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

Percentage Accurate: 89.2% → 96.3%

Time: 13.9s

Alternatives: 17

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: 89.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \left(t - z\right) \cdot \left(y - z\right)\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+284}:\\ \;\;\;\;\frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (- t z) (- y z))))
   (if (<= t_1 2e+284) (/ x t_1) (/ (/ x (- t z)) (- y z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= 2e+284) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - z) * (y - z)
    if (t_1 <= 2d+284) then
        tmp = x / t_1
    else
        tmp = (x / (t - z)) / (y - z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (t - z) * (y - z);
	double tmp;
	if (t_1 <= 2e+284) {
		tmp = x / t_1;
	} else {
		tmp = (x / (t - z)) / (y - z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (t - z) * (y - z)
	tmp = 0
	if t_1 <= 2e+284:
		tmp = x / t_1
	else:
		tmp = (x / (t - z)) / (y - z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(t - z) * Float64(y - z))
	tmp = 0.0
	if (t_1 <= 2e+284)
		tmp = Float64(x / t_1);
	else
		tmp = Float64(Float64(x / Float64(t - z)) / 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)
	t_1 = (t - z) * (y - z);
	tmp = 0.0;
	if (t_1 <= 2e+284)
		tmp = x / t_1;
	else
		tmp = (x / (t - z)) / (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+284], N[(x / t$95$1), $MachinePrecision], N[(N[(x / N[(t - z), $MachinePrecision]), $MachinePrecision] / N[(y - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 y z) (-.f64 t z)) < 2.00000000000000016e284

   1. Initial program 97.4%

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

   if 2.00000000000000016e284 < (*.f64 (-.f64 y z) (-.f64 t z))

   1. Initial program 73.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 99.9%

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

   4. Applied egg-rr 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - z\right) \cdot \left(y - z\right) \leq 2 \cdot 10^{+284}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t - z}}{y - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.5e+46)
   (/ (/ x (- z t)) z)
   (if (<= z -8.2e-113)
     (/ (/ x y) (- t z))
     (if (<= z 4.2e-36) (/ x (* t (- y z))) (/ (/ x z) (- z y))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+46) {
		tmp = (x / (z - t)) / z;
	} else if (z <= -8.2e-113) {
		tmp = (x / y) / (t - z);
	} else if (z <= 4.2e-36) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.5d+46)) then
        tmp = (x / (z - t)) / z
    else if (z <= (-8.2d-113)) then
        tmp = (x / y) / (t - z)
    else if (z <= 4.2d-36) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / z) / (z - y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.5e+46) {
		tmp = (x / (z - t)) / z;
	} else if (z <= -8.2e-113) {
		tmp = (x / y) / (t - z);
	} else if (z <= 4.2e-36) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.5e+46:
		tmp = (x / (z - t)) / z
	elif z <= -8.2e-113:
		tmp = (x / y) / (t - z)
	elif z <= 4.2e-36:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.5e+46)
		tmp = Float64(Float64(x / Float64(z - t)) / z);
	elseif (z <= -8.2e-113)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 4.2e-36)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.5e+46)
		tmp = (x / (z - t)) / z;
	elseif (z <= -8.2e-113)
		tmp = (x / y) / (t - z);
	elseif (z <= 4.2e-36)
		tmp = x / (t * (y - z));
	else
		tmp = (x / z) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.5e+46], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -8.2e-113], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e-36], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.5000000000000001e46

   1. Initial program 76.1%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 91.1%

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

   7. Simplified 91.1%

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

      1. clear-num N/A

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

      2. inv-pow N/A

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

      3. associate-/r/ N/A

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

      4. neg-sub0 N/A

         \[\leadsto {\left(\frac{0 - \left(t - z\right)}{x} \cdot z\right)}^{-1} \]

      5. associate--r- N/A

         \[\leadsto {\left(\frac{\left(0 - t\right) + z}{x} \cdot z\right)}^{-1} \]

      6. neg-sub0 N/A

         \[\leadsto {\left(\frac{\left(\mathsf{neg}\left(t\right)\right) + z}{x} \cdot z\right)}^{-1} \]

      7. +-commutative N/A

         \[\leadsto {\left(\frac{z + \left(\mathsf{neg}\left(t\right)\right)}{x} \cdot z\right)}^{-1} \]

