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

Percentage Accurate: 89.0% → 97.0%

Time: 12.0s

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: 89.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 1.0× speedup

Math

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

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 88.9%

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

   1. associate-/l/ 97.5%

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

3. Simplified 97.5%

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

4. Final simplification 97.5%

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

Alternative 2: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t - z}}{y}\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-221}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-259}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x (- t z)) y)))
   (if (<= y -3.9e+208)
     t_1
     (if (<= y -7.2e-7)
       (/ x (* (- t z) y))
       (if (<= y -6.5e-81)
         t_1
         (if (<= y -1.2e-221)
           (/ 1.0 (/ z (/ x z)))
           (if (<= y -7.5e-259)
             (/ (/ x t) (- y z))
             (if (<= y 1.25e-259)
               (* (/ x z) (/ 1.0 z))
               (/ x (* t (- y z)))))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / (t - z)) / y;
	double tmp;
	if (y <= -3.9e+208) {
		tmp = t_1;
	} else if (y <= -7.2e-7) {
		tmp = x / ((t - z) * y);
	} else if (y <= -6.5e-81) {
		tmp = t_1;
	} else if (y <= -1.2e-221) {
		tmp = 1.0 / (z / (x / z));
	} else if (y <= -7.5e-259) {
		tmp = (x / t) / (y - z);
	} else if (y <= 1.25e-259) {
		tmp = (x / z) * (1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (x / (t - z)) / y
    if (y <= (-3.9d+208)) then
        tmp = t_1
    else if (y <= (-7.2d-7)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-6.5d-81)) then
        tmp = t_1
    else if (y <= (-1.2d-221)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (y <= (-7.5d-259)) then
        tmp = (x / t) / (y - z)
    else if (y <= 1.25d-259) then
        tmp = (x / z) * (1.0d0 / 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 t_1 = (x / (t - z)) / y;
	double tmp;
	if (y <= -3.9e+208) {
		tmp = t_1;
	} else if (y <= -7.2e-7) {
		tmp = x / ((t - z) * y);
	} else if (y <= -6.5e-81) {
		tmp = t_1;
	} else if (y <= -1.2e-221) {
		tmp = 1.0 / (z / (x / z));
	} else if (y <= -7.5e-259) {
		tmp = (x / t) / (y - z);
	} else if (y <= 1.25e-259) {
		tmp = (x / z) * (1.0 / z);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / (t - z)) / y
	tmp = 0
	if y <= -3.9e+208:
		tmp = t_1
	elif y <= -7.2e-7:
		tmp = x / ((t - z) * y)
	elif y <= -6.5e-81:
		tmp = t_1
	elif y <= -1.2e-221:
		tmp = 1.0 / (z / (x / z))
	elif y <= -7.5e-259:
		tmp = (x / t) / (y - z)
	elif y <= 1.25e-259:
		tmp = (x / z) * (1.0 / z)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / Float64(t - z)) / y)
	tmp = 0.0
	if (y <= -3.9e+208)
		tmp = t_1;
	elseif (y <= -7.2e-7)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -6.5e-81)
		tmp = t_1;
	elseif (y <= -1.2e-221)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (y <= -7.5e-259)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (y <= 1.25e-259)
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / (t - z)) / y;
	tmp = 0.0;
	if (y <= -3.9e+208)
		tmp = t_1;
	elseif (y <= -7.2e-7)
		tmp = x / ((t - z) * y);
	elseif (y <= -6.5e-81)
		tmp = t_1;
	elseif (y <= -1.2e-221)
		tmp = 1.0 / (z / (x / z));
	elseif (y <= -7.5e-259)
		tmp = (x / t) / (y - z);
	elseif (y <= 1.25e-259)
		tmp = (x / z) * (1.0 / 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_] := Block[{t$95$1 = N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -3.9e+208], t$95$1, If[LessEqual[y, -7.2e-7], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.5e-81], t$95$1, If[LessEqual[y, -1.2e-221], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.5e-259], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-259], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -3.9000000000000001e208 or -7.19999999999999989e-7 < y < -6.5000000000000002e-81

   1. Initial program 86.2%

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

   2. Taylor expanded in y around inf 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-/r* 90.1%

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

   4. Simplified 90.1%

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

   if -3.9000000000000001e208 < y < -7.19999999999999989e-7

   1. Initial program 95.0%

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

   2. Taylor expanded in y around inf 88.8%

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

      1. *-commutative 88.8%

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

   4. Simplified 88.8%

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

   if -6.5000000000000002e-81 < y < -1.20000000000000012e-221

   1. Initial program 85.8%

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

      1. associate-/r* 99.7%

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

      2. div-inv 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. associate-*l/ 99.6%

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

      2. clear-num 99.7%

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

      3. div-inv 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around inf 56.9%

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

      1. unpow2 56.9%

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

      2. associate-/l* 70.9%

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

   8. Simplified 70.9%

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

   if -1.20000000000000012e-221 < y < -7.50000000000000052e-259

   1. Initial program 99.5%

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

      1. associate-/l/ 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in t around inf 47.3%

