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

Percentage Accurate: 89.0% → 97.0%

Time: 13.5s

Alternatives: 15

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 89.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (1.0 / (y - z)) / ((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 = (1.0d0 / (y - z)) / ((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 (1.0 / (y - z)) / ((t - z) / x);
}

Python

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

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(1.0 / Float64(y - z)) / 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 = (1.0 / (y - z)) / ((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[(1.0 / N[(y - z), $MachinePrecision]), $MachinePrecision] / N[(N[(t - z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.0%

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

   1. clear-num N/A

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

   2. associate-/l* N/A

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

   3. associate-/r* N/A

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

   4. flip3-- N/A

      \[\leadsto \frac{\frac{1}{\frac{{y}^{3} - {z}^{3}}{y \cdot y + \left(z \cdot z + y \cdot z\right)}}}{\frac{t - \color{blue}{z}}{x}} \]

   5. clear-num N/A

      \[\leadsto \frac{\frac{y \cdot y + \left(z \cdot z + y \cdot z\right)}{{y}^{3} - {z}^{3}}}{\frac{\color{blue}{t - z}}{x}} \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{y \cdot y + \left(z \cdot z + y \cdot z\right)}{{y}^{3} - {z}^{3}}\right), \color{blue}{\left(\frac{t - z}{x}\right)}\right) \]

   7. clear-num N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{\frac{{y}^{3} - {z}^{3}}{y \cdot y + \left(z \cdot z + y \cdot z\right)}}\right), \left(\frac{\color{blue}{t - z}}{x}\right)\right) \]

   8. flip3-- N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{y - z}\right), \left(\frac{t - \color{blue}{z}}{x}\right)\right) \]

   9. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \left(y - z\right)\right), \left(\frac{\color{blue}{t - z}}{x}\right)\right) \]

   10. --lowering--.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, z\right)\right), \left(\frac{t - \color{blue}{z}}{x}\right)\right) \]

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{/.f64}\left(\left(t - z\right), \color{blue}{x}\right)\right) \]

   12. --lowering--.f64 96.4%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{/.f64}\left(\mathsf{\_.f64}\left(t, z\right), x\right)\right) \]

4. Applied egg-rr 96.4%

   \[\leadsto \color{blue}{\frac{\frac{1}{y - z}}{\frac{t - z}{x}}} \]
5. Add Preprocessing

Alternative 2: 72.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ t_2 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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)) (t_2 (/ x (* z (- z y)))))
   (if (<= z -8.6e+155)
     t_1
     (if (<= z -1.75e-94)
       t_2
       (if (<= z 2.3e-39) (/ (/ x t) y) (if (<= z 6.2e+157) t_2 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 t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -8.6e+155) {
		tmp = t_1;
	} else if (z <= -1.75e-94) {
		tmp = t_2;
	} else if (z <= 2.3e-39) {
		tmp = (x / t) / y;
	} else if (z <= 6.2e+157) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x / z) / z
    t_2 = x / (z * (z - y))
    if (z <= (-8.6d+155)) then
        tmp = t_1
    else if (z <= (-1.75d-94)) then
        tmp = t_2
    else if (z <= 2.3d-39) then
        tmp = (x / t) / y
    else if (z <= 6.2d+157) then
        tmp = t_2
    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 t_2 = x / (z * (z - y));
	double tmp;
	if (z <= -8.6e+155) {
		tmp = t_1;
	} else if (z <= -1.75e-94) {
		tmp = t_2;
	} else if (z <= 2.3e-39) {
		tmp = (x / t) / y;
	} else if (z <= 6.2e+157) {
		tmp = t_2;
	} 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
	t_2 = x / (z * (z - y))
	tmp = 0
	if z <= -8.6e+155:
		tmp = t_1
	elif z <= -1.75e-94:
		tmp = t_2
	elif z <= 2.3e-39:
		tmp = (x / t) / y
	elif z <= 6.2e+157:
		tmp = t_2
	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(Float64(x / z) / z)
	t_2 = Float64(x / Float64(z * Float64(z - y)))
	tmp = 0.0
	if (z <= -8.6e+155)
		tmp = t_1;
	elseif (z <= -1.75e-94)
		tmp = t_2;
	elseif (z <= 2.3e-39)
		tmp = Float64(Float64(x / t) / y);
	elseif (z <= 6.2e+157)
		tmp = t_2;
	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;
	t_2 = x / (z * (z - y));
	tmp = 0.0;
	if (z <= -8.6e+155)
		tmp = t_1;
	elseif (z <= -1.75e-94)
		tmp = t_2;
	elseif (z <= 2.3e-39)
		tmp = (x / t) / y;
	elseif (z <= 6.2e+157)
		tmp = t_2;
	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[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.6e+155], t$95$1, If[LessEqual[z, -1.75e-94], t$95$2, If[LessEqual[z, 2.3e-39], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 6.2e+157], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000005e155 or 6.1999999999999994e157 < z

