+62) t_2 t_1))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double t_2 = (x / t) / y;
	double tmp;
	if (z <= -11.0) {
		tmp = t_1;
	} else if (z <= -2.7e-201) {
		tmp = t_2;
	} else if (z <= 8.8e-197) {
		tmp = x / (y * t);
	} else if (z <= 6e+62) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x / (z * z)
    t_2 = (x / t) / y
    if (z <= (-11.0d0)) then
        tmp = t_1
    else if (z <= (-2.7d-201)) then
        tmp = t_2
    else if (z <= 8.8d-197) then
        tmp = x / (y * t)
    else if (z <= 6d+62) then
        tmp = t_2
    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 t_2 = (x / t) / y;
	double tmp;
	if (z <= -11.0) {
		tmp = t_1;
	} else if (z <= -2.7e-201) {
		tmp = t_2;
	} else if (z <= 8.8e-197) {
		tmp = x / (y * t);
	} else if (z <= 6e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	t_2 = (x / t) / y
	tmp = 0
	if z <= -11.0:
		tmp = t_1
	elif z <= -2.7e-201:
		tmp = t_2
	elif z <= 8.8e-197:
		tmp = x / (y * t)
	elif z <= 6e+62:
		tmp = t_2
	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))
	t_2 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (z <= -11.0)
		tmp = t_1;
	elseif (z <= -2.7e-201)
		tmp = t_2;
	elseif (z <= 8.8e-197)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 6e+62)
		tmp = t_2;
	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);
	t_2 = (x / t) / y;
	tmp = 0.0;
	if (z <= -11.0)
		tmp = t_1;
	elseif (z <= -2.7e-201)
		tmp = t_2;
	elseif (z <= 8.8e-197)
		tmp = x / (y * t);
	elseif (z <= 6e+62)
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[z, -11.0], t$95$1, If[LessEqual[z, -2.7e-201], t$95$2, If[LessEqual[z, 8.8e-197], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+62], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -11 or 6e62 < z

   1. Initial program 86.2%

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

   2. Taylor expanded in z around inf 72.7%

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

      1. unpow2 72.7%

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

   4. Simplified 72.7%

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

   if -11 < z < -2.70000000000000005e-201 or 8.8000000000000001e-197 < z < 6e62

   1. Initial program 90.7%

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

   2. Taylor expanded in z around 0 42.1%

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

      1. *-un-lft-identity 42.1%

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

      2. times-frac 51.1%

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

   4. Applied egg-rr 51.1%

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

      1. associate-*l/ 51.1%

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

      2. *-lft-identity 51.1%

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

   6. Simplified 51.1%

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

   if -2.70000000000000005e-201 < z < 8.8000000000000001e-197

   1. Initial program 93.7%

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

   2. Taylor expanded in z around 0 83.3%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-201}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 4: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.8e+20)
   (/ (/ x z) z)
   (if (<= z -8.4e-160)
     (/ (/ x t) (- y z))
     (if (<= z 2.6e+74) (/ x (* y (- t z))) (/ 1.0 (* z (/ z x)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.8e+20) {
		tmp = (x / z) / z;
	} else if (z <= -8.4e-160) {
		tmp = (x / t) / (y - z);
	} else if (z <= 2.6e+74) {
		tmp = x / (y * (t - z));
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	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 <= (-5.8d+20)) then
        tmp = (x / z) / z
    else if (z <= (-8.4d-160)) then
        tmp = (x / t) / (y - z)
    else if (z <= 2.6d+74) then
        tmp = x / (y * (t - z))
    else
        tmp = 1.0d0 / (z * (z / x))
    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 <= -5.8e+20) {
		tmp = (x / z) / z;
	} else if (z <= -8.4e-160) {
		tmp = (x / t) / (y - z);
	} else if (z <= 2.6e+74) {
		tmp = x / (y * (t - z));
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -5.8e+20:
		tmp = (x / z) / z
	elif z <= -8.4e-160:
		tmp = (x / t) / (y - z)
	elif z <= 2.6e+74:
		tmp = x / (y * (t - z))
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.8e+20)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= -8.4e-160)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (z <= 2.6e+74)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.8e+20)
		tmp = (x / z) / z;
	elseif (z <= -8.4e-160)
		tmp = (x / t) / (y - z);
	elseif (z <= 2.6e+74)
		tmp = x / (y * (t - z));
	else
		tmp = 1.0 / (z * (z / x));
	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, -5.8e+20], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8.4e-160], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.6e+74], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.8e20

