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

Percentage Accurate: 88.8% → 96.9%

Time: 14.6s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (1.0d0 / (y - z)) / ((t - z) / x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

   1. add-cube-cbrt 86.2%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. *-commutative 86.2%

      \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

   3. times-frac 97.2%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

   4. pow2 97.2%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

3. Applied egg-rr 97.2%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
4. Step-by-step derivation

   1. frac-times 86.2%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

   2. unpow2 86.2%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

   3. add-cube-cbrt 87.0%

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

   4. associate-/r* 96.8%

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

   5. clear-num 96.7%

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

   6. associate-/l/ 96.0%

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

   7. associate-/r* 96.7%

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

5. Applied egg-rr 96.7%

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

6. Final simplification 96.7%

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

Alternative 2: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-104} \lor \neg \left(y \leq 2.35 \cdot 10^{-194}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* y (/ t x)))))
   (if (<= y -3.3e+106)
     (/ (/ (- x) y) z)
     (if (<= y -7.5e+47)
       t_1
       (if (<= y -1.8e-10)
         (/ (- x) (* y z))
         (if (or (<= y -5.4e-104) (not (<= y 2.35e-194)))
           t_1
           (/ (- x) (* z t))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (y * (t / x));
	double tmp;
	if (y <= -3.3e+106) {
		tmp = (-x / y) / z;
	} else if (y <= -7.5e+47) {
		tmp = t_1;
	} else if (y <= -1.8e-10) {
		tmp = -x / (y * z);
	} else if ((y <= -5.4e-104) || !(y <= 2.35e-194)) {
		tmp = t_1;
	} else {
		tmp = -x / (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) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (y * (t / x))
    if (y <= (-3.3d+106)) then
        tmp = (-x / y) / z
    else if (y <= (-7.5d+47)) then
        tmp = t_1
    else if (y <= (-1.8d-10)) then
        tmp = -x / (y * z)
    else if ((y <= (-5.4d-104)) .or. (.not. (y <= 2.35d-194))) then
        tmp = t_1
    else
        tmp = -x / (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 t_1 = 1.0 / (y * (t / x));
	double tmp;
	if (y <= -3.3e+106) {
		tmp = (-x / y) / z;
	} else if (y <= -7.5e+47) {
		tmp = t_1;
	} else if (y <= -1.8e-10) {
		tmp = -x / (y * z);
	} else if ((y <= -5.4e-104) || !(y <= 2.35e-194)) {
		tmp = t_1;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (y * (t / x))
	tmp = 0
	if y <= -3.3e+106:
		tmp = (-x / y) / z
	elif y <= -7.5e+47:
		tmp = t_1
	elif y <= -1.8e-10:
		tmp = -x / (y * z)
	elif (y <= -5.4e-104) or not (y <= 2.35e-194):
		tmp = t_1
	else:
		tmp = -x / (z * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(y * Float64(t / x)))
	tmp = 0.0
	if (y <= -3.3e+106)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (y <= -7.5e+47)
		tmp = t_1;
	elseif (y <= -1.8e-10)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif ((y <= -5.4e-104) || !(y <= 2.35e-194))
		tmp = t_1;
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (y * (t / x));
	tmp = 0.0;
	if (y <= -3.3e+106)
		tmp = (-x / y) / z;
	elseif (y <= -7.5e+47)
		tmp = t_1;
	elseif (y <= -1.8e-10)
		tmp = -x / (y * z);
	elseif ((y <= -5.4e-104) || ~((y <= 2.35e-194)))
		tmp = t_1;
	else
		tmp = -x / (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_] := Block[{t$95$1 = N[(1.0 / N[(y * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e+106], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -7.5e+47], t$95$1, If[LessEqual[y, -1.8e-10], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.4e-104], N[Not[LessEqual[y, 2.35e-194]], $MachinePrecision]], t$95$1, N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.30000000000000008e106

   1. Initial program 82.8%

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

   2. Taylor expanded in t around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/r* 67.9%

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

      3. distribute-neg-frac 67.9%

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

      4. distribute-neg-frac 67.9%

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

   7. Simplified 67.9%

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

   if -3.30000000000000008e106 < y < -7.4999999999999999e47 or -1.8e-10 < y < -5.3999999999999997e-104 or 2.3500000000000001e-194 < y

   1. Initial program 85.6%

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

   2. Taylor expanded in z around 0 39.0%

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

      1. clear-num 39.0%

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

      2. inv-pow 39.0%

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

      3. associate-/l* 41.7%

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

   4. Applied egg-rr 41.7%

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

      1. unpow-1 41.7%

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

      2. associate-/r/ 41.8%

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

   6. Simplified 41.8%

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

   if -7.4999999999999999e47 < y < -1.8e-10

   1. Initial program 90.4%

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

   2. Taylor expanded in y around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-/r* 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in t around 0 42.9%

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

      1. associate-*r/ 42.9%

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

      2. neg-mul-1 42.9%

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

      3. *-commutative 42.9%

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

   7. Simplified 42.9%

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

   if -5.3999999999999997e-104 < y < 2.3500000000000001e-194

   1. Initial program 90.7%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 89.8%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 89.8%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 90.7%

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

      4. associate-/r* 98.5%

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

      5. clear-num 98.4%

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

      6. associate-/l/ 97.6%

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

      7. associate-/r* 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in t around inf 60.2%

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

      1. associate-/r* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in y around 0 51.6%

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

       1. associate-*r/ 51.6%

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

       2. neg-mul-1 51.6%

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

       3. *-commutative 51.6%

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

   11. Simplified 51.6%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-104} \lor \neg \left(y \leq 2.35 \cdot 10^{-194}\right):\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]