   1. Initial program 70.9%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({z}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 70.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   5. Simplified 70.9%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{z}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 85.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), z\right) \]

   7. Applied egg-rr 85.5%

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

   if -8.6000000000000005e155 < z < -1.74999999999999999e-94 or 2.30000000000000008e-39 < z < 6.1999999999999994e157

   1. Initial program 95.0%

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

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(y - z\right)\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(y - z\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(z - y\right)\right)\right) \]

      15. --lowering--.f64 63.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 63.9%

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

   if -1.74999999999999999e-94 < z < 2.30000000000000008e-39

   1. Initial program 97.9%

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

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right) \]

      2. *-lowering-*.f64 72.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{y}\right)\right) \]

   5. Simplified 72.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 74.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), y\right) \]

   7. Applied egg-rr 74.8%

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

Alternative 3: 75.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -3.2e+47)
     t_1
     (if (<= z 1.6e-23)
       (/ x (* y (- t z)))
       (if (<= z 6.2e+157) (/ x (* z (- 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 <= -3.2e+47) {
		tmp = t_1;
	} else if (z <= 1.6e-23) {
		tmp = x / (y * (t - z));
	} else if (z <= 6.2e+157) {
		tmp = x / (z * (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 <= (-3.2d+47)) then
        tmp = t_1
    else if (z <= 1.6d-23) then
        tmp = x / (y * (t - z))
    else if (z <= 6.2d+157) then
        tmp = x / (z * (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 <= -3.2e+47) {
		tmp = t_1;
	} else if (z <= 1.6e-23) {
		tmp = x / (y * (t - z));
	} else if (z <= 6.2e+157) {
		tmp = x / (z * (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 <= -3.2e+47:
		tmp = t_1
	elif z <= 1.6e-23:
		tmp = x / (y * (t - z))
	elif z <= 6.2e+157:
		tmp = x / (z * (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(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -3.2e+47)
		tmp = t_1;
	elseif (z <= 1.6e-23)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (z <= 6.2e+157)
		tmp = Float64(x / Float64(z * 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 <= -3.2e+47)
		tmp = t_1;
	elseif (z <= 1.6e-23)
		tmp = x / (y * (t - z));
	elseif (z <= 6.2e+157)
		tmp = x / (z * (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[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -3.2e+47], t$95$1, If[LessEqual[z, 1.6e-23], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+157], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.2e47 or 6.1999999999999994e157 < z

   1. Initial program 75.4%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({z}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   5. Simplified 70.0%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{z}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 81.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), z\right) \]

   7. Applied egg-rr 81.6%

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

   if -3.2e47 < z < 1.59999999999999988e-23

   1. Initial program 97.0%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(y \cdot \left(t - z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t - z\right) \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{y}\right)\right) \]

      4. --lowering--.f64 76.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), y\right)\right) \]

   5. Simplified 76.5%

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

   if 1.59999999999999988e-23 < z < 6.1999999999999994e157

   1. Initial program 96.1%

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

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(y - z\right)\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(y - z\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(z - y\right)\right)\right) \]

      15. --lowering--.f64 74.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 74.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+155}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