   1. Initial program 87.5%

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

   2. Taylor expanded in z around inf 73.5%

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

      1. unpow2 73.5%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -5.8e20 < z < -8.4000000000000002e-160

   1. Initial program 91.1%

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

      1. associate-/l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in t around inf 59.8%

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

   if -8.4000000000000002e-160 < z < 2.6000000000000001e74

   1. Initial program 92.3%

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

   2. Taylor expanded in y around inf 73.1%

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

      1. *-commutative 73.1%

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

   4. Simplified 73.1%

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

   if 2.6000000000000001e74 < z

   1. Initial program 82.6%

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

      1. associate-/r* 99.9%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.8%

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

      5. clear-num 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 77.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 77.5%

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

   8. Simplified 77.5%

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

   9. Taylor expanded in z around 0 77.5%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   10. Step-by-step derivation

       1. unpow2 77.5%

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

       2. associate-*r/ 89.0%

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

   11. Simplified 89.0%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-160}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+74}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 5: 78.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e-175)
   (/ (/ x y) (- t z))
   (if (<= t 2.3e-32) (/ (- x) (* z (- y z))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e-175) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2.3e-32) {
		tmp = -x / (z * (y - 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 (t <= (-3.7d-175)) then
        tmp = (x / y) / (t - z)
    else if (t <= 2.3d-32) then
        tmp = -x / (z * (y - 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 (t <= -3.7e-175) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2.3e-32) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -3.7e-175:
		tmp = (x / y) / (t - z)
	elif t <= 2.3e-32:
		tmp = -x / (z * (y - 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 (t <= -3.7e-175)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 2.3e-32)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - 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 (t <= -3.7e-175)
		tmp = (x / y) / (t - z);
	elseif (t <= 2.3e-32)
		tmp = -x / (z * (y - 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[LessEqual[t, -3.7e-175], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e-32], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.69999999999999998e-175

   1. Initial program 81.7%

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

      1. associate-/r* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 58.7%

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

   if -3.69999999999999998e-175 < t < 2.3000000000000001e-32

   1. Initial program 91.5%

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

   2. Taylor expanded in t around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. neg-mul-1 79.2%

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

      3. *-commutative 79.2%

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

   4. Simplified 79.2%

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

   if 2.3000000000000001e-32 < t

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 83.8%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-175}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 6: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-32}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e-174)
   (/ (/ x y) (- t z))
   (if (<= t 7e-32) (/ (/ (- x) z) (- y z)) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-174) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7e-32) {
		tmp = (-x / z) / (y - 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 (t <= (-1.7d-174)) then
        tmp = (x / y) / (t - z)
    else if (t <= 7d-32) then
        tmp = (-x / z) / (y - 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 (t <= -1.7e-174) {
		tmp = (x / y) / (t - z);
	} else if (t <= 7e-32) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e-174:
		tmp = (x / y) / (t - z)
	elif t <= 7e-32:
		tmp = (-x / z) / (y - 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 (t <= -1.7e-174)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 7e-32)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - 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 (t <= -1.7e-174)
		tmp = (x / y) / (t - z);
	elseif (t <= 7e-32)
		tmp = (-x / z) / (y - 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[LessEqual[t, -1.7e-174], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-32], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.7000000000000001e-174

   1. Initial program 81.7%

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

      1. associate-/r* 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in y around inf 58.7%

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

   if -1.7000000000000001e-174 < t < 6.9999999999999997e-32

   1. Initial program 91.5%

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

   2. Taylor expanded in t around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. neg-mul-1 79.2%

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

      3. *-commutative 79.2%

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

      4. associate-/r* 83.3%

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

   4. Simplified 83.3%

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

   if 6.9999999999999997e-32 < t

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 83.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-174}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-32}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 7: 67.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -36:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -36.0)
   (/ (/ x z) z)
   (if (<= z 5.5e+62) (/ (/ x y) t) (/ 1.0 (* z (/ z x))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -36.0) {
		tmp = (x / z) / z;
	} else if (z <= 5.5e+62) {
		tmp = (x / y) / t;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	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 <= (-36.0d0)) then
        tmp = (x / z) / z
    else if (z <= 5.5d+62) then
        tmp = (x / y) / t
    else
        tmp = 1.0d0 / (z * (z / x))
    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 <= -36.0) {
		tmp = (x / z) / z;
	} else if (z <= 5.5e+62) {
		tmp = (x / y) / t;
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -36.0:
		tmp = (x / z) / z
	elif z <= 5.5e+62:
		tmp = (x / y) / t
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -36.0)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 5.5e+62)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -36.0)
		tmp = (x / z) / z;
	elseif (z <= 5.5e+62)
		tmp = (x / y) / t;
	else
		tmp = 1.0 / (z * (z / x));
	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, -36.0], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.5e+62], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -36

