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

Percentage Accurate: 95.7% → 99.6%

Time: 8.7s

Alternatives: 8

Speedup: 0.3×

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: 95.7% 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 10^{+214}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) (- INFINITY)) (not (<= (* z t) 1e+214)))
   (/ (/ x z) (- t))
   (/ x (- y (* z t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -((double) INFINITY)) || !((z * t) <= 1e+214)) {
		tmp = (x / z) / -t;
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

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) <= -Double.POSITIVE_INFINITY) || !((z * t) <= 1e+214)) {
		tmp = (x / z) / -t;
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -math.inf) or not ((z * t) <= 1e+214):
		tmp = (x / z) / -t
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= Float64(-Inf)) || !(Float64(z * t) <= 1e+214))
		tmp = Float64(Float64(x / z) / Float64(-t));
	else
		tmp = Float64(x / Float64(y - 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) <= -Inf) || ~(((z * t) <= 1e+214)))
		tmp = (x / z) / -t;
	else
		tmp = x / (y - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+214]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -inf.0 or 9.9999999999999995e213 < (*.f64 z t)

   1. Initial program 57.9%

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

      1. clear-num 57.9%

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

      2. inv-pow 57.9%

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

   4. Applied egg-rr 57.9%

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

   5. Taylor expanded in y around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. associate-/l/ 99.8%

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

      3. distribute-neg-frac2 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (*.f64 z t) < 9.9999999999999995e213

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 10^{+214}\right):\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51} \lor \neg \left(z \cdot t \leq -5 \cdot 10^{+15}\right) \land \left(z \cdot t \leq -2 \cdot 10^{-117} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-13}\right)\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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) -1e+51)
         (and (not (<= (* z t) -5e+15))
              (or (<= (* z t) -2e-117) (not (<= (* z t) 2e-13)))))
   (/ (- 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) <= -1e+51) || (!((z * t) <= -5e+15) && (((z * t) <= -2e-117) || !((z * t) <= 2e-13)))) {
		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) <= (-1d+51)) .or. (.not. ((z * t) <= (-5d+15))) .and. ((z * t) <= (-2d-117)) .or. (.not. ((z * t) <= 2d-13))) 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) <= -1e+51) || (!((z * t) <= -5e+15) && (((z * t) <= -2e-117) || !((z * t) <= 2e-13)))) {
		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) <= -1e+51) or (not ((z * t) <= -5e+15) and (((z * t) <= -2e-117) or not ((z * t) <= 2e-13))):
		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) <= -1e+51) || (!(Float64(z * t) <= -5e+15) && ((Float64(z * t) <= -2e-117) || !(Float64(z * t) <= 2e-13))))
		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) <= -1e+51) || (~(((z * t) <= -5e+15)) && (((z * t) <= -2e-117) || ~(((z * t) <= 2e-13)))))
		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], -1e+51], And[N[Not[LessEqual[N[(z * t), $MachinePrecision], -5e+15]], $MachinePrecision], Or[LessEqual[N[(z * t), $MachinePrecision], -2e-117], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e-13]], $MachinePrecision]]]], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1e51 or -5e15 < (*.f64 z t) < -2.00000000000000006e-117 or 2.0000000000000001e-13 < (*.f64 z t)

   1. Initial program 86.8%

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

   3. Taylor expanded in y around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. neg-mul-1 69.2%

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

   5. Simplified 69.2%

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

   if -1e51 < (*.f64 z t) < -5e15 or -2.00000000000000006e-117 < (*.f64 z t) < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.4%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51} \lor \neg \left(z \cdot t \leq -5 \cdot 10^{+15}\right) \land \left(z \cdot t \leq -2 \cdot 10^{-117} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{-13}\right)\right):\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{t}}{-z}\\ \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 t) (- z))))
   (if (<= (* z t) -1e+51)
     t_1
     (if (<= (* z t) -5e+15)
       (/ x y)
       (if (<= (* z t) -2e-117)
         (/ (- x) (* z t))
         (if (<= (* z t) 2e-13) (/ x 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 / t) / -z;
	double tmp;
	if ((z * t) <= -1e+51) {
		tmp = t_1;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 2e-13) {
		tmp = x / 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 / t) / -z
    if ((z * t) <= (-1d+51)) then
        tmp = t_1
    else if ((z * t) <= (-5d+15)) then
        tmp = x / y
    else if ((z * t) <= (-2d-117)) then
        tmp = -x / (z * t)
    else if ((z * t) <= 2d-13) then
        tmp = x / 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 / t) / -z;
	double tmp;
	if ((z * t) <= -1e+51) {
		tmp = t_1;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 2e-13) {
		tmp = x / 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 / t) / -z
	tmp = 0
	if (z * t) <= -1e+51:
		tmp = t_1
	elif (z * t) <= -5e+15:
		tmp = x / y
	elif (z * t) <= -2e-117:
		tmp = -x / (z * t)
	elif (z * t) <= 2e-13:
		tmp = x / y
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / t) / Float64(-z))
	tmp = 0.0
	if (Float64(z * t) <= -1e+51)
		tmp = t_1;
	elseif (Float64(z * t) <= -5e+15)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -2e-117)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (Float64(z * t) <= 2e-13)
		tmp = Float64(x / 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 / t) / -z;
	tmp = 0.0;
	if ((z * t) <= -1e+51)
		tmp = t_1;
	elseif ((z * t) <= -5e+15)
		tmp = x / y;
	elseif ((z * t) <= -2e-117)
		tmp = -x / (z * t);
	elseif ((z * t) <= 2e-13)
		tmp = x / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -1e+51], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], -5e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-117], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-13], N[(x / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1e51 or 2.0000000000000001e-13 < (*.f64 z t)