Alternative 3: 91.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ t_2 := \frac{\frac{-x}{z}}{y - z}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-198}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* (- y z) (- t z)))) (t_2 (/ (/ (- x) z) (- y z))))
   (if (<= z -2.1e+162)
     t_2
     (if (<= z -3.1e-250)
       t_1
       (if (<= z 1.62e-198)
         (/ (/ x (- t z)) y)
         (if (<= z 3.1e+29) t_1 t_2))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double t_2 = (-x / z) / (y - z);
	double tmp;
	if (z <= -2.1e+162) {
		tmp = t_2;
	} else if (z <= -3.1e-250) {
		tmp = t_1;
	} else if (z <= 1.62e-198) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 3.1e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / ((y - z) * (t - z))
    t_2 = (-x / z) / (y - z)
    if (z <= (-2.1d+162)) then
        tmp = t_2
    else if (z <= (-3.1d-250)) then
        tmp = t_1
    else if (z <= 1.62d-198) then
        tmp = (x / (t - z)) / y
    else if (z <= 3.1d+29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / ((y - z) * (t - z));
	double t_2 = (-x / z) / (y - z);
	double tmp;
	if (z <= -2.1e+162) {
		tmp = t_2;
	} else if (z <= -3.1e-250) {
		tmp = t_1;
	} else if (z <= 1.62e-198) {
		tmp = (x / (t - z)) / y;
	} else if (z <= 3.1e+29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = x / ((y - z) * (t - z))
	t_2 = (-x / z) / (y - z)
	tmp = 0
	if z <= -2.1e+162:
		tmp = t_2
	elif z <= -3.1e-250:
		tmp = t_1
	elif z <= 1.62e-198:
		tmp = (x / (t - z)) / y
	elif z <= 3.1e+29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(y - z) * Float64(t - z)))
	t_2 = Float64(Float64(Float64(-x) / z) / Float64(y - z))
	tmp = 0.0
	if (z <= -2.1e+162)
		tmp = t_2;
	elseif (z <= -3.1e-250)
		tmp = t_1;
	elseif (z <= 1.62e-198)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (z <= 3.1e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / ((y - z) * (t - z));
	t_2 = (-x / z) / (y - z);
	tmp = 0.0;
	if (z <= -2.1e+162)
		tmp = t_2;
	elseif (z <= -3.1e-250)
		tmp = t_1;
	elseif (z <= 1.62e-198)
		tmp = (x / (t - z)) / y;
	elseif (z <= 3.1e+29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+162], t$95$2, If[LessEqual[z, -3.1e-250], t$95$1, If[LessEqual[z, 1.62e-198], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 3.1e+29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e162 or 3.0999999999999999e29 < z

   1. Initial program 76.2%

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

      1. add-cube-cbrt 76.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 76.0%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 99.2%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 99.2%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 76.0%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 76.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 76.2%

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

      4. associate-/r* 99.8%

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

      5. clear-num 99.7%

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

      6. associate-/l/ 98.7%

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

      7. associate-/r* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in t around 0 71.4%

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

      1. associate-/r* 89.6%

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

      2. associate-*r/ 89.6%

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

      3. neg-mul-1 89.6%

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

      4. distribute-neg-frac 89.6%

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

   8. Simplified 89.6%

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

   if -2.1e162 < z < -3.1000000000000001e-250 or 1.62e-198 < z < 3.0999999999999999e29

   1. Initial program 95.7%

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

   if -3.1000000000000001e-250 < z < 1.62e-198

   1. Initial program 77.8%

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

   2. Taylor expanded in y around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-/r* 90.4%

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

   4. Simplified 90.4%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+162}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-250}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{-198}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \end{array} \]

Alternative 4: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.82 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-102} \lor \neg \left(y \leq 1.85 \cdot 10^{-194}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)))
   (if (<= y -1.3e+106)
     (/ (/ (- x) y) z)
     (if (<= y -2.85e+47)
       t_1
       (if (<= y -1.82e-10)
         (/ (- x) (* y z))
         (if (or (<= y -6.6e-102) (not (<= y 1.85e-194)))
           t_1
           (/ (- x) (* z t))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (y <= -1.3e+106) {
		tmp = (-x / y) / z;
	} else if (y <= -2.85e+47) {
		tmp = t_1;
	} else if (y <= -1.82e-10) {
		tmp = -x / (y * z);
	} else if ((y <= -6.6e-102) || !(y <= 1.85e-194)) {
		tmp = t_1;
	} else {
		tmp = -x / (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) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / y
    if (y <= (-1.3d+106)) then
        tmp = (-x / y) / z
    else if (y <= (-2.85d+47)) then
        tmp = t_1
    else if (y <= (-1.82d-10)) then
        tmp = -x / (y * z)
    else if ((y <= (-6.6d-102)) .or. (.not. (y <= 1.85d-194))) then
        tmp = t_1
    else
        tmp = -x / (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 t_1 = (x / t) / y;
	double tmp;
	if (y <= -1.3e+106) {
		tmp = (-x / y) / z;
	} else if (y <= -2.85e+47) {
		tmp = t_1;
	} else if (y <= -1.82e-10) {
		tmp = -x / (y * z);
	} else if ((y <= -6.6e-102) || !(y <= 1.85e-194)) {
		tmp = t_1;
	} else {
		tmp = -x / (z * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	tmp = 0
	if y <= -1.3e+106:
		tmp = (-x / y) / z
	elif y <= -2.85e+47:
		tmp = t_1
	elif y <= -1.82e-10:
		tmp = -x / (y * z)
	elif (y <= -6.6e-102) or not (y <= 1.85e-194):
		tmp = t_1
	else:
		tmp = -x / (z * t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (y <= -1.3e+106)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (y <= -2.85e+47)
		tmp = t_1;
	elseif (y <= -1.82e-10)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif ((y <= -6.6e-102) || !(y <= 1.85e-194))
		tmp = t_1;
	else
		tmp = Float64(Float64(-x) / Float64(z * t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	tmp = 0.0;
	if (y <= -1.3e+106)
		tmp = (-x / y) / z;
	elseif (y <= -2.85e+47)
		tmp = t_1;
	elseif (y <= -1.82e-10)
		tmp = -x / (y * z);
	elseif ((y <= -6.6e-102) || ~((y <= 1.85e-194)))
		tmp = t_1;
	else
		tmp = -x / (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_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1.3e+106], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -2.85e+47], t$95$1, If[LessEqual[y, -1.82e-10], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -6.6e-102], N[Not[LessEqual[y, 1.85e-194]], $MachinePrecision]], t$95$1, N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3000000000000001e106