      8. sub-neg N/A

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

      9. unpow-prod-down N/A

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

      10. inv-pow N/A

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

      11. clear-num N/A

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

      12. inv-pow N/A

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

      13. div-inv N/A

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

      14. /-lowering-/.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. neg-sub0 N/A

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

      18. associate--r- N/A

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

      19. neg-sub0 N/A

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

      20. /-lowering-/.f64 N/A

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

      21. neg-sub0 N/A

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

      22. associate--r- N/A

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

      23. neg-sub0 N/A

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

      24. +-commutative N/A

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

      25. sub-neg N/A

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

      26. --lowering--.f64 91.2%

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

   9. Applied egg-rr 91.2%

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

   if -2.5000000000000001e46 < z < -8.1999999999999999e-113

   1. Initial program 93.0%

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

      1. associate-/r* N/A

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

      2. /-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 96.1%

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

   4. Applied egg-rr 96.1%

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

   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 69.6%

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

   if -8.1999999999999999e-113 < z < 4.19999999999999982e-36

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 78.0%

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

   if 4.19999999999999982e-36 < z

   1. Initial program 87.8%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

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

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

      7. distribute-neg-frac2 N/A

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

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

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

      9. neg-sub0 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

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

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

      16. neg-sub0 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. associate--r+ N/A

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

      20. neg-sub0 N/A

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

      21. remove-double-neg N/A

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

      22. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 83.0%

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

   9. Simplified 83.0%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z - y}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{-77}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- z y))))
   (if (<= z -5.2e-77)
     t_1
     (if (<= z -3.8e-113)
       (/ (/ x y) (- t z))
       (if (<= z 1.02e-38) (/ x (* t (- y z))) t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - y);
	double tmp;
	if (z <= -5.2e-77) {
		tmp = t_1;
	} else if (z <= -3.8e-113) {
		tmp = (x / y) / (t - z);
	} else if (z <= 1.02e-38) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / z) / (z - y)
    if (z <= (-5.2d-77)) then
        tmp = t_1
    else if (z <= (-3.8d-113)) then
        tmp = (x / y) / (t - z)
    else if (z <= 1.02d-38) then
        tmp = x / (t * (y - z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / (z - y);
	double tmp;
	if (z <= -5.2e-77) {
		tmp = t_1;
	} else if (z <= -3.8e-113) {
		tmp = (x / y) / (t - z);
	} else if (z <= 1.02e-38) {
		tmp = x / (t * (y - z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = (x / z) / (z - y)
	tmp = 0
	if z <= -5.2e-77:
		tmp = t_1
	elif z <= -3.8e-113:
		tmp = (x / y) / (t - z)
	elif z <= 1.02e-38:
		tmp = x / (t * (y - z))
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(z - y))
	tmp = 0.0
	if (z <= -5.2e-77)
		tmp = t_1;
	elseif (z <= -3.8e-113)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (z <= 1.02e-38)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = (x / z) / (z - y);
	tmp = 0.0;
	if (z <= -5.2e-77)
		tmp = t_1;
	elseif (z <= -3.8e-113)
		tmp = (x / y) / (t - z);
	elseif (z <= 1.02e-38)
		tmp = x / (t * (y - z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e-77], t$95$1, If[LessEqual[z, -3.8e-113], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e-38], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2000000000000002e-77 or 1.01999999999999998e-38 < z

   1. Initial program 83.4%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 99.1%

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

   4. Applied egg-rr 99.1%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

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

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

      7. distribute-neg-frac2 N/A

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

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

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

      9. neg-sub0 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

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

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

      16. neg-sub0 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. associate--r+ N/A