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

   if -7.50000000000000052e-259 < y < 1.24999999999999994e-259

   1. Initial program 78.2%

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

   2. Taylor expanded in z around inf 55.6%

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

      1. unpow2 55.6%

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

   4. Simplified 55.6%

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

      1. associate-/r* 66.5%

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

      2. div-inv 66.5%

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

   6. Applied egg-rr 66.5%

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

   if 1.24999999999999994e-259 < y

   1. Initial program 89.4%

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

   2. Taylor expanded in t around inf 54.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-81}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-221}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-259}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 3: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-258}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ x z) (/ 1.0 z))))
   (if (<= y -4.2e+208)
     (/ (/ x y) (- t z))
     (if (<= y -1.85e-66)
       (/ x (* (- t z) y))
       (if (<= y -1.1e-221)
         t_1
         (if (<= y -2.8e-258)
           (/ (/ x t) (- y z))
           (if (<= y 3.2e-262) t_1 (/ x (* t (- y z))))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (y <= -4.2e+208) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.85e-66) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.1e-221) {
		tmp = t_1;
	} else if (y <= -2.8e-258) {
		tmp = (x / t) / (y - z);
	} else if (y <= 3.2e-262) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / z) * (1.0d0 / z)
    if (y <= (-4.2d+208)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-1.85d-66)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-1.1d-221)) then
        tmp = t_1
    else if (y <= (-2.8d-258)) then
        tmp = (x / t) / (y - z)
    else if (y <= 3.2d-262) then
        tmp = t_1
    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 t_1 = (x / z) * (1.0 / z);
	double tmp;
	if (y <= -4.2e+208) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.85e-66) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.1e-221) {
		tmp = t_1;
	} else if (y <= -2.8e-258) {
		tmp = (x / t) / (y - z);
	} else if (y <= 3.2e-262) {
		tmp = t_1;
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) * (1.0 / z)
	tmp = 0
	if y <= -4.2e+208:
		tmp = (x / y) / (t - z)
	elif y <= -1.85e-66:
		tmp = x / ((t - z) * y)
	elif y <= -1.1e-221:
		tmp = t_1
	elif y <= -2.8e-258:
		tmp = (x / t) / (y - z)
	elif y <= 3.2e-262:
		tmp = t_1
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) * Float64(1.0 / z))
	tmp = 0.0
	if (y <= -4.2e+208)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -1.85e-66)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -1.1e-221)
		tmp = t_1;
	elseif (y <= -2.8e-258)
		tmp = Float64(Float64(x / t) / Float64(y - z));
	elseif (y <= 3.2e-262)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) * (1.0 / z);
	tmp = 0.0;
	if (y <= -4.2e+208)
		tmp = (x / y) / (t - z);
	elseif (y <= -1.85e-66)
		tmp = x / ((t - z) * y);
	elseif (y <= -1.1e-221)
		tmp = t_1;
	elseif (y <= -2.8e-258)
		tmp = (x / t) / (y - z);
	elseif (y <= 3.2e-262)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+208], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.85e-66], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.1e-221], t$95$1, If[LessEqual[y, -2.8e-258], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-262], t$95$1, N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.1999999999999997e208

   1. Initial program 79.8%

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

      1. associate-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 99.9%

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

   if -4.1999999999999997e208 < y < -1.8500000000000001e-66

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 84.8%

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

      1. *-commutative 84.8%

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

   4. Simplified 84.8%

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

   if -1.8500000000000001e-66 < y < -1.10000000000000001e-221 or -2.8000000000000002e-258 < y < 3.2e-262

   1. Initial program 84.3%

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

   2. Taylor expanded in z around inf 57.7%

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

      1. unpow2 57.7%

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

   4. Simplified 57.7%

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

      1. associate-/r* 69.3%

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

      2. div-inv 69.4%

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

   6. Applied egg-rr 69.4%

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

   if -1.10000000000000001e-221 < y < -2.8000000000000002e-258

   1. Initial program 99.5%

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

      1. associate-/l/ 68.6%

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

   3. Simplified 68.6%

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

   4. Taylor expanded in t around inf 47.3%

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

   if 3.2e-262 < y

   1. Initial program 89.4%

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

   2. Taylor expanded in t around inf 54.6%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-221}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-258}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-262}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 4: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+124} \lor \neg \left(z \leq 5.2 \cdot 10^{+167}\right):\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.9e+33)
   (/ (/ x z) z)
   (if (<= z 5.2e+35)
     (/ x (* t (- y z)))
     (if (or (<= z 3.6e+124) (not (<= z 5.2e+167)))
       (/ 1.0 (/ z (/ x z)))
       (* (/ x z) (/ -1.0 t))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+33) {
		tmp = (x / z) / z;
	} else if (z <= 5.2e+35) {
		tmp = x / (t * (y - z));
	} else if ((z <= 3.6e+124) || !(z <= 5.2e+167)) {
		tmp = 1.0 / (z / (x / z));
	} else {
		tmp = (x / z) * (-1.0 / t);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4.9d+33)) then
        tmp = (x / z) / z
    else if (z <= 5.2d+35) then
        tmp = x / (t * (y - z))
    else if ((z <= 3.6d+124) .or. (.not. (z <= 5.2d+167))) then
        tmp = 1.0d0 / (z / (x / z))
    else
        tmp = (x / z) * ((-1.0d0) / t)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.9e+33) {
		tmp = (x / z) / z;
	} else if (z <= 5.2e+35) {
		tmp = x / (t * (y - z));
	} else if ((z <= 3.6e+124) || !(z <= 5.2e+167)) {
		tmp = 1.0 / (z / (x / z));
	} else {
		tmp = (x / z) * (-1.0 / t);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -4.9e+33:
		tmp = (x / z) / z
	elif z <= 5.2e+35:
		tmp = x / (t * (y - z))
	elif (z <= 3.6e+124) or not (z <= 5.2e+167):
		tmp = 1.0 / (z / (x / z))
	else:
		tmp = (x / z) * (-1.0 / t)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.9e+33)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 5.2e+35)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif ((z <= 3.6e+124) || !(z <= 5.2e+167))
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	else
		tmp = Float64(Float64(x / z) * Float64(-1.0 / t));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.9e+33)
		tmp = (x / z) / z;
	elseif (z <= 5.2e+35)
		tmp = x / (t * (y - z));
	elseif ((z <= 3.6e+124) || ~((z <= 5.2e+167)))
		tmp = 1.0 / (z / (x / z));
	else
		tmp = (x / z) * (-1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -4.9e+33], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.2e+35], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.6e+124], N[Not[LessEqual[z, 5.2e+167]], $MachinePrecision]], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.90000000000000014e33