   1. Initial program 84.2%

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

   3. Taylor expanded in y around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. associate-/r* 82.2%

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

      3. distribute-neg-frac2 82.2%

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

   5. Simplified 82.2%

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

   if -1e51 < (*.f64 z t) < -5e15 or -2.00000000000000006e-117 < (*.f64 z t) < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.4%

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

   if -5e15 < (*.f64 z t) < -2.00000000000000006e-117

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 65.3%

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

      1. associate-*r/ 65.3%

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

      2. neg-mul-1 65.3%

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

   5. Simplified 65.3%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

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+51)
   (/ (/ x t) (- z))
   (if (<= (* z t) -5e+15)
     (/ x y)
     (if (<= (* z t) -2e-117)
       (/ (- x) (* z t))
       (if (<= (* z t) 2e-13) (/ 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+51) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 2e-13) {
		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+51)) then
        tmp = (x / t) / -z
    else if ((z * t) <= (-5d+15)) then
        tmp = x / y
    else if ((z * t) <= (-2d-117)) then
        tmp = -x / (z * t)
    else if ((z * t) <= 2d-13) 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+51) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = -x / (z * t);
	} else if ((z * t) <= 2e-13) {
		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+51:
		tmp = (x / t) / -z
	elif (z * t) <= -5e+15:
		tmp = x / y
	elif (z * t) <= -2e-117:
		tmp = -x / (z * t)
	elif (z * t) <= 2e-13:
		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+51)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(z * t) <= -5e+15)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -2e-117)
		tmp = Float64(Float64(-x) / Float64(z * t));
	elseif (Float64(z * t) <= 2e-13)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / z) / Float64(-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+51)
		tmp = (x / t) / -z;
	elseif ((z * t) <= -5e+15)
		tmp = x / y;
	elseif ((z * t) <= -2e-117)
		tmp = -x / (z * t);
	elseif ((z * t) <= 2e-13)
		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+51], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -5e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-117], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-13], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -1e51

   1. Initial program 75.6%

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

   3. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-/r* 89.5%

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

      3. distribute-neg-frac2 89.5%

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

   5. Simplified 89.5%

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

   if -1e51 < (*.f64 z t) < -5e15 or -2.00000000000000006e-117 < (*.f64 z t) < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.4%

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

   if -5e15 < (*.f64 z t) < -2.00000000000000006e-117

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 65.3%

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

      1. associate-*r/ 65.3%

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

      2. neg-mul-1 65.3%

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

   5. Simplified 65.3%

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

   if 2.0000000000000001e-13 < (*.f64 z t)

   1. Initial program 92.0%

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

      1. clear-num 91.9%

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

      2. inv-pow 91.9%

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

   4. Applied egg-rr 91.9%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. associate-/l/ 74.1%

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

      3. distribute-neg-frac2 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

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+51)
   (/ (/ x t) (- z))
   (if (<= (* z t) -5e+15)
     (/ x y)
     (if (<= (* z t) -2e-117)
       (* x (/ (/ -1.0 z) t))
       (if (<= (* z t) 2e-13) (/ 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+51) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = x * ((-1.0 / z) / t);
	} else if ((z * t) <= 2e-13) {
		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+51)) then
        tmp = (x / t) / -z
    else if ((z * t) <= (-5d+15)) then
        tmp = x / y
    else if ((z * t) <= (-2d-117)) then
        tmp = x * (((-1.0d0) / z) / t)
    else if ((z * t) <= 2d-13) 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+51) {
		tmp = (x / t) / -z;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = x * ((-1.0 / z) / t);
	} else if ((z * t) <= 2e-13) {
		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+51:
		tmp = (x / t) / -z
	elif (z * t) <= -5e+15:
		tmp = x / y
	elif (z * t) <= -2e-117:
		tmp = x * ((-1.0 / z) / t)
	elif (z * t) <= 2e-13:
		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+51)
		tmp = Float64(Float64(x / t) / Float64(-z));
	elseif (Float64(z * t) <= -5e+15)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -2e-117)
		tmp = Float64(x * Float64(Float64(-1.0 / z) / t));
	elseif (Float64(z * t) <= 2e-13)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / z) / Float64(-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+51)
		tmp = (x / t) / -z;
	elseif ((z * t) <= -5e+15)
		tmp = x / y;
	elseif ((z * t) <= -2e-117)
		tmp = x * ((-1.0 / z) / t);
	elseif ((z * t) <= 2e-13)
		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+51], N[(N[(x / t), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -5e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-117], N[(x * N[(N[(-1.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-13], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -1e51