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

      20. neg-sub0 N/A

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

      21. remove-double-neg N/A

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

      22. --lowering--.f64 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 86.4%

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

   9. Simplified 86.4%

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

   if -5.2000000000000002e-77 < z < -3.79999999999999983e-113

   1. Initial program 99.1%

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

      1. associate-/r* N/A

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

      2. /-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 89.3%

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

   4. Applied egg-rr 89.3%

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

   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 81.7%

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

   if -3.79999999999999983e-113 < z < 1.01999999999999998e-38

   1. Initial program 96.0%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 78.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-113}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+160}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+160)
   (/ 1.0 (/ z (/ x z)))
   (if (<= z -6.5e-113)
     (/ x (* z (- z y)))
     (if (<= z 8e+42) (/ x (* t (- y z))) (* (/ x z) (/ 1.0 z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+160) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= -6.5e-113) {
		tmp = x / (z * (z - y));
	} else if (z <= 8e+42) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.7d+160)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= (-6.5d-113)) then
        tmp = x / (z * (z - y))
    else if (z <= 8d+42) then
        tmp = x / (t * (y - z))
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+160) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= -6.5e-113) {
		tmp = x / (z * (z - y));
	} else if (z <= 8e+42) {
		tmp = x / (t * (y - z));
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+160:
		tmp = 1.0 / (z / (x / z))
	elif z <= -6.5e-113:
		tmp = x / (z * (z - y))
	elif z <= 8e+42:
		tmp = x / (t * (y - z))
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+160)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= -6.5e-113)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (z <= 8e+42)
		tmp = Float64(x / Float64(t * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e+160)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= -6.5e-113)
		tmp = x / (z * (z - y));
	elseif (z <= 8e+42)
		tmp = x / (t * (y - z));
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+160], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.5e-113], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8e+42], N[(x / N[(t * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7e160

   1. Initial program 64.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.7%

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

   5. Simplified 64.7%

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

      1. clear-num N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. clear-num N/A

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

      6. associate-/r* N/A

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

      7. clear-num N/A

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

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

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

      9. /-lowering-/.f64 90.4%

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

   7. Applied egg-rr 90.4%

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

   if -2.7e160 < z < -6.49999999999999979e-113

   1. Initial program 92.8%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 96.5%

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

   4. Applied egg-rr 96.5%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. frac-2neg N/A

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

      5. distribute-frac-neg2 N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-out N/A

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

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

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 N/A

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

      18. distribute-neg-frac N/A

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

      19. metadata-eval N/A

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 75.5%

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

   9. Simplified 75.5%

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

   if -6.49999999999999979e-113 < z < 8.00000000000000036e42

   1. Initial program 96.4%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 76.2%

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

   if 8.00000000000000036e42 < z

   1. Initial program 84.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 78.5%

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

   5. Simplified 78.5%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

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

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval 86.1%

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

   7. Applied egg-rr 86.1%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+160}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-113}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{t \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.4e+160)
   (/ 1.0 (/ z (/ x z)))
   (if (<= z -1.15e-76)
     (/ x (* z (- z y)))
     (if (<= z 2.5e+21) (/ x (* (- t z) y)) (* (/ x z) (/ 1.0 z))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+160) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= -1.15e-76) {
		tmp = x / (z * (z - y));
	} else if (z <= 2.5e+21) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.4d+160)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= (-1.15d-76)) then
        tmp = x / (z * (z - y))
    else if (z <= 2.5d+21) then
        tmp = x / ((t - z) * y)
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.4e+160) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= -1.15e-76) {
		tmp = x / (z * (z - y));
	} else if (z <= 2.5e+21) {
		tmp = x / ((t - z) * y);
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.4e+160:
		tmp = 1.0 / (z / (x / z))
	elif z <= -1.15e-76:
		tmp = x / (z * (z - y))
	elif z <= 2.5e+21:
		tmp = x / ((t - z) * y)
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.4e+160)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= -1.15e-76)
		tmp = Float64(x / Float64(z * Float64(z - y)));
	elseif (z <= 2.5e+21)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.4e+160)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= -1.15e-76)
		tmp = x / (z * (z - y));
	elseif (z <= 2.5e+21)
		tmp = x / ((t - z) * y);
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.4e+160], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-76], N[(x / N[(z * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e+21], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.4000000000000001e160

   1. Initial program 64.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.7%

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

   5. Simplified 64.7%

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

      1. clear-num N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. clear-num N/A

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

      6. associate-/r* N/A

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

      7. clear-num N/A

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

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

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

      9. /-lowering-/.f64 90.4%

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

   7. Applied egg-rr 90.4%

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

   if -2.4000000000000001e160 < z < -1.15000000000000003e-76

   1. Initial program 91.7%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 97.8%

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

   4. Applied egg-rr 97.8%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. frac-2neg N/A

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

      5. distribute-frac-neg2 N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-out N/A