   1. Initial program 82.8%

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

   2. Taylor expanded in t around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/r* 67.9%

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

      3. distribute-neg-frac 67.9%

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

      4. distribute-neg-frac 67.9%

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

   7. Simplified 67.9%

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

   if -1.3000000000000001e106 < y < -2.8499999999999998e47 or -1.8199999999999999e-10 < y < -6.6e-102 or 1.85000000000000004e-194 < y

   1. Initial program 85.6%

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

   2. Taylor expanded in y around inf 58.3%

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

      1. *-commutative 58.3%

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

      2. associate-/r* 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in t around inf 41.8%

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

   if -2.8499999999999998e47 < y < -1.8199999999999999e-10

   1. Initial program 90.4%

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

   2. Taylor expanded in y around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-/r* 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in t around 0 42.9%

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

      1. associate-*r/ 42.9%

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

      2. neg-mul-1 42.9%

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

      3. *-commutative 42.9%

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

   7. Simplified 42.9%

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

   if -6.6e-102 < y < 1.85000000000000004e-194

   1. Initial program 90.7%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 89.8%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 89.8%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 90.7%

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

      4. associate-/r* 98.5%

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

      5. clear-num 98.4%

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

      6. associate-/l/ 97.6%

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

      7. associate-/r* 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in t around inf 60.2%

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

      1. associate-/r* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in y around 0 51.6%

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

       1. associate-*r/ 51.6%

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

       2. neg-mul-1 51.6%

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

       3. *-commutative 51.6%

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

   11. Simplified 51.6%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq -1.82 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-102} \lor \neg \left(y \leq 1.85 \cdot 10^{-194}\right):\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \end{array} \]

Alternative 5: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-194}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x t) y)))
   (if (<= y -4.2e+106)
     (/ (/ (- x) y) z)
     (if (<= y -5.6e+47)
       t_1
       (if (<= y -1.8e-10)
         (/ (- x) (* y z))
         (if (<= y -2.3e-104)
           (* (/ x t) (/ 1.0 y))
           (if (<= y 2.1e-194) (/ (- x) (* z t)) t_1)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (y <= -4.2e+106) {
		tmp = (-x / y) / z;
	} else if (y <= -5.6e+47) {
		tmp = t_1;
	} else if (y <= -1.8e-10) {
		tmp = -x / (y * z);
	} else if (y <= -2.3e-104) {
		tmp = (x / t) * (1.0 / y);
	} else if (y <= 2.1e-194) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / t) / y
    if (y <= (-4.2d+106)) then
        tmp = (-x / y) / z
    else if (y <= (-5.6d+47)) then
        tmp = t_1
    else if (y <= (-1.8d-10)) then
        tmp = -x / (y * z)
    else if (y <= (-2.3d-104)) then
        tmp = (x / t) * (1.0d0 / y)
    else if (y <= 2.1d-194) then
        tmp = -x / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / t) / y;
	double tmp;
	if (y <= -4.2e+106) {
		tmp = (-x / y) / z;
	} else if (y <= -5.6e+47) {
		tmp = t_1;
	} else if (y <= -1.8e-10) {
		tmp = -x / (y * z);
	} else if (y <= -2.3e-104) {
		tmp = (x / t) * (1.0 / y);
	} else if (y <= 2.1e-194) {
		tmp = -x / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / t) / y
	tmp = 0
	if y <= -4.2e+106:
		tmp = (-x / y) / z
	elif y <= -5.6e+47:
		tmp = t_1
	elif y <= -1.8e-10:
		tmp = -x / (y * z)
	elif y <= -2.3e-104:
		tmp = (x / t) * (1.0 / y)
	elif y <= 2.1e-194:
		tmp = -x / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / y)
	tmp = 0.0
	if (y <= -4.2e+106)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif (y <= -5.6e+47)
		tmp = t_1;
	elseif (y <= -1.8e-10)
		tmp = Float64(Float64(-x) / Float64(y * z));
	elseif (y <= -2.3e-104)
		tmp = Float64(Float64(x / t) * Float64(1.0 / y));
	elseif (y <= 2.1e-194)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / t) / y;
	tmp = 0.0;
	if (y <= -4.2e+106)
		tmp = (-x / y) / z;
	elseif (y <= -5.6e+47)
		tmp = t_1;
	elseif (y <= -1.8e-10)
		tmp = -x / (y * z);
	elseif (y <= -2.3e-104)
		tmp = (x / t) * (1.0 / y);
	elseif (y <= 2.1e-194)
		tmp = -x / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.2e+106], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -5.6e+47], t$95$1, If[LessEqual[y, -1.8e-10], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-104], N[(N[(x / t), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-194], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.2000000000000001e106

   1. Initial program 82.8%

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

   2. Taylor expanded in t around 0 51.6%

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

      1. associate-*r/ 51.6%

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

      2. neg-mul-1 51.6%

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

   4. Simplified 51.6%

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

   5. Taylor expanded in z around 0 51.6%

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

      1. mul-1-neg 51.6%

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

      2. associate-/r* 67.9%

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

      3. distribute-neg-frac 67.9%

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

      4. distribute-neg-frac 67.9%

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

   7. Simplified 67.9%

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

   if -4.2000000000000001e106 < y < -5.59999999999999976e47 or 2.1e-194 < y

   1. Initial program 83.7%

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

   2. Taylor expanded in y around inf 58.4%

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

      1. *-commutative 58.4%

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

      2. associate-/r* 59.0%

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

   4. Simplified 59.0%

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

   5. Taylor expanded in t around inf 41.2%

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

   if -5.59999999999999976e47 < y < -1.8e-10

   1. Initial program 90.4%

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

   2. Taylor expanded in y around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-/r* 52.3%

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

   4. Simplified 52.3%

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

   5. Taylor expanded in t around 0 42.9%

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

      1. associate-*r/ 42.9%

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

      2. neg-mul-1 42.9%

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

      3. *-commutative 42.9%

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

   7. Simplified 42.9%

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

   if -1.8e-10 < y < -2.2999999999999999e-104

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 40.9%

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

      1. associate-/r* 46.4%

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

      2. div-inv 46.4%

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

   4. Applied egg-rr 46.4%

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

   if -2.2999999999999999e-104 < y < 2.1e-194

   1. Initial program 90.7%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 89.8%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 89.8%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 90.7%