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 -8.6e+155)
   (/ (/ x (- z t)) z)
   (if (<= z 6.2e+157) (/ x (* (- y z) (- t 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 <= -8.6e+155) {
		tmp = (x / (z - t)) / z;
	} else if (z <= 6.2e+157) {
		tmp = x / ((y - z) * (t - 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 <= (-8.6d+155)) then
        tmp = (x / (z - t)) / z
    else if (z <= 6.2d+157) then
        tmp = x / ((y - z) * (t - 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 <= -8.6e+155) {
		tmp = (x / (z - t)) / z;
	} else if (z <= 6.2e+157) {
		tmp = x / ((y - z) * (t - 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 <= -8.6e+155:
		tmp = (x / (z - t)) / z
	elif z <= 6.2e+157:
		tmp = x / ((y - z) * (t - 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 <= -8.6e+155)
		tmp = Float64(Float64(x / Float64(z - t)) / z);
	elseif (z <= 6.2e+157)
		tmp = Float64(x / Float64(Float64(y - z) * Float64(t - 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 <= -8.6e+155)
		tmp = (x / (z - t)) / z;
	elseif (z <= 6.2e+157)
		tmp = x / ((y - z) * (t - 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, -8.6e+155], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 6.2e+157], N[(x / N[(N[(y - z), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6000000000000005e155

   1. Initial program 66.5%

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

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{t - z}\right), \color{blue}{z}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{x}{t - z}\right)\right), z\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), z\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{-1 \cdot \left(t - z\right)}\right), z\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(-1 \cdot \left(t - z\right)\right)\right), z\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), z\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right), z\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right)\right), z\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right)\right), z\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right), z\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(z - t\right)\right), z\right) \]

      16. --lowering--.f64 82.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), z\right) \]

   5. Simplified 82.5%

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

   if -8.6000000000000005e155 < z < 6.1999999999999994e157

   1. Initial program 96.5%

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

   if 6.1999999999999994e157 < z

   1. Initial program 74.6%

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

      1. associate-/r* N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. distribute-neg-frac2 N/A

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

      5. associate-*l/ N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - \color{blue}{z}\right)\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(t - z\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      12. associate--r+ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(z - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \color{blue}{\left(y - z\right)}\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \left(y + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{y}\right)\right)\right) \]

      19. associate--r+ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - \color{blue}{y}\right)\right) \]

      20. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - y\right)\right) \]

      21. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(z - y\right)\right) \]

      22. --lowering--.f64 99.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{z}\right)}, \mathsf{\_.f64}\left(z, y\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 91.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\color{blue}{z}, y\right)\right) \]

   7. Simplified 91.0%

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

Alternative 5: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-145}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t}\\ \end{array} \end{array} \]

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 -8e-19)
   (/ (/ x y) (- t z))
   (if (<= y 4.6e-145) (/ (/ 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 <= -8e-19) {
		tmp = (x / y) / (t - z);
	} else if (y <= 4.6e-145) {
		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 <= (-8d-19)) then
        tmp = (x / y) / (t - z)
    else if (y <= 4.6d-145) 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 <= -8e-19) {
		tmp = (x / y) / (t - z);
	} else if (y <= 4.6e-145) {
		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 <= -8e-19:
		tmp = (x / y) / (t - z)
	elif y <= 4.6e-145:
		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 <= -8e-19)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (y <= 4.6e-145)
		tmp = Float64(Float64(x / Float64(z - t)) / z);
	else
		tmp = Float64(Float64(x / 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 <= -8e-19)
		tmp = (x / y) / (t - z);
	elseif (y <= 4.6e-145)
		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, -8e-19], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-145], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.9999999999999998e-19

   1. Initial program 94.1%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{\left(t - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 96.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{y}\right), \mathsf{\_.f64}\left(t, z\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 89.2%

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

   if -7.9999999999999998e-19 < y < 4.60000000000000014e-145

   1. Initial program 88.9%

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

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-*r/ N/A

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

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(-1 \cdot \frac{x}{t - z}\right), \color{blue}{z}\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{x}{t - z}\right)\right), z\right) \]

      7. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), z\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{-1 \cdot \left(t - z\right)}\right), z\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(-1 \cdot \left(t - z\right)\right)\right), z\right) \]

      10. mul-1-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right), z\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right), z\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right)\right), z\right) \]

      13. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \left(\mathsf{neg}\left(t\right)\right)\right)\right), z\right) \]

      14. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right), z\right) \]

      15. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(z - t\right)\right), z\right) \]

      16. --lowering--.f64 81.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(z, t\right)\right), z\right) \]

   5. Simplified 81.5%

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

   if 4.60000000000000014e-145 < y

   1. Initial program 91.2%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{\left(t - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 99.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \color{blue}{t}\right) \]
   6. Step-by-step derivation