   1. Initial program 88.2%

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

   2. Taylor expanded in z around inf 72.3%

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

      1. unpow2 72.3%

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

      2. associate-/r* 74.0%

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

   4. Simplified 74.0%

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

   if -36 < z < 5.4999999999999997e62

   1. Initial program 91.7%

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

      1. associate-/l/ 91.4%

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

   3. Simplified 91.4%

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

      1. flip-- 68.6%

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

      2. associate-/r/ 64.0%

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

      3. +-commutative 64.0%

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

   5. Applied egg-rr 64.0%

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

      1. associate-*l/ 60.6%

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

      2. difference-of-squares 61.4%

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

      3. +-commutative 61.4%

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

      4. times-frac 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in z around 0 56.2%

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

      1. associate-/r* 63.1%

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

   10. Simplified 63.1%

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

   if 5.4999999999999997e62 < z

   1. Initial program 83.3%

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

      1. associate-/r* 99.9%

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

      2. clear-num 99.8%

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

      3. inv-pow 99.8%

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

      4. div-inv 99.8%

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

      5. clear-num 99.8%

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

   3. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 74.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 74.8%

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

   8. Simplified 74.8%

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

   9. Taylor expanded in z around 0 74.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   10. Step-by-step derivation

       1. unpow2 74.8%

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

       2. associate-*r/ 85.9%

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

   11. Simplified 85.9%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 8: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.1e+20)
   (/ (/ x z) z)
   (if (<= z 1.38e+14) (/ x (* (- y z) t)) (/ 1.0 (* z (/ z x))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.1e+20) {
		tmp = (x / z) / z;
	} else if (z <= 1.38e+14) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	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+20)) then
        tmp = (x / z) / z
    else if (z <= 1.38d+14) then
        tmp = x / ((y - z) * t)
    else
        tmp = 1.0d0 / (z * (z / x))
    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+20) {
		tmp = (x / z) / z;
	} else if (z <= 1.38e+14) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = 1.0 / (z * (z / x));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -5.1e+20:
		tmp = (x / z) / z
	elif z <= 1.38e+14:
		tmp = x / ((y - z) * t)
	else:
		tmp = 1.0 / (z * (z / x))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.1e+20)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 1.38e+14)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	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+20)
		tmp = (x / z) / z;
	elseif (z <= 1.38e+14)
		tmp = x / ((y - z) * t);
	else
		tmp = 1.0 / (z * (z / x));
	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, -5.1e+20], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.38e+14], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.1e20

   1. Initial program 87.5%

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

   2. Taylor expanded in z around inf 73.5%

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

      1. unpow2 73.5%

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

      2. associate-/r* 75.2%

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

   4. Simplified 75.2%

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

   if -5.1e20 < z < 1.38e14

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf 70.6%

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

   if 1.38e14 < z

   1. Initial program 83.5%

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

      1. associate-/r* 99.8%

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

      2. clear-num 99.7%

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

      3. inv-pow 99.7%

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

      4. div-inv 99.7%

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

      5. clear-num 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. unpow-1 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in z around inf 68.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 68.9%

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

   8. Simplified 68.9%

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

   9. Taylor expanded in z around 0 68.9%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   10. Step-by-step derivation