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

      4. associate-/r* 98.5%

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

      5. clear-num 98.4%

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

      6. associate-/l/ 97.6%

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

      7. associate-/r* 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in t around inf 60.2%

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

      1. associate-/r* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in y around 0 51.6%

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

       1. associate-*r/ 51.6%

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

       2. neg-mul-1 51.6%

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

       3. *-commutative 51.6%

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

   11. Simplified 51.6%

       \[\leadsto \color{blue}{\frac{-x}{z \cdot t}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+106}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{t} \cdot \frac{1}{y}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-194}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 6: 81.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.8e+213)
   (/ (/ x (- t z)) y)
   (if (<= y -3.5e+46)
     (/ x (* y (- t z)))
     (if (<= y -3.6e-103)
       (/ (- x) (* z (- y z)))
       (if (<= y 3.4e-133) (/ (/ (- 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 <= -8.8e+213) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -3.5e+46) {
		tmp = x / (y * (t - z));
	} else if (y <= -3.6e-103) {
		tmp = -x / (z * (y - z));
	} else if (y <= 3.4e-133) {
		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 <= (-8.8d+213)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-3.5d+46)) then
        tmp = x / (y * (t - z))
    else if (y <= (-3.6d-103)) then
        tmp = -x / (z * (y - z))
    else if (y <= 3.4d-133) 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 <= -8.8e+213) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -3.5e+46) {
		tmp = x / (y * (t - z));
	} else if (y <= -3.6e-103) {
		tmp = -x / (z * (y - z));
	} else if (y <= 3.4e-133) {
		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 <= -8.8e+213:
		tmp = (x / (t - z)) / y
	elif y <= -3.5e+46:
		tmp = x / (y * (t - z))
	elif y <= -3.6e-103:
		tmp = -x / (z * (y - z))
	elif y <= 3.4e-133:
		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 <= -8.8e+213)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -3.5e+46)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= -3.6e-103)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - z)));
	elseif (y <= 3.4e-133)
		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 <= -8.8e+213)
		tmp = (x / (t - z)) / y;
	elseif (y <= -3.5e+46)
		tmp = x / (y * (t - z));
	elseif (y <= -3.6e-103)
		tmp = -x / (z * (y - z));
	elseif (y <= 3.4e-133)
		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, -8.8e+213], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -3.5e+46], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.6e-103], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-133], 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 5 regimes

2. if y < -8.7999999999999995e213

   1. Initial program 72.9%

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

   2. Taylor expanded in y around inf 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/r* 95.4%

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

   4. Simplified 95.4%

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

   if -8.7999999999999995e213 < y < -3.49999999999999985e46

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 93.7%

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

      1. *-commutative 93.7%

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

   4. Simplified 93.7%

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

   if -3.49999999999999985e46 < y < -3.5999999999999998e-103

   1. Initial program 96.1%

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

      1. add-cube-cbrt 95.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 95.0%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 95.0%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 95.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 96.1%

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

      4. associate-/r* 96.1%

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

      5. clear-num 96.1%

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

      6. associate-/l/ 96.1%

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

      7. associate-/r* 96.2%

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

   5. Applied egg-rr 96.2%

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

      1. clear-num 96.1%

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

      2. associate-/r/ 96.1%

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

   7. Applied egg-rr 96.1%

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

   8. Taylor expanded in t around 0 65.4%

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

      1. mul-1-neg 65.4%

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

   10. Simplified 65.4%

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

   if -3.5999999999999998e-103 < y < 3.40000000000000006e-133

   1. Initial program 86.9%

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

      1. add-cube-cbrt 86.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 86.0%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 86.0%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 86.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 86.9%

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

      4. associate-/r* 98.7%

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

      5. clear-num 98.6%

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

      6. associate-/l/ 97.9%

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

      7. associate-/r* 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. mul-1-neg 79.1%

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

      2. associate-/r* 82.9%

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

      3. distribute-neg-frac 82.9%

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

      4. distribute-neg-frac 82.9%

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

   8. Simplified 82.9%

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

   if 3.40000000000000006e-133 < y

   1. Initial program 85.5%

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

      1. add-cube-cbrt 84.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 84.7%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 96.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 96.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 96.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 84.7%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 84.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 85.5%

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

      4. associate-/r* 95.2%

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

      5. clear-num 95.2%

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

      6. associate-/l/ 94.1%

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

      7. associate-/r* 95.2%

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

   5. Applied egg-rr 95.2%

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

   6. Taylor expanded in t around inf 51.0%

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

      1. associate-/r* 55.3%

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

   8. Simplified 55.3%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+213}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-103}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-133}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 7: 64.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-79} \lor \neg \left(t \leq 5.5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{z}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.15e-122)
   (/ (/ x y) t)
   (if (<= t 1.48e-148)
     (/ (/ (- x) y) z)
     (if (or (<= t 3.2e-79) (not (<= t 5.5e-37)))
       (/ x (* (- y z) t))
       (- (/ (/ x z) y))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.15e-122) {
		tmp = (x / y) / t;
	} else if (t <= 1.48e-148) {
		tmp = (-x / y) / z;
	} else if ((t <= 3.2e-79) || !(t <= 5.5e-37)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = -((x / z) / y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.15d-122)) then
        tmp = (x / y) / t
    else if (t <= 1.48d-148) then
        tmp = (-x / y) / z
    else if ((t <= 3.2d-79) .or. (.not. (t <= 5.5d-37))) then
        tmp = x / ((y - z) * t)
    else
        tmp = -((x / z) / y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.15e-122) {
		tmp = (x / y) / t;
	} else if (t <= 1.48e-148) {
		tmp = (-x / y) / z;
	} else if ((t <= 3.2e-79) || !(t <= 5.5e-37)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = -((x / z) / y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.15e-122:
		tmp = (x / y) / t
	elif t <= 1.48e-148:
		tmp = (-x / y) / z
	elif (t <= 3.2e-79) or not (t <= 5.5e-37):
		tmp = x / ((y - z) * t)
	else:
		tmp = -((x / z) / y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.15e-122)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 1.48e-148)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif ((t <= 3.2e-79) || !(t <= 5.5e-37))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(-Float64(Float64(x / z) / y));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.15e-122)
		tmp = (x / y) / t;
	elseif (t <= 1.48e-148)
		tmp = (-x / y) / z;
	elseif ((t <= 3.2e-79) || ~((t <= 5.5e-37)))
		tmp = x / ((y - z) * t);
	else
		tmp = -((x / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -2.15e-122], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 1.48e-148], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t, 3.2e-79], N[Not[LessEqual[t, 5.5e-37]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], (-N[(N[(x / z), $MachinePrecision] / y), $MachinePrecision])]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.15000000000000009e-122

