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

Percentage Accurate: 95.8% → 99.7%

Time: 8.3s

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: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+243}\right):\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: 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) 5e+243)))
   (* (/ -1.0 z) (/ x t))
   (/ x (fma z (- t) y))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -((double) INFINITY)) || !((z * t) <= 5e+243)) {
		tmp = (-1.0 / z) * (x / t);
	} else {
		tmp = x / fma(z, -t, y);
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= Float64(-Inf)) || !(Float64(z * t) <= 5e+243))
		tmp = Float64(Float64(-1.0 / z) * Float64(x / t));
	else
		tmp = Float64(x / fma(z, Float64(-t), y));
	end
	return tmp
end

Wolfram

NOTE: 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], 5e+243]], $MachinePrecision]], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(x / N[(z * (-t) + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -inf.0 or 5.00000000000000037e243 < (*.f64 z t)

   1. Initial program 72.0%

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

      1. sub-neg 72.0%

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

      2. +-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. fma-udef 72.0%

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

      5. clear-num 72.0%

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

      6. inv-pow 72.0%

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

      7. add-sqr-sqrt 41.6%

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

      8. sqrt-unprod 72.0%

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

      9. sqr-neg 72.0%

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

      10. sqrt-unprod 30.4%

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

      11. add-sqr-sqrt 67.0%

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

   3. Applied egg-rr 67.0%

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

   4. Taylor expanded in z around inf 67.0%

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

      1. add-sqr-sqrt 33.2%

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

      2. sqrt-unprod 68.2%

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

      3. sqr-neg 68.2%

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

      4. sqrt-unprod 36.3%

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

      5. add-sqr-sqrt 72.0%

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

      6. neg-mul-1 72.0%

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

      7. *-commutative 72.0%

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

      8. times-frac 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 z t) < 5.00000000000000037e243

   1. Initial program 99.8%

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

      1. cancel-sign-sub-inv 99.8%

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

      2. +-commutative 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. distribute-rgt-neg-out 99.8%

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

      5. fma-def 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+243}\right):\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(z, -t, y\right)}\\ \end{array} \]

Alternative 2: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ t_2 := \frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+243}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))) (t_2 (* (/ -1.0 z) (/ x t))))
   (if (<= (* z t) -5e+89)
     t_2
     (if (<= (* z t) -5e+15)
       (/ x y)
       (if (<= (* z t) -5e-133)
         t_1
         (if (<= (* z t) 4e-17) (/ x y) (if (<= (* z t) 5e+243) t_1 t_2)))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double t_2 = (-1.0 / z) * (x / t);
	double tmp;
	if ((z * t) <= -5e+89) {
		tmp = t_2;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -5e-133) {
		tmp = t_1;
	} else if ((z * t) <= 4e-17) {
		tmp = x / y;
	} else if ((z * t) <= 5e+243) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -x / (z * t)
    t_2 = ((-1.0d0) / z) * (x / t)
    if ((z * t) <= (-5d+89)) then
        tmp = t_2
    else if ((z * t) <= (-5d+15)) then
        tmp = x / y
    else if ((z * t) <= (-5d-133)) then
        tmp = t_1
    else if ((z * t) <= 4d-17) then
        tmp = x / y
    else if ((z * t) <= 5d+243) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double t_2 = (-1.0 / z) * (x / t);
	double tmp;
	if ((z * t) <= -5e+89) {
		tmp = t_2;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -5e-133) {
		tmp = t_1;
	} else if ((z * t) <= 4e-17) {
		tmp = x / y;
	} else if ((z * t) <= 5e+243) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	t_1 = -x / (z * t)
	t_2 = (-1.0 / z) * (x / t)
	tmp = 0
	if (z * t) <= -5e+89:
		tmp = t_2
	elif (z * t) <= -5e+15:
		tmp = x / y
	elif (z * t) <= -5e-133:
		tmp = t_1
	elif (z * t) <= 4e-17:
		tmp = x / y
	elif (z * t) <= 5e+243:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	t_2 = Float64(Float64(-1.0 / z) * Float64(x / t))
	tmp = 0.0
	if (Float64(z * t) <= -5e+89)
		tmp = t_2;
	elseif (Float64(z * t) <= -5e+15)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -5e-133)
		tmp = t_1;
	elseif (Float64(z * t) <= 4e-17)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 5e+243)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	t_2 = (-1.0 / z) * (x / t);
	tmp = 0.0;
	if ((z * t) <= -5e+89)
		tmp = t_2;
	elseif ((z * t) <= -5e+15)
		tmp = x / y;
	elseif ((z * t) <= -5e-133)
		tmp = t_1;
	elseif ((z * t) <= 4e-17)
		tmp = x / y;
	elseif ((z * t) <= 5e+243)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+89], t$95$2, If[LessEqual[N[(z * t), $MachinePrecision], -5e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -5e-133], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 4e-17], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+243], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999983e89 or 5.00000000000000037e243 < (*.f64 z t)