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

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

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 N/A

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

      18. distribute-neg-frac N/A

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

      19. metadata-eval N/A

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 99.1%

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

   6. Applied egg-rr 99.1%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 80.9%

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

   9. Simplified 80.9%

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

   if -1.15000000000000003e-76 < z < 2.5e21

   1. Initial program 96.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 78.8%

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

   5. Simplified 78.8%

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

   if 2.5e21 < z

   1. Initial program 85.3%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 76.1%

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

   5. Simplified 76.1%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

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

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval 83.3%

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

   7. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+160}:\\ \;\;\;\;\frac{1}{\frac{z}{\frac{x}{z}}}\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-116}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 y)))))
   (if (<= z -2.4e+160)
     (/ 1.0 (/ z (/ x z)))
     (if (<= z -2.35e-116) t_1 (if (<= z 3.7e-60) (/ (/ 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 - y));
	double tmp;
	if (z <= -2.4e+160) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= -2.35e-116) {
		tmp = t_1;
	} else if (z <= 3.7e-60) {
		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 - y))
    if (z <= (-2.4d+160)) then
        tmp = 1.0d0 / (z / (x / z))
    else if (z <= (-2.35d-116)) then
        tmp = t_1
    else if (z <= 3.7d-60) 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 - y));
	double tmp;
	if (z <= -2.4e+160) {
		tmp = 1.0 / (z / (x / z));
	} else if (z <= -2.35e-116) {
		tmp = t_1;
	} else if (z <= 3.7e-60) {
		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 - y))
	tmp = 0
	if z <= -2.4e+160:
		tmp = 1.0 / (z / (x / z))
	elif z <= -2.35e-116:
		tmp = t_1
	elif z <= 3.7e-60:
		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 * Float64(z - y)))
	tmp = 0.0
	if (z <= -2.4e+160)
		tmp = Float64(1.0 / Float64(z / Float64(x / z)));
	elseif (z <= -2.35e-116)
		tmp = t_1;
	elseif (z <= 3.7e-60)
		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 - y));
	tmp = 0.0;
	if (z <= -2.4e+160)
		tmp = 1.0 / (z / (x / z));
	elseif (z <= -2.35e-116)
		tmp = t_1;
	elseif (z <= 3.7e-60)
		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 * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+160], N[(1.0 / N[(z / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.35e-116], t$95$1, If[LessEqual[z, 3.7e-60], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4000000000000001e160

   1. Initial program 64.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.7%

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

   5. Simplified 64.7%

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

      1. clear-num N/A

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

      2. metadata-eval N/A

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

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

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

      4. metadata-eval N/A

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

      5. clear-num N/A

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

      6. associate-/r* N/A

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

      7. clear-num N/A

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

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

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

      9. /-lowering-/.f64 90.4%

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

   7. Applied egg-rr 90.4%

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

   if -2.4000000000000001e160 < z < -2.34999999999999997e-116 or 3.70000000000000025e-60 < z

   1. Initial program 90.7%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 98.3%

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

   4. Applied egg-rr 98.3%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. frac-2neg N/A

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

      5. distribute-frac-neg2 N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-out N/A

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

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

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 N/A

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

      18. distribute-neg-frac N/A

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

      19. metadata-eval N/A

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 98.8%

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

   6. Applied egg-rr 98.8%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 72.1%

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

   9. Simplified 72.1%

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

   if -2.34999999999999997e-116 < z < 3.70000000000000025e-60

   1. Initial program 95.7%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 71.5%

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

   5. Simplified 71.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   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 74.2%