   1. Initial program 87.8%

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

   2. Taylor expanded in z around 0 41.2%

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

      1. associate-/r* 45.2%

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

      2. div-inv 45.2%

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

   4. Applied egg-rr 45.2%

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

      1. associate-*l/ 41.1%

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

      2. un-div-inv 41.2%

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

   6. Applied egg-rr 41.2%

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

   if -2.15000000000000009e-122 < t < 1.47999999999999996e-148

   1. Initial program 84.3%

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

   2. Taylor expanded in t around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in z around 0 44.7%

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

      1. mul-1-neg 44.7%

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

      2. associate-/r* 48.3%

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

      3. distribute-neg-frac 48.3%

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

      4. distribute-neg-frac 48.3%

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

   7. Simplified 48.3%

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

   if 1.47999999999999996e-148 < t < 3.19999999999999988e-79 or 5.4999999999999998e-37 < t

   1. Initial program 87.8%

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

   2. Taylor expanded in t around inf 77.3%

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

   if 3.19999999999999988e-79 < t < 5.4999999999999998e-37

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 53.2%

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

      1. *-commutative 53.2%

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

      2. associate-/r* 76.2%

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

   4. Simplified 76.2%

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

   5. Taylor expanded in t around 0 52.3%

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

      1. associate-*r/ 52.3%

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

      2. neg-mul-1 52.3%

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

   7. Simplified 52.3%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 1.48 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-79} \lor \neg \left(t \leq 5.5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{z}}{y}\\ \end{array} \]

Alternative 8: 65.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-81} \lor \neg \left(t \leq 5.2 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.8e-122)
   (/ (/ x y) t)
   (if (<= t 2.95e-148)
     (/ (/ (- x) y) z)
     (if (or (<= t 1.02e-81) (not (<= t 5.2e-34)))
       (/ x (* (- y z) t))
       (/ x (* z (- y z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.8e-122) {
		tmp = (x / y) / t;
	} else if (t <= 2.95e-148) {
		tmp = (-x / y) / z;
	} else if ((t <= 1.02e-81) || !(t <= 5.2e-34)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = x / (z * (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 (t <= (-1.8d-122)) then
        tmp = (x / y) / t
    else if (t <= 2.95d-148) then
        tmp = (-x / y) / z
    else if ((t <= 1.02d-81) .or. (.not. (t <= 5.2d-34))) then
        tmp = x / ((y - z) * t)
    else
        tmp = x / (z * (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 (t <= -1.8e-122) {
		tmp = (x / y) / t;
	} else if (t <= 2.95e-148) {
		tmp = (-x / y) / z;
	} else if ((t <= 1.02e-81) || !(t <= 5.2e-34)) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = x / (z * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.8e-122:
		tmp = (x / y) / t
	elif t <= 2.95e-148:
		tmp = (-x / y) / z
	elif (t <= 1.02e-81) or not (t <= 5.2e-34):
		tmp = x / ((y - z) * t)
	else:
		tmp = x / (z * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.8e-122)
		tmp = Float64(Float64(x / y) / t);
	elseif (t <= 2.95e-148)
		tmp = Float64(Float64(Float64(-x) / y) / z);
	elseif ((t <= 1.02e-81) || !(t <= 5.2e-34))
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = Float64(x / Float64(z * 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 (t <= -1.8e-122)
		tmp = (x / y) / t;
	elseif (t <= 2.95e-148)
		tmp = (-x / y) / z;
	elseif ((t <= 1.02e-81) || ~((t <= 5.2e-34)))
		tmp = x / ((y - z) * t);
	else
		tmp = x / (z * (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[t, -1.8e-122], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[t, 2.95e-148], N[(N[((-x) / y), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[t, 1.02e-81], N[Not[LessEqual[t, 5.2e-34]], $MachinePrecision]], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.79999999999999997e-122

   1. Initial program 87.8%

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

   2. Taylor expanded in z around 0 41.2%

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

      1. associate-/r* 45.2%

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

      2. div-inv 45.2%

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

   4. Applied egg-rr 45.2%

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

      1. associate-*l/ 41.1%

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

      2. un-div-inv 41.2%

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

   6. Applied egg-rr 41.2%

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

   if -1.79999999999999997e-122 < t < 2.95000000000000008e-148

   1. Initial program 84.3%

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

   2. Taylor expanded in t around 0 77.1%

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

      1. associate-*r/ 77.1%

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

      2. neg-mul-1 77.1%

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

   4. Simplified 77.1%

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

   5. Taylor expanded in z around 0 44.7%

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

      1. mul-1-neg 44.7%

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

      2. associate-/r* 48.3%

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

      3. distribute-neg-frac 48.3%

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

      4. distribute-neg-frac 48.3%

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

   7. Simplified 48.3%

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

   if 2.95000000000000008e-148 < t < 1.01999999999999998e-81 or 5.1999999999999999e-34 < t

