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

Percentage Accurate: 88.6% → 96.9%

Time: 16.5s

Alternatives: 15

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. frac-2neg 89.7%

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

   2. div-inv 89.3%

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

   3. distribute-rgt-neg-in 89.3%

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

3. Applied egg-rr 89.3%

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

   1. associate-*r/ 89.7%

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

   2. *-commutative 89.7%

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

   3. *-rgt-identity 89.7%

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

   4. associate-/r* 97.2%

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

5. Simplified 97.2%

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

   1. expm1-log1p-u 82.3%

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

   2. expm1-udef 59.6%

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

   3. frac-2neg 59.6%

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

7. Applied egg-rr 59.6%

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

   1. expm1-def 82.3%

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

   2. expm1-log1p 97.2%

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

9. Simplified 97.2%

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

10. Final simplification 97.2%

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

Alternative 2: 73.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-304}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e-43)
   (/ x (* (- t z) y))
   (if (<= y -1.75e-304)
     (/ 1.0 (* z (/ z x)))
     (if (<= y 1.02e-73)
       (/ x (* t (- y z)))
       (if (<= y 8.2e-58) (/ x (* z z)) (/ (/ x t) (- y z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.75e-304) {
		tmp = 1.0 / (z * (z / x));
	} else if (y <= 1.02e-73) {
		tmp = x / (t * (y - z));
	} else if (y <= 8.2e-58) {
		tmp = x / (z * 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 <= (-2.1d-43)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-1.75d-304)) then
        tmp = 1.0d0 / (z * (z / x))
    else if (y <= 1.02d-73) then
        tmp = x / (t * (y - z))
    else if (y <= 8.2d-58) then
        tmp = x / (z * 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 <= -2.1e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= -1.75e-304) {
		tmp = 1.0 / (z * (z / x));
	} else if (y <= 1.02e-73) {
		tmp = x / (t * (y - z));
	} else if (y <= 8.2e-58) {
		tmp = x / (z * 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 <= -2.1e-43:
		tmp = x / ((t - z) * y)
	elif y <= -1.75e-304:
		tmp = 1.0 / (z * (z / x))
	elif y <= 1.02e-73:
		tmp = x / (t * (y - z))
	elif y <= 8.2e-58:
		tmp = x / (z * 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 <= -2.1e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -1.75e-304)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	elseif (y <= 1.02e-73)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (y <= 8.2e-58)
		tmp = Float64(x / Float64(z * 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 <= -2.1e-43)
		tmp = x / ((t - z) * y);
	elseif (y <= -1.75e-304)
		tmp = 1.0 / (z * (z / x));
	elseif (y <= 1.02e-73)
		tmp = x / (t * (y - z));
	elseif (y <= 8.2e-58)
		tmp = x / (z * 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, -2.1e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e-304], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.02e-73], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-58], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.1000000000000001e-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 -2.1000000000000001e-43 < y < -1.75e-304