   1. Initial program 80.7%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. unpow2 71.9%

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

      2. associate-/r* 79.4%

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

   4. Simplified 79.4%

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

   if -4.90000000000000014e33 < z < 5.20000000000000013e35

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 73.8%

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

   if 5.20000000000000013e35 < z < 3.59999999999999986e124 or 5.2000000000000004e167 < z

   1. Initial program 85.6%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.8%

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

      2. clear-num 98.2%

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

      3. div-inv 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in z around inf 81.5%

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

      1. unpow2 81.5%

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

      2. associate-/l* 87.5%

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

   8. Simplified 87.5%

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

   if 3.59999999999999986e124 < z < 5.2000000000000004e167

   1. Initial program 87.8%

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

   2. Taylor expanded in y around 0 64.2%

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

      1. associate-*r/ 64.2%

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

      2. neg-mul-1 64.2%

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

   4. Simplified 64.2%

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

      1. neg-mul-1 64.2%

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

      2. *-commutative 64.2%

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

      3. times-frac 52.9%

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

   6. Applied egg-rr 52.9%

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

   7. Taylor expanded in t around inf 46.2%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+124} \lor \neg \left(z \leq 5.2 \cdot 10^{+167}\right):\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{-1}{t}\\ \end{array} \]

Alternative 5: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-221} \lor \neg \left(y \leq -8 \cdot 10^{-259}\right) \land y \leq 3.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.4e-67)
   (/ x (* (- t z) y))
   (if (or (<= y -1.1e-221) (and (not (<= y -8e-259)) (<= y 3.2e-258)))
     (* (/ x z) (/ 1.0 z))
     (/ x (* t (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7.4e-67) {
		tmp = x / ((t - z) * y);
	} else if ((y <= -1.1e-221) || (!(y <= -8e-259) && (y <= 3.2e-258))) {
		tmp = (x / z) * (1.0 / 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 <= (-7.4d-67)) then
        tmp = x / ((t - z) * y)
    else if ((y <= (-1.1d-221)) .or. (.not. (y <= (-8d-259))) .and. (y <= 3.2d-258)) then
        tmp = (x / z) * (1.0d0 / 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 <= -7.4e-67) {
		tmp = x / ((t - z) * y);
	} else if ((y <= -1.1e-221) || (!(y <= -8e-259) && (y <= 3.2e-258))) {
		tmp = (x / z) * (1.0 / 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 <= -7.4e-67:
		tmp = x / ((t - z) * y)
	elif (y <= -1.1e-221) or (not (y <= -8e-259) and (y <= 3.2e-258)):
		tmp = (x / z) * (1.0 / 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 <= -7.4e-67)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif ((y <= -1.1e-221) || (!(y <= -8e-259) && (y <= 3.2e-258)))
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	else
		tmp = Float64(x / Float64(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 <= -7.4e-67)
		tmp = x / ((t - z) * y);
	elseif ((y <= -1.1e-221) || (~((y <= -8e-259)) && (y <= 3.2e-258)))
		tmp = (x / z) * (1.0 / 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, -7.4e-67], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.1e-221], And[N[Not[LessEqual[y, -8e-259]], $MachinePrecision], LessEqual[y, 3.2e-258]]], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.3999999999999999e-67

   1. Initial program 89.6%

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

   2. Taylor expanded in y around inf 83.1%

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

      1. *-commutative 83.1%

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

   4. Simplified 83.1%

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

   if -7.3999999999999999e-67 < y < -1.10000000000000001e-221 or -8.0000000000000006e-259 < y < 3.2000000000000002e-258

   1. Initial program 84.3%

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

   2. Taylor expanded in z around inf 57.7%

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

      1. unpow2 57.7%

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

   4. Simplified 57.7%

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

      1. associate-/r* 69.3%

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

      2. div-inv 69.4%

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

   6. Applied egg-rr 69.4%

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

   if -1.10000000000000001e-221 < y < -8.0000000000000006e-259 or 3.2000000000000002e-258 < y