   1. Initial program 86.6%

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

      1. sub-neg 86.6%

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

      2. +-commutative 86.6%

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

      3. distribute-rgt-neg-in 86.6%

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

      4. fma-udef 86.6%

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

      5. clear-num 84.9%

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

      6. inv-pow 84.9%

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

      7. add-sqr-sqrt 51.5%

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

      8. sqrt-unprod 64.0%

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

      9. sqr-neg 64.0%

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

      10. sqrt-unprod 23.3%

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

      11. add-sqr-sqrt 50.8%

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

   3. Applied egg-rr 50.8%

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

   4. Taylor expanded in z around inf 44.1%

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

      1. add-sqr-sqrt 21.4%

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

      2. sqrt-unprod 54.8%

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

      3. sqr-neg 54.8%

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

      4. sqrt-unprod 40.6%

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

      5. add-sqr-sqrt 79.5%

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

      6. neg-mul-1 79.5%

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

      7. *-commutative 79.5%

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

      8. times-frac 90.4%

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

   6. Applied egg-rr 90.4%

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

   if -4.99999999999999983e89 < (*.f64 z t) < -5e15 or -4.9999999999999999e-133 < (*.f64 z t) < 4.00000000000000029e-17

   1. Initial program 100.0%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 86.6%

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

   if -5e15 < (*.f64 z t) < -4.9999999999999999e-133 or 4.00000000000000029e-17 < (*.f64 z t) < 5.00000000000000037e243

   1. Initial program 99.6%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   4. Simplified 75.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{-133}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+243}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \end{array} \]

Alternative 3: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot t}\\ t_2 := \frac{-\frac{x}{t}}{z}\\ \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+243}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z t))) (t_2 (/ (- (/ x t)) z)))
   (if (<= (* z t) -5e+89)
     t_2
     (if (<= (* z t) -5e+15)
       (/ x y)
       (if (<= (* z t) -5e-133)
         t_1
         (if (<= (* z t) 4e-17) (/ x y) (if (<= (* z t) 5e+243) t_1 t_2)))))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double t_2 = -(x / t) / z;
	double tmp;
	if ((z * t) <= -5e+89) {
		tmp = t_2;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -5e-133) {
		tmp = t_1;
	} else if ((z * t) <= 4e-17) {
		tmp = x / y;
	} else if ((z * t) <= 5e+243) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -x / (z * t)
    t_2 = -(x / t) / z
    if ((z * t) <= (-5d+89)) then
        tmp = t_2
    else if ((z * t) <= (-5d+15)) then
        tmp = x / y
    else if ((z * t) <= (-5d-133)) then
        tmp = t_1
    else if ((z * t) <= 4d-17) then
        tmp = x / y
    else if ((z * t) <= 5d+243) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = -x / (z * t);
	double t_2 = -(x / t) / z;
	double tmp;
	if ((z * t) <= -5e+89) {
		tmp = t_2;
	} else if ((z * t) <= -5e+15) {
		tmp = x / y;
	} else if ((z * t) <= -5e-133) {
		tmp = t_1;
	} else if ((z * t) <= 4e-17) {
		tmp = x / y;
	} else if ((z * t) <= 5e+243) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	t_1 = -x / (z * t)
	t_2 = -(x / t) / z
	tmp = 0
	if (z * t) <= -5e+89:
		tmp = t_2
	elif (z * t) <= -5e+15:
		tmp = x / y
	elif (z * t) <= -5e-133:
		tmp = t_1
	elif (z * t) <= 4e-17:
		tmp = x / y
	elif (z * t) <= 5e+243:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(-x) / Float64(z * t))
	t_2 = Float64(Float64(-Float64(x / t)) / z)
	tmp = 0.0
	if (Float64(z * t) <= -5e+89)
		tmp = t_2;
	elseif (Float64(z * t) <= -5e+15)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= -5e-133)
		tmp = t_1;
	elseif (Float64(z * t) <= 4e-17)
		tmp = Float64(x / y);
	elseif (Float64(z * t) <= 5e+243)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = -x / (z * t);
	t_2 = -(x / t) / z;
	tmp = 0.0;
	if ((z * t) <= -5e+89)
		tmp = t_2;
	elseif ((z * t) <= -5e+15)
		tmp = x / y;
	elseif ((z * t) <= -5e-133)
		tmp = t_1;
	elseif ((z * t) <= 4e-17)
		tmp = x / y;
	elseif ((z * t) <= 5e+243)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-N[(x / t), $MachinePrecision]) / z), $MachinePrecision]}, If[LessEqual[N[(z * t), $MachinePrecision], -5e+89], t$95$2, If[LessEqual[N[(z * t), $MachinePrecision], -5e+15], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], -5e-133], t$95$1, If[LessEqual[N[(z * t), $MachinePrecision], 4e-17], N[(x / y), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+243], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.99999999999999983e89 or 5.00000000000000037e243 < (*.f64 z t)

