Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 95.8% → 97.7%

Time: 8.2s

Alternatives: 8

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

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))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

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 t) 5e+285) (/ x (- y (* z t))) (/ -1.0 (* t (/ z x)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 5e+285) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -1.0 / (t * (z / x));
	}
	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 * t) <= 5d+285) then
        tmp = x / (y - (z * t))
    else
        tmp = (-1.0d0) / (t * (z / x))
    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 * t) <= 5e+285) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -1.0 / (t * (z / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= 5e+285:
		tmp = x / (y - (z * t))
	else:
		tmp = -1.0 / (t * (z / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 5e+285)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	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 * t) <= 5e+285)
		tmp = x / (y - (z * t));
	else
		tmp = -1.0 / (t * (z / x));
	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[N[(z * t), $MachinePrecision], 5e+285], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 5.00000000000000016e285

   1. Initial program 99.1%

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

   if 5.00000000000000016e285 < (*.f64 z t)

   1. Initial program 53.3%

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

      1. clear-num 53.3%

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

      2. associate-/r/ 53.3%

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

   4. Applied egg-rr 53.3%

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

   5. Taylor expanded in y around 0 53.3%

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

      1. associate-/r* 61.6%

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

   7. Simplified 61.6%

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

      1. associate-*l/ 99.4%

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

      2. clear-num 99.6%

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

   9. Applied egg-rr 99.6%

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

       1. associate-*l/ 99.6%

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

       2. neg-mul-1 99.6%

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

       3. associate-/r/ 99.7%

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

       4. add-sqr-sqrt 68.5%

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

       5. sqrt-unprod 56.8%

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

       6. sqr-neg 56.8%

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

       7. sqrt-unprod 7.5%

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

       8. add-sqr-sqrt 46.4%

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

       9. associate-/r/ 46.4%

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

       10. frac-2neg 46.4%

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

       11. associate-/r/ 46.4%

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

       12. add-sqr-sqrt 38.9%

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

       13. sqrt-unprod 45.3%

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

       14. sqr-neg 45.3%

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

       15. sqrt-unprod 31.2%

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

       16. add-sqr-sqrt 99.7%

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

   11. Applied egg-rr 99.7%

       \[\leadsto \frac{1}{\color{blue}{\frac{z}{x} \cdot \left(-t\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+91} \lor \neg \left(z \cdot t \leq 10^{-59}\right):\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (or (<= (* z t) -4e+91) (not (<= (* z t) 1e-59)))
   (/ (/ x (- z)) t)
   (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -4e+91) || !((z * t) <= 1e-59)) {
		tmp = (x / -z) / t;
	} else {
		tmp = x / 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 * t) <= (-4d+91)) .or. (.not. ((z * t) <= 1d-59))) then
        tmp = (x / -z) / t
    else
        tmp = x / 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 * t) <= -4e+91) || !((z * t) <= 1e-59)) {
		tmp = (x / -z) / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -4e+91) or not ((z * t) <= 1e-59):
		tmp = (x / -z) / t
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -4e+91) || !(Float64(z * t) <= 1e-59))
		tmp = Float64(Float64(x / Float64(-z)) / t);
	else
		tmp = Float64(x / 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 * t) <= -4e+91) || ~(((z * t) <= 1e-59)))
		tmp = (x / -z) / t;
	else
		tmp = x / 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[Or[LessEqual[N[(z * t), $MachinePrecision], -4e+91], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e-59]], $MachinePrecision]], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.00000000000000032e91 or 1e-59 < (*.f64 z t)

   1. Initial program 92.2%

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

      1. clear-num 92.0%

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

      2. associate-/r/ 92.1%

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

   4. Applied egg-rr 92.1%

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

   5. Taylor expanded in t around inf 72.9%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   6. Step-by-step derivation

      1. distribute-lft-out 72.9%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}\right)}}{t} \]

      2. associate-*r/ 72.9%

         \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      3. mul-1-neg 72.9%

         \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      4. associate-/r* 72.8%

         \[\leadsto -\frac{\frac{x}{z} + \color{blue}{\frac{\frac{x \cdot y}{t}}{{z}^{2}}}}{t} \]

   7. Simplified 72.8%

      \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{\frac{x \cdot y}{t}}{{z}^{2}}}{t}} \]

