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

Percentage Accurate: 88.6% → 96.9%

Time: 12.9s

Alternatives: 19

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 88.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 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 89.7%

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

   1. associate-/r* 98.1%

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

   2. div-inv 98.1%

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

3. Applied egg-rr 98.1%

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

   1. associate-*l/ 97.2%

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

   2. div-inv 97.2%

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

5. Applied egg-rr 97.2%

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

6. Final simplification 97.2%

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

Alternative 2: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) z)))
   (if (<= y -1e+43)
     (/ (/ x y) (- t z))
     (if (<= y -1.45e-12)
       (/ t_1 (- y z))
       (if (<= y -3.5e-43)
         (/ x (* (- t z) y))
         (if (<= y 1.3e-57) (/ t_1 (- t z)) (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -1e+43) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.45e-12) {
		tmp = t_1 / (y - z);
	} else if (y <= -3.5e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.3e-57) {
		tmp = t_1 / (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) :: t_1
    real(8) :: tmp
    t_1 = -x / z
    if (y <= (-1d+43)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-1.45d-12)) then
        tmp = t_1 / (y - z)
    else if (y <= (-3.5d-43)) then
        tmp = x / ((t - z) * y)
    else if (y <= 1.3d-57) then
        tmp = t_1 / (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 t_1 = -x / z;
	double tmp;
	if (y <= -1e+43) {
		tmp = (x / y) / (t - z);
	} else if (y <= -1.45e-12) {
		tmp = t_1 / (y - z);
	} else if (y <= -3.5e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 1.3e-57) {
		tmp = t_1 / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -x / z
	tmp = 0
	if y <= -1e+43:
		tmp = (x / y) / (t - z)
	elif y <= -1.45e-12:
		tmp = t_1 / (y - z)
	elif y <= -3.5e-43:
		tmp = x / ((t - z) * y)
	elif y <= 1.3e-57:
		tmp = t_1 / (t - 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) / z)
	tmp = 0.0
	if (y <= -1e+43)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -1.45e-12)
		tmp = Float64(t_1 / Float64(y - z));
	elseif (y <= -3.5e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 1.3e-57)
		tmp = Float64(t_1 / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / z;
	tmp = 0.0;
	if (y <= -1e+43)
		tmp = (x / y) / (t - z);
	elseif (y <= -1.45e-12)
		tmp = t_1 / (y - z);
	elseif (y <= -3.5e-43)
		tmp = x / ((t - z) * y);
	elseif (y <= 1.3e-57)
		tmp = t_1 / (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_] := Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[y, -1e+43], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-12], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-57], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.00000000000000001e43

   1. Initial program 84.0%

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

      1. associate-/r* 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 91.4%

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

   if -1.00000000000000001e43 < y < -1.4500000000000001e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. neg-mul-1 68.5%