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

   7. Applied egg-rr 74.2%

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

Alternative 7: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+105)
   (/ (/ x (- z t)) z)
   (if (<= z 2.8e+134) (/ x (* (- t z) (- y z))) (/ (/ x z) (- z y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+105) {
		tmp = (x / (z - t)) / z;
	} else if (z <= 2.8e+134) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-4d+105)) then
        tmp = (x / (z - t)) / z
    else if (z <= 2.8d+134) then
        tmp = x / ((t - z) * (y - z))
    else
        tmp = (x / z) / (z - y)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+105) {
		tmp = (x / (z - t)) / z;
	} else if (z <= 2.8e+134) {
		tmp = x / ((t - z) * (y - z));
	} else {
		tmp = (x / z) / (z - y);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -4e+105:
		tmp = (x / (z - t)) / z
	elif z <= 2.8e+134:
		tmp = x / ((t - z) * (y - z))
	else:
		tmp = (x / z) / (z - y)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+105)
		tmp = Float64(Float64(x / Float64(z - t)) / z);
	elseif (z <= 2.8e+134)
		tmp = Float64(x / Float64(Float64(t - z) * Float64(y - z)));
	else
		tmp = Float64(Float64(x / z) / Float64(z - y));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e+105)
		tmp = (x / (z - t)) / z;
	elseif (z <= 2.8e+134)
		tmp = x / ((t - z) * (y - z));
	else
		tmp = (x / z) / (z - y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -4e+105], N[(N[(x / N[(z - t), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 2.8e+134], N[(x / N[(N[(t - z), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999998e105

   1. Initial program 70.9%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. associate-/r* N/A

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

      3. distribute-neg-frac2 N/A

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

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

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

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

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

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

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

      7. --lowering--.f64 94.9%

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

   7. Simplified 94.9%

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

      1. clear-num N/A

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

      2. inv-pow N/A

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

      3. associate-/r/ N/A

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

      4. neg-sub0 N/A

         \[\leadsto {\left(\frac{0 - \left(t - z\right)}{x} \cdot z\right)}^{-1} \]

      5. associate--r- N/A

         \[\leadsto {\left(\frac{\left(0 - t\right) + z}{x} \cdot z\right)}^{-1} \]

      6. neg-sub0 N/A

         \[\leadsto {\left(\frac{\left(\mathsf{neg}\left(t\right)\right) + z}{x} \cdot z\right)}^{-1} \]

      7. +-commutative N/A

         \[\leadsto {\left(\frac{z + \left(\mathsf{neg}\left(t\right)\right)}{x} \cdot z\right)}^{-1} \]

      8. sub-neg N/A

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

      9. unpow-prod-down N/A

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

      10. inv-pow N/A

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

      11. clear-num N/A

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

      12. inv-pow N/A

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

      13. div-inv N/A

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

      14. /-lowering-/.f64 N/A

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

      15. sub-neg N/A

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

      16. +-commutative N/A

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

      17. neg-sub0 N/A

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

      18. associate--r- N/A

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

      19. neg-sub0 N/A

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

      20. /-lowering-/.f64 N/A

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

      21. neg-sub0 N/A

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

      22. associate--r- N/A

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

      23. neg-sub0 N/A

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

      24. +-commutative N/A

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

      25. sub-neg N/A

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

      26. --lowering--.f64 94.9%

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

   9. Applied egg-rr 94.9%

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

   if -3.9999999999999998e105 < z < 2.7999999999999999e134

   1. Initial program 95.0%

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

   if 2.7999999999999999e134 < z

   1. Initial program 85.4%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. associate-/r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. div-inv N/A

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

      5. frac-2neg N/A

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

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

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

      7. distribute-neg-frac2 N/A

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

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

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

      9. neg-sub0 N/A

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

      10. sub-neg N/A

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

      11. +-commutative N/A

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

      12. associate--r+ N/A

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

      13. neg-sub0 N/A

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

      14. remove-double-neg N/A

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

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

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

      16. neg-sub0 N/A

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

      17. sub-neg N/A

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

      18. +-commutative N/A

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

      19. associate--r+ N/A

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

      20. neg-sub0 N/A

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

      21. remove-double-neg N/A

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

      22. --lowering--.f64 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around inf

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

      1. /-lowering-/.f64 95.2%

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

   9. Simplified 95.2%

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

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{x}{z - t}}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot \left(y - z\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-157}:\\ \;\;\;\;\frac{\frac{x}{y}}{t - z}\\ \mathbf{elif}\;t \leq 980:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -1.2e-157)
   (/ (/ x y) (- t z))
   (if (<= t 980.0) (/ 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 <= -1.2e-157) {
		tmp = (x / y) / (t - z);
	} else if (t <= 980.0) {
		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 <= (-1.2d-157)) then
        tmp = (x / y) / (t - z)
    else if (t <= 980.0d0) 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 <= -1.2e-157) {
		tmp = (x / y) / (t - z);
	} else if (t <= 980.0) {
		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 <= -1.2e-157:
		tmp = (x / y) / (t - z)
	elif t <= 980.0:
		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 <= -1.2e-157)
		tmp = Float64(Float64(x / y) / Float64(t - z));
	elseif (t <= 980.0)
		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 <= -1.2e-157)
		tmp = (x / y) / (t - z);
	elseif (t <= 980.0)
		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, -1.2e-157], N[(N[(x / y), $MachinePrecision] / N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 980.0], 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 < -1.2e-157