   8. Taylor expanded in z around inf 80.6%

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

   if -4.00000000000000032e91 < (*.f64 z t) < 1e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 81.9%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+91} \lor \neg \left(z \cdot t \leq 10^{-59}\right):\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -5e-7)
   (/ (- x) (* z t))
   (if (<= (* z t) 1e-59) (/ x y) (/ (/ x (- z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-7) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 1e-59) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-5d-7)) then
        tmp = -x / (z * t)
    else if ((z * t) <= 1d-59) then
        tmp = x / y
    else
        tmp = (x / -z) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -5e-7) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 1e-59) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -5e-7:
		tmp = -x / (z * t)
	elif (z * t) <= 1e-59:
		tmp = x / y
	else:
		tmp = (x / -z) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -5e-7)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (Float64(z * t) <= 1e-59)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / Float64(-z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -5e-7)
		tmp = -x / (z * t);
	elseif ((z * t) <= 1e-59)
		tmp = x / y;
	else
		tmp = (x / -z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -5e-7], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-59], N[(x / y), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999977e-7

   1. Initial program 97.0%

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

   3. Taylor expanded in y around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. neg-mul-1 78.3%

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

   5. Simplified 78.3%

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

   if -4.99999999999999977e-7 < (*.f64 z t) < 1e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 86.7%

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

   if 1e-59 < (*.f64 z t)

   1. Initial program 89.2%

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

      1. clear-num 88.9%

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

      2. associate-/r/ 88.9%

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

   4. Applied egg-rr 88.9%

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

   5. Taylor expanded in t around inf 68.8%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   6. Step-by-step derivation

      1. distribute-lft-out 68.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}\right)}}{t} \]

      2. associate-*r/ 68.8%

         \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      3. mul-1-neg 68.8%

         \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      4. associate-/r* 68.7%

         \[\leadsto -\frac{\frac{x}{z} + \color{blue}{\frac{\frac{x \cdot y}{t}}{{z}^{2}}}}{t} \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{\frac{x \cdot y}{t}}{{z}^{2}}}{t}} \]

   8. Taylor expanded in z around inf 76.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{-7}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1e+38)
   (/ (/ x t) (- z))
   (if (<= (* z t) 1e-59) (/ x y) (/ (/ x (- z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+38) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 1e-59) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-1d+38)) then
        tmp = (x / t) / -z
    else if ((z * t) <= 1d-59) then
        tmp = x / y
    else
        tmp = (x / -z) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+38) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= 1e-59) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1e+38:
		tmp = (x / t) / -z
	elif (z * t) <= 1e-59:
		tmp = x / y
	else:
		tmp = (x / -z) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+38)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(z * t) <= 1e-59)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / Float64(-z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1e+38)
		tmp = (x / t) / -z;
	elseif ((z * t) <= 1e-59)
		tmp = x / y;
	else
		tmp = (x / -z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+38], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-59], N[(x / y), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -9.99999999999999977e37

   1. Initial program 96.4%

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

      1. clear-num 96.3%

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

      2. associate-/r/ 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in y around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-/r* 81.9%

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

      3. distribute-neg-frac2 81.9%

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

   7. Simplified 81.9%

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

   if -9.99999999999999977e37 < (*.f64 z t) < 1e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 83.0%

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

   if 1e-59 < (*.f64 z t)

   1. Initial program 89.2%

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

      1. clear-num 88.9%

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

      2. associate-/r/ 88.9%

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

   4. Applied egg-rr 88.9%

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

   5. Taylor expanded in t around inf 68.8%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   6. Step-by-step derivation

      1. distribute-lft-out 68.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}\right)}}{t} \]

      2. associate-*r/ 68.8%

         \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      3. mul-1-neg 68.8%

         \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      4. associate-/r* 68.7%

         \[\leadsto -\frac{\frac{x}{z} + \color{blue}{\frac{\frac{x \cdot y}{t}}{{z}^{2}}}}{t} \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{\frac{x \cdot y}{t}}{{z}^{2}}}{t}} \]

   8. Taylor expanded in z around inf 76.0%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+38}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+38}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1e+38)
   (/ -1.0 (* z (/ t x)))
   (if (<= (* z t) 1e-59) (/ x y) (/ (/ x (- z)) t))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+38) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= 1e-59) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * t) <= (-1d+38)) then
        tmp = (-1.0d0) / (z * (t / x))
    else if ((z * t) <= 1d-59) then
        tmp = x / y
    else
        tmp = (x / -z) / t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+38) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= 1e-59) {
		tmp = x / y;
	} else {
		tmp = (x / -z) / t;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1e+38:
		tmp = -1.0 / (z * (t / x))
	elif (z * t) <= 1e-59:
		tmp = x / y
	else:
		tmp = (x / -z) / t
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+38)
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	elseif (Float64(z * t) <= 1e-59)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / Float64(-z)) / t);
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1e+38)
		tmp = -1.0 / (z * (t / x));
	elseif ((z * t) <= 1e-59)
		tmp = x / y;
	else
		tmp = (x / -z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+38], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 1e-59], N[(x / y), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -9.99999999999999977e37