   1. Initial program 87.8%

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

   2. Taylor expanded in t around inf 77.3%

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

   if 1.01999999999999998e-81 < t < 5.1999999999999999e-34

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 76.6%

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

      1. associate-*r/ 76.6%

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

      2. neg-mul-1 76.6%

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

   4. Simplified 76.6%

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

      1. expm1-log1p-u 73.9%

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

      2. expm1-udef 73.9%

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

      3. add-sqr-sqrt 50.0%

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

      4. sqrt-unprod 50.0%

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

      5. sqr-neg 50.0%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 50.0%

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

      8. associate-/r* 50.0%

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

   6. Applied egg-rr 50.0%

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

      1. expm1-def 50.0%

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

      2. expm1-log1p 50.2%

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

      3. associate-/r* 50.3%

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

   8. Simplified 50.3%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{-x}{y}}{z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-81} \lor \neg \left(t \leq 5.2 \cdot 10^{-34}\right):\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 9: 79.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.2e-122)
   (/ (/ x (- t z)) y)
   (if (<= t 2.1e+16) (/ (- x) (* z (- y z))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e-122) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.1e+16) {
		tmp = -x / (z * (y - 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 (t <= (-2.2d-122)) then
        tmp = (x / (t - z)) / y
    else if (t <= 2.1d+16) then
        tmp = -x / (z * (y - 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 (t <= -2.2e-122) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.1e+16) {
		tmp = -x / (z * (y - z));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -2.2e-122:
		tmp = (x / (t - z)) / y
	elif t <= 2.1e+16:
		tmp = -x / (z * (y - 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 (t <= -2.2e-122)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 2.1e+16)
		tmp = Float64(Float64(-x) / Float64(z * Float64(y - 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 (t <= -2.2e-122)
		tmp = (x / (t - z)) / y;
	elseif (t <= 2.1e+16)
		tmp = -x / (z * (y - 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[t, -2.2e-122], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.1e+16], N[((-x) / N[(z * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2e-122

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-/r* 55.6%

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

   4. Simplified 55.6%

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

   if -2.2e-122 < t < 2.1e16

   1. Initial program 86.5%

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

      1. add-cube-cbrt 85.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 85.5%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 95.1%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 95.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 95.1%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 85.5%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 85.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 86.5%

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

      4. associate-/r* 94.3%

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

      5. clear-num 94.2%

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

      6. associate-/l/ 94.2%

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

      7. associate-/r* 94.1%

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

   5. Applied egg-rr 94.1%

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

      1. clear-num 94.0%

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

      2. associate-/r/ 94.0%

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

   7. Applied egg-rr 94.0%

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

   8. Taylor expanded in t around 0 68.3%

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

      1. mul-1-neg 68.3%

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

   10. Simplified 68.3%

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

   if 2.1e16 < t

   1. Initial program 86.6%

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

      1. add-cube-cbrt 85.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 85.7%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 85.7%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 85.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 86.6%

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

      4. associate-/r* 99.7%

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

      5. clear-num 99.6%

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

      6. associate-/l/ 99.7%

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

      7. associate-/r* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in t around inf 83.3%

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

      1. associate-/r* 88.1%

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

   8. Simplified 88.1%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{-x}{z \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 10: 81.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.95e-122)
   (/ (/ x (- t z)) y)
   (if (<= t 2.35e+16) (/ (/ (- x) z) (- y z)) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.95e-122) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.35e+16) {
		tmp = (-x / z) / (y - 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 (t <= (-1.95d-122)) then
        tmp = (x / (t - z)) / y
    else if (t <= 2.35d+16) then
        tmp = (-x / z) / (y - 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 (t <= -1.95e-122) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 2.35e+16) {
		tmp = (-x / z) / (y - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.95e-122:
		tmp = (x / (t - z)) / y
	elif t <= 2.35e+16:
		tmp = (-x / z) / (y - 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 (t <= -1.95e-122)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 2.35e+16)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - 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 (t <= -1.95e-122)
		tmp = (x / (t - z)) / y;
	elseif (t <= 2.35e+16)
		tmp = (-x / z) / (y - 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[t, -1.95e-122], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.35e+16], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999995e-122

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-/r* 55.6%

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

   4. Simplified 55.6%

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

   if -1.94999999999999995e-122 < t < 2.35e16

   1. Initial program 86.5%

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

      1. add-cube-cbrt 85.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 85.5%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 95.1%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 95.1%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 95.1%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 85.5%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 85.5%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 86.5%

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

      4. associate-/r* 94.3%

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

      5. clear-num 94.2%

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

      6. associate-/l/ 94.2%

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

      7. associate-/r* 94.1%

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

   5. Applied egg-rr 94.1%

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

   6. Taylor expanded in t around 0 68.3%

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

      1. associate-/r* 74.8%

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

      2. associate-*r/ 74.8%

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

      3. neg-mul-1 74.8%

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

      4. distribute-neg-frac 74.8%

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

   8. Simplified 74.8%

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

   if 2.35e16 < t

   1. Initial program 86.6%

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

      1. add-cube-cbrt 85.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 85.7%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 85.7%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 85.7%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 86.6%

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

      4. associate-/r* 99.7%

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

      5. clear-num 99.6%

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

      6. associate-/l/ 99.7%

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

      7. associate-/r* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in t around inf 83.3%

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

      1. associate-/r* 88.1%

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

   8. Simplified 88.1%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{+16}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 11: 48.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-113} \lor \neg \left(z \leq 8 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e-113) (not (<= z 8e-23))) (/ (- x) (* y z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-113) || !(z <= 8e-23)) {
		tmp = -x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-2d-113)) .or. (.not. (z <= 8d-23))) then
        tmp = -x / (y * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e-113) || !(z <= 8e-23)) {
		tmp = -x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -2e-113) or not (z <= 8e-23):
		tmp = -x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e-113) || !(z <= 8e-23))
		tmp = Float64(Float64(-x) / Float64(y * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2e-113) || ~((z <= 8e-23)))
		tmp = -x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e-113], N[Not[LessEqual[z, 8e-23]], $MachinePrecision]], N[((-x) / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999996e-113 or 7.99999999999999968e-23 < z

   1. Initial program 84.1%

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

   2. Taylor expanded in y around inf 34.8%

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

      1. *-commutative 34.8%

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

      2. associate-/r* 42.4%

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

   4. Simplified 42.4%

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

   5. Taylor expanded in t around 0 30.3%

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

      1. associate-*r/ 30.3%

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

      2. neg-mul-1 30.3%

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

      3. *-commutative 30.3%

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

   7. Simplified 30.3%

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

   if -1.99999999999999996e-113 < z < 7.99999999999999968e-23

   1. Initial program 91.9%

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

   2. Taylor expanded in y around inf 73.5%

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

      1. *-commutative 73.5%

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

      2. associate-/r* 78.1%

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

   4. Simplified 78.1%

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

   5. Taylor expanded in t around inf 67.0%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-113} \lor \neg \left(z \leq 8 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{-x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 12: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-104}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-194}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e-104)
   (/ (/ x y) t)
   (if (<= y 2.35e-194) (/ (- x) (* z t)) (/ (/ x t) y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-104) {
		tmp = (x / y) / t;
	} else if (y <= 2.35e-194) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.7d-104)) then
        tmp = (x / y) / t
    else if (y <= 2.35d-194) then
        tmp = -x / (z * t)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-104) {
		tmp = (x / y) / t;
	} else if (y <= 2.35e-194) {
		tmp = -x / (z * t);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e-104:
		tmp = (x / y) / t
	elif y <= 2.35e-194:
		tmp = -x / (z * t)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e-104)
		tmp = Float64(Float64(x / y) / t);
	elseif (y <= 2.35e-194)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e-104)
		tmp = (x / y) / t;
	elseif (y <= 2.35e-194)
		tmp = -x / (z * t);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e-104], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[y, 2.35e-194], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999998e-104