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

      3. *-commutative 68.5%

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

      4. associate-/r* 68.4%

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

   4. Simplified 68.4%

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

   if -1.4500000000000001e-12 < y < -3.49999999999999997e-43

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 99.6%

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

      1. *-commutative 99.6%

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

   4. Simplified 99.6%

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

   if -3.49999999999999997e-43 < y < 1.29999999999999993e-57

   1. Initial program 91.3%

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

   2. Taylor expanded in y around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-frac-neg 75.4%

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

      3. associate-/r* 81.8%

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

   4. Simplified 81.8%

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

   if 1.29999999999999993e-57 < y

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. associate-/r* 61.3%

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

   4. Simplified 61.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 81.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t - z}}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{t_1}{y - z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-58}:\\ \;\;\;\;\frac{t_1}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) z)))
   (if (<= y -5.8e+42)
     (/ 1.0 (/ y (/ x (- t z))))
     (if (<= y -3.5e-13)
       (/ t_1 (- y z))
       (if (<= y -3.5e-43)
         (/ x (* (- t z) y))
         (if (<= y 2.55e-58) (/ t_1 (- t z)) (/ (/ x t) (- y z))))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / z;
	double tmp;
	if (y <= -5.8e+42) {
		tmp = 1.0 / (y / (x / (t - z)));
	} else if (y <= -3.5e-13) {
		tmp = t_1 / (y - z);
	} else if (y <= -3.5e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 2.55e-58) {
		tmp = t_1 / (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) :: t_1
    real(8) :: tmp
    t_1 = -x / z
    if (y <= (-5.8d+42)) then
        tmp = 1.0d0 / (y / (x / (t - z)))
    else if (y <= (-3.5d-13)) then
        tmp = t_1 / (y - z)
    else if (y <= (-3.5d-43)) then
        tmp = x / ((t - z) * y)
    else if (y <= 2.55d-58) then
        tmp = t_1 / (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 t_1 = -x / z;
	double tmp;
	if (y <= -5.8e+42) {
		tmp = 1.0 / (y / (x / (t - z)));
	} else if (y <= -3.5e-13) {
		tmp = t_1 / (y - z);
	} else if (y <= -3.5e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 2.55e-58) {
		tmp = t_1 / (t - z);
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = -x / z
	tmp = 0
	if y <= -5.8e+42:
		tmp = 1.0 / (y / (x / (t - z)))
	elif y <= -3.5e-13:
		tmp = t_1 / (y - z)
	elif y <= -3.5e-43:
		tmp = x / ((t - z) * y)
	elif y <= 2.55e-58:
		tmp = t_1 / (t - 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) / z)
	tmp = 0.0
	if (y <= -5.8e+42)
		tmp = Float64(1.0 / Float64(y / Float64(x / Float64(t - z))));
	elseif (y <= -3.5e-13)
		tmp = Float64(t_1 / Float64(y - z));
	elseif (y <= -3.5e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 2.55e-58)
		tmp = Float64(t_1 / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / z;
	tmp = 0.0;
	if (y <= -5.8e+42)
		tmp = 1.0 / (y / (x / (t - z)));
	elseif (y <= -3.5e-13)
		tmp = t_1 / (y - z);
	elseif (y <= -3.5e-43)
		tmp = x / ((t - z) * y);
	elseif (y <= 2.55e-58)
		tmp = t_1 / (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_] := Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[y, -5.8e+42], N[(1.0 / N[(y / N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-13], N[(t$95$1 / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.55e-58], N[(t$95$1 / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.79999999999999961e42

   1. Initial program 84.0%

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

   2. Taylor expanded in y around inf 84.0%

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

      1. *-commutative 84.0%

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

   4. Simplified 84.0%

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

      1. clear-num 83.9%

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

      2. inv-pow 83.9%

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

      3. *-commutative 83.9%

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

   6. Applied egg-rr 83.9%

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

      1. unpow-1 83.9%

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

      2. associate-/l* 92.0%

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

   8. Simplified 92.0%

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

   if -5.79999999999999961e42 < y < -3.5000000000000002e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 68.5%

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

      1. associate-*r/ 68.5%

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

      2. neg-mul-1 68.5%

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

      3. *-commutative 68.5%

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

      4. associate-/r* 68.4%

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

   4. Simplified 68.4%

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

   if -3.5000000000000002e-13 < y < -3.49999999999999997e-43

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 99.6%

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

      1. *-commutative 99.6%

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

   4. Simplified 99.6%

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

   if -3.49999999999999997e-43 < y < 2.55e-58

   1. Initial program 91.3%

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

   2. Taylor expanded in y around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-frac-neg 75.4%

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

      3. associate-/r* 81.8%

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

   4. Simplified 81.8%

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

   if 2.55e-58 < y

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. associate-/r* 61.3%

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

   4. Simplified 61.3%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t - z}}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 4: 67.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -1.5e+47)
     t_1
     (if (<= z -6.5e-12)
       (/ (- (/ x y)) z)
       (if (<= z 2.8e+65) (/ 1.0 (* t (/ y x))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.5e+47) {
		tmp = t_1;
	} else if (z <= -6.5e-12) {
		tmp = -(x / y) / z;
	} else if (z <= 2.8e+65) {
		tmp = 1.0 / (t * (y / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-1.5d+47)) then
        tmp = t_1
    else if (z <= (-6.5d-12)) then
        tmp = -(x / y) / z
    else if (z <= 2.8d+65) then
        tmp = 1.0d0 / (t * (y / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.5e+47) {
		tmp = t_1;
	} else if (z <= -6.5e-12) {
		tmp = -(x / y) / z;
	} else if (z <= 2.8e+65) {
		tmp = 1.0 / (t * (y / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.5e+47:
		tmp = t_1
	elif z <= -6.5e-12:
		tmp = -(x / y) / z
	elif z <= 2.8e+65:
		tmp = 1.0 / (t * (y / x))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.5e+47)
		tmp = t_1;
	elseif (z <= -6.5e-12)
		tmp = Float64(Float64(-Float64(x / y)) / z);
	elseif (z <= 2.8e+65)
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.5e+47)
		tmp = t_1;
	elseif (z <= -6.5e-12)
		tmp = -(x / y) / z;
	elseif (z <= 2.8e+65)
		tmp = 1.0 / (t * (y / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.5e+47], t$95$1, If[LessEqual[z, -6.5e-12], N[((-N[(x / y), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[z, 2.8e+65], N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5000000000000001e47 or 2.7999999999999999e65 < z