   1. Initial program 96.4%

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

      1. clear-num 96.3%

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

      2. associate-/r/ 96.4%

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

   4. Applied egg-rr 96.4%

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

   5. Taylor expanded in y around 0 83.7%

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

      1. associate-/r* 83.7%

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

   7. Simplified 83.7%

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

      1. *-commutative 83.7%

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

      2. associate-/l/ 83.7%

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

      3. frac-2neg 83.7%

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

      4. metadata-eval 83.7%

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

      5. distribute-lft-neg-out 83.7%

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

      6. div-inv 83.7%

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

      7. associate-/l/ 81.9%

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

      8. clear-num 81.8%

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

      9. frac-2neg 81.8%

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

      10. metadata-eval 81.8%

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

      11. add-sqr-sqrt 40.5%

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

      12. sqrt-unprod 49.5%

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

      13. sqr-neg 49.5%

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

      14. sqrt-prod 17.1%

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

      15. add-sqr-sqrt 35.6%

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

      16. distribute-frac-neg 35.6%

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

      17. div-inv 35.6%

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

      18. add-sqr-sqrt 18.5%

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

      19. sqrt-unprod 42.6%

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

      20. sqr-neg 42.6%

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

      21. sqrt-prod 39.9%

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

      22. add-sqr-sqrt 80.5%

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

      23. clear-num 82.4%

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

   9. Applied egg-rr 82.4%

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

   if -9.99999999999999977e37 < (*.f64 z t) < 1e-59

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 83.0%

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

   if 1e-59 < (*.f64 z t)

   1. Initial program 89.2%

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

      1. clear-num 88.9%

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

      2. associate-/r/ 88.9%

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

   4. Applied egg-rr 88.9%

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

   5. Taylor expanded in t around inf 68.8%

      \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{z} + -1 \cdot \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]
   6. Step-by-step derivation

      1. distribute-lft-out 68.8%

         \[\leadsto \frac{\color{blue}{-1 \cdot \left(\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}\right)}}{t} \]

      2. associate-*r/ 68.8%

         \[\leadsto \color{blue}{-1 \cdot \frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      3. mul-1-neg 68.8%

         \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{x \cdot y}{t \cdot {z}^{2}}}{t}} \]

      4. associate-/r* 68.7%

         \[\leadsto -\frac{\frac{x}{z} + \color{blue}{\frac{\frac{x \cdot y}{t}}{{z}^{2}}}}{t} \]

   7. Simplified 68.7%

      \[\leadsto \color{blue}{-\frac{\frac{x}{z} + \frac{\frac{x \cdot y}{t}}{{z}^{2}}}{t}} \]

   8. Taylor expanded in z around inf 76.0%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+38}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq 10^{-59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+167} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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 (or (<= (* z t) -5e+167) (not (<= (* z t) 2e+129)))
   (/ x (* z t))
   (/ x y)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -5e+167) || !((z * t) <= 2e+129)) {
		tmp = x / (z * t);
	} else {
		tmp = x / 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 * t) <= (-5d+167)) .or. (.not. ((z * t) <= 2d+129))) then
        tmp = x / (z * t)
    else
        tmp = x / 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 * t) <= -5e+167) || !((z * t) <= 2e+129)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -5e+167) or not ((z * t) <= 2e+129):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -5e+167) || !(Float64(z * t) <= 2e+129))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / 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 * t) <= -5e+167) || ~(((z * t) <= 2e+129)))
		tmp = x / (z * t);
	else
		tmp = x / 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[Or[LessEqual[N[(z * t), $MachinePrecision], -5e+167], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+129]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999997e167 or 2e129 < (*.f64 z t)

