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

Percentage Accurate: 89.2% → 96.7%

Time: 8.9s

Alternatives: 12

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.2% 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: 96.7% accurate, 0.8× speedup

Math

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

FPCore

NOTE: x, y, z, 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(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (x / (t - z)) / (y - z);
}

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, 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 91.3%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l/ N/A

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

   4. lower-/.f64 N/A

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

   5. lower-/.f64 97.6

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

4. Applied rewrites 97.6%

   \[\leadsto \color{blue}{\frac{\frac{x}{t - z}}{y - z}} \]
5. Add Preprocessing

Alternative 2: 60.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, 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 -4.7e-42)
     t_1
     (if (<= z 2e-148)
       (/ x (* y t))
       (if (<= z 3.1e+29) (/ x (* (- z) y)) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -4.7e-42) {
		tmp = t_1;
	} else if (z <= 2e-148) {
		tmp = x / (y * t);
	} else if (z <= 3.1e+29) {
		tmp = x / (-z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-4.7d-42)) then
        tmp = t_1
    else if (z <= 2d-148) then
        tmp = x / (y * t)
    else if (z <= 3.1d+29) then
        tmp = x / (-z * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -4.7e-42) {
		tmp = t_1;
	} else if (z <= 2e-148) {
		tmp = x / (y * t);
	} else if (z <= 3.1e+29) {
		tmp = x / (-z * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -4.7e-42:
		tmp = t_1
	elif z <= 2e-148:
		tmp = x / (y * t)
	elif z <= 3.1e+29:
		tmp = x / (-z * y)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -4.7e-42)
		tmp = t_1;
	elseif (z <= 2e-148)
		tmp = Float64(x / Float64(y * t));
	elseif (z <= 3.1e+29)
		tmp = Float64(x / Float64(Float64(-z) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -4.7e-42)
		tmp = t_1;
	elseif (z <= 2e-148)
		tmp = x / (y * t);
	elseif (z <= 3.1e+29)
		tmp = x / (-z * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, 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, -4.7e-42], t$95$1, If[LessEqual[z, 2e-148], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.1e+29], N[(x / N[((-z) * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.7000000000000001e-42 or 3.0999999999999999e29 < z

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 72.6

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

   5. Applied rewrites 72.6%

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

   if -4.7000000000000001e-42 < z < 1.99999999999999987e-148

   1. Initial program 97.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 69.0

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

   5. Applied rewrites 69.0%

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

   if 1.99999999999999987e-148 < z < 3.0999999999999999e29

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 61.1

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

   5. Applied rewrites 61.1%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 34.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-48)
   (/ x (* y (- t z)))
   (if (<= y 3.5e-32) (/ x (* (- z t) z)) (/ (/ x y) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-48) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.5e-32) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-9d-48)) then
        tmp = x / (y * (t - z))
    else if (y <= 3.5d-32) then
        tmp = x / ((z - t) * z)
    else
        tmp = (x / y) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-48) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.5e-32) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = (x / y) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -9e-48:
		tmp = x / (y * (t - z))
	elif y <= 3.5e-32:
		tmp = x / ((z - t) * z)
	else:
		tmp = (x / y) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-48)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 3.5e-32)
		tmp = Float64(x / Float64(Float64(z - t) * z));
	else
		tmp = Float64(Float64(x / y) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e-48)
		tmp = x / (y * (t - z));
	elseif (y <= 3.5e-32)
		tmp = x / ((z - t) * z);
	else
		tmp = (x / y) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -9e-48], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-32], N[(x / N[(N[(z - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999977e-48

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -8.99999999999999977e-48 < y < 3.4999999999999999e-32

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. remove-double-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if 3.4999999999999999e-32 < y

   1. Initial program 86.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 96.5

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

   4. Applied rewrites 96.5%

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

   5. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 58.6

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

   7. Applied rewrites 58.6%

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

   9. Applied rewrites 58.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-48)
   (/ x (* y (- t z)))
   (if (<= y 3.5e-32) (/ x (* (- z t) z)) (/ (/ x t) y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-48) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.5e-32) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-9d-48)) then
        tmp = x / (y * (t - z))
    else if (y <= 3.5d-32) then
        tmp = x / ((z - t) * z)
    else
        tmp = (x / t) / y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-48) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.5e-32) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = (x / t) / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -9e-48:
		tmp = x / (y * (t - z))
	elif y <= 3.5e-32:
		tmp = x / ((z - t) * z)
	else:
		tmp = (x / t) / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-48)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 3.5e-32)
		tmp = Float64(x / Float64(Float64(z - t) * z));
	else
		tmp = Float64(Float64(x / t) / y);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e-48)
		tmp = x / (y * (t - z));
	elseif (y <= 3.5e-32)
		tmp = x / ((z - t) * z);
	else
		tmp = (x / t) / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -9e-48], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e-32], N[(x / N[(N[(z - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999977e-48