   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. /-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 96.1%

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

   4. Applied egg-rr 96.1%

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

   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 62.3%

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

   if -1.2e-157 < t < 980

   1. Initial program 88.7%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 94.9%

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

   4. Applied egg-rr 94.9%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. frac-2neg N/A

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

      5. distribute-frac-neg2 N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-out N/A

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

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

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 N/A

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

      18. distribute-neg-frac N/A

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

      19. metadata-eval N/A

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 70.8%

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

   9. Simplified 70.8%

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

   if 980 < t

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 79.0%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. --lowering--.f64 88.0%

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

   7. Applied egg-rr 88.0%

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

Alternative 9: 79.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-161}:\\ \;\;\;\;\frac{x}{\left(t - z\right) \cdot y}\\ \mathbf{elif}\;t \leq 980:\\ \;\;\;\;\frac{x}{z \cdot \left(z - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{y - z}\\ \end{array} \end{array} \]

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 -3.5e-161)
   (/ x (* (- t z) y))
   (if (<= t 980.0) (/ 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 <= -3.5e-161) {
		tmp = x / ((t - z) * y);
	} else if (t <= 980.0) {
		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 <= (-3.5d-161)) then
        tmp = x / ((t - z) * y)
    else if (t <= 980.0d0) 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 <= -3.5e-161) {
		tmp = x / ((t - z) * y);
	} else if (t <= 980.0) {
		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 <= -3.5e-161:
		tmp = x / ((t - z) * y)
	elif t <= 980.0:
		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 <= -3.5e-161)
		tmp = Float64(x / Float64(Float64(t - z) * y));
	elseif (t <= 980.0)
		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 <= -3.5e-161)
		tmp = x / ((t - z) * y);
	elseif (t <= 980.0)
		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, -3.5e-161], N[(x / N[(N[(t - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 980.0], 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 < -3.5000000000000002e-161