   1. Initial program 90.1%

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

   2. Taylor expanded in t around inf 56.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-221} \lor \neg \left(y \leq -8 \cdot 10^{-259}\right) \land y \leq 3.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 6: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+37} \lor \neg \left(z \leq 3.6 \cdot 10^{+124}\right) \land z \leq 5.2 \cdot 10^{+167}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.1e+34)
   (/ (/ x z) z)
   (if (or (<= z 3.6e+37) (and (not (<= z 3.6e+124)) (<= z 5.2e+167)))
     (/ (/ x t) (- y z))
     (/ 1.0 (/ z (/ x z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.1e+34) {
		tmp = (x / z) / z;
	} else if ((z <= 3.6e+37) || (!(z <= 3.6e+124) && (z <= 5.2e+167))) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z / (x / 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 (z <= (-1.1d+34)) then
        tmp = (x / z) / z
    else if ((z <= 3.6d+37) .or. (.not. (z <= 3.6d+124)) .and. (z <= 5.2d+167)) then
        tmp = (x / t) / (y - z)
    else
        tmp = 1.0d0 / (z / (x / 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 (z <= -1.1e+34) {
		tmp = (x / z) / z;
	} else if ((z <= 3.6e+37) || (!(z <= 3.6e+124) && (z <= 5.2e+167))) {
		tmp = (x / t) / (y - z);
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.1e+34:
		tmp = (x / z) / z
	elif (z <= 3.6e+37) or (not (z <= 3.6e+124) and (z <= 5.2e+167)):
		tmp = (x / t) / (y - z)
	else:
		tmp = 1.0 / (z / (x / z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.1e+34)
		tmp = Float64(Float64(x / z) / z);
	elseif ((z <= 3.6e+37) || (!(z <= 3.6e+124) && (z <= 5.2e+167)))
		tmp = Float64(Float64(x / t) / Float64(y - z));
	else
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.1e+34)
		tmp = (x / z) / z;
	elseif ((z <= 3.6e+37) || (~((z <= 3.6e+124)) && (z <= 5.2e+167)))
		tmp = (x / t) / (y - z);
	else
		tmp = 1.0 / (z / (x / 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[z, -1.1e+34], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[z, 3.6e+37], And[N[Not[LessEqual[z, 3.6e+124]], $MachinePrecision], LessEqual[z, 5.2e+167]]], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e34

   1. Initial program 80.7%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. unpow2 71.9%

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

      2. associate-/r* 79.4%

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

   4. Simplified 79.4%

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

   if -1.1000000000000001e34 < z < 3.59999999999999998e37 or 3.59999999999999986e124 < z < 5.2000000000000004e167

   1. Initial program 93.5%

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

      1. associate-/l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around inf 74.1%

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

   if 3.59999999999999998e37 < z < 3.59999999999999986e124 or 5.2000000000000004e167 < z

   1. Initial program 85.6%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.8%

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

      2. clear-num 98.2%

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

      3. div-inv 98.2%

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

   5. Applied egg-rr 98.2%

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

   6. Taylor expanded in z around inf 81.5%

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

      1. unpow2 81.5%

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

      2. associate-/l* 87.5%

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

   8. Simplified 87.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+37} \lor \neg \left(z \leq 3.6 \cdot 10^{+124}\right) \land z \leq 5.2 \cdot 10^{+167}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 7: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e+208)
   (/ (/ x (- t z)) y)
   (if (<= y -3.6e-35)
     (/ x (* (- t z) y))
     (if (<= y 1.8e-174) (* (/ -1.0 (- t z)) (/ x z)) (/ x (* t (- y z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e+208) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -3.6e-35) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.8e-174) {
		tmp = (-1.0 / (t - z)) * (x / 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 <= (-4.4d+208)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-3.6d-35)) then
        tmp = x / ((t - z) * y)
    else if (y <= 1.8d-174) then
        tmp = ((-1.0d0) / (t - z)) * (x / 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 <= -4.4e+208) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -3.6e-35) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.8e-174) {
		tmp = (-1.0 / (t - z)) * (x / 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 <= -4.4e+208:
		tmp = (x / (t - z)) / y
	elif y <= -3.6e-35:
		tmp = x / ((t - z) * y)
	elif y <= 1.8e-174:
		tmp = (-1.0 / (t - z)) * (x / 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 <= -4.4e+208)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -3.6e-35)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 1.8e-174)
		tmp = Float64(Float64(-1.0 / Float64(t - z)) * Float64(x / z));
	else
		tmp = Float64(x / Float64(t * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e+208)
		tmp = (x / (t - z)) / y;
	elseif (y <= -3.6e-35)
		tmp = x / ((t - z) * y);
	elseif (y <= 1.8e-174)
		tmp = (-1.0 / (t - z)) * (x / 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, -4.4e+208], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -3.6e-35], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e-174], N[(N[(-1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.40000000000000029e208