   1. Initial program 88.8%

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

   2. Taylor expanded in z around 0 47.9%

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

      1. associate-/r* 49.2%

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

      2. div-inv 49.2%

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

   4. Applied egg-rr 49.2%

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

      1. associate-*l/ 48.2%

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

      2. un-div-inv 48.2%

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

   6. Applied egg-rr 48.2%

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

   if -2.6999999999999998e-104 < y < 2.3500000000000001e-194

   1. Initial program 90.7%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 89.8%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.4%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 89.8%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 89.8%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 90.7%

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

      4. associate-/r* 98.5%

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

      5. clear-num 98.4%

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

      6. associate-/l/ 97.6%

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

      7. associate-/r* 98.4%

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

   5. Applied egg-rr 98.4%

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

   6. Taylor expanded in t around inf 60.2%

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

      1. associate-/r* 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in y around 0 51.6%

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

       1. associate-*r/ 51.6%

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

       2. neg-mul-1 51.6%

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

       3. *-commutative 51.6%

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

   11. Simplified 51.6%

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

   if 2.3500000000000001e-194 < y

   1. Initial program 82.5%

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

   2. Taylor expanded in y around inf 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-/r* 54.9%

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

   4. Simplified 54.9%

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

   5. Taylor expanded in t around inf 36.8%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-104}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-194}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 13: 45.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-43} \lor \neg \left(z \leq 80\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \end{array} \]

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 -6.1e-43) (not (<= z 80.0))) (/ x (* y z)) (/ x (* y t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.1e-43) || !(z <= 80.0)) {
		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 <= (-6.1d-43)) .or. (.not. (z <= 80.0d0))) 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 <= -6.1e-43) || !(z <= 80.0)) {
		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 <= -6.1e-43) or not (z <= 80.0):
		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 <= -6.1e-43) || !(z <= 80.0))
		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 <= -6.1e-43) || ~((z <= 80.0)))
		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, -6.1e-43], N[Not[LessEqual[z, 80.0]], $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 < -6.10000000000000037e-43 or 80 < z

   1. Initial program 82.4%

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

   2. Taylor expanded in y around inf 32.6%

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

      1. *-commutative 32.6%

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

      2. associate-/r* 41.9%

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

   4. Simplified 41.9%

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

   5. Taylor expanded in t around 0 31.0%

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

      1. associate-*r/ 31.0%

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

      2. neg-mul-1 31.0%

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

      3. *-commutative 31.0%

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

   7. Simplified 31.0%

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

      1. expm1-log1p-u 29.8%

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

      2. expm1-udef 44.5%

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

      3. add-sqr-sqrt 18.0%

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

      4. sqrt-unprod 41.5%

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

      5. sqr-neg 41.5%

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

      6. sqrt-unprod 26.3%

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

      7. add-sqr-sqrt 43.0%

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

      8. *-commutative 43.0%

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

      9. associate-/r* 43.0%

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

   9. Applied egg-rr 43.0%

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

       1. expm1-def 21.2%

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

       2. expm1-log1p 21.7%

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

       3. associate-/l/ 24.5%

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

   11. Simplified 24.5%

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

   if -6.10000000000000037e-43 < z < 80

   1. Initial program 92.5%

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

   2. Taylor expanded in z around 0 56.5%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{-43} \lor \neg \left(z \leq 80\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \end{array} \]

Alternative 14: 49.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+121} \lor \neg \left(z \leq 2.7 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.6e+121) (not (<= z 2.7e+29))) (/ x (* y z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.6e+121) || !(z <= 2.7e+29)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-9.6d+121)) .or. (.not. (z <= 2.7d+29))) then
        tmp = x / (y * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.6e+121) || !(z <= 2.7e+29)) {
		tmp = x / (y * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -9.6e+121) or not (z <= 2.7e+29):
		tmp = x / (y * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.6e+121) || !(z <= 2.7e+29))
		tmp = Float64(x / Float64(y * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -9.6e+121) || ~((z <= 2.7e+29)))
		tmp = x / (y * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.6e+121], N[Not[LessEqual[z, 2.7e+29]], $MachinePrecision]], N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.600000000000001e121 or 2.7e29 < z

   1. Initial program 78.9%

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

   2. Taylor expanded in y around inf 30.8%

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

      1. *-commutative 30.8%

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

      2. associate-/r* 38.3%

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

   4. Simplified 38.3%

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

   5. Taylor expanded in t around 0 29.6%

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

      1. associate-*r/ 29.6%

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

      2. neg-mul-1 29.6%

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

      3. *-commutative 29.6%

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

   7. Simplified 29.6%

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

      1. expm1-log1p-u 29.4%

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

      2. expm1-udef 51.7%

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

      3. add-sqr-sqrt 18.6%

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

      4. sqrt-unprod 48.4%

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

      5. sqr-neg 48.4%

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

      6. sqrt-unprod 32.7%

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

      7. add-sqr-sqrt 51.4%

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

      8. *-commutative 51.4%

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

      9. associate-/r* 51.3%

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

   9. Applied egg-rr 51.3%

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

       1. expm1-def 24.9%

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

       2. expm1-log1p 25.3%

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

       3. associate-/l/ 29.4%

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

   11. Simplified 29.4%

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

   if -9.600000000000001e121 < z < 2.7e29

   1. Initial program 92.0%

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

   2. Taylor expanded in y around inf 60.8%

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

      1. *-commutative 60.8%

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

      2. associate-/r* 66.5%

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

   4. Simplified 66.5%

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

   5. Taylor expanded in t around inf 51.3%

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

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+121} \lor \neg \left(z \leq 2.7 \cdot 10^{+29}\right):\\ \;\;\;\;\frac{x}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 71.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.15e-104) (/ x (* y (- t z))) (/ x (* (- y z) t))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e-104) {
		tmp = x / (y * (t - 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 (y <= (-2.15d-104)) then
        tmp = x / (y * (t - 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 (y <= -2.15e-104) {
		tmp = x / (y * (t - z));
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.15e-104:
		tmp = x / (y * (t - 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 (y <= -2.15e-104)
		tmp = Float64(x / Float64(y * Float64(t - 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 (y <= -2.15e-104)
		tmp = x / (y * (t - 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[y, -2.15e-104], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15000000000000005e-104

