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

Percentage Accurate: 88.5% → 96.6%

Time: 8.7s

Alternatives: 11

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: 88.5% 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: 96.6% accurate, 0.2× speedup

Math

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

FPCore

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

C

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

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 = ((y - z) ** (-1.0d0)) / ((t - z) / x)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = ((y - z) ^ -1.0) / ((t - z) / x);
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[Power[N[(y - z), $MachinePrecision], -1.0], $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.1%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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. clear-num N/A

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

   3. lift-*.f64 N/A

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

   4. associate-/l* N/A

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

   5. associate-/r* N/A

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

   6. lift--.f64 N/A

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

   7. flip-- N/A

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

   8. clear-num N/A

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

   9. lower-/.f64 N/A

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

   10. clear-num N/A

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

   11. flip-- N/A

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

   12. lift--.f64 N/A

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

   13. inv-pow N/A

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

   14. lower-pow.f64 N/A

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

   15. lower-/.f64 97.4

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

4. Applied rewrites 97.4%

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

Alternative 2: 91.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \end{array} \end{array} \]

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 (* (- t z) (- y z))))
   (if (<= t_1 5e+297) (/ x t_1) (/ (/ x (- z y)) z))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= 5e+297) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - y)) / 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) :: t_1
    real(8) :: tmp
    t_1 = (t - z) * (y - z)
    if (t_1 <= 5d+297) then
        tmp = x / t_1
    else
        tmp = (x / (z - y)) / 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 t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= 5e+297) {
		tmp = x / t_1;
	} else {
		tmp = (x / (z - y)) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= 5e+297:
		tmp = x / t_1
	else:
		tmp = (x / (z - y)) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= 5e+297)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(z - y)) / z);
	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 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= 5e+297)
		tmp = x / t_1;
	else
		tmp = (x / (z - y)) / 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_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+297], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(z - y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 4.9999999999999998e297

   1. Initial program 95.1%

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

   if 4.9999999999999998e297 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 77.0%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 84.9

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

   5. Applied rewrites 84.9%

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

   7. Applied rewrites 87.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq 5 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z - y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -4.8e+32)
     t_1
     (if (<= z 5.8e-57)
       (/ x (* t (- y z)))
       (if (<= z 8.5e+82) (/ 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 <= -4.8e+32) {
		tmp = t_1;
	} else if (z <= 5.8e-57) {
		tmp = x / (t * (y - z));
	} else if (z <= 8.5e+82) {
		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 <= (-4.8d+32)) then
        tmp = t_1
    else if (z <= 5.8d-57) then
        tmp = x / (t * (y - z))
    else if (z <= 8.5d+82) 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 <= -4.8e+32) {
		tmp = t_1;
	} else if (z <= 5.8e-57) {
		tmp = x / (t * (y - z));
	} else if (z <= 8.5e+82) {
		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 <= -4.8e+32:
		tmp = t_1
	elif z <= 5.8e-57:
		tmp = x / (t * (y - z))
	elif z <= 8.5e+82:
		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 <= -4.8e+32)
		tmp = t_1;
	elseif (z <= 5.8e-57)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	elseif (z <= 8.5e+82)
		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 <= -4.8e+32)
		tmp = t_1;
	elseif (z <= 5.8e-57)
		tmp = x / (t * (y - z));
	elseif (z <= 8.5e+82)
		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, -4.8e+32], t$95$1, If[LessEqual[z, 5.8e-57], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+82], N[(x / N[((-z) * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.79999999999999983e32 or 8.4999999999999995e82 < z