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf 76.0%

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

      1. unpow2 76.0%

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

      2. associate-/r* 79.9%

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

   4. Simplified 79.9%

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

   if -1.5000000000000001e47 < z < -6.5000000000000002e-12

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in t around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/r* 52.7%

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

      3. distribute-neg-frac 52.7%

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

   7. Simplified 52.7%

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

   if -6.5000000000000002e-12 < z < 2.7999999999999999e65

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 57.1%

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

      1. clear-num 56.5%

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

      2. inv-pow 56.5%

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

   4. Applied egg-rr 56.5%

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

      1. unpow-1 56.5%

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

      2. associate-/l* 60.3%

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

   6. Simplified 60.3%

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

      1. associate-/r/ 61.4%

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

   8. Applied egg-rr 61.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 5: 67.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ z x)))))
   (if (<= z -2.1e+49)
     t_1
     (if (<= z -5.2e-13)
       (/ (- (/ x y)) z)
       (if (<= z 4.5e+60) (/ 1.0 (* t (/ y x))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -2.1e+49) {
		tmp = t_1;
	} else if (z <= -5.2e-13) {
		tmp = -(x / y) / z;
	} else if (z <= 4.5e+60) {
		tmp = 1.0 / (t * (y / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (z * (z / x))
    if (z <= (-2.1d+49)) then
        tmp = t_1
    else if (z <= (-5.2d-13)) then
        tmp = -(x / y) / z
    else if (z <= 4.5d+60) then
        tmp = 1.0d0 / (t * (y / x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -2.1e+49) {
		tmp = t_1;
	} else if (z <= -5.2e-13) {
		tmp = -(x / y) / z;
	} else if (z <= 4.5e+60) {
		tmp = 1.0 / (t * (y / x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (z * (z / x))
	tmp = 0
	if z <= -2.1e+49:
		tmp = t_1
	elif z <= -5.2e-13:
		tmp = -(x / y) / z
	elif z <= 4.5e+60:
		tmp = 1.0 / (t * (y / x))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(z * Float64(z / x)))
	tmp = 0.0
	if (z <= -2.1e+49)
		tmp = t_1;
	elseif (z <= -5.2e-13)
		tmp = Float64(Float64(-Float64(x / y)) / z);
	elseif (z <= 4.5e+60)
		tmp = Float64(1.0 / Float64(t * Float64(y / x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (z * (z / x));
	tmp = 0.0;
	if (z <= -2.1e+49)
		tmp = t_1;
	elseif (z <= -5.2e-13)
		tmp = -(x / y) / z;
	elseif (z <= 4.5e+60)
		tmp = 1.0 / (t * (y / x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+49], t$95$1, If[LessEqual[z, -5.2e-13], N[((-N[(x / y), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[z, 4.5e+60], N[(1.0 / N[(t * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.10000000000000011e49 or 4.50000000000000013e60 < z

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf 76.0%

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

      1. unpow2 76.0%

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

   4. Simplified 76.0%

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

      1. clear-num 76.4%

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

      2. inv-pow 76.4%

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

      3. associate-/l* 80.4%

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

   6. Applied egg-rr 80.4%

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

      1. unpow-1 80.4%

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

      2. associate-/r/ 80.4%

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

   8. Simplified 80.4%

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

   if -2.10000000000000011e49 < z < -5.2000000000000001e-13

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in t around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/r* 52.7%