   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%

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

   6. Applied egg-rr 72.3%

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

      1. unpow-1 72.3%

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

      2. *-lft-identity 72.3%

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

      3. times-frac 76.3%

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

      4. /-rgt-identity 76.3%

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

   8. Simplified 76.3%

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

   if -1.75e-304 < y < 1.0199999999999999e-73

   1. Initial program 88.1%

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

   2. Taylor expanded in t around inf 63.7%

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

   if 1.0199999999999999e-73 < y < 8.20000000000000056e-58

   1. Initial program 91.9%

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

   2. Taylor expanded in z around inf 53.5%

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

      1. unpow2 53.5%

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

   4. Simplified 53.5%

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

   if 8.20000000000000056e-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 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-304}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 3: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-308}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.8e-44)
   (/ (/ x y) (- t z))
   (if (<= y 2e-308)
     (/ 1.0 (* z (/ z x)))
     (if (<= y 5.5e-84)
       (/ x (* t (- y z)))
       (if (<= y 1.65e-57) (/ x (* z z)) (/ (/ x t) (- y z)))))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.8e-44) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2e-308) {
		tmp = 1.0 / (z * (z / x));
	} else if (y <= 5.5e-84) {
		tmp = x / (t * (y - z));
	} else if (y <= 1.65e-57) {
		tmp = x / (z * 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 <= (-5.8d-44)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2d-308) then
        tmp = 1.0d0 / (z * (z / x))
    else if (y <= 5.5d-84) then
        tmp = x / (t * (y - z))
    else if (y <= 1.65d-57) then
        tmp = x / (z * 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 <= -5.8e-44) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2e-308) {
		tmp = 1.0 / (z * (z / x));
	} else if (y <= 5.5e-84) {
		tmp = x / (t * (y - z));
	} else if (y <= 1.65e-57) {
		tmp = x / (z * 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 <= -5.8e-44:
		tmp = (x / y) / (t - z)
	elif y <= 2e-308:
		tmp = 1.0 / (z * (z / x))
	elif y <= 5.5e-84:
		tmp = x / (t * (y - z))
	elif y <= 1.65e-57:
		tmp = x / (z * 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 <= -5.8e-44)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2e-308)
		tmp = Float64(1.0 / Float64(z * Float64(z / x)));
	elseif (y <= 5.5e-84)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (y <= 1.65e-57)
		tmp = Float64(x / Float64(z * 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 <= -5.8e-44)
		tmp = (x / y) / (t - z);
	elseif (y <= 2e-308)
		tmp = 1.0 / (z * (z / x));
	elseif (y <= 5.5e-84)
		tmp = x / (t * (y - z));
	elseif (y <= 1.65e-57)
		tmp = x / (z * 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, -5.8e-44], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-308], N[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e-84], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-57], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.8000000000000003e-44

   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. associate-/r* 87.2%

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

   4. Simplified 87.2%

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

   if -5.8000000000000003e-44 < y < 1.9999999999999998e-308

   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%

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

   6. Applied egg-rr 72.3%

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

      1. unpow-1 72.3%

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

      2. *-lft-identity 72.3%

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

      3. times-frac 76.3%

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

      4. /-rgt-identity 76.3%

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

   8. Simplified 76.3%

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

   if 1.9999999999999998e-308 < y < 5.50000000000000019e-84

   1. Initial program 87.8%

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

   2. Taylor expanded in t around inf 65.2%

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

   if 5.50000000000000019e-84 < y < 1.6499999999999999e-57

   1. Initial program 93.3%

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

   2. Taylor expanded in z around inf 61.3%

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

      1. unpow2 61.3%

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

   4. Simplified 61.3%

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

   if 1.6499999999999999e-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 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-308}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 4: 81.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.6e+42)
   (/ (/ x y) (- t z))
   (if (<= y -3.3e-13)
     (/ (/ (- x) z) (- y z))
     (if (<= y -1.9e-43)
       (/ x (* (- t z) y))
       (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 <= -7.6e+42) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3.3e-13) {
		tmp = (-x / z) / (y - z);
	} else if (y <= -1.9e-43) {
		tmp = x / ((t - z) * y);
	} 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 <= (-7.6d+42)) then
        tmp = (x / y) / (t - z)
    else if (y <= (-3.3d-13)) then
        tmp = (-x / z) / (y - z)
    else if (y <= (-1.9d-43)) then
        tmp = x / ((t - z) * y)
    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 <= -7.6e+42) {
		tmp = (x / y) / (t - z);
	} else if (y <= -3.3e-13) {
		tmp = (-x / z) / (y - z);
	} else if (y <= -1.9e-43) {
		tmp = x / ((t - z) * y);
	} 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 <= -7.6e+42:
		tmp = (x / y) / (t - z)
	elif y <= -3.3e-13:
		tmp = (-x / z) / (y - z)
	elif y <= -1.9e-43:
		tmp = x / ((t - z) * y)
	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 <= -7.6e+42)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= -3.3e-13)
		tmp = Float64(Float64(Float64(-x) / z) / Float64(y - z));
	elseif (y <= -1.9e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= 1.7e-57)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7.6e+42)
		tmp = (x / y) / (t - z);
	elseif (y <= -3.3e-13)
		tmp = (-x / z) / (y - z);
	elseif (y <= -1.9e-43)
		tmp = x / ((t - z) * y);
	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, -7.6e+42], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-13], N[(N[((-x) / z), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.9e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-57], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.5999999999999997e42