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -8.99999999999999977e-48 < y < 3.4999999999999999e-32

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. remove-double-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 78.3

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

   5. Applied rewrites 78.3%

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

   if 3.4999999999999999e-32 < y

   1. Initial program 86.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 96.5

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

   4. Applied rewrites 96.5%

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

   5. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 58.6

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

   7. Applied rewrites 58.6%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-48)
   (/ x (* y (- t z)))
   (if (<= y 3.7e-84) (/ x (* (- z t) z)) (/ x (* (- y z) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-48) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.7e-84) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-9d-48)) then
        tmp = x / (y * (t - z))
    else if (y <= 3.7d-84) then
        tmp = x / ((z - t) * z)
    else
        tmp = x / ((y - z) * t)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-48) {
		tmp = x / (y * (t - z));
	} else if (y <= 3.7e-84) {
		tmp = x / ((z - t) * z);
	} else {
		tmp = x / ((y - z) * t);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -9e-48:
		tmp = x / (y * (t - z))
	elif y <= 3.7e-84:
		tmp = x / ((z - t) * z)
	else:
		tmp = x / ((y - z) * t)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-48)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (y <= 3.7e-84)
		tmp = Float64(x / Float64(Float64(z - t) * z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * t));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e-48)
		tmp = x / (y * (t - z));
	elseif (y <= 3.7e-84)
		tmp = x / ((z - t) * z);
	else
		tmp = x / ((y - z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -9e-48], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-84], N[(x / N[(N[(z - t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.99999999999999977e-48

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 82.0

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

   5. Applied rewrites 82.0%

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

   if -8.99999999999999977e-48 < y < 3.6999999999999999e-84

   1. Initial program 93.7%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. remove-double-neg N/A

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

      9. unsub-neg N/A

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

      10. lower--.f64 79.4

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

   5. Applied rewrites 79.4%

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

   if 3.6999999999999999e-84 < y

   1. Initial program 88.7%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 60.6

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

   5. Applied rewrites 60.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-48}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{\left(z - t\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -8.4 \cdot 10^{+83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, 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 -8.4e+83) t_1 (if (<= z 7.2e+30) (/ x (* y (- t z))) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -8.4e+83) {
		tmp = t_1;
	} else if (z <= 7.2e+30) {
		tmp = x / (y * (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-8.4d+83)) then
        tmp = t_1
    else if (z <= 7.2d+30) then
        tmp = x / (y * (t - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -8.4e+83) {
		tmp = t_1;
	} else if (z <= 7.2e+30) {
		tmp = x / (y * (t - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -8.4e+83:
		tmp = t_1
	elif z <= 7.2e+30:
		tmp = x / (y * (t - z))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -8.4e+83)
		tmp = t_1;
	elseif (z <= 7.2e+30)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -8.4e+83)
		tmp = t_1;
	elseif (z <= 7.2e+30)
		tmp = x / (y * (t - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, 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, -8.4e+83], t$95$1, If[LessEqual[z, 7.2e+30], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4000000000000001e83 or 7.2000000000000004e30 < z

   1. Initial program 86.9%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 81.9

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

   5. Applied rewrites 81.9%

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

   if -8.4000000000000001e83 < z < 7.2000000000000004e30

   1. Initial program 94.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 69.7

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

   5. Applied rewrites 69.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -6 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, 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 -6e-41) t_1 (if (<= z 5.6e+30) (/ x (* (- y z) t)) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -6e-41) {
		tmp = t_1;
	} else if (z <= 5.6e+30) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-6d-41)) then
        tmp = t_1
    else if (z <= 5.6d+30) then
        tmp = x / ((y - z) * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -6e-41) {
		tmp = t_1;
	} else if (z <= 5.6e+30) {
		tmp = x / ((y - z) * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -6e-41:
		tmp = t_1
	elif z <= 5.6e+30:
		tmp = x / ((y - z) * t)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -6e-41)
		tmp = t_1;
	elseif (z <= 5.6e+30)
		tmp = Float64(x / Float64(Float64(y - z) * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -6e-41)
		tmp = t_1;
	elseif (z <= 5.6e+30)
		tmp = x / ((y - z) * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, 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, -6e-41], t$95$1, If[LessEqual[z, 5.6e+30], N[(x / N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999978e-41 or 5.59999999999999966e30 < z