   1. Initial program 92.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 62.5%

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

   5. Simplified 62.5%

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

   if -3.5000000000000002e-161 < t < 980

   1. Initial program 88.7%

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

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

      3. associate-/l* N/A

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

      4. associate-/r* N/A

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

      5. flip3-- N/A

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

      6. clear-num N/A

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

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

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

      8. clear-num N/A

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

      9. flip3-- N/A

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

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

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

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

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

      12. /-lowering-/.f64 N/A

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

      13. --lowering--.f64 94.9%

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

   4. Applied egg-rr 94.9%

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

      1. associate-/l/ N/A

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

      2. associate-/r* N/A

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

      3. clear-num N/A

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

      4. frac-2neg N/A

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

      5. distribute-frac-neg2 N/A

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

      6. div-inv N/A

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

      7. distribute-rgt-neg-out N/A

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

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

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

      9. distribute-neg-frac2 N/A

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

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

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

      11. neg-sub0 N/A

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

      12. sub-neg N/A

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

      13. +-commutative N/A

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

      14. associate--r+ N/A

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

      15. neg-sub0 N/A

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

      16. remove-double-neg N/A

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

      17. --lowering--.f64 N/A

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

      18. distribute-neg-frac N/A

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

      19. metadata-eval N/A

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

      20. /-lowering-/.f64 N/A

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

      21. --lowering--.f64 95.6%

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

   6. Applied egg-rr 95.6%

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

   7. Taylor expanded in t around 0

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

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

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

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

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

      3. --lowering--.f64 70.8%

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

   9. Simplified 70.8%

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

   if 980 < t

   1. Initial program 82.4%

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

   3. Taylor expanded in t around inf

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

   5. Simplified 79.0%

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

      1. *-commutative N/A

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

      2. associate-/r* N/A

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

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

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

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

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

      5. --lowering--.f64 88.0%

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

   7. Applied egg-rr 88.0%

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

Alternative 10: 67.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{\frac{x}{z}}{z}\\ \mathbf{elif}\;z \leq 11000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{1}{z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.9e+46)
   (/ (/ x z) z)
   (if (<= z 11000000.0) (/ (/ x y) t) (* (/ x z) (/ 1.0 z)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+46) {
		tmp = (x / z) / z;
	} else if (z <= 11000000.0) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.9d+46)) then
        tmp = (x / z) / z
    else if (z <= 11000000.0d0) then
        tmp = (x / y) / t
    else
        tmp = (x / z) * (1.0d0 / z)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.9e+46) {
		tmp = (x / z) / z;
	} else if (z <= 11000000.0) {
		tmp = (x / y) / t;
	} else {
		tmp = (x / z) * (1.0 / z);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.9e+46:
		tmp = (x / z) / z
	elif z <= 11000000.0:
		tmp = (x / y) / t
	else:
		tmp = (x / z) * (1.0 / z)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.9e+46)
		tmp = Float64(Float64(x / z) / z);
	elseif (z <= 11000000.0)
		tmp = Float64(Float64(x / y) / t);
	else
		tmp = Float64(Float64(x / z) * Float64(1.0 / z));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.9e+46)
		tmp = (x / z) / z;
	elseif (z <= 11000000.0)
		tmp = (x / y) / t;
	else
		tmp = (x / z) * (1.0 / z);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.9e+46], N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 11000000.0], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000002e46

   1. Initial program 76.1%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 85.1%

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

   7. Applied egg-rr 85.1%

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

   if -2.9000000000000002e46 < z < 1.1e7

   1. Initial program 95.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 57.5%

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

   5. Simplified 57.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   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 59.9%

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

   7. Applied egg-rr 59.9%

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

   if 1.1e7 < z

   1. Initial program 85.6%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 74.8%

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

   5. Simplified 74.8%

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

      1. associate-/r* N/A

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

      2. div-inv N/A

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

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

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

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

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

      5. metadata-eval N/A

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

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

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

      7. metadata-eval 81.9%

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

   7. Applied egg-rr 81.9%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{1}{z}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 11: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{z}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 46000000:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -3.3e+46) t_1 (if (<= z 46000000.0) (/ (/ 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 <= -3.3e+46) {
		tmp = t_1;
	} else if (z <= 46000000.0) {
		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 <= (-3.3d+46)) then
        tmp = t_1
    else if (z <= 46000000.0d0) 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 <= -3.3e+46) {
		tmp = t_1;
	} else if (z <= 46000000.0) {
		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 <= -3.3e+46:
		tmp = t_1
	elif z <= 46000000.0:
		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 <= -3.3e+46)
		tmp = t_1;
	elseif (z <= 46000000.0)
		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 <= -3.3e+46)
		tmp = t_1;
	elseif (z <= 46000000.0)
		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, -3.3e+46], t$95$1, If[LessEqual[z, 46000000.0], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999998e46 or 4.6e7 < z

   1. Initial program 80.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 72.2%

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

   5. Simplified 72.2%

      \[\leadsto \color{blue}{\frac{x}{z \cdot z}} \]
   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 83.6%

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

   7. Applied egg-rr 83.6%

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

   if -3.2999999999999998e46 < z < 4.6e7

   1. Initial program 95.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 57.5%

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

   5. Simplified 57.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   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 59.9%

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

   7. Applied egg-rr 59.9%

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

Alternative 12: 63.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 165:\\ \;\;\;\;\frac{\frac{x}{y}}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2.5e+46) t_1 (if (<= z 165.0) (/ (/ 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 <= -2.5e+46) {
		tmp = t_1;
	} else if (z <= 165.0) {
		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 <= (-2.5d+46)) then
        tmp = t_1
    else if (z <= 165.0d0) 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 <= -2.5e+46) {
		tmp = t_1;
	} else if (z <= 165.0) {
		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 <= -2.5e+46:
		tmp = t_1
	elif z <= 165.0:
		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 <= -2.5e+46)
		tmp = t_1;
	elseif (z <= 165.0)
		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 <= -2.5e+46)
		tmp = t_1;
	elseif (z <= 165.0)
		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, -2.5e+46], t$95$1, If[LessEqual[z, 165.0], N[(N[(x / y), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e46 or 165 < z