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/r* 99.9%

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

   4. Simplified 99.9%

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

   if -4.40000000000000029e208 < y < -3.60000000000000019e-35

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 87.8%

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

      1. *-commutative 87.8%

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

   4. Simplified 87.8%

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

   if -3.60000000000000019e-35 < y < 1.79999999999999999e-174

   1. Initial program 85.8%

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

   2. Taylor expanded in y around 0 70.4%

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

      1. associate-*r/ 70.4%

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

      2. neg-mul-1 70.4%

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

   4. Simplified 70.4%

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

      1. neg-mul-1 70.4%

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

      2. *-commutative 70.4%

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

      3. times-frac 82.1%

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

   6. Applied egg-rr 82.1%

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

   if 1.79999999999999999e-174 < y

   1. Initial program 90.8%

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

   2. Taylor expanded in t around inf 58.2%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-174}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 8: 80.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4e+208)
   (/ (/ x (- t z)) y)
   (if (<= y -7.5e-36)
     (/ x (* (- t z) y))
     (if (<= y 4.8e-170) (/ (- 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 <= -4e+208) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -7.5e-36) {
		tmp = x / ((t - z) * y);
	} else if (y <= 4.8e-170) {
		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 <= (-4d+208)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-7.5d-36)) then
        tmp = x / ((t - z) * y)
    else if (y <= 4.8d-170) 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 <= -4e+208) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -7.5e-36) {
		tmp = x / ((t - z) * y);
	} else if (y <= 4.8e-170) {
		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 <= -4e+208:
		tmp = (x / (t - z)) / y
	elif y <= -7.5e-36:
		tmp = x / ((t - z) * y)
	elif y <= 4.8e-170:
		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 <= -4e+208)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -7.5e-36)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 4.8e-170)
		tmp = Float64(Float64(-x) / Float64(z * Float64(t - z)));
	else
		tmp = Float64(x / Float64(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 <= -4e+208)
		tmp = (x / (t - z)) / y;
	elseif (y <= -7.5e-36)
		tmp = x / ((t - z) * y);
	elseif (y <= 4.8e-170)
		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, -4e+208], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -7.5e-36], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-170], N[((-x) / N[(z * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.9999999999999999e208

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/r* 99.9%

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

   4. Simplified 99.9%

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

   if -3.9999999999999999e208 < y < -7.49999999999999972e-36

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 87.8%

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

      1. *-commutative 87.8%

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

   4. Simplified 87.8%

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

   if -7.49999999999999972e-36 < y < 4.7999999999999999e-170

   1. Initial program 85.8%

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

   2. Taylor expanded in y around 0 70.4%

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

      1. associate-*r/ 70.4%

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

      2. neg-mul-1 70.4%

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

   4. Simplified 70.4%

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

   if 4.7999999999999999e-170 < y

   1. Initial program 90.8%

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

   2. Taylor expanded in t around inf 58.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-170}:\\ \;\;\;\;\frac{-x}{z \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 9: 82.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-169}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+208)
   (/ (/ x (- t z)) y)
   (if (<= y -2.6e-35)
     (/ x (* (- t z) y))
     (if (<= y 1.15e-169) (/ (/ (- 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 <= -6.8e+208) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.6e-35) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.15e-169) {
		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 <= (-6.8d+208)) then
        tmp = (x / (t - z)) / y
    else if (y <= (-2.6d-35)) then
        tmp = x / ((t - z) * y)
    else if (y <= 1.15d-169) 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 <= -6.8e+208) {
		tmp = (x / (t - z)) / y;
	} else if (y <= -2.6e-35) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.15e-169) {
		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 <= -6.8e+208:
		tmp = (x / (t - z)) / y
	elif y <= -2.6e-35:
		tmp = x / ((t - z) * y)
	elif y <= 1.15e-169:
		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 <= -6.8e+208)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (y <= -2.6e-35)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 1.15e-169)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(x / Float64(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 <= -6.8e+208)
		tmp = (x / (t - z)) / y;
	elseif (y <= -2.6e-35)
		tmp = x / ((t - z) * y);
	elseif (y <= 1.15e-169)
		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, -6.8e+208], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.6e-35], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-169], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.7999999999999997e208

   1. Initial program 79.8%

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

   2. Taylor expanded in y around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/r* 99.9%

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

   4. Simplified 99.9%

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

   if -6.7999999999999997e208 < y < -2.60000000000000005e-35

   1. Initial program 95.6%

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

   2. Taylor expanded in y around inf 87.8%

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

      1. *-commutative 87.8%

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

   4. Simplified 87.8%

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

   if -2.60000000000000005e-35 < y < 1.15e-169

   1. Initial program 86.0%

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

   2. Taylor expanded in y around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-frac-neg 70.8%

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

      3. associate-/r* 82.3%

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

   4. Simplified 82.3%

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

   if 1.15e-169 < y

   1. Initial program 90.7%

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

   2. Taylor expanded in t around inf 57.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+208}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-169}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 10: 93.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+124)
   (/ (/ (- x) (- y z)) z)
   (if (<= z 2.5e+150)
     (/ x (* (- t z) (- y z)))
     (* (/ -1.0 (- t z)) (/ x z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+124) {
		tmp = (-x / (y - z)) / z;
	} else if (z <= 2.5e+150) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (-1.0 / (t - z)) * (x / 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 (z <= (-9.5d+124)) then
        tmp = (-x / (y - z)) / z
    else if (z <= 2.5d+150) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = ((-1.0d0) / (t - z)) * (x / 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 (z <= -9.5e+124) {
		tmp = (-x / (y - z)) / z;
	} else if (z <= 2.5e+150) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (-1.0 / (t - z)) * (x / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+124:
		tmp = (-x / (y - z)) / z
	elif z <= 2.5e+150:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (-1.0 / (t - z)) * (x / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+124)
		tmp = Float64(Float64(Float64(-x) / Float64(y - z)) / z);
	elseif (z <= 2.5e+150)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(-1.0 / Float64(t - z)) * Float64(x / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e+124)
		tmp = (-x / (y - z)) / z;
	elseif (z <= 2.5e+150)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (-1.0 / (t - z)) * (x / 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[z, -9.5e+124], N[(N[((-x) / N[(y - z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.5e+150], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(t - z), $MachinePrecision]), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.50000000000000004e124