   1. Initial program 86.5%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 73.1

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

   5. Applied rewrites 73.1%

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

   if -5.99999999999999978e-41 < z < 5.59999999999999966e30

   1. Initial program 95.8%

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

   3. Taylor expanded in t around inf

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

      1. lower-*.f64 N/A

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

      2. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+200}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.9e+200) (/ (/ x y) (- t z)) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.9e+200) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-4.9d+200)) then
        tmp = (x / y) / (t - z)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.9e+200) {
		tmp = (x / y) / (t - z);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -4.9e+200:
		tmp = (x / y) / (t - z)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.9e+200)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.9e+200)
		tmp = (x / y) / (t - z);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -4.9e+200], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.89999999999999982e200

   1. Initial program 84.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around 0

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

      1. lower-/.f64 99.8

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

   7. Applied rewrites 99.8%

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

   if -4.89999999999999982e200 < y

   1. Initial program 91.9%

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

Alternative 9: 91.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+115}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -3.05e+115) (/ (/ x z) (- z t)) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.05e+115) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-3.05d+115)) then
        tmp = (x / z) / (z - t)
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -3.05e+115) {
		tmp = (x / z) / (z - t);
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -3.05e+115:
		tmp = (x / z) / (z - t)
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -3.05e+115)
		tmp = Float64(Float64(x / z) / Float64(z - t));
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -3.05e+115)
		tmp = (x / z) / (z - t);
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -3.05e+115], N[(N[(x / z), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.04999999999999983e115

   1. Initial program 85.5%

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

   3. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. remove-double-neg N/A

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

      12. unsub-neg N/A

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

      13. lower--.f64 96.7

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

   5. Applied rewrites 96.7%

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

   if -3.04999999999999983e115 < z

   1. Initial program 92.7%

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

Alternative 10: 61.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -4.7 \cdot 10^{-42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, 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 -4.7e-42) t_1 (if (<= z 9.5e-5) (/ x (* y t)) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -4.7e-42) {
		tmp = t_1;
	} else if (z <= 9.5e-5) {
		tmp = x / (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, 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 <= (-4.7d-42)) then
        tmp = t_1
    else if (z <= 9.5d-5) then
        tmp = x / (y * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -4.7e-42) {
		tmp = t_1;
	} else if (z <= 9.5e-5) {
		tmp = x / (y * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -4.7e-42:
		tmp = t_1
	elif z <= 9.5e-5:
		tmp = x / (y * t)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -4.7e-42)
		tmp = t_1;
	elseif (z <= 9.5e-5)
		tmp = Float64(x / Float64(y * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -4.7e-42)
		tmp = t_1;
	elseif (z <= 9.5e-5)
		tmp = x / (y * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, 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, -4.7e-42], t$95$1, If[LessEqual[z, 9.5e-5], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.7000000000000001e-42 or 9.5000000000000005e-5 < z

   1. Initial program 87.2%

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

   3. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. lower-*.f64 70.3

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

   5. Applied rewrites 70.3%

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

   if -4.7000000000000001e-42 < z < 9.5000000000000005e-5

   1. Initial program 95.6%

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

   3. Taylor expanded in z around 0

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

      1. lower-*.f64 60.1

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

   5. Applied rewrites 60.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 89.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.8e+94) (/ (/ x t) y) (/ x (* (- y z) (- t z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e+94) {
		tmp = (x / t) / y;
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.8d+94)) then
        tmp = (x / t) / y
    else
        tmp = x / ((y - z) * (t - z))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.8e+94) {
		tmp = (x / t) / y;
	} else {
		tmp = x / ((y - z) * (t - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -4.8e+94:
		tmp = (x / t) / y
	else:
		tmp = x / ((y - z) * (t - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.8e+94)
		tmp = Float64(Float64(x / t) / y);
	else
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - z)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.8e+94)
		tmp = (x / t) / y;
	else
		tmp = x / ((y - z) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[t, -4.8e+94], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.79999999999999965e94

   1. Initial program 79.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 97.9

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

   4. Applied rewrites 97.9%

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

   5. Taylor expanded in z around 0

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

      1. associate-/r* N/A

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

      2. lower-/.f64 N/A

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

      3. lower-/.f64 63.8

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

   7. Applied rewrites 63.8%

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

   if -4.79999999999999965e94 < t

   1. Initial program 94.2%

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

Alternative 12: 40.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

3. Taylor expanded in z around 0

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

   1. lower-*.f64 38.2

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

5. Applied rewrites 38.2%

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

6. Final simplification 38.2%

   \[\leadsto \frac{x}{y \cdot t} \]
7. Add Preprocessing

Developer Target 1: 88.0% 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 2024267 
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (/ x (* (- y z) (- t z))) 0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z))))))

  (/ x (* (- y z) (- t z))))