   7. Simplified 66.5%

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

Alternative 6: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-28}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.6e-158)
   (/ (/ x (- t z)) y)
   (if (<= t 1.65e-28) (/ (/ x z) (- z y)) (/ (/ 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 <= -2.6e-158) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.65e-28) {
		tmp = (x / z) / (z - y);
	} 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 <= (-2.6d-158)) then
        tmp = (x / (t - z)) / y
    else if (t <= 1.65d-28) then
        tmp = (x / z) / (z - y)
    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 <= -2.6e-158) {
		tmp = (x / (t - z)) / y;
	} else if (t <= 1.65e-28) {
		tmp = (x / z) / (z - y);
	} 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 <= -2.6e-158:
		tmp = (x / (t - z)) / y
	elif t <= 1.65e-28:
		tmp = (x / z) / (z - y)
	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 <= -2.6e-158)
		tmp = Float64(Float64(x / Float64(t - z)) / y);
	elseif (t <= 1.65e-28)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / 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 <= -2.6e-158)
		tmp = (x / (t - z)) / y;
	elseif (t <= 1.65e-28)
		tmp = (x / z) / (z - y);
	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, -2.6e-158], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.65e-28], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6e-158

   1. Initial program 90.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{\left(t - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 96.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{y}\right), \mathsf{\_.f64}\left(t, z\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 56.8%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), y\right) \]

      5. --lowering--.f64 62.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), y\right) \]

   9. Applied egg-rr 62.2%

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

   if -2.6e-158 < t < 1.6500000000000001e-28

   1. Initial program 92.4%

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

      1. associate-/r* N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. distribute-neg-frac2 N/A

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

      5. associate-*l/ N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - \color{blue}{z}\right)\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(t - z\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      12. associate--r+ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(z - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \color{blue}{\left(y - z\right)}\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \left(y + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{y}\right)\right)\right) \]

      19. associate--r+ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - \color{blue}{y}\right)\right) \]

      20. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - y\right)\right) \]

      21. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(z - y\right)\right) \]

      22. --lowering--.f64 95.1%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 95.1%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{z}\right)}, \mathsf{\_.f64}\left(z, y\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 78.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\color{blue}{z}, y\right)\right) \]

   7. Simplified 78.7%

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

   if 1.6500000000000001e-28 < t

   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 inf

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(y - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\color{blue}{y} - z\right)\right) \]

      4. --lowering--.f64 86.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 86.0%

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

Alternative 7: 82.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-27}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.3e-158)
   (/ (/ x y) (- t z))
   (if (<= t 4.8e-27) (/ (/ x z) (- z y)) (/ (/ 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 <= -2.3e-158) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.8e-27) {
		tmp = (x / z) / (z - y);
	} 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 <= (-2.3d-158)) then
        tmp = (x / y) / (t - z)
    else if (t <= 4.8d-27) then
        tmp = (x / z) / (z - y)
    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 <= -2.3e-158) {
		tmp = (x / y) / (t - z);
	} else if (t <= 4.8e-27) {
		tmp = (x / z) / (z - y);
	} 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 <= -2.3e-158:
		tmp = (x / y) / (t - z)
	elif t <= 4.8e-27:
		tmp = (x / z) / (z - y)
	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 <= -2.3e-158)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 4.8e-27)
		tmp = Float64(Float64(x / z) / Float64(z - y));
	else
		tmp = Float64(Float64(x / 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 <= -2.3e-158)
		tmp = (x / y) / (t - z);
	elseif (t <= 4.8e-27)
		tmp = (x / z) / (z - y);
	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, -2.3e-158], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-27], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2999999999999999e-158

   1. Initial program 90.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{\left(t - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 96.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{y}\right), \mathsf{\_.f64}\left(t, z\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 56.8%

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

   if -2.2999999999999999e-158 < t < 4.80000000000000004e-27

   1. Initial program 92.5%

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

      1. associate-/r* N/A

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

      2. frac-2neg N/A

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

      3. div-inv N/A

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

      4. distribute-neg-frac2 N/A

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

      5. associate-*l/ N/A

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

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{\mathsf{neg}\left(\left(t - z\right)\right)}\right), \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \left(\frac{1}{\mathsf{neg}\left(\left(t - z\right)\right)}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\left(y - z\right)}\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\mathsf{neg}\left(\left(t - z\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - \color{blue}{z}\right)\right)\right)\right) \]