   1. Initial program 80.4%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in t around 0 80.3%

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

      1. mul-1-neg 80.3%

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

      2. associate-/r* 94.1%

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

      3. distribute-neg-frac 94.1%

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

      4. distribute-frac-neg 94.1%

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

   6. Simplified 94.1%

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

   if -9.50000000000000004e124 < z < 2.50000000000000004e150

   1. Initial program 92.7%

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

   if 2.50000000000000004e150 < z

   1. Initial program 82.0%

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

   2. Taylor expanded in y around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. neg-mul-1 82.0%

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

   4. Simplified 82.0%

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

      1. neg-mul-1 82.0%

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

      2. *-commutative 82.0%

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

      3. times-frac 97.2%

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

   6. Applied egg-rr 97.2%

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

4. Final simplification 93.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+124}:\\ \;\;\;\;\frac{\frac{-x}{y - z}}{z}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t - z} \cdot \frac{x}{z}\\ \end{array} \]

Alternative 11: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.6e+33)
   (/ (/ x z) z)
   (if (<= z 7.8e+39) (/ (/ x t) y) (* (/ x z) (/ 1.0 z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.6e+33) {
		tmp = (x / z) / z;
	} else if (z <= 7.8e+39) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) * (1.0 / 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 (z <= (-1.6d+33)) then
        tmp = (x / z) / z
    else if (z <= 7.8d+39) then
        tmp = (x / t) / y
    else
        tmp = (x / z) * (1.0d0 / 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 (z <= -1.6e+33) {
		tmp = (x / z) / z;
	} else if (z <= 7.8e+39) {
		tmp = (x / t) / y;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.6e+33:
		tmp = (x / z) / z
	elif z <= 7.8e+39:
		tmp = (x / t) / y
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.6e+33)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 7.8e+39)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.6e+33)
		tmp = (x / z) / z;
	elseif (z <= 7.8e+39)
		tmp = (x / t) / y;
	else
		tmp = (x / z) * (1.0 / 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[z, -1.6e+33], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 7.8e+39], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.60000000000000009e33

   1. Initial program 80.7%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. unpow2 71.9%

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

      2. associate-/r* 79.4%

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

   4. Simplified 79.4%

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

   if -1.60000000000000009e33 < z < 7.8000000000000002e39

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/r* 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in t around inf 62.3%

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

   if 7.8000000000000002e39 < z

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. unpow2 71.1%

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

   4. Simplified 71.1%

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

      1. associate-/r* 75.2%

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

      2. div-inv 75.3%

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

   6. Applied egg-rr 75.3%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 12: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -9.5e+33)
   (/ (/ x z) z)
   (if (<= z 7e+35) (/ 1.0 (* y (/ t x))) (* (/ x z) (/ 1.0 z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -9.5e+33) {
		tmp = (x / z) / z;
	} else if (z <= 7e+35) {
		tmp = 1.0 / (y * (t / x));
	} else {
		tmp = (x / z) * (1.0 / 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 (z <= (-9.5d+33)) then
        tmp = (x / z) / z
    else if (z <= 7d+35) then
        tmp = 1.0d0 / (y * (t / x))
    else
        tmp = (x / z) * (1.0d0 / 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 (z <= -9.5e+33) {
		tmp = (x / z) / z;
	} else if (z <= 7e+35) {
		tmp = 1.0 / (y * (t / x));
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -9.5e+33:
		tmp = (x / z) / z
	elif z <= 7e+35:
		tmp = 1.0 / (y * (t / x))
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -9.5e+33)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 7e+35)
		tmp = Float64(1.0 / Float64(y * Float64(t / x)));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -9.5e+33)
		tmp = (x / z) / z;
	elseif (z <= 7e+35)
		tmp = 1.0 / (y * (t / x));
	else
		tmp = (x / z) * (1.0 / 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[z, -9.5e+33], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 7e+35], N[(1.0 / N[(y * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5000000000000003e33

   1. Initial program 80.7%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. unpow2 71.9%

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

      2. associate-/r* 79.4%

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

   4. Simplified 79.4%

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

   if -9.5000000000000003e33 < z < 7.0000000000000001e35

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/r* 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in t around inf 62.3%