   1. Initial program 86.6%

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

      1. sub-neg 86.6%

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

      2. +-commutative 86.6%

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

      3. distribute-rgt-neg-in 86.6%

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

      4. fma-udef 86.6%

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

      5. frac-2neg 86.6%

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

      6. div-inv 86.6%

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

      7. fma-udef 86.6%

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

      8. distribute-rgt-neg-in 86.6%

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

      9. distribute-neg-in 86.6%

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

   3. Applied egg-rr 86.6%

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

      1. /-rgt-identity 86.6%

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

      2. add-cube-cbrt 86.1%

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

      3. associate-/l* 86.0%

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

      4. pow2 86.0%

         \[\leadsto \left(-x\right) \cdot \frac{1}{\frac{\color{blue}{{\left(\sqrt[3]{z \cdot t - y}\right)}^{2}}}{\frac{1}{\sqrt[3]{z \cdot t - y}}}} \]

   5. Applied egg-rr 86.0%

      \[\leadsto \left(-x\right) \cdot \frac{1}{\color{blue}{\frac{{\left(\sqrt[3]{z \cdot t - y}\right)}^{2}}{\frac{1}{\sqrt[3]{z \cdot t - y}}}}} \]

   6. Taylor expanded in z around inf 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-/r* 90.4%

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

      3. distribute-neg-frac 90.4%

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

   8. Simplified 90.4%

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

   if -4.99999999999999983e89 < (*.f64 z t) < -5e15 or -4.9999999999999999e-133 < (*.f64 z t) < 4.00000000000000029e-17

   1. Initial program 100.0%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 86.6%

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

   if -5e15 < (*.f64 z t) < -4.9999999999999999e-133 or 4.00000000000000029e-17 < (*.f64 z t) < 5.00000000000000037e243

   1. Initial program 99.6%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   4. Simplified 75.8%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+89}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq -5 \cdot 10^{-133}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{elif}\;z \cdot t \leq 4 \cdot 10^{-17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+243}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{x}{t}}{z}\\ \end{array} \]

Alternative 4: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+243}\right):\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: 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) 5e+243)))
   (* (/ -1.0 z) (/ x t))
   (/ x (- y (* z t)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -((double) INFINITY)) || !((z * t) <= 5e+243)) {
		tmp = (-1.0 / z) * (x / t);
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -Double.POSITIVE_INFINITY) || !((z * t) <= 5e+243)) {
		tmp = (-1.0 / z) * (x / t);
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -math.inf) or not ((z * t) <= 5e+243):
		tmp = (-1.0 / z) * (x / t)
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= Float64(-Inf)) || !(Float64(z * t) <= 5e+243))
		tmp = Float64(Float64(-1.0 / z) * Float64(x / t));
	else
		tmp = Float64(x / Float64(y - Float64(z * t)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -Inf) || ~(((z * t) <= 5e+243)))
		tmp = (-1.0 / z) * (x / t);
	else
		tmp = x / (y - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: 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], 5e+243]], $MachinePrecision]], N[(N[(-1.0 / z), $MachinePrecision] * N[(x / t), $MachinePrecision]), $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 5.00000000000000037e243 < (*.f64 z t)