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

      3. distribute-neg-frac 52.7%

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

   7. Simplified 52.7%

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

   if -5.2000000000000001e-13 < z < 4.50000000000000013e60

   1. Initial program 92.9%

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

   2. Taylor expanded in z around 0 57.1%

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

      1. clear-num 56.5%

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

      2. inv-pow 56.5%

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

   4. Applied egg-rr 56.5%

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

      1. unpow-1 56.5%

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

      2. associate-/l* 60.3%

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

   6. Simplified 60.3%

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

      1. associate-/r/ 61.4%

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

   8. Applied egg-rr 61.4%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+49}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+60}:\\ \;\;\;\;\frac{1}{t \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 6: 67.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{if}\;z \leq -7.7 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-11}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ z x)))))
   (if (<= z -7.7e+46)
     t_1
     (if (<= z -2.1e-11)
       (/ (- (/ x y)) z)
       (if (<= z 6.2e+16) (/ 1.0 (/ y (/ x t))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -7.7e+46) {
		tmp = t_1;
	} else if (z <= -2.1e-11) {
		tmp = -(x / y) / z;
	} else if (z <= 6.2e+16) {
		tmp = 1.0 / (y / (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (z * (z / x))
    if (z <= (-7.7d+46)) then
        tmp = t_1
    else if (z <= (-2.1d-11)) then
        tmp = -(x / y) / z
    else if (z <= 6.2d+16) then
        tmp = 1.0d0 / (y / (x / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -7.7e+46) {
		tmp = t_1;
	} else if (z <= -2.1e-11) {
		tmp = -(x / y) / z;
	} else if (z <= 6.2e+16) {
		tmp = 1.0 / (y / (x / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (z * (z / x))
	tmp = 0
	if z <= -7.7e+46:
		tmp = t_1
	elif z <= -2.1e-11:
		tmp = -(x / y) / z
	elif z <= 6.2e+16:
		tmp = 1.0 / (y / (x / t))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(z * Float64(z / x)))
	tmp = 0.0
	if (z <= -7.7e+46)
		tmp = t_1;
	elseif (z <= -2.1e-11)
		tmp = Float64(Float64(-Float64(x / y)) / z);
	elseif (z <= 6.2e+16)
		tmp = Float64(1.0 / Float64(y / Float64(x / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (z * (z / x));
	tmp = 0.0;
	if (z <= -7.7e+46)
		tmp = t_1;
	elseif (z <= -2.1e-11)
		tmp = -(x / y) / z;
	elseif (z <= 6.2e+16)
		tmp = 1.0 / (y / (x / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.7e+46], t$95$1, If[LessEqual[z, -2.1e-11], N[((-N[(x / y), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[z, 6.2e+16], N[(1.0 / N[(y / N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.70000000000000038e46 or 6.2e16 < z

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 73.4%

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

      1. unpow2 73.4%

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

   4. Simplified 73.4%

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

      1. clear-num 73.7%

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

      2. inv-pow 73.7%

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

      3. associate-/l* 77.4%

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

   6. Applied egg-rr 77.4%

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

      1. unpow-1 77.4%

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

      2. associate-/r/ 77.4%

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

   8. Simplified 77.4%

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

   if -7.70000000000000038e46 < z < -2.0999999999999999e-11

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in t around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/r* 52.7%

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

      3. distribute-neg-frac 52.7%

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

   7. Simplified 52.7%

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

   if -2.0999999999999999e-11 < z < 6.2e16

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 59.3%

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

      1. clear-num 58.7%

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

      2. inv-pow 58.7%

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

   4. Applied egg-rr 58.7%

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

      1. unpow-1 58.7%

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

      2. associate-/l* 62.1%

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

   6. Simplified 62.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.7 \cdot 10^{+46}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-11}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 7: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* z (/ z x)))))
   (if (<= z -2.6e+48)
     t_1
     (if (<= z -1.8e-11)
       (/ (- (/ x y)) z)
       (if (<= z 9.2e+29) (/ x (* t (- y z))) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -2.6e+48) {
		tmp = t_1;
	} else if (z <= -1.8e-11) {
		tmp = -(x / y) / z;
	} else if (z <= 9.2e+29) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / (z * (z / x))
    if (z <= (-2.6d+48)) then
        tmp = t_1
    else if (z <= (-1.8d-11)) then
        tmp = -(x / y) / z
    else if (z <= 9.2d+29) then
        tmp = x / (t * (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -2.6e+48) {
		tmp = t_1;
	} else if (z <= -1.8e-11) {
		tmp = -(x / y) / z;
	} else if (z <= 9.2e+29) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = 1.0 / (z * (z / x))
	tmp = 0
	if z <= -2.6e+48:
		tmp = t_1
	elif z <= -1.8e-11:
		tmp = -(x / y) / z
	elif z <= 9.2e+29:
		tmp = x / (t * (y - z))
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(z * Float64(z / x)))
	tmp = 0.0
	if (z <= -2.6e+48)
		tmp = t_1;
	elseif (z <= -1.8e-11)
		tmp = Float64(Float64(-Float64(x / y)) / z);
	elseif (z <= 9.2e+29)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / (z * (z / x));
	tmp = 0.0;
	if (z <= -2.6e+48)
		tmp = t_1;
	elseif (z <= -1.8e-11)
		tmp = -(x / y) / z;
	elseif (z <= 9.2e+29)
		tmp = x / (t * (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+48], t$95$1, If[LessEqual[z, -1.8e-11], N[((-N[(x / y), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[z, 9.2e+29], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.59999999999999995e48 or 9.2000000000000004e29 < z