      9. neg-sub0 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(t - z\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(t + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + t\right)\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      12. associate--r+ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      13. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \left(z - t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      15. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right) \]

      16. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \color{blue}{\left(y - z\right)}\right)\right) \]

      17. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \left(y + \color{blue}{\left(\mathsf{neg}\left(z\right)\right)}\right)\right)\right) \]

      18. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(0 - \left(\left(\mathsf{neg}\left(z\right)\right) + \color{blue}{y}\right)\right)\right) \]

      19. associate--r+ N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\left(0 - \left(\mathsf{neg}\left(z\right)\right)\right) - \color{blue}{y}\right)\right) \]

      20. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - y\right)\right) \]

      21. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \left(z - y\right)\right) \]

      22. --lowering--.f64 95.2%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(z, t\right)\right)\right), \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right) \]

   4. Applied egg-rr 95.2%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(\frac{x}{z}\right)}, \mathsf{\_.f64}\left(z, y\right)\right) \]
   6. Step-by-step derivation

      1. /-lowering-/.f64 78.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), \mathsf{\_.f64}\left(\color{blue}{z}, y\right)\right) \]

   7. Simplified 78.0%

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

   if 4.80000000000000004e-27 < t

   1. Initial program 89.5%

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

   3. Taylor expanded in t around inf

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(y - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\color{blue}{y} - z\right)\right) \]

      4. --lowering--.f64 85.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 85.8%

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

Alternative 8: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-28}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.5e-158)
   (/ (/ x y) (- t z))
   (if (<= t 2.6e-28) (/ x (* z (- z y))) (/ (/ 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 <= -2.5e-158) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2.6e-28) {
		tmp = x / (z * (z - y));
	} 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 <= (-2.5d-158)) then
        tmp = (x / y) / (t - z)
    else if (t <= 2.6d-28) then
        tmp = x / (z * (z - y))
    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 <= -2.5e-158) {
		tmp = (x / y) / (t - z);
	} else if (t <= 2.6e-28) {
		tmp = x / (z * (z - y));
	} 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 <= -2.5e-158:
		tmp = (x / y) / (t - z)
	elif t <= 2.6e-28:
		tmp = x / (z * (z - y))
	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 <= -2.5e-158)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 2.6e-28)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(Float64(x / 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 <= -2.5e-158)
		tmp = (x / y) / (t - z);
	elseif (t <= 2.6e-28)
		tmp = x / (z * (z - y));
	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, -2.5e-158], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-28], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.49999999999999986e-158

   1. Initial program 90.5%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y - z}\right), \color{blue}{\left(t - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(y - z\right)\right), \left(\color{blue}{t} - z\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \left(t - z\right)\right) \]

      5. --lowering--.f64 96.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(y, z\right)\right), \mathsf{\_.f64}\left(t, \color{blue}{z}\right)\right) \]

   3. Simplified 96.5%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \color{blue}{y}\right), \mathsf{\_.f64}\left(t, z\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 56.8%

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

   if -2.49999999999999986e-158 < t < 2.6e-28

   1. Initial program 92.4%

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

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(y - z\right)\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(y - z\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(z - y\right)\right)\right) \]

      15. --lowering--.f64 74.5%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 74.5%

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

   if 2.6e-28 < t

   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 inf

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(y - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\color{blue}{y} - z\right)\right) \]

      4. --lowering--.f64 86.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 86.0%

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

Alternative 9: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.2e-158)
   (/ x (* y (- t z)))
   (if (<= t 7.5e-29) (/ x (* z (- z y))) (/ (/ 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 <= -2.2e-158) {
		tmp = x / (y * (t - z));
	} else if (t <= 7.5e-29) {
		tmp = x / (z * (z - y));
	} 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 <= (-2.2d-158)) then
        tmp = x / (y * (t - z))
    else if (t <= 7.5d-29) then
        tmp = x / (z * (z - y))
    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 <= -2.2e-158) {
		tmp = x / (y * (t - z));
	} else if (t <= 7.5e-29) {
		tmp = x / (z * (z - y));
	} 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 <= -2.2e-158:
		tmp = x / (y * (t - z))
	elif t <= 7.5e-29:
		tmp = x / (z * (z - y))
	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 <= -2.2e-158)
		tmp = Float64(x / Float64(y * Float64(t - z)));
	elseif (t <= 7.5e-29)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	else
		tmp = Float64(Float64(x / 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 <= -2.2e-158)
		tmp = x / (y * (t - z));
	elseif (t <= 7.5e-29)
		tmp = x / (z * (z - y));
	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, -2.2e-158], N[(x / N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-29], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2000000000000001e-158