   1. Initial program 72.0%

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

      1. sub-neg 72.0%

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

      2. +-commutative 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. fma-udef 72.0%

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

      5. clear-num 72.0%

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

      6. inv-pow 72.0%

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

      7. add-sqr-sqrt 41.6%

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

      8. sqrt-unprod 72.0%

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

      9. sqr-neg 72.0%

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

      10. sqrt-unprod 30.4%

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

      11. add-sqr-sqrt 67.0%

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

   3. Applied egg-rr 67.0%

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

   4. Taylor expanded in z around inf 67.0%

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

      1. add-sqr-sqrt 33.2%

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

      2. sqrt-unprod 68.2%

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

      3. sqr-neg 68.2%

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

      4. sqrt-unprod 36.3%

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

      5. add-sqr-sqrt 72.0%

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

      6. neg-mul-1 72.0%

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

      7. *-commutative 72.0%

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

      8. times-frac 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 z t) < 5.00000000000000037e243

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+243}\right):\\ \;\;\;\;\frac{-1}{z} \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]

Alternative 5: 73.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.5e+32) (/ x y) (if (<= y 4.8e-72) (/ (- x) (* z t)) (/ x y))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+32) {
		tmp = x / y;
	} else if (y <= 4.8e-72) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.5d+32)) then
        tmp = x / y
    else if (y <= 4.8d-72) then
        tmp = -x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.5e+32) {
		tmp = x / y;
	} else if (y <= 4.8e-72) {
		tmp = -x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= -1.5e+32:
		tmp = x / y
	elif y <= 4.8e-72:
		tmp = -x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.5e+32)
		tmp = Float64(x / y);
	elseif (y <= 4.8e-72)
		tmp = Float64(Float64(-x) / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.5e+32)
		tmp = x / y;
	elseif (y <= 4.8e-72)
		tmp = -x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, -1.5e+32], N[(x / y), $MachinePrecision], If[LessEqual[y, 4.8e-72], N[((-x) / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5e32 or 4.8e-72 < y

   1. Initial program 95.9%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 76.7%

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

   if -1.5e32 < y < 4.8e-72

   1. Initial program 95.7%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around 0 83.0%

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

      1. associate-*r/ 83.0%

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

      2. neg-mul-1 83.0%

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

   4. Simplified 83.0%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{-x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 6: 58.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \leq -2100000000 \lor \neg \left(t \leq 6.8 \cdot 10^{+181}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2100000000.0) (not (<= t 6.8e+181))) (/ x (* z t)) (/ x y)))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2100000000.0) || !(t <= 6.8e+181)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2100000000.0d0)) .or. (.not. (t <= 6.8d+181))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2100000000.0) || !(t <= 6.8e+181)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if (t <= -2100000000.0) or not (t <= 6.8e+181):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2100000000.0) || !(t <= 6.8e+181))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2100000000.0) || ~((t <= 6.8e+181)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2100000000.0], N[Not[LessEqual[t, 6.8e+181]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1e9 or 6.80000000000000062e181 < t

   1. Initial program 91.3%

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

      1. sub-neg 91.3%

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

      2. +-commutative 91.3%

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

      3. distribute-rgt-neg-in 91.3%

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

      4. fma-udef 91.3%

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

      5. clear-num 88.6%

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

      6. inv-pow 88.6%

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

      7. add-sqr-sqrt 65.4%

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

      8. sqrt-unprod 57.2%

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

      9. sqr-neg 57.2%

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

      10. sqrt-unprod 14.3%

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

      11. add-sqr-sqrt 50.9%

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

   3. Applied egg-rr 50.9%

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

   4. Taylor expanded in z around inf 32.3%

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

   if -2.1e9 < t < 6.80000000000000062e181

   1. Initial program 98.7%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 61.4%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2100000000 \lor \neg \left(t \leq 6.8 \cdot 10^{+181}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 7: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+140) (/ (/ x z) t) (if (<= z 5.2e+80) (/ x y) (/ x (* z t)))))