   1. Initial program 80.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 72.2%

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

   5. Simplified 72.2%

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

   if -2.5000000000000001e46 < z < 165

   1. Initial program 95.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 57.5%

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

   5. Simplified 57.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   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 59.9%

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

   7. Applied egg-rr 59.9%

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

Alternative 13: 63.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+46}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 260000:\\ \;\;\;\;\frac{\frac{x}{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 -2.5e+46) t_1 (if (<= z 260000.0) (/ (/ x t) y) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -2.5e+46) {
		tmp = t_1;
	} else if (z <= 260000.0) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * z)
    if (z <= (-2.5d+46)) then
        tmp = t_1
    else if (z <= 260000.0d0) then
        tmp = (x / t) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -2.5e+46) {
		tmp = t_1;
	} else if (z <= 260000.0) {
		tmp = (x / t) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -2.5e+46:
		tmp = t_1
	elif z <= 260000.0:
		tmp = (x / t) / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -2.5e+46)
		tmp = t_1;
	elseif (z <= 260000.0)
		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 <= -2.5e+46)
		tmp = t_1;
	elseif (z <= 260000.0)
		tmp = (x / t) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.5e+46], t$95$1, If[LessEqual[z, 260000.0], N[(N[(x / t), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e46 or 2.6e5 < z

   1. Initial program 80.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 72.2%

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

   5. Simplified 72.2%

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

   if -2.5000000000000001e46 < z < 2.6e5

   1. Initial program 95.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 57.5%

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

   5. Simplified 57.5%

      \[\leadsto \color{blue}{\frac{x}{t \cdot y}} \]
   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 60.3%

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

   7. Applied egg-rr 60.3%

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

Alternative 14: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4000000:\\ \;\;\;\;\frac{x}{t \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (* z z))))
   (if (<= z -2.6e-76) t_1 (if (<= z 4000000.0) (/ x (* t y)) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -2.6e-76) {
		tmp = t_1;
	} else if (z <= 4000000.0) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (z * z)
    if (z <= (-2.6d-76)) then
        tmp = t_1
    else if (z <= 4000000.0d0) then
        tmp = x / (t * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = x / (z * z);
	double tmp;
	if (z <= -2.6e-76) {
		tmp = t_1;
	} else if (z <= 4000000.0) {
		tmp = x / (t * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = x / (z * z)
	tmp = 0
	if z <= -2.6e-76:
		tmp = t_1
	elif z <= 4000000.0:
		tmp = x / (t * y)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(x / Float64(z * z))
	tmp = 0.0
	if (z <= -2.6e-76)
		tmp = t_1;
	elseif (z <= 4000000.0)
		tmp = Float64(x / Float64(t * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = x / (z * z);
	tmp = 0.0;
	if (z <= -2.6e-76)
		tmp = t_1;
	elseif (z <= 4000000.0)
		tmp = x / (t * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e-76], t$95$1, If[LessEqual[z, 4000000.0], N[(x / N[(t * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-76 or 4e6 < z

   1. Initial program 82.4%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 63.7%

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

   5. Simplified 63.7%

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

   if -2.6e-76 < z < 4e6

   1. Initial program 96.5%

      \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
   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 64.4%

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

   5. Simplified 64.4%

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

Alternative 15: 97.0% accurate, 0.8× speedup

Math

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

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 88.9%

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

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

   3. associate-/l* N/A

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

   4. associate-/r* N/A

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

   5. flip3-- N/A

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

   6. clear-num N/A

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

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

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

   8. clear-num N/A

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

   9. flip3-- N/A

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

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

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

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

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

   12. /-lowering-/.f64 N/A

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

   13. --lowering--.f64 95.9%

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

4. Applied egg-rr 95.9%

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

Alternative 16: 97.0% accurate, 1.0× speedup

Math

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

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 (- y z)) (- t z)))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 88.9%

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

   1. associate-/r* N/A

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

   2. /-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 96.0%

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

4. Applied egg-rr 96.0%

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

Alternative 17: 39.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.9%

   \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \]
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 41.4%

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

5. Simplified 41.4%

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

Developer Target 1: 88.1% 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 2024158 
(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))))