   1. Initial program 84.9%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 75.1

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

   5. Applied rewrites 75.1%

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

   if -4.79999999999999983e32 < z < 5.8000000000000005e-57

   1. Initial program 94.0%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 71.4

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

   5. Applied rewrites 71.4%

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

   if 5.8000000000000005e-57 < z < 8.4999999999999995e82

   1. Initial program 91.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 47.5

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

   5. Applied rewrites 47.5%

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

   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 38.2%

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

Alternative 4: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-154}:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+82}:\\ \;\;\;\;\frac{x}{\left(-z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2.65e-34)
     t_1
     (if (<= z 2.5e-154)
       (/ x (* t y))
       (if (<= z 8.5e+82) (/ 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 <= -2.65e-34) {
		tmp = t_1;
	} else if (z <= 2.5e-154) {
		tmp = x / (t * y);
	} else if (z <= 8.5e+82) {
		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 <= (-2.65d-34)) then
        tmp = t_1
    else if (z <= 2.5d-154) then
        tmp = x / (t * y)
    else if (z <= 8.5d+82) 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 <= -2.65e-34) {
		tmp = t_1;
	} else if (z <= 2.5e-154) {
		tmp = x / (t * y);
	} else if (z <= 8.5e+82) {
		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 <= -2.65e-34:
		tmp = t_1
	elif z <= 2.5e-154:
		tmp = x / (t * y)
	elif z <= 8.5e+82:
		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 <= -2.65e-34)
		tmp = t_1;
	elseif (z <= 2.5e-154)
		tmp = Float64(x / Float64(t * y));
	elseif (z <= 8.5e+82)
		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 <= -2.65e-34)
		tmp = t_1;
	elseif (z <= 2.5e-154)
		tmp = x / (t * y);
	elseif (z <= 8.5e+82)
		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, -2.65e-34], t$95$1, If[LessEqual[z, 2.5e-154], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+82], N[(x / N[((-z) * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6499999999999998e-34 or 8.4999999999999995e82 < z

   1. Initial program 85.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 70.6

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

   5. Applied rewrites 70.6%

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

   if -2.6499999999999998e-34 < z < 2.5000000000000001e-154

   1. Initial program 93.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 71.9

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

   5. Applied rewrites 71.9%

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

   if 2.5000000000000001e-154 < z < 8.4999999999999995e82

   1. Initial program 94.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 57.6

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

   5. Applied rewrites 57.6%

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

   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 43.4%

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

Alternative 5: 77.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{\left(z - y\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 -1.85e-93)
   (/ x (* (- t z) y))
   (if (<= t 3e-63) (/ x (* (- z y) z)) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.85e-93) {
		tmp = x / ((t - z) * y);
	} else if (t <= 3e-63) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / (t * (y - 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 <= (-1.85d-93)) then
        tmp = x / ((t - z) * y)
    else if (t <= 3d-63) then
        tmp = x / ((z - y) * z)
    else
        tmp = x / (t * (y - 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 <= -1.85e-93) {
		tmp = x / ((t - z) * y);
	} else if (t <= 3e-63) {
		tmp = x / ((z - y) * z);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if t <= -1.85e-93:
		tmp = x / ((t - z) * y)
	elif t <= 3e-63:
		tmp = x / ((z - y) * z)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.85e-93)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 3e-63)
		tmp = Float64(x / Float64(Float64(z - y) * z));
	else
		tmp = Float64(x / Float64(t * Float64(y - 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 <= -1.85e-93)
		tmp = x / ((t - z) * y);
	elseif (t <= 3e-63)
		tmp = x / ((z - y) * z);
	else
		tmp = x / (t * (y - 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, -1.85e-93], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-63], N[(x / N[(N[(z - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.85000000000000001e-93

   1. Initial program 91.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 63.0

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

   5. Applied rewrites 63.0%

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

   if -1.85000000000000001e-93 < t < 2.99999999999999979e-63

   1. Initial program 89.6%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. associate-*r* N/A

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

      3. lower-*.f64 N/A

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

      4. mul-1-neg N/A

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

      5. sub-neg N/A

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

      6. +-commutative N/A

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

      7. distribute-neg-in N/A

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

      8. unsub-neg N/A

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

      9. remove-double-neg N/A

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

      10. lower--.f64 70.1

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

   5. Applied rewrites 70.1%

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

   if 2.99999999999999979e-63 < t

   1. Initial program 89.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 79.0

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

   5. Applied rewrites 79.0%

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

Alternative 6: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \end{array} \end{array} \]

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 -6.1e-65)
   (/ x (* (- t z) y))
   (if (<= y -6e-242) (/ x (* z z)) (/ x (* t (- y z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.1e-65) {
		tmp = x / ((t - z) * y);
	} else if (y <= -6e-242) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * (y - 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 <= (-6.1d-65)) then
        tmp = x / ((t - z) * y)
    else if (y <= (-6d-242)) then
        tmp = x / (z * z)
    else
        tmp = x / (t * (y - 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 <= -6.1e-65) {
		tmp = x / ((t - z) * y);
	} else if (y <= -6e-242) {
		tmp = x / (z * z);
	} else {
		tmp = x / (t * (y - z));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -6.1e-65:
		tmp = x / ((t - z) * y)
	elif y <= -6e-242:
		tmp = x / (z * z)
	else:
		tmp = x / (t * (y - z))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.1e-65)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (y <= -6e-242)
		tmp = Float64(x / Float64(z * z));
	else
		tmp = Float64(x / Float64(t * Float64(y - 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 <= -6.1e-65)
		tmp = x / ((t - z) * y);
	elseif (y <= -6e-242)
		tmp = x / (z * z);
	else
		tmp = x / (t * (y - 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, -6.1e-65], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6e-242], N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.10000000000000014e-65