   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. associate-/r* 91.4%

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

   4. Simplified 91.4%

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

   if -7.5999999999999997e42 < y < -3.3000000000000001e-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%

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

      1. mul-1-neg 68.5%

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

      2. distribute-frac-neg 68.5%

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

      3. 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 -3.3000000000000001e-13 < y < -1.89999999999999985e-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 -1.89999999999999985e-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/ 91.3%

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

      2. *-commutative 91.3%

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

      3. *-rgt-identity 91.3%

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

      4. associate-/r* 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in y around 0 75.4%

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

      1. associate-/r* 81.8%

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

   8. Simplified 81.8%

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

   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 5 regimes into one program.

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{-x}{z}}{y - z}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 5: 67.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (/ 1.0 (* z (/ z x)))))
   (if (<= z -6.2e+46)
     t_1
     (if (<= z -1.7e-13)
       (/ (- x) (* z y))
       (if (<= z 2.15e+17) (/ (/ x t) y) 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 <= -6.2e+46) {
		tmp = t_1;
	} else if (z <= -1.7e-13) {
		tmp = -x / (z * y);
	} else if (z <= 2.15e+17) {
		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 = 1.0d0 / (z * (z / x))
    if (z <= (-6.2d+46)) then
        tmp = t_1
    else if (z <= (-1.7d-13)) then
        tmp = -x / (z * y)
    else if (z <= 2.15d+17) 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 = 1.0 / (z * (z / x));
	double tmp;
	if (z <= -6.2e+46) {
		tmp = t_1;
	} else if (z <= -1.7e-13) {
		tmp = -x / (z * y);
	} else if (z <= 2.15e+17) {
		tmp = (x / t) / y;
	} 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 <= -6.2e+46:
		tmp = t_1
	elif z <= -1.7e-13:
		tmp = -x / (z * y)
	elif z <= 2.15e+17:
		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(1.0 / Float64(z * Float64(z / x)))
	tmp = 0.0
	if (z <= -6.2e+46)
		tmp = t_1;
	elseif (z <= -1.7e-13)
		tmp = Float64(Float64(-x) / Float64(z * y));
	elseif (z <= 2.15e+17)
		tmp = Float64(Float64(x / 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 = 1.0 / (z * (z / x));
	tmp = 0.0;
	if (z <= -6.2e+46)
		tmp = t_1;
	elseif (z <= -1.7e-13)
		tmp = -x / (z * y);
	elseif (z <= 2.15e+17)
		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[(1.0 / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+46], t$95$1, If[LessEqual[z, -1.7e-13], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+17], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1999999999999995e46 or 2.15e17 < 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%

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

   6. Applied egg-rr 73.7%

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

      1. unpow-1 73.7%

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

      2. *-lft-identity 73.7%

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

      3. times-frac 77.4%

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

      4. /-rgt-identity 77.4%

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

   8. Simplified 77.4%

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

   if -6.1999999999999995e46 < z < -1.70000000000000008e-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. associate-*r/ 52.9%

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

      2. neg-mul-1 52.9%

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

   7. Simplified 52.9%

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

   if -1.70000000000000008e-13 < z < 2.15e17

   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%

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

      1. associate-/r* 62.7%

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

   4. Simplified 62.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-13}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 6: 72.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-13}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -2.65e+53)
     t_1
     (if (<= z -3e-13)
       (/ (- x) (* z y))
       (if (<= z 1.26e+28) (/ 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 <= -2.65e+53) {
		tmp = t_1;
	} else if (z <= -3e-13) {
		tmp = -x / (z * y);
	} else if (z <= 1.26e+28) {
		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 <= (-2.65d+53)) then
        tmp = t_1
    else if (z <= (-3d-13)) then
        tmp = -x / (z * y)
    else if (z <= 1.26d+28) 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 <= -2.65e+53) {
		tmp = t_1;
	} else if (z <= -3e-13) {
		tmp = -x / (z * y);
	} else if (z <= 1.26e+28) {
		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 <= -2.65e+53:
		tmp = t_1
	elif z <= -3e-13:
		tmp = -x / (z * y)
	elif z <= 1.26e+28:
		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 <= -2.65e+53)
		tmp = t_1;
	elseif (z <= -3e-13)
		tmp = Float64(Float64(-x) / Float64(z * y));
	elseif (z <= 1.26e+28)
		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 <= -2.65e+53)
		tmp = t_1;
	elseif (z <= -3e-13)
		tmp = -x / (z * y);
	elseif (z <= 1.26e+28)
		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, -2.65e+53], t$95$1, If[LessEqual[z, -3e-13], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.26e+28], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6500000000000001e53 or 1.26e28 < 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%