   1. Initial program 86.2%

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

   2. Taylor expanded in z around inf 73.5%

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

      1. unpow2 73.5%

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

   4. Simplified 73.5%

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

      1. clear-num 73.9%

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

      2. inv-pow 73.9%

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

      3. associate-/l* 77.6%

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

   6. Applied egg-rr 77.6%

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

      1. unpow-1 77.6%

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

      2. associate-/r/ 77.6%

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

   8. Simplified 77.6%

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

   if -2.59999999999999995e48 < z < -1.79999999999999992e-11

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in t around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/r* 52.7%

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

      3. distribute-neg-frac 52.7%

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

   7. Simplified 52.7%

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

   if -1.79999999999999992e-11 < z < 9.2000000000000004e29

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 68.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 8: 82.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e-43)
   (/ (/ x y) (- t z))
   (if (<= y 6.1e-58) (/ (/ (- 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 <= -2.6e-43) {
		tmp = (x / y) / (t - z);
	} else if (y <= 6.1e-58) {
		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 <= (-2.6d-43)) then
        tmp = (x / y) / (t - z)
    else if (y <= 6.1d-58) 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 <= -2.6e-43) {
		tmp = (x / y) / (t - z);
	} else if (y <= 6.1e-58) {
		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 <= -2.6e-43:
		tmp = (x / y) / (t - z)
	elif y <= 6.1e-58:
		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 <= -2.6e-43)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 6.1e-58)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(t - z));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e-43)
		tmp = (x / y) / (t - z);
	elseif (y <= 6.1e-58)
		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, -2.6e-43], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e-58], N[(N[((-x) / z), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6e-43

   1. Initial program 87.1%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 87.2%

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

   if -2.6e-43 < y < 6.1000000000000003e-58

   1. Initial program 91.3%

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

   2. Taylor expanded in y around 0 75.4%

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

      1. mul-1-neg 75.4%

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

      2. distribute-frac-neg 75.4%

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

      3. associate-/r* 81.8%

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

   4. Simplified 81.8%

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

   if 6.1000000000000003e-58 < y

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. associate-/r* 61.3%

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

   4. Simplified 61.3%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 9: 66.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.62 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 510000000000:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -1.62e+44)
     t_1
     (if (<= z -1.65e-17)
       (/ x (* y (- z)))
       (if (<= z 510000000000.0) (/ x (* t y)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.62e+44) {
		tmp = t_1;
	} else if (z <= -1.65e-17) {
		tmp = x / (y * -z);
	} else if (z <= 510000000000.0) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-1.62d+44)) then
        tmp = t_1
    else if (z <= (-1.65d-17)) then
        tmp = x / (y * -z)
    else if (z <= 510000000000.0d0) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -1.62e+44) {
		tmp = t_1;
	} else if (z <= -1.65e-17) {
		tmp = x / (y * -z);
	} else if (z <= 510000000000.0) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -1.62e+44:
		tmp = t_1
	elif z <= -1.65e-17:
		tmp = x / (y * -z)
	elif z <= 510000000000.0:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.62e+44)
		tmp = t_1;
	elseif (z <= -1.65e-17)
		tmp = Float64(x / Float64(y * Float64(-z)));
	elseif (z <= 510000000000.0)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -1.62e+44)
		tmp = t_1;
	elseif (z <= -1.65e-17)
		tmp = x / (y * -z);
	elseif (z <= 510000000000.0)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.62e+44], t$95$1, If[LessEqual[z, -1.65e-17], N[(x / N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 510000000000.0], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6199999999999999e44 or 5.1e11 < z

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 73.4%

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

      1. unpow2 73.4%

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

      2. associate-/r* 77.0%

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

   4. Simplified 77.0%

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

   if -1.6199999999999999e44 < z < -1.65e-17

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in t around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. *-commutative 52.9%