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

      1. clear-num 62.0%

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

      2. inv-pow 62.1%

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

      3. div-inv 61.6%

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

      4. clear-num 62.1%

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

   7. Applied egg-rr 62.1%

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

      1. unpow-1 62.1%

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

   9. Simplified 62.1%

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

   if 7.0000000000000001e35 < z

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. unpow2 71.1%

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

   4. Simplified 71.1%

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

      1. associate-/r* 75.2%

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

      2. div-inv 75.3%

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

   6. Applied egg-rr 75.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{y \cdot \frac{t}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 13: 67.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -8e+33)
   (/ (/ x z) z)
   (if (<= z 3.3e+35) (/ 1.0 (/ y (/ x t))) (* (/ x z) (/ 1.0 z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8e+33) {
		tmp = (x / z) / z;
	} else if (z <= 3.3e+35) {
		tmp = 1.0 / (y / (x / t));
	} else {
		tmp = (x / z) * (1.0 / 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 (z <= (-8d+33)) then
        tmp = (x / z) / z
    else if (z <= 3.3d+35) then
        tmp = 1.0d0 / (y / (x / t))
    else
        tmp = (x / z) * (1.0d0 / 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 (z <= -8e+33) {
		tmp = (x / z) / z;
	} else if (z <= 3.3e+35) {
		tmp = 1.0 / (y / (x / t));
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -8e+33:
		tmp = (x / z) / z
	elif z <= 3.3e+35:
		tmp = 1.0 / (y / (x / t))
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8e+33)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 3.3e+35)
		tmp = Float64(1.0 / Float64(y / Float64(x / t)));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8e+33)
		tmp = (x / z) / z;
	elseif (z <= 3.3e+35)
		tmp = 1.0 / (y / (x / t));
	else
		tmp = (x / z) * (1.0 / 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[z, -8e+33], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 3.3e+35], N[(1.0 / N[(y / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.9999999999999996e33

   1. Initial program 80.7%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. unpow2 71.9%

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

      2. associate-/r* 79.4%

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

   4. Simplified 79.4%

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

   if -7.9999999999999996e33 < z < 3.3000000000000002e35

   1. Initial program 93.8%

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

      1. associate-/r* 96.7%

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

      2. div-inv 96.6%

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

   3. Applied egg-rr 96.6%

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

      1. associate-*l/ 95.6%

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

      2. clear-num 95.2%

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

      3. div-inv 95.3%

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

   5. Applied egg-rr 95.3%

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

   6. Taylor expanded in z around 0 61.0%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

   if 3.3000000000000002e35 < z

   1. Initial program 85.9%

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

   2. Taylor expanded in z around inf 71.1%

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

      1. unpow2 71.1%

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

   4. Simplified 71.1%

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

      1. associate-/r* 75.2%

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

      2. div-inv 75.3%

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

   6. Applied egg-rr 75.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+35}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]

Alternative 14: 66.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.5e+33)
   (/ (/ x z) z)
   (if (<= z 5.1e+38) (/ 1.0 (/ y (/ x t))) (/ 1.0 (/ z (/ x z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.5e+33) {
		tmp = (x / z) / z;
	} else if (z <= 5.1e+38) {
		tmp = 1.0 / (y / (x / t));
	} else {
		tmp = 1.0 / (z / (x / 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 (z <= (-1.5d+33)) then
        tmp = (x / z) / z
    else if (z <= 5.1d+38) then
        tmp = 1.0d0 / (y / (x / t))
    else
        tmp = 1.0d0 / (z / (x / 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 (z <= -1.5e+33) {
		tmp = (x / z) / z;
	} else if (z <= 5.1e+38) {
		tmp = 1.0 / (y / (x / t));
	} else {
		tmp = 1.0 / (z / (x / z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -1.5e+33:
		tmp = (x / z) / z
	elif z <= 5.1e+38:
		tmp = 1.0 / (y / (x / t))
	else:
		tmp = 1.0 / (z / (x / z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.5e+33)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 5.1e+38)
		tmp = Float64(1.0 / Float64(y / Float64(x / t)));
	else
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.5e+33)
		tmp = (x / z) / z;
	elseif (z <= 5.1e+38)
		tmp = 1.0 / (y / (x / t));
	else
		tmp = 1.0 / (z / (x / 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[z, -1.5e+33], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.1e+38], N[(1.0 / N[(y / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.49999999999999992e33

   1. Initial program 80.7%

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

   2. Taylor expanded in z around inf 71.9%

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

      1. unpow2 71.9%

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

      2. associate-/r* 79.4%

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

   4. Simplified 79.4%

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

   if -1.49999999999999992e33 < z < 5.1000000000000001e38

   1. Initial program 93.8%

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

      1. associate-/r* 96.7%

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

      2. div-inv 96.6%

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

   3. Applied egg-rr 96.6%

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

      1. associate-*l/ 95.6%

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

      2. clear-num 95.2%

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

      3. div-inv 95.3%

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

   5. Applied egg-rr 95.3%

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

   6. Taylor expanded in z around 0 61.0%

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

      1. associate-/l* 62.0%

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

   8. Simplified 62.0%

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

   if 5.1000000000000001e38 < z

   1. Initial program 85.9%

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

      1. associate-/r* 99.9%

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

      2. div-inv 99.9%

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

   3. Applied egg-rr 99.9%

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

      1. associate-*l/ 99.8%

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

      2. clear-num 98.4%

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

      3. div-inv 98.5%

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

   5. Applied egg-rr 98.5%

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

   6. Taylor expanded in z around inf 71.6%

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

      1. unpow2 71.6%

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

      2. associate-/l* 76.6%

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

   8. Simplified 76.6%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 15: 45.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 4.9 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -9.8e+33) (not (<= z 4.9e+113))) (/ x (* z y)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.8e+33) || !(z <= 4.9e+113)) {
		tmp = x / (z * y);
	} 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 <= (-9.8d+33)) .or. (.not. (z <= 4.9d+113))) then
        tmp = x / (z * y)
    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 <= -9.8e+33) || !(z <= 4.9e+113)) {
		tmp = x / (z * y);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -9.8e+33) or not (z <= 4.9e+113):
		tmp = x / (z * y)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.8e+33) || !(z <= 4.9e+113))
		tmp = Float64(x / Float64(z * y));
	else
		tmp = Float64(x / Float64(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 <= -9.8e+33) || ~((z <= 4.9e+113)))
		tmp = x / (z * y);
	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, -9.8e+33], N[Not[LessEqual[z, 4.9e+113]], $MachinePrecision]], N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.80000000000000027e33 or 4.90000000000000021e113 < z