   1. Initial program 87.6%

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

      1. clear-num 87.5%

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

      2. associate-/r/ 87.6%

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

   4. Applied egg-rr 87.6%

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

   5. Taylor expanded in y around 0 86.3%

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

      1. associate-/r* 88.0%

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

   7. Simplified 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-/l/ 86.3%

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

      3. frac-2neg 86.3%

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

      4. metadata-eval 86.3%

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

      5. distribute-lft-neg-out 86.3%

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

      6. div-inv 86.3%

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

      7. add-sqr-sqrt 47.1%

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

      8. sqrt-unprod 59.2%

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

      9. sqr-neg 59.2%

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

      10. sqrt-prod 20.4%

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

      11. add-sqr-sqrt 45.1%

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

   9. Applied egg-rr 45.1%

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

   if -4.9999999999999997e167 < (*.f64 z t) < 2e129

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.3%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+167} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+129}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+288}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \end{array} \]

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 t) 1e+288) (/ x (- y (* z t))) (/ -1.0 (* z (/ t x)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= 1e+288) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	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 * t) <= 1d+288) then
        tmp = x / (y - (z * t))
    else
        tmp = (-1.0d0) / (z * (t / x))
    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 * t) <= 1e+288) {
		tmp = x / (y - (z * t));
	} else {
		tmp = -1.0 / (z * (t / x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if (z * t) <= 1e+288:
		tmp = x / (y - (z * t))
	else:
		tmp = -1.0 / (z * (t / x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= 1e+288)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	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 * t) <= 1e+288)
		tmp = x / (y - (z * t));
	else
		tmp = -1.0 / (z * (t / x));
	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[N[(z * t), $MachinePrecision], 1e+288], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 1e288

   1. Initial program 99.1%

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

   if 1e288 < (*.f64 z t)

   1. Initial program 50.2%

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

      1. clear-num 50.2%

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

      2. associate-/r/ 50.2%

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

   4. Applied egg-rr 50.2%

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

   5. Taylor expanded in y around 0 50.2%

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

      1. associate-/r* 59.1%

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

   7. Simplified 59.1%

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

      1. *-commutative 59.1%

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

      2. associate-/l/ 50.2%

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

      3. frac-2neg 50.2%

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

      4. metadata-eval 50.2%

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

      5. distribute-lft-neg-out 50.2%

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

      6. div-inv 50.2%

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

      7. associate-/l/ 99.5%

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

      8. clear-num 99.6%

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

      9. frac-2neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. add-sqr-sqrt 59.8%

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

      12. sqrt-unprod 62.2%

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

      13. sqr-neg 62.2%

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

      14. sqrt-prod 20.9%

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

      15. add-sqr-sqrt 49.4%

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

      16. distribute-frac-neg 49.4%

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

      17. div-inv 49.4%

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

      18. add-sqr-sqrt 28.4%

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

      19. sqrt-unprod 56.4%

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

      20. sqr-neg 56.4%

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

      21. sqrt-prod 40.0%

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

      22. add-sqr-sqrt 99.8%

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

      23. clear-num 100.0%

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

   9. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{-1}{z \cdot \frac{t}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 10^{+288}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 54.3% accurate, 2.3× speedup

Math

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

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 y))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in y around inf 54.4%

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

4. Final simplification 54.4%

   \[\leadsto \frac{x}{y} \]
5. Add Preprocessing

Developer target: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{y}{x} - \frac{z}{x} \cdot t}\\ \mathbf{if}\;x < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x < 2.1378306434876444 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (- (/ y x) (* (/ z x) t)))))
   (if (< x -1.618195973607049e+50)
     t_1
     (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = 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 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((y / x) - ((z / x) * t));
	double tmp;
	if (x < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (x < 2.1378306434876444e+131) {
		tmp = x / (y - (z * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 / ((y / x) - ((z / x) * t))
	tmp = 0
	if x < -1.618195973607049e+50:
		tmp = t_1
	elif x < 2.1378306434876444e+131:
		tmp = x / (y - (z * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(y / x) - Float64(Float64(z / x) * t)))
	tmp = 0.0
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = Float64(x / Float64(y - Float64(z * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 / ((y / x) - ((z / x) * t));
	tmp = 0.0;
	if (x < -1.618195973607049e+50)
		tmp = t_1;
	elseif (x < 2.1378306434876444e+131)
		tmp = x / (y - (z * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 / N[(N[(y / x), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[x, -1.618195973607049e+50], t$95$1, If[Less[x, 2.1378306434876444e+131], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (if (< x -1.618195973607049e+50) (/ 1.0 (- (/ y x) (* (/ z x) t))) (if (< x 2.1378306434876444e+131) (/ x (- y (* z t))) (/ 1.0 (- (/ y x) (* (/ z x) t)))))

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