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

      3. distribute-rgt-neg-in 52.9%

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

   7. Simplified 52.9%

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

   if -1.65e-17 < z < 5.1e11

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 59.3%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.62 \cdot 10^{+44}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y \cdot \left(-z\right)}\\ \mathbf{elif}\;z \leq 510000000000:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 10: 66.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 12200000000:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) z)))
   (if (<= z -5.5e+49)
     t_1
     (if (<= z -1.1e-13)
       (/ (- (/ x y)) z)
       (if (<= z 12200000000.0) (/ x (* t y)) t_1)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.5e+49) {
		tmp = t_1;
	} else if (z <= -1.1e-13) {
		tmp = -(x / y) / z;
	} else if (z <= 12200000000.0) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / z
    if (z <= (-5.5d+49)) then
        tmp = t_1
    else if (z <= (-1.1d-13)) then
        tmp = -(x / y) / z
    else if (z <= 12200000000.0d0) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / z;
	double tmp;
	if (z <= -5.5e+49) {
		tmp = t_1;
	} else if (z <= -1.1e-13) {
		tmp = -(x / y) / z;
	} else if (z <= 12200000000.0) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	t_1 = (x / z) / z
	tmp = 0
	if z <= -5.5e+49:
		tmp = t_1
	elif z <= -1.1e-13:
		tmp = -(x / y) / z
	elif z <= 12200000000.0:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -5.5e+49)
		tmp = t_1;
	elseif (z <= -1.1e-13)
		tmp = Float64(Float64(-Float64(x / y)) / z);
	elseif (z <= 12200000000.0)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / z;
	tmp = 0.0;
	if (z <= -5.5e+49)
		tmp = t_1;
	elseif (z <= -1.1e-13)
		tmp = -(x / y) / z;
	elseif (z <= 12200000000.0)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -5.5e+49], t$95$1, If[LessEqual[z, -1.1e-13], N[((-N[(x / y), $MachinePrecision]) / z), $MachinePrecision], If[LessEqual[z, 12200000000.0], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.50000000000000042e49 or 1.22e10 < z

   1. Initial program 86.5%

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

   2. Taylor expanded in z around inf 73.4%

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

      1. unpow2 73.4%

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

      2. associate-/r* 77.0%

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

   4. Simplified 77.0%

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

   if -5.50000000000000042e49 < z < -1.09999999999999998e-13

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in t around 0 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/r* 52.7%

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

      3. distribute-neg-frac 52.7%

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

   7. Simplified 52.7%

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

   if -1.09999999999999998e-13 < z < 1.22e10

   1. Initial program 92.1%

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

   2. Taylor expanded in z around 0 59.3%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-13}:\\ \;\;\;\;\frac{-\frac{x}{y}}{z}\\ \mathbf{elif}\;z \leq 12200000000:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 11: 72.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-307}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e-43)
   (/ x (* (- t z) y))
   (if (<= y 6.1e-307) (/ 1.0 (* z (/ z x))) (/ x (* t (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 6.1e-307) {
		tmp = 1.0 / (z * (z / x));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.4d-43)) then
        tmp = x / ((t - z) * y)
    else if (y <= 6.1d-307) then
        tmp = 1.0d0 / (z * (z / x))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 6.1e-307) {
		tmp = 1.0 / (z * (z / x));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e-43:
		tmp = x / ((t - z) * y)
	elif y <= 6.1e-307:
		tmp = 1.0 / (z * (z / x))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 6.1e-307)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	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 <= -2.4e-43)
		tmp = x / ((t - z) * y);
	elseif (y <= 6.1e-307)
		tmp = 1.0 / (z * (z / x));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e-307], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4000000000000002e-43

   1. Initial program 87.1%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -2.4000000000000002e-43 < y < 6.09999999999999974e-307

   1. Initial program 93.9%

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

   2. Taylor expanded in z around inf 71.3%

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

      1. unpow2 71.3%

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

   4. Simplified 71.3%

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

      1. clear-num 72.3%

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

      2. inv-pow 72.3%

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

      3. associate-/l* 76.3%

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

   6. Applied egg-rr 76.3%

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

      1. unpow-1 76.3%

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

      2. associate-/r/ 76.3%

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

   8. Simplified 76.3%

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

   if 6.09999999999999974e-307 < y

   1. Initial program 89.8%

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

   2. Taylor expanded in t around inf 58.3%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-307}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 12: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.05e-43)
   (/ x (* (- t z) y))
   (if (<= y 4.7e-58) (/ x (* z (- z t))) (/ x (* t (- y z))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.05e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 4.7e-58) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.05d-43)) then
        tmp = x / ((t - z) * y)
    else if (y <= 4.7d-58) then
        tmp = x / (z * (z - t))
    else
        tmp = x / (t * (y - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.05e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 4.7e-58) {
		tmp = x / (z * (z - t));
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -3.05e-43:
		tmp = x / ((t - z) * y)
	elif y <= 4.7e-58:
		tmp = x / (z * (z - t))
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.05e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 4.7e-58)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	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 <= -3.05e-43)
		tmp = x / ((t - z) * y);
	elseif (y <= 4.7e-58)
		tmp = x / (z * (z - t));
	else
		tmp = x / (t * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -3.05e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e-58], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.05000000000000019e-43