       1. unpow2 68.9%

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

       2. associate-*r/ 77.8%

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

   11. Simplified 77.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.38 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 9: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.02e-302)
   (/ x (* y (- t z)))
   (if (<= t 5.9e-33) (/ 1.0 (* z (/ z x))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.02e-302) {
		tmp = x / (y * (t - z));
	} else if (t <= 5.9e-33) {
		tmp = 1.0 / (z * (z / x));
	} 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 (t <= 1.02d-302) then
        tmp = x / (y * (t - z))
    else if (t <= 5.9d-33) then
        tmp = 1.0d0 / (z * (z / x))
    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 (t <= 1.02e-302) {
		tmp = x / (y * (t - z));
	} else if (t <= 5.9e-33) {
		tmp = 1.0 / (z * (z / x));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 1.02e-302:
		tmp = x / (y * (t - z))
	elif t <= 5.9e-33:
		tmp = 1.0 / (z * (z / x))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.02e-302)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 5.9e-33)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	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 (t <= 1.02e-302)
		tmp = x / (y * (t - z));
	elseif (t <= 5.9e-33)
		tmp = 1.0 / (z * (z / x));
	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[LessEqual[t, 1.02e-302], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.9e-33], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 1.02e-302

   1. Initial program 83.2%

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

   2. Taylor expanded in y around inf 50.5%

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

      1. *-commutative 50.5%

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

   4. Simplified 50.5%

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

   if 1.02e-302 < t < 5.89999999999999985e-33

   1. Initial program 93.5%

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

      1. associate-/r* 96.5%

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

      2. clear-num 96.0%

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

      3. inv-pow 96.0%

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

      4. div-inv 96.0%

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

      5. clear-num 96.1%

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

   3. Applied egg-rr 96.1%

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

      1. unpow-1 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in z around inf 56.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in z around 0 56.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   10. Step-by-step derivation

       1. unpow2 56.8%

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

       2. associate-*r/ 61.6%

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

   11. Simplified 61.6%

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

   if 5.89999999999999985e-33 < t

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 83.8%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 10: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.7 \cdot 10^{-303}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 5.7e-303)
   (/ (/ x y) (- t z))
   (if (<= t 9e-33) (/ 1.0 (* z (/ z x))) (/ x (* (- y z) t)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.7e-303) {
		tmp = (x / y) / (t - z);
	} else if (t <= 9e-33) {
		tmp = 1.0 / (z * (z / x));
	} 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 (t <= 5.7d-303) then
        tmp = (x / y) / (t - z)
    else if (t <= 9d-33) then
        tmp = 1.0d0 / (z * (z / x))
    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 (t <= 5.7e-303) {
		tmp = (x / y) / (t - z);
	} else if (t <= 9e-33) {
		tmp = 1.0 / (z * (z / x));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 5.7e-303:
		tmp = (x / y) / (t - z)
	elif t <= 9e-33:
		tmp = 1.0 / (z * (z / x))
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 5.7e-303)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 9e-33)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	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 (t <= 5.7e-303)
		tmp = (x / y) / (t - z);
	elseif (t <= 9e-33)
		tmp = 1.0 / (z * (z / x));
	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[LessEqual[t, 5.7e-303], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-33], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 5.69999999999999981e-303

   1. Initial program 83.2%

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

      1. associate-/r* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in y around inf 56.2%

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

   if 5.69999999999999981e-303 < t < 8.99999999999999982e-33

   1. Initial program 93.5%

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

      1. associate-/r* 96.5%

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

      2. clear-num 96.0%

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

      3. inv-pow 96.0%

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

      4. div-inv 96.0%

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

      5. clear-num 96.1%

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

   3. Applied egg-rr 96.1%

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

      1. unpow-1 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in z around inf 56.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   7. Step-by-step derivation

      1. unpow2 56.8%

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

   8. Simplified 56.8%

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

   9. Taylor expanded in z around 0 56.8%

      \[\leadsto \frac{1}{\color{blue}{\frac{{z}^{2}}{x}}} \]
   10. Step-by-step derivation

       1. unpow2 56.8%

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

       2. associate-*r/ 61.6%

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

   11. Simplified 61.6%

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

   if 8.99999999999999982e-33 < t

   1. Initial program 97.0%

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

   2. Taylor expanded in t around inf 83.8%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.7 \cdot 10^{-303}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-33}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 11: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e+161) (/ (/ x y) (- t z)) (/ x (* (- y z) (- t z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e+161) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - 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 <= (-5.8d+161)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * (t - 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 <= -5.8e+161) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -5.8e+161:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.8e+161)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - 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 <= -5.8e+161)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * (t - 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, -5.8e+161], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000032e161

   1. Initial program 77.8%

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

      1. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 92.1%

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

   if -5.80000000000000032e161 < y

   1. Initial program 90.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+161}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \]