   1. Initial program 75.6%

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

   3. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-/r* 89.5%

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

      3. distribute-neg-frac2 89.5%

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

   5. Simplified 89.5%

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

   if -1e51 < (*.f64 z t) < -5e15 or -2.00000000000000006e-117 < (*.f64 z t) < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.4%

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

   if -5e15 < (*.f64 z t) < -2.00000000000000006e-117

   1. Initial program 99.7%

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

      1. clear-num 99.3%

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

      2. inv-pow 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in y around 0 65.2%

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

      1. associate-*r* 65.2%

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

      2. neg-mul-1 65.2%

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

      3. *-commutative 65.2%

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

   7. Simplified 65.2%

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

      1. unpow-1 65.2%

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

      2. clear-num 65.3%

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

      3. associate-/r* 50.1%

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

      4. add-sqr-sqrt 23.0%

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

      5. sqrt-unprod 19.5%

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

      6. sqr-neg 19.5%

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

      7. sqrt-unprod 0.5%

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

      8. add-sqr-sqrt 2.0%

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

      9. associate-/r* 2.3%

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

   9. Applied egg-rr 2.3%

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

       1. add-sqr-sqrt 1.1%

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

       2. sqrt-unprod 20.1%

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

       3. sqr-neg 20.1%

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

       4. sqrt-unprod 38.2%

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

       5. add-sqr-sqrt 65.3%

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

       6. neg-mul-1 65.3%

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

       7. times-frac 53.3%

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

       8. clear-num 53.3%

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

       9. div-inv 53.3%

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

       10. associate-/r/ 65.1%

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

   11. Applied egg-rr 65.1%

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

   if 2.0000000000000001e-13 < (*.f64 z t)

   1. Initial program 92.0%

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

      1. clear-num 91.9%

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

      2. inv-pow 91.9%

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

   4. Applied egg-rr 91.9%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. associate-/l/ 74.1%

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

      3. distribute-neg-frac2 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{\frac{x}{t}}{-z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \end{array} \]

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+51)
   (/ -1.0 (* z (/ t x)))
   (if (<= (* z t) -5e+15)
     (/ x y)
     (if (<= (* z t) -2e-117)
       (* x (/ (/ -1.0 z) t))
       (if (<= (* z t) 2e-13) (/ 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+51) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = x * ((-1.0 / z) / t);
	} else if ((z * t) <= 2e-13) {
		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+51)) then
        tmp = (-1.0d0) / (z * (t / x))
    else if ((z * t) <= (-5d+15)) then
        tmp = x / y
    else if ((z * t) <= (-2d-117)) then
        tmp = x * (((-1.0d0) / z) / t)
    else if ((z * t) <= 2d-13) 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+51) {
		tmp = -1.0 / (z * (t / x));
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -2e-117) {
		tmp = x * ((-1.0 / z) / t);
	} else if ((z * t) <= 2e-13) {
		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+51:
		tmp = -1.0 / (z * (t / x))
	elif (z * t) <= -5e+15:
		tmp = x / y
	elif (z * t) <= -2e-117:
		tmp = x * ((-1.0 / z) / t)
	elif (z * t) <= 2e-13:
		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+51)
		tmp = Float64(-1.0 / Float64(z * Float64(t / x)));
	elseif (Float64(z * t) <= -5e+15)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -2e-117)
		tmp = Float64(x * Float64(Float64(-1.0 / z) / t));
	elseif (Float64(z * t) <= 2e-13)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(x / z) / Float64(-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+51)
		tmp = -1.0 / (z * (t / x));
	elseif ((z * t) <= -5e+15)
		tmp = x / y;
	elseif ((z * t) <= -2e-117)
		tmp = x * ((-1.0 / z) / t);
	elseif ((z * t) <= 2e-13)
		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+51], N[(-1.0 / N[(z * N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -5e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -2e-117], N[(x * N[(N[(-1.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e-13], N[(x / y), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 z t) < -1e51