   1. Initial program 87.1%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -3.05000000000000019e-43 < y < 4.69999999999999994e-58

   1. Initial program 91.3%

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

      1. frac-2neg 91.3%

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

      2. div-inv 90.3%

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

      3. distribute-rgt-neg-in 90.3%

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

   3. Applied egg-rr 90.3%

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

      1. associate-/r* 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in y around 0 75.4%

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

   if 4.69999999999999994e-58 < y

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 56.6%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.05 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 13: 78.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.35e-43)
   (/ x (* (- t z) y))
   (if (<= y 2e-57) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 2e-57) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.35d-43)) then
        tmp = x / ((t - z) * y)
    else if (y <= 2d-57) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= 2e-57) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -2.35e-43:
		tmp = x / ((t - z) * y)
	elif y <= 2e-57:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.35e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 2e-57)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.35e-43)
		tmp = x / ((t - z) * y);
	elseif (y <= 2e-57)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -2.35e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-57], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.35e-43

   1. Initial program 87.1%

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

   2. Taylor expanded in y around inf 81.3%

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

      1. *-commutative 81.3%

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

   4. Simplified 81.3%

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

   if -2.35e-43 < y < 1.99999999999999991e-57

   1. Initial program 91.3%

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

      1. frac-2neg 91.3%

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

      2. div-inv 90.3%

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

      3. distribute-rgt-neg-in 90.3%

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

   3. Applied egg-rr 90.3%

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

      1. associate-/r* 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in y around 0 75.4%

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

   if 1.99999999999999991e-57 < y

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. associate-/r* 61.3%

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

   4. Simplified 61.3%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 14: 79.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-43)
   (/ (/ x y) (- t z))
   (if (<= y 1.7e-57) (/ x (* z (- z t))) (/ (/ x t) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-43) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.7e-57) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.8d-43)) then
        tmp = (x / y) / (t - z)
    else if (y <= 1.7d-57) then
        tmp = x / (z * (z - t))
    else
        tmp = (x / t) / (y - z)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-43) {
		tmp = (x / y) / (t - z);
	} else if (y <= 1.7e-57) {
		tmp = x / (z * (z - t));
	} else {
		tmp = (x / t) / (y - z);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-43:
		tmp = (x / y) / (t - z)
	elif y <= 1.7e-57:
		tmp = x / (z * (z - t))
	else:
		tmp = (x / t) / (y - z)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-43)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 1.7e-57)
		tmp = Float64(x / Float64(z * Float64(z - t)));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e-43)
		tmp = (x / y) / (t - z);
	elseif (y <= 1.7e-57)
		tmp = x / (z * (z - t));
	else
		tmp = (x / t) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-43], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-57], N[(x / N[(z * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000004e-43

   1. Initial program 87.1%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 87.2%

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

   if -4.8000000000000004e-43 < y < 1.70000000000000008e-57

   1. Initial program 91.3%

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

      1. frac-2neg 91.3%

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

      2. div-inv 90.3%

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

      3. distribute-rgt-neg-in 90.3%

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

   3. Applied egg-rr 90.3%

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

      1. associate-/r* 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in y around 0 75.4%

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

   if 1.70000000000000008e-57 < y

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 56.6%

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

      1. associate-/r* 61.3%

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

   4. Simplified 61.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - t\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 15: 90.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t - z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e+161) (/ 1.0 (/ y (/ x (- t z)))) (/ x (* (- t z) (- y z)))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+161) {
		tmp = 1.0 / (y / (x / (t - z)));
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d+161)) then
        tmp = 1.0d0 / (y / (x / (t - z)))
    else
        tmp = x / ((t - z) * (y - z))
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e+161) {
		tmp = 1.0 / (y / (x / (t - z)));
	} else {
		tmp = x / ((t - z) * (y - z));
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e+161:
		tmp = 1.0 / (y / (x / (t - z)))
	else:
		tmp = x / ((t - z) * (y - z))
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e+161)
		tmp = Float64(1.0 / Float64(y / Float64(x / Float64(t - z))));
	else
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e+161)
		tmp = 1.0 / (y / (x / (t - z)));
	else
		tmp = x / ((t - z) * (y - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e+161], N[(1.0 / N[(y / N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e161