Alternative 12: 46.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+80} \lor \neg \left(z \leq 2.4 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -2.35e+80) (not (<= z 2.4e+166))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.35e+80) || !(z <= 2.4e+166)) {
		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 <= (-2.35d+80)) .or. (.not. (z <= 2.4d+166))) 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 <= -2.35e+80) || !(z <= 2.4e+166)) {
		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 <= -2.35e+80) or not (z <= 2.4e+166):
		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 <= -2.35e+80) || !(z <= 2.4e+166))
		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 <= -2.35e+80) || ~((z <= 2.4e+166)))
		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, -2.35e+80], N[Not[LessEqual[z, 2.4e+166]], $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 < -2.35000000000000005e80 or 2.39999999999999992e166 < z

   1. Initial program 79.1%

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

   2. Taylor expanded in t around 0 79.1%

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

      1. associate-*r/ 79.1%

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

      2. neg-mul-1 79.1%

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

      3. *-commutative 79.1%

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

   4. Simplified 79.1%

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

   5. Taylor expanded in z around 0 36.8%

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

      1. expm1-log1p-u 36.6%

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

      2. expm1-udef 62.5%

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

      3. add-sqr-sqrt 35.3%

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

      4. sqrt-unprod 61.7%

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

      5. sqr-neg 61.7%

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

      6. sqrt-unprod 27.2%

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

      7. add-sqr-sqrt 62.5%

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

      8. *-commutative 62.5%

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

   7. Applied egg-rr 62.5%

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

      1. expm1-def 36.6%

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

      2. expm1-log1p 36.9%

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

      3. *-commutative 36.9%

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

   9. Simplified 36.9%

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

   if -2.35000000000000005e80 < z < 2.39999999999999992e166

   1. Initial program 93.6%

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

   2. Taylor expanded in z around 0 47.7%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+80} \lor \neg \left(z \leq 2.4 \cdot 10^{+166}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 13: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -530000000000 \lor \neg \left(z \leq 9 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -530000000000.0) (not (<= z 9e+75)))
   (/ x (* z t))
   (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -530000000000.0) || !(z <= 9e+75)) {
		tmp = x / (z * t);
	} 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 <= (-530000000000.0d0)) .or. (.not. (z <= 9d+75))) then
        tmp = x / (z * t)
    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 <= -530000000000.0) || !(z <= 9e+75)) {
		tmp = x / (z * t);
	} else {
		tmp = x / (y * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -530000000000.0) or not (z <= 9e+75):
		tmp = x / (z * t)
	else:
		tmp = x / (y * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -530000000000.0) || !(z <= 9e+75))
		tmp = Float64(x / Float64(z * t));
	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 <= -530000000000.0) || ~((z <= 9e+75)))
		tmp = x / (z * t);
	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, -530000000000.0], N[Not[LessEqual[z, 9e+75]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.3e11 or 9.0000000000000007e75 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around 0 49.6%

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

      1. distribute-lft-out 49.6%

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

      2. +-commutative 49.6%

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

      3. mul-1-neg 49.6%

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

      4. distribute-lft-neg-in 49.6%

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

      5. *-commutative 49.6%

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

      6. unsub-neg 49.6%

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

      7. *-commutative 49.6%

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

      8. +-commutative 49.6%

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

   4. Simplified 49.6%

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

   5. Taylor expanded in y around 0 37.6%

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

      1. associate-*r/ 37.6%

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

      2. neg-mul-1 37.6%

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

      3. *-commutative 37.6%

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

   7. Simplified 37.6%

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

      1. expm1-log1p-u 36.4%

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

      2. expm1-udef 58.1%

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

      3. associate-/r* 58.1%

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

      4. add-sqr-sqrt 29.3%

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

      5. sqrt-unprod 56.9%

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

      6. sqr-neg 56.9%

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

      7. sqrt-unprod 28.8%

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

      8. add-sqr-sqrt 57.9%

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

   9. Applied egg-rr 57.9%

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

       1. expm1-def 38.6%

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

       2. expm1-log1p 39.1%

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

       3. associate-/r* 34.4%

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

   11. Simplified 34.4%

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

   if -5.3e11 < z < 9.0000000000000007e75

   1. Initial program 91.9%

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

   2. Taylor expanded in z around 0 54.8%

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

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -530000000000 \lor \neg \left(z \leq 9 \cdot 10^{+75}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 62.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-16} \lor \neg \left(z \leq 1950\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -3.6e-16) (not (<= z 1950.0))) (/ x (* z z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.6e-16) || !(z <= 1950.0)) {
		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 <= (-3.6d-16)) .or. (.not. (z <= 1950.0d0))) 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 <= -3.6e-16) || !(z <= 1950.0)) {
		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 <= -3.6e-16) or not (z <= 1950.0):
		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 <= -3.6e-16) || !(z <= 1950.0))
		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 <= -3.6e-16) || ~((z <= 1950.0)))
		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, -3.6e-16], N[Not[LessEqual[z, 1950.0]], $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 < -3.59999999999999983e-16 or 1950 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf 67.9%