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 74.8%

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

      1. *-commutative 74.8%

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

   4. Simplified 74.8%

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

   if -2.15000000000000005e-104 < y

   1. Initial program 86.1%

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

   2. Taylor expanded in t around inf 53.3%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]

Alternative 16: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.15e-104) (/ x (* y (- t z))) (/ (/ x t) (- y z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.15e-104) {
		tmp = x / (y * (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 <= (-2.15d-104)) then
        tmp = x / (y * (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 <= -2.15e-104) {
		tmp = x / (y * (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 <= -2.15e-104:
		tmp = x / (y * (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 <= -2.15e-104)
		tmp = Float64(x / Float64(y * 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 <= -2.15e-104)
		tmp = x / (y * (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, -2.15e-104], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15000000000000005e-104

   1. Initial program 88.9%

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

   2. Taylor expanded in y around inf 74.8%

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

      1. *-commutative 74.8%

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

   4. Simplified 74.8%

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

   if -2.15000000000000005e-104 < y

   1. Initial program 86.1%

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

      1. add-cube-cbrt 85.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 85.3%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 97.6%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 97.6%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 97.6%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 85.3%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 85.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 86.1%

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

      4. associate-/r* 97.0%

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

      5. clear-num 96.9%

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

      6. associate-/l/ 96.0%

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

      7. associate-/r* 97.0%

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

   5. Applied egg-rr 97.0%

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

   6. Taylor expanded in t around inf 53.3%

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

      1. associate-/r* 57.9%

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

   8. Simplified 57.9%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-104}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 17: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t 5.7e-36) (/ (/ x (- t z)) y) (/ (/ x t) (- y z))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 5.7e-36) {
		tmp = (x / (t - z)) / y;
	} 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 (t <= 5.7d-36) then
        tmp = (x / (t - z)) / y
    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 (t <= 5.7e-36) {
		tmp = (x / (t - z)) / y;
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if t <= 5.7e-36:
		tmp = (x / (t - z)) / y
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= 5.7e-36)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	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 (t <= 5.7e-36)
		tmp = (x / (t - z)) / y;
	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[t, 5.7e-36], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 5.6999999999999999e-36

   1. Initial program 87.3%

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

   2. Taylor expanded in y around inf 51.0%

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

      1. *-commutative 51.0%

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

      2. associate-/r* 56.5%

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

   4. Simplified 56.5%

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

   if 5.6999999999999999e-36 < t

   1. Initial program 86.2%

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

      1. add-cube-cbrt 85.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

      2. *-commutative 85.3%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      3. times-frac 98.7%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

      4. pow2 98.7%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

   3. Applied egg-rr 98.7%

      \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]
   4. Step-by-step derivation

      1. frac-times 85.3%

         \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)}} \]

      2. unpow2 85.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)} \cdot \sqrt[3]{x}}{\left(t - z\right) \cdot \left(y - z\right)} \]

      3. add-cube-cbrt 86.2%

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

      4. associate-/r* 99.7%

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

      5. clear-num 99.6%

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

      6. associate-/l/ 99.7%

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

      7. associate-/r* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in t around inf 78.7%

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

      1. associate-/r* 81.2%

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

   8. Simplified 81.2%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 18: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 87.0%

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

   1. add-cube-cbrt 86.2%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(y - z\right) \cdot \left(t - z\right)} \]

   2. *-commutative 86.2%

      \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}{\color{blue}{\left(t - z\right) \cdot \left(y - z\right)}} \]

   3. times-frac 97.2%

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

   4. pow2 97.2%

      \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z} \]

3. Applied egg-rr 97.2%

   \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{t - z} \cdot \frac{\sqrt[3]{x}}{y - z}} \]

4. Taylor expanded in x around 0 87.0%

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

   1. associate-/r* 96.8%

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

6. Simplified 96.8%

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

7. Final simplification 96.8%

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

Alternative 19: 39.7% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.0%

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

2. Taylor expanded in z around 0 33.4%

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

3. Final simplification 33.4%

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

Developer target: 87.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y - z\right) \cdot \left(t - z\right)\\ \mathbf{if}\;\frac{x}{t_1} < 0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- y z) (- t z))))
   (if (< (/ x t_1) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1.0 t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - z) * (t - z)
    if ((x / t_1) < 0.0d0) then
        tmp = (x / (y - z)) / (t - z)
    else
        tmp = x * (1.0d0 / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y - z) * (t - z);
	double tmp;
	if ((x / t_1) < 0.0) {
		tmp = (x / (y - z)) / (t - z);
	} else {
		tmp = x * (1.0 / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y - z) * (t - z)
	tmp = 0
	if (x / t_1) < 0.0:
		tmp = (x / (y - z)) / (t - z)
	else:
		tmp = x * (1.0 / t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y - z) * Float64(t - z))
	tmp = 0.0
	if (Float64(x / t_1) < 0.0)
		tmp = Float64(Float64(x / Float64(y - z)) / Float64(t - z));
	else
		tmp = Float64(x * Float64(1.0 / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y - z) * (t - z);
	tmp = 0.0;
	if ((x / t_1) < 0.0)
		tmp = (x / (y - z)) / (t - z);
	else
		tmp = x * (1.0 / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[Less[N[(x / t$95$1), $MachinePrecision], 0.0], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023320 
(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))))