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

   6. Applied egg-rr 73.9%

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

      1. unpow-1 73.9%

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

      2. *-lft-identity 73.9%

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

      3. times-frac 77.6%

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

      4. /-rgt-identity 77.6%

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

   8. Simplified 77.6%

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

   if -2.6500000000000001e53 < z < -2.99999999999999984e-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. associate-*r/ 52.9%

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

      2. neg-mul-1 52.9%

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

   7. Simplified 52.9%

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

   if -2.99999999999999984e-13 < z < 1.26e28

   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 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+53}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-13}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 7: 63.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-11}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2120000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 -1.65e+47)
     t_1
     (if (<= z -1.06e-11)
       (/ (- x) (* z y))
       (if (<= z 2120000000.0) (/ (/ 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 <= -1.65e+47) {
		tmp = t_1;
	} else if (z <= -1.06e-11) {
		tmp = -x / (z * y);
	} else if (z <= 2120000000.0) {
		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 <= (-1.65d+47)) then
        tmp = t_1
    else if (z <= (-1.06d-11)) then
        tmp = -x / (z * y)
    else if (z <= 2120000000.0d0) 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 <= -1.65e+47) {
		tmp = t_1;
	} else if (z <= -1.06e-11) {
		tmp = -x / (z * y);
	} else if (z <= 2120000000.0) {
		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 <= -1.65e+47:
		tmp = t_1
	elif z <= -1.06e-11:
		tmp = -x / (z * y)
	elif z <= 2120000000.0:
		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(x / Float64(z * z))
	tmp = 0.0
	if (z <= -1.65e+47)
		tmp = t_1;
	elseif (z <= -1.06e-11)
		tmp = Float64(Float64(-x) / Float64(z * y));
	elseif (z <= 2120000000.0)
		tmp = Float64(Float64(x / 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 <= -1.65e+47)
		tmp = t_1;
	elseif (z <= -1.06e-11)
		tmp = -x / (z * y);
	elseif (z <= 2120000000.0)
		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[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.65e+47], t$95$1, If[LessEqual[z, -1.06e-11], N[((-x) / N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2120000000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65e47 or 2.12e9 < 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%

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

   if -1.65e47 < z < -1.05999999999999993e-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. associate-*r/ 52.9%

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

      2. neg-mul-1 52.9%

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

   7. Simplified 52.9%

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

   if -1.05999999999999993e-11 < z < 2.12e9

   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%

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

      1. associate-/r* 62.7%

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

   4. Simplified 62.7%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+47}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-11}:\\ \;\;\;\;\frac{-x}{z \cdot y}\\ \mathbf{elif}\;z \leq 2120000000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]

Alternative 8: 72.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-305}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.55e-43)
   (/ x (* (- t z) y))
   (if (<= y -4.2e-305) (/ 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 <= -3.55e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= -4.2e-305) {
		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 <= (-3.55d-43)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-4.2d-305)) 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 <= -3.55e-43) {
		tmp = x / ((t - z) * y);
	} else if (y <= -4.2e-305) {
		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 <= -3.55e-43:
		tmp = x / ((t - z) * y)
	elif y <= -4.2e-305:
		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 <= -3.55e-43)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -4.2e-305)
		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 <= -3.55e-43)
		tmp = x / ((t - z) * y);
	elseif (y <= -4.2e-305)
		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, -3.55e-43], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.2e-305], 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 < -3.55000000000000013e-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 -3.55000000000000013e-43 < y < -4.2e-305