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

      1. unpow2 67.9%

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

   4. Simplified 67.9%

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

   if -3.59999999999999983e-16 < z < 1950

   1. Initial program 93.0%

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

   2. Taylor expanded in z around 0 61.1%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-16} \lor \neg \left(z \leq 1950\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 15: 63.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \lor \neg \left(z \leq 7.6 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

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 -7.0) (not (<= z 7.6e+62))) (/ x (* z z)) (/ (/ x y) t)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.0) || !(z <= 7.6e+62)) {
		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 <= (-7.0d0)) .or. (.not. (z <= 7.6d+62))) 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 <= -7.0) || !(z <= 7.6e+62)) {
		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 <= -7.0) or not (z <= 7.6e+62):
		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 <= -7.0) || !(z <= 7.6e+62))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / 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 <= -7.0) || ~((z <= 7.6e+62)))
		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, -7.0], N[Not[LessEqual[z, 7.6e+62]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7 or 7.59999999999999967e62 < z

   1. Initial program 86.2%

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

   2. Taylor expanded in z around inf 72.7%

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

      1. unpow2 72.7%

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

   4. Simplified 72.7%

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

   if -7 < z < 7.59999999999999967e62

   1. Initial program 91.7%

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

      1. associate-/l/ 91.4%

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

   3. Simplified 91.4%

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

      1. flip-- 68.6%

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

      2. associate-/r/ 64.0%

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

      3. +-commutative 64.0%

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

   5. Applied egg-rr 64.0%

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

      1. associate-*l/ 60.6%

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

      2. difference-of-squares 61.4%

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

      3. +-commutative 61.4%

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

      4. times-frac 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in z around 0 56.2%

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

      1. associate-/r* 63.1%

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

   10. Simplified 63.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \lor \neg \left(z \leq 7.6 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 16: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \lor \neg \left(z \leq 9.2 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

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 -4.4) (not (<= z 9.2e+62))) (/ (/ x z) z) (/ (/ x y) t)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4) || !(z <= 9.2e+62)) {
		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 <= (-4.4d0)) .or. (.not. (z <= 9.2d+62))) 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 <= -4.4) || !(z <= 9.2e+62)) {
		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 <= -4.4) or not (z <= 9.2e+62):
		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 <= -4.4) || !(z <= 9.2e+62))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / 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 <= -4.4) || ~((z <= 9.2e+62)))
		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, -4.4], N[Not[LessEqual[z, 9.2e+62]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000004 or 9.19999999999999936e62 < z

   1. Initial program 86.2%

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

   2. Taylor expanded in z around inf 72.7%

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

      1. unpow2 72.7%

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

      2. associate-/r* 78.3%

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

   4. Simplified 78.3%

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

   if -4.4000000000000004 < z < 9.19999999999999936e62

   1. Initial program 91.7%

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

      1. associate-/l/ 91.4%

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

   3. Simplified 91.4%

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

      1. flip-- 68.6%

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

      2. associate-/r/ 64.0%

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

      3. +-commutative 64.0%

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

   5. Applied egg-rr 64.0%

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

      1. associate-*l/ 60.6%

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

      2. difference-of-squares 61.4%

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

      3. +-commutative 61.4%

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

      4. times-frac 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in z around 0 56.2%

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

      1. associate-/r* 63.1%

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

   10. Simplified 63.1%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \lor \neg \left(z \leq 9.2 \cdot 10^{+62}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]

Alternative 17: 97.0% 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 89.1%

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

   1. associate-/r* 97.2%

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

3. Simplified 97.2%

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

4. Final simplification 97.2%

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

Alternative 18: 40.1% 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 89.1%

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

2. Taylor expanded in z around 0 37.6%

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

3. Final simplification 37.6%

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

Developer target: 87.6% 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 2023196 
(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))))