   1. Initial program 77.1%

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

   2. Taylor expanded in y around inf 77.1%

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

      1. *-commutative 77.1%

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

   4. Simplified 77.1%

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

      1. clear-num 77.0%

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

      2. inv-pow 77.0%

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

      3. *-commutative 77.0%

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

   6. Applied egg-rr 77.0%

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

      1. unpow-1 77.0%

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

      2. associate-/l* 98.8%

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

   8. Simplified 98.8%

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

   if -1.4000000000000001e161 < y

   1. Initial program 91.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\frac{y}{\frac{x}{t - z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 16: 46.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+26} \lor \neg \left(z \leq 6.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -3.5e+26) (not (<= z 6.4e+57))) (/ x (* z y)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.5e+26) || !(z <= 6.4e+57)) {
		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 <= (-3.5d+26)) .or. (.not. (z <= 6.4d+57))) 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 <= -3.5e+26) || !(z <= 6.4e+57)) {
		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 <= -3.5e+26) or not (z <= 6.4e+57):
		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 <= -3.5e+26) || !(z <= 6.4e+57))
		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 <= -3.5e+26) || ~((z <= 6.4e+57)))
		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, -3.5e+26], N[Not[LessEqual[z, 6.4e+57]], $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 < -3.4999999999999999e26 or 6.40000000000000059e57 < z

   1. Initial program 86.0%

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

   2. Taylor expanded in y around inf 47.9%

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

      1. *-commutative 47.9%

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

   4. Simplified 47.9%

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

   5. Taylor expanded in t around 0 43.6%

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

      1. mul-1-neg 43.6%

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

      2. *-commutative 43.6%

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

      3. distribute-rgt-neg-in 43.6%

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

   7. Simplified 43.6%

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

      1. expm1-log1p-u 42.5%

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

      2. expm1-udef 63.2%

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

      3. add-sqr-sqrt 31.9%

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

      4. sqrt-unprod 56.5%

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

      5. sqr-neg 56.5%

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

      6. sqrt-unprod 30.9%

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

      7. add-sqr-sqrt 63.0%

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

   9. Applied egg-rr 63.0%

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

       1. expm1-def 40.3%

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

       2. expm1-log1p 40.6%

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

       3. *-commutative 40.6%

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

   11. Simplified 40.6%

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

   if -3.4999999999999999e26 < z < 6.40000000000000059e57

   1. Initial program 93.3%

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

   2. Taylor expanded in z around 0 55.3%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+26} \lor \neg \left(z \leq 6.4 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{x}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 17: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-9} \lor \neg \left(z \leq 4 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -4.2e-9) (not (<= z 4e+16))) (/ x (* z z)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.2e-9) || !(z <= 4e+16)) {
		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 <= (-4.2d-9)) .or. (.not. (z <= 4d+16))) 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 <= -4.2e-9) || !(z <= 4e+16)) {
		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 <= -4.2e-9) or not (z <= 4e+16):
		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 <= -4.2e-9) || !(z <= 4e+16))
		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 <= -4.2e-9) || ~((z <= 4e+16)))
		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, -4.2e-9], N[Not[LessEqual[z, 4e+16]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000039e-9 or 4e16 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 69.7%

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

      1. unpow2 69.7%

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

   4. Simplified 69.7%

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

   if -4.20000000000000039e-9 < z < 4e16

   1. Initial program 92.2%

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

   2. Taylor expanded in z around 0 58.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-9} \lor \neg \left(z \leq 4 \cdot 10^{+16}\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 18: 66.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-9} \lor \neg \left(z \leq 34500000000000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -1.45e-9) (not (<= z 34500000000000.0)))
   (/ (/ x z) z)
   (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.45e-9) || !(z <= 34500000000000.0)) {
		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 <= (-1.45d-9)) .or. (.not. (z <= 34500000000000.0d0))) 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 <= -1.45e-9) || !(z <= 34500000000000.0)) {
		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 <= -1.45e-9) or not (z <= 34500000000000.0):
		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 <= -1.45e-9) || !(z <= 34500000000000.0))
		tmp = Float64(Float64(x / 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 <= -1.45e-9) || ~((z <= 34500000000000.0)))
		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, -1.45e-9], N[Not[LessEqual[z, 34500000000000.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.44999999999999996e-9 or 3.45e13 < z

   1. Initial program 87.8%

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

   2. Taylor expanded in z around inf 69.7%

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

      1. unpow2 69.7%

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

      2. associate-/r* 72.9%

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

   4. Simplified 72.9%

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

   if -1.44999999999999996e-9 < z < 3.45e13

   1. Initial program 92.2%

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

   2. Taylor expanded in z around 0 58.9%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-9} \lor \neg \left(z \leq 34500000000000\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 19: 40.3% 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 89.7%

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

2. Taylor expanded in z around 0 41.0%

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

3. Final simplification 41.0%

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

Developer target: 87.6% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(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))))