   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%

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

   6. Applied egg-rr 72.3%

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

      1. unpow-1 72.3%

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

      2. *-lft-identity 72.3%

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

      3. times-frac 76.3%

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

      4. /-rgt-identity 76.3%

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

   8. Simplified 76.3%

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

   if -4.2e-305 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.55 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-305}:\\ \;\;\;\;\frac{1}{z \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 9: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.8e-43)
   (/ (/ x y) (- t z))
   (if (<= y 2.1e-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 <= -2.8e-43) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.1e-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 <= (-2.8d-43)) then
        tmp = (x / y) / (t - z)
    else if (y <= 2.1d-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 <= -2.8e-43) {
		tmp = (x / y) / (t - z);
	} else if (y <= 2.1e-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 <= -2.8e-43:
		tmp = (x / y) / (t - z)
	elif y <= 2.1e-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 <= -2.8e-43)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 2.1e-57)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(Float64(x / t) / Float64(y - z));
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.8e-43)
		tmp = (x / y) / (t - z);
	elseif (y <= 2.1e-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, -2.8e-43], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e-57], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7999999999999998e-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. associate-/r* 87.2%

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

   4. Simplified 87.2%

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

   if -2.7999999999999998e-43 < y < 2.0999999999999999e-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/ 91.3%

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

      2. *-commutative 91.3%

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

      3. *-rgt-identity 91.3%

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

      4. associate-/r* 95.8%

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

   5. Simplified 95.8%

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

   6. Taylor expanded in y around 0 75.4%

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

      1. associate-/r* 81.8%

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

   8. Simplified 81.8%

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

   if 2.0999999999999999e-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 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-43}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]

Alternative 10: 90.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.95e+159) (/ (/ x y) (- 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 <= -2.95e+159) {
		tmp = (x / y) / (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 <= (-2.95d+159)) then
        tmp = (x / y) / (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 <= -2.95e+159) {
		tmp = (x / y) / (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 <= -2.95e+159:
		tmp = (x / y) / (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 <= -2.95e+159)
		tmp = Float64(Float64(x / y) / 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 <= -2.95e+159)
		tmp = (x / y) / (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, -2.95e+159], N[(N[(x / y), $MachinePrecision] / N[(t - z), $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 < -2.94999999999999996e159

   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. associate-/r* 95.9%

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

   4. Simplified 95.9%

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

   if -2.94999999999999996e159 < 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 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+159}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 11: 90.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+161}:\\ \;\;\;\;\frac{x \cdot \frac{1}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -7.2e+161) (/ (* x (/ 1.0 y)) (- 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 <= -7.2e+161) {
		tmp = (x * (1.0 / y)) / (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 <= (-7.2d+161)) then
        tmp = (x * (1.0d0 / y)) / (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 <= -7.2e+161) {
		tmp = (x * (1.0 / y)) / (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 <= -7.2e+161:
		tmp = (x * (1.0 / y)) / (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 <= -7.2e+161)
		tmp = Float64(Float64(x * Float64(1.0 / y)) / 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 <= -7.2e+161)
		tmp = (x * (1.0 / y)) / (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, -7.2e+161], N[(N[(x * N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / N[(t - z), $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 < -7.19999999999999967e161

   1. Initial program 77.1%

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

      1. associate-/r* 96.9%

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

   3. Simplified 96.9%

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

      1. clear-num 96.8%

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

      2. associate-/r/ 96.8%

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

   5. Applied egg-rr 96.8%

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

   6. Taylor expanded in y around inf 95.8%

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

   if -7.19999999999999967e161 < 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 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+161}:\\ \;\;\;\;\frac{x \cdot \frac{1}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \end{array} \]

Alternative 12: 46.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+154} \lor \neg \left(z \leq 4.4 \cdot 10^{+69}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -3.4e+154) (not (<= z 4.4e+69))) (/ x (* t z)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+154) || !(z <= 4.4e+69)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Fortran

NOTE: y and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.4d+154)) .or. (.not. (z <= 4.4d+69))) then
        tmp = x / (t * z)
    else
        tmp = x / (t * y)
    end if
    code = tmp
end function