   1. Initial program 90.5%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(y \cdot \left(t - z\right)\right)}\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\left(t - z\right) \cdot \color{blue}{y}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(t - z\right), \color{blue}{y}\right)\right) \]

      4. --lowering--.f64 53.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(t, z\right), y\right)\right) \]

   5. Simplified 53.7%

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

   if -2.2000000000000001e-158 < t < 7.50000000000000006e-29

   1. Initial program 92.4%

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

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

      2. distribute-neg-frac2 N/A

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

      3. mul-1-neg N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(-1 \cdot \left(z \cdot \left(y - z\right)\right)\right)}\right) \]

      5. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(\mathsf{neg}\left(z \cdot \left(y - z\right)\right)\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{\left(\mathsf{neg}\left(\left(y - z\right)\right)\right)}\right)\right) \]

      7. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \left(-1 \cdot \color{blue}{\left(y - z\right)}\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{\left(-1 \cdot \left(y - z\right)\right)}\right)\right) \]

      9. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y - z\right)\right)\right)\right)\right) \]

      10. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(y + \left(\mathsf{neg}\left(z\right)\right)\right)\right)\right)\right)\right) \]

      11. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\mathsf{neg}\left(\left(\left(\mathsf{neg}\left(z\right)\right) + y\right)\right)\right)\right)\right) \]

      12. distribute-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right)\right)\right) \]

      13. unsub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(z\right)\right)\right)\right) - \color{blue}{y}\right)\right)\right) \]

      14. remove-double-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \left(z - y\right)\right)\right) \]

      15. --lowering--.f64 74.5%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \mathsf{\_.f64}\left(z, \color{blue}{y}\right)\right)\right) \]

   5. Simplified 74.5%

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

   if 7.50000000000000006e-29 < t

   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 inf

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t}\right), \color{blue}{\left(y - z\right)}\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \left(\color{blue}{y} - z\right)\right) \]

      4. --lowering--.f64 86.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 86.0%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{y \cdot \left(t - z\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1.25e+45) t_1 (if (<= z 1.8e-23) (/ (/ 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 <= -1.25e+45) {
		tmp = t_1;
	} else if (z <= 1.8e-23) {
		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 <= (-1.25d+45)) then
        tmp = t_1
    else if (z <= 1.8d-23) 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 <= -1.25e+45) {
		tmp = t_1;
	} else if (z <= 1.8e-23) {
		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 <= -1.25e+45:
		tmp = t_1
	elif z <= 1.8e-23:
		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(Float64(x / z) / z)
	tmp = 0.0
	if (z <= -1.25e+45)
		tmp = t_1;
	elseif (z <= 1.8e-23)
		tmp = Float64(Float64(x / 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 <= -1.25e+45)
		tmp = t_1;
	elseif (z <= 1.8e-23)
		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[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.25e+45], t$95$1, If[LessEqual[z, 1.8e-23], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e45 or 1.7999999999999999e-23 < z

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({z}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 66.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   5. Simplified 66.4%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{z}\right), \color{blue}{z}\right) \]

      3. /-lowering-/.f64 73.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, z\right), z\right) \]

   7. Applied egg-rr 73.0%

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

   if -1.25e45 < z < 1.7999999999999999e-23

   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

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right) \]

      2. *-lowering-*.f64 62.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{y}\right)\right) \]

   5. Simplified 62.3%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), t\right) \]

   7. Applied egg-rr 63.6%

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

Alternative 11: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-24}:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -4.6e+45) t_1 (if (<= z 1.3e-24) (/ (/ 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 <= -4.6e+45) {
		tmp = t_1;
	} else if (z <= 1.3e-24) {
		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 <= (-4.6d+45)) then
        tmp = t_1
    else if (z <= 1.3d-24) 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 <= -4.6e+45) {
		tmp = t_1;
	} else if (z <= 1.3e-24) {
		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 <= -4.6e+45:
		tmp = t_1
	elif z <= 1.3e-24:
		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 <= -4.6e+45)
		tmp = t_1;
	elseif (z <= 1.3e-24)
		tmp = Float64(Float64(x / 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 <= -4.6e+45)
		tmp = t_1;
	elseif (z <= 1.3e-24)
		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, -4.6e+45], t$95$1, If[LessEqual[z, 1.3e-24], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000025e45 or 1.3e-24 < z