   1. Initial program 75.6%

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

      1. clear-num 75.5%

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

      2. inv-pow 75.5%

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

   4. Applied egg-rr 75.5%

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

   5. Taylor expanded in y around 0 70.3%

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

      1. associate-*r* 70.3%

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

      2. neg-mul-1 70.3%

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

      3. *-commutative 70.3%

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

   7. Simplified 70.3%

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

      1. unpow-1 70.3%

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

      2. clear-num 70.3%

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

      3. distribute-rgt-neg-out 70.3%

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

      4. distribute-frac-neg2 70.3%

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

      5. clear-num 70.3%

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

      6. associate-*r/ 89.9%

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

      7. distribute-neg-frac 89.9%

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

      8. metadata-eval 89.9%

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

   9. Applied egg-rr 89.9%

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

   if -1e51 < (*.f64 z t) < -5e15 or -2.00000000000000006e-117 < (*.f64 z t) < 2.0000000000000001e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 88.4%

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

   if -5e15 < (*.f64 z t) < -2.00000000000000006e-117

   1. Initial program 99.7%

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

      1. clear-num 99.3%

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

      2. inv-pow 99.3%

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

   4. Applied egg-rr 99.3%

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

   5. Taylor expanded in y around 0 65.2%

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

      1. associate-*r* 65.2%

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

      2. neg-mul-1 65.2%

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

      3. *-commutative 65.2%

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

   7. Simplified 65.2%

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

      1. unpow-1 65.2%

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

      2. clear-num 65.3%

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

      3. associate-/r* 50.1%

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

      4. add-sqr-sqrt 23.0%

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

      5. sqrt-unprod 19.5%

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

      6. sqr-neg 19.5%

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

      7. sqrt-unprod 0.5%

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

      8. add-sqr-sqrt 2.0%

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

      9. associate-/r* 2.3%

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

   9. Applied egg-rr 2.3%

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

       1. add-sqr-sqrt 1.1%

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

       2. sqrt-unprod 20.1%

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

       3. sqr-neg 20.1%

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

       4. sqrt-unprod 38.2%

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

       5. add-sqr-sqrt 65.3%

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

       6. neg-mul-1 65.3%

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

       7. times-frac 53.3%

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

       8. clear-num 53.3%

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

       9. div-inv 53.3%

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

       10. associate-/r/ 65.1%

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

   11. Applied egg-rr 65.1%

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

   if 2.0000000000000001e-13 < (*.f64 z t)

   1. Initial program 92.0%

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

      1. clear-num 91.9%

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

      2. inv-pow 91.9%

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

   4. Applied egg-rr 91.9%

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

   5. Taylor expanded in y around 0 69.6%

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

      1. mul-1-neg 69.6%

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

      2. associate-/l/ 74.1%

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

      3. distribute-neg-frac2 74.1%

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

   7. Simplified 74.1%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+51}:\\ \;\;\;\;\frac{-1}{z \cdot \frac{t}{x}}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -2 \cdot 10^{-117}:\\ \;\;\;\;x \cdot \frac{\frac{-1}{z}}{t}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+114} \lor \neg \left(z \cdot t \leq 10^{+171}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

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) -2e+114) (not (<= (* z t) 1e+171)))
   (/ 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) <= -2e+114) || !((z * t) <= 1e+171)) {
		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) <= (-2d+114)) .or. (.not. ((z * t) <= 1d+171))) 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) <= -2e+114) || !((z * t) <= 1e+171)) {
		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) <= -2e+114) or not ((z * t) <= 1e+171):
		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) <= -2e+114) || !(Float64(z * t) <= 1e+171))
		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) <= -2e+114) || ~(((z * t) <= 1e+171)))
		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], -2e+114], N[Not[LessEqual[N[(z * t), $MachinePrecision], 1e+171]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -2e114 or 9.99999999999999954e170 < (*.f64 z t)

   1. Initial program 75.8%

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

      1. clear-num 75.7%

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

      2. inv-pow 75.7%

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

   4. Applied egg-rr 75.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. associate-*r* 74.5%

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

      2. neg-mul-1 74.5%

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

      3. *-commutative 74.5%

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

   7. Simplified 74.5%

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

      1. unpow-1 74.5%

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

      2. clear-num 74.5%

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

      3. associate-/r* 97.3%

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

      4. add-sqr-sqrt 47.7%

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

      5. sqrt-unprod 60.1%

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

      6. sqr-neg 60.1%

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

      7. sqrt-unprod 24.9%

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

      8. add-sqr-sqrt 43.1%

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

      9. associate-/r* 43.5%

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

   9. Applied egg-rr 43.5%

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

   if -2e114 < (*.f64 z t) < 9.99999999999999954e170

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 69.8%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -2 \cdot 10^{+114} \lor \neg \left(z \cdot t \leq 10^{+171}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.9% 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 92.8%

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

3. Taylor expanded in y around inf 52.2%

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

4. Final simplification 52.2%

   \[\leadsto \frac{x}{y} \]
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 2024039 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (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))))