Java

assert y < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+154) || !(z <= 4.4e+69)) {
		tmp = x / (t * z);
	} else {
		tmp = x / (t * y);
	}
	return tmp;
}

Python

[y, t] = sort([y, t])
def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e+154) or not (z <= 4.4e+69):
		tmp = x / (t * z)
	else:
		tmp = x / (t * y)
	return tmp

Julia

y, t = sort([y, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e+154) || !(z <= 4.4e+69))
		tmp = Float64(x / Float64(t * 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 <= -3.4e+154) || ~((z <= 4.4e+69)))
		tmp = x / (t * z);
	else
		tmp = x / (t * y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e+154], N[Not[LessEqual[z, 4.4e+69]], $MachinePrecision]], N[(x / N[(t * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.39999999999999974e154 or 4.4000000000000003e69 < z

   1. Initial program 82.8%

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

   2. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. distribute-frac-neg 79.8%

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

      3. associate-/r* 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in z around 0 38.1%

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

      1. associate-*r/ 38.1%

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

      2. neg-mul-1 38.1%

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

      3. *-commutative 38.1%

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

   7. Simplified 38.1%

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

      1. expm1-log1p-u 37.9%

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

      2. expm1-udef 65.8%

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

      3. add-sqr-sqrt 34.0%

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

      4. sqrt-unprod 62.5%

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

      5. sqr-neg 62.5%

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

      6. sqrt-unprod 31.3%

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

      7. add-sqr-sqrt 65.3%

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

      8. *-commutative 65.3%

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

   9. Applied egg-rr 65.3%

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

       1. expm1-def 36.3%

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

       2. expm1-log1p 36.5%

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

   11. Simplified 36.5%

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

   if -3.39999999999999974e154 < z < 4.4000000000000003e69

   1. Initial program 93.8%

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

   2. Taylor expanded in z around 0 51.2%

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

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+154} \lor \neg \left(z \leq 4.4 \cdot 10^{+69}\right):\\ \;\;\;\;\frac{x}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 13: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-9} \lor \neg \left(z \leq 27000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \end{array} \]

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 -1.35e-9) (not (<= z 27000000.0))) (/ x (* z z)) (/ x (* t y))))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.35e-9) || !(z <= 27000000.0)) {
		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 <= (-1.35d-9)) .or. (.not. (z <= 27000000.0d0))) 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 <= -1.35e-9) || !(z <= 27000000.0)) {
		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 <= -1.35e-9) or not (z <= 27000000.0):
		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 <= -1.35e-9) || !(z <= 27000000.0))
		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 <= -1.35e-9) || ~((z <= 27000000.0)))
		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, -1.35e-9], N[Not[LessEqual[z, 27000000.0]], $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 < -1.3500000000000001e-9 or 2.7e7 < 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 -1.3500000000000001e-9 < z < 2.7e7

   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%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-9} \lor \neg \left(z \leq 27000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \end{array} \]

Alternative 14: 64.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [y, t] = \mathsf{sort}([y, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-9} \lor \neg \left(z \leq 135000000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: y and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.4e-9) (not (<= z 135000000000.0)))
   (/ x (* z z))
   (/ (/ x t) y)))

C

assert(y < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.4e-9) || !(z <= 135000000000.0)) {
		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 <= (-7.4d-9)) .or. (.not. (z <= 135000000000.0d0))) 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 <= -7.4e-9) || !(z <= 135000000000.0)) {
		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 <= -7.4e-9) or not (z <= 135000000000.0):
		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 <= -7.4e-9) || !(z <= 135000000000.0))
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

y, t = num2cell(sort([y, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.4e-9) || ~((z <= 135000000000.0)))
		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, -7.4e-9], N[Not[LessEqual[z, 135000000000.0]], $MachinePrecision]], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.4e-9 or 1.35e11 < 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 -7.4e-9 < z < 1.35e11

   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%

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

      1. associate-/r* 62.2%

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

   4. Simplified 62.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.4 \cdot 10^{-9} \lor \neg \left(z \leq 135000000000\right):\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]

Alternative 15: 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%

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

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))))