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({z}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 66.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   5. Simplified 66.4%

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

   if -4.60000000000000025e45 < z < 1.3e-24

   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

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right) \]

      2. *-lowering-*.f64 62.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{y}\right)\right) \]

   5. Simplified 62.3%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{t}\right) \]

      4. /-lowering-/.f64 63.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), t\right) \]

   7. Applied egg-rr 63.6%

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

Alternative 12: 63.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -8.8e+45) t_1 (if (<= z 5.5e-25) (/ (/ 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 <= -8.8e+45) {
		tmp = t_1;
	} else if (z <= 5.5e-25) {
		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 <= (-8.8d+45)) then
        tmp = t_1
    else if (z <= 5.5d-25) 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 <= -8.8e+45) {
		tmp = t_1;
	} else if (z <= 5.5e-25) {
		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 <= -8.8e+45:
		tmp = t_1
	elif z <= 5.5e-25:
		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 <= -8.8e+45)
		tmp = t_1;
	elseif (z <= 5.5e-25)
		tmp = Float64(Float64(x / 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 <= -8.8e+45)
		tmp = t_1;
	elseif (z <= 5.5e-25)
		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, -8.8e+45], t$95$1, If[LessEqual[z, 5.5e-25], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000001e45 or 5.50000000000000004e-25 < z

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({z}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 66.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   5. Simplified 66.4%

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

   if -8.8000000000000001e45 < z < 5.50000000000000004e-25

   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

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right) \]

      2. *-lowering-*.f64 62.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{y}\right)\right) \]

   5. Simplified 62.3%

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

      1. associate-/r* N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t}\right), \color{blue}{y}\right) \]

      3. /-lowering-/.f64 65.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, t\right), y\right) \]

   7. Applied egg-rr 65.7%

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

Alternative 13: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -1.25e+45) t_1 (if (<= z 1.7e-23) (/ 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 <= -1.25e+45) {
		tmp = t_1;
	} else if (z <= 1.7e-23) {
		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 <= (-1.25d+45)) then
        tmp = t_1
    else if (z <= 1.7d-23) 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 <= -1.25e+45) {
		tmp = t_1;
	} else if (z <= 1.7e-23) {
		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 <= -1.25e+45:
		tmp = t_1
	elif z <= 1.7e-23:
		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 <= -1.25e+45)
		tmp = t_1;
	elseif (z <= 1.7e-23)
		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 <= -1.25e+45)
		tmp = t_1;
	elseif (z <= 1.7e-23)
		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, -1.25e+45], t$95$1, If[LessEqual[z, 1.7e-23], N[(x / N[(y * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e45 or 1.7e-23 < z

   1. Initial program 84.2%

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

   3. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left({z}^{2}\right)}\right) \]

      2. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \left(z \cdot \color{blue}{z}\right)\right) \]

      3. *-lowering-*.f64 66.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(z, \color{blue}{z}\right)\right) \]

   5. Simplified 66.4%

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

   if -1.25e45 < z < 1.7e-23

   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

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right) \]

      2. *-lowering-*.f64 62.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{y}\right)\right) \]

   5. Simplified 62.3%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{y \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.2% accurate, 1.0× 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 91.0%

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

   1. associate-/l/ N/A

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

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{t - z}\right), \color{blue}{\left(y - z\right)}\right) \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \left(t - z\right)\right), \left(\color{blue}{y} - z\right)\right) \]

   4. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \left(y - z\right)\right) \]

   5. --lowering--.f64 96.7%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(t, z\right)\right), \mathsf{\_.f64}\left(y, \color{blue}{z}\right)\right) \]

4. Applied egg-rr 96.7%

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

Alternative 15: 39.1% accurate, 1.8× 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 91.0%

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

3. Taylor expanded in z around 0

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(t \cdot y\right)}\right) \]

   2. *-lowering-*.f64 41.0%

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(t, \color{blue}{y}\right)\right) \]

5. Simplified 41.0%

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

6. Final simplification 41.0%

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

Developer Target 1: 87.8% 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 2024192 
(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))))