   1. Initial program 91.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 83.2

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

   5. Applied rewrites 83.2%

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

   if -6.10000000000000014e-65 < y < -6e-242

   1. Initial program 87.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 70.1

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

   5. Applied rewrites 70.1%

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

   if -6e-242 < y

   1. Initial program 89.8%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 62.7

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

   5. Applied rewrites 62.7%

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

Alternative 7: 90.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

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 (<= z 4.5e+133) (/ x (* (- t z) (- y z))) (/ (/ x z) (- z y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 4.5e+133) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - 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 (z <= 4.5d+133) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = (x / z) / (z - 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 (z <= 4.5e+133) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 4.5e+133:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 4.5e+133)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - 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 (z <= 4.5e+133)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (x / z) / (z - 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[z, 4.5e+133], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.49999999999999985e133

   1. Initial program 92.2%

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

   if 4.49999999999999985e133 < z

   1. Initial program 79.4%

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

   3. Taylor expanded in t around 0

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

      4. mul-1-neg N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. mul-1-neg N/A

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

      8. sub-neg N/A

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

      9. +-commutative N/A

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

      10. distribute-neg-in N/A

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

      11. unsub-neg N/A

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

      12. remove-double-neg N/A

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

      13. lower--.f64 97.6

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

   5. Applied rewrites 97.6%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 61.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{-34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2.65e-34) t_1 (if (<= z 0.0018) (/ x (* t 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 <= -2.65e-34) {
		tmp = t_1;
	} else if (z <= 0.0018) {
		tmp = x / (t * 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 <= (-2.65d-34)) then
        tmp = t_1
    else if (z <= 0.0018d0) then
        tmp = x / (t * 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 <= -2.65e-34) {
		tmp = t_1;
	} else if (z <= 0.0018) {
		tmp = x / (t * 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 <= -2.65e-34:
		tmp = t_1
	elif z <= 0.0018:
		tmp = x / (t * 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 <= -2.65e-34)
		tmp = t_1;
	elseif (z <= 0.0018)
		tmp = Float64(x / Float64(t * 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 <= -2.65e-34)
		tmp = t_1;
	elseif (z <= 0.0018)
		tmp = x / (t * 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, -2.65e-34], t$95$1, If[LessEqual[z, 0.0018], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6499999999999998e-34 or 0.0018 < z

   1. Initial program 85.2%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 66.3

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

   5. Applied rewrites 66.3%

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

   if -2.6499999999999998e-34 < z < 0.0018

   1. Initial program 95.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 58.5

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

   5. Applied rewrites 58.5%

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

Alternative 9: 90.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 9 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

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 9e+136) (/ x (* (- t z) (- y z))) (/ (/ x z) z)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 9e+136) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / 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 <= 9d+136) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = (x / z) / 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 <= 9e+136) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / z;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 9e+136:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (x / z) / z
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 9e+136)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / 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 <= 9e+136)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (x / z) / 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, 9e+136], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.9999999999999999e136

   1. Initial program 91.8%

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

   if 8.9999999999999999e136 < z

   1. Initial program 80.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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. clear-num N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. associate-/r* N/A

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

      6. lift--.f64 N/A

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

      7. flip-- N/A

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

      8. clear-num N/A

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

      9. lower-/.f64 N/A

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

      10. clear-num N/A

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

      11. flip-- N/A

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

      12. lift--.f64 N/A

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

      13. inv-pow N/A

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

      14. lower-pow.f64 N/A

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

      15. lower-/.f64 99.8

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in z around inf

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

      1. unpow2 N/A

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

      2. associate-/r* N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 100.0

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

   7. Applied rewrites 100.0%

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

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 9 \cdot 10^{+136}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 96.6% 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 90.1%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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 97.3

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

4. Applied rewrites 97.3%

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

Alternative 11: 40.6% accurate, 1.4× speedup

Math

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

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 y)))

C

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

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 * y)
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 * y);
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 90.1%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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 40.3

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

5. Applied rewrites 40.3%

   \[\leadsto \frac{x}{\color{blue}{t \cdot y}} \]
6. Add Preprocessing

Developer Target 1: 87.4% 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 2024244 
(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))))