   1. Initial program 82.5%

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

   2. Taylor expanded in y around inf 41.7%

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

      1. *-commutative 41.7%

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

      2. associate-/r* 50.2%

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

   4. Simplified 50.2%

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

   5. Taylor expanded in t around 0 46.4%

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

      1. associate-*r/ 46.4%

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

      2. neg-mul-1 46.4%

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

   7. Simplified 46.4%

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

      1. expm1-log1p-u 45.5%

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

      2. expm1-udef 59.0%

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

      3. associate-/l/ 59.0%

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

      4. add-sqr-sqrt 32.5%

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

      5. sqrt-unprod 54.1%

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

      6. sqr-neg 54.1%

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

      7. sqrt-unprod 26.5%

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

      8. add-sqr-sqrt 59.0%

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

   9. Applied egg-rr 59.0%

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

       1. expm1-def 37.1%

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

       2. expm1-log1p 37.5%

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

   11. Simplified 37.5%

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

   if -9.80000000000000027e33 < z < 4.90000000000000021e113

   1. Initial program 93.5%

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

   2. Taylor expanded in z around 0 58.8%

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

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+33} \lor \neg \left(z \leq 4.9 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 16: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-21} \lor \neg \left(z \leq 2.85 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -6.8e-21) (not (<= z 2.85e+35))) (/ x (* z z)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e-21) || !(z <= 2.85e+35)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.8d-21)) .or. (.not. (z <= 2.85d+35))) then
        tmp = x / (z * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.8e-21) || !(z <= 2.85e+35)) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -6.8e-21) or not (z <= 2.85e+35):
		tmp = x / (z * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.8e-21) || !(z <= 2.85e+35))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(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 <= -6.8e-21) || ~((z <= 2.85e+35)))
		tmp = x / (z * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.8e-21], N[Not[LessEqual[z, 2.85e+35]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8e-21 or 2.84999999999999997e35 < z

   1. Initial program 83.1%

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

   2. Taylor expanded in z around inf 67.5%

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

      1. unpow2 67.5%

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

   4. Simplified 67.5%

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

   if -6.8e-21 < z < 2.84999999999999997e35

   1. Initial program 94.7%

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

   2. Taylor expanded in z around 0 65.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-21} \lor \neg \left(z \leq 2.85 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 17: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+33} \lor \neg \left(z \leq 7.2 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.5e+33) (not (<= z 7.2e+40))) (/ x (* z z)) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e+33) || !(z <= 7.2e+40)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.5d+33)) .or. (.not. (z <= 7.2d+40))) then
        tmp = x / (z * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.5e+33) || !(z <= 7.2e+40)) {
		tmp = x / (z * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -1.5e+33) or not (z <= 7.2e+40):
		tmp = x / (z * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.5e+33) || !(z <= 7.2e+40))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.5e+33) || ~((z <= 7.2e+40)))
		tmp = x / (z * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.5e+33], N[Not[LessEqual[z, 7.2e+40]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999992e33 or 7.19999999999999993e40 < z

   1. Initial program 83.0%

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

   2. Taylor expanded in z around inf 71.5%

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

      1. unpow2 71.5%

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

   4. Simplified 71.5%

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

   if -1.49999999999999992e33 < z < 7.19999999999999993e40

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/r* 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in t around inf 62.3%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+33} \lor \neg \left(z \leq 7.2 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 18: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+33} \lor \neg \left(z \leq 4.2 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

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 -3.2e+33) (not (<= z 4.2e+35))) (/ (/ x z) z) (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+33) || !(z <= 4.2e+35)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.2d+33)) .or. (.not. (z <= 4.2d+35))) then
        tmp = (x / z) / z
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e+33) || !(z <= 4.2e+35)) {
		tmp = (x / z) / z;
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e+33) or not (z <= 4.2e+35):
		tmp = (x / z) / z
	else:
		tmp = (x / t) / y
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e+33) || !(z <= 4.2e+35))
		tmp = Float64(Float64(x / z) / z);
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e+33) || ~((z <= 4.2e+35)))
		tmp = (x / z) / z;
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e+33], N[Not[LessEqual[z, 4.2e+35]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000017e33 or 4.1999999999999998e35 < z

   1. Initial program 83.0%

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

   2. Taylor expanded in z around inf 71.5%

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

      1. unpow2 71.5%

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

      2. associate-/r* 77.6%

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

   4. Simplified 77.6%

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

   if -3.20000000000000017e33 < z < 4.1999999999999998e35

   1. Initial program 93.8%

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

   2. Taylor expanded in y around inf 75.6%

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

      1. *-commutative 75.6%

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

      2. associate-/r* 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in t around inf 62.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+33} \lor \neg \left(z \leq 4.2 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 19: 38.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

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

2. Taylor expanded in z around 0 41.8%

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

3. Final simplification 41.8%

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

Developer target: 87.9% 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 2023200 
(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))))