C

assert(z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+140) {
		tmp = (x / z) / t;
	} else if (z <= 5.2e+80) {
		tmp = x / y;
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.8d+140)) then
        tmp = (x / z) / t
    else if (z <= 5.2d+80) then
        tmp = x / y
    else
        tmp = x / (z * t)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+140) {
		tmp = (x / z) / t;
	} else if (z <= 5.2e+80) {
		tmp = x / y;
	} else {
		tmp = x / (z * t);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+140:
		tmp = (x / z) / t
	elif z <= 5.2e+80:
		tmp = x / y
	else:
		tmp = x / (z * t)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+140)
		tmp = Float64(Float64(x / z) / t);
	elseif (z <= 5.2e+80)
		tmp = Float64(x / y);
	else
		tmp = Float64(x / Float64(z * t));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+140)
		tmp = (x / z) / t;
	elseif (z <= 5.2e+80)
		tmp = x / y;
	else
		tmp = x / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+140], N[(N[(x / z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 5.2e+80], N[(x / y), $MachinePrecision], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999983e140

   1. Initial program 94.5%

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

      1. sub-neg 94.5%

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

      2. +-commutative 94.5%

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

      3. distribute-rgt-neg-in 94.5%

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

      4. fma-udef 94.5%

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

      5. frac-2neg 94.5%

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

      6. div-inv 94.3%

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

      7. fma-udef 94.3%

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

      8. distribute-rgt-neg-in 94.3%

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

      9. distribute-neg-in 94.3%

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

   3. Applied egg-rr 94.3%

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

      1. un-div-inv 94.5%

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

      2. sub-neg 94.5%

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

      3. add-sqr-sqrt 0.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 25.8%

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

      6. sqr-neg 25.8%

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

      7. sqrt-unprod 31.1%

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

      8. add-sqr-sqrt 31.1%

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

      9. associate-*l* 31.1%

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

      10. distribute-lft-neg-out 31.1%

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

      11. distribute-lft-neg-out 31.1%

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

      12. associate-*r* 31.1%

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

      13. add-sqr-sqrt 69.1%

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

      14. distribute-neg-in 69.1%

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

      15. fma-udef 69.1%

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

      16. frac-2neg 69.1%

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

      17. clear-num 69.2%

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

      18. frac-2neg 69.2%

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

      19. metadata-eval 69.2%

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

      20. add-sqr-sqrt 31.8%

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

      21. sqrt-unprod 74.2%

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

   5. Applied egg-rr 82.6%

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

   6. Taylor expanded in z around inf 80.1%

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

      1. associate-/l* 88.2%

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

      2. associate-/r/ 80.6%

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

   8. Simplified 80.6%

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

      1. expm1-log1p-u 76.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{-1}{\frac{t}{x} \cdot z}\right)\right)} \]

      2. expm1-udef 58.2%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{-1}{\frac{t}{x} \cdot z}\right)} - 1} \]

      3. associate-/r* 58.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\frac{-1}{\frac{t}{x}}}{z}}\right)} - 1 \]

      4. frac-2neg 58.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{--1}{-\frac{t}{x}}}}{z}\right)} - 1 \]

      5. metadata-eval 58.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{\color{blue}{1}}{-\frac{t}{x}}}{z}\right)} - 1 \]

      6. add-sqr-sqrt 23.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{1}{-\frac{t}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}}}{z}\right)} - 1 \]

      7. sqrt-unprod 57.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{1}{-\frac{t}{\color{blue}{\sqrt{x \cdot x}}}}}{z}\right)} - 1 \]

      8. sqr-neg 57.9%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{1}{-\frac{t}{\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}}}}{z}\right)} - 1 \]

      9. sqrt-unprod 34.6%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{1}{-\frac{t}{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}}}{z}\right)} - 1 \]

      10. add-sqr-sqrt 58.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{1}{-\frac{t}{\color{blue}{-x}}}}{z}\right)} - 1 \]

      11. distribute-frac-neg 58.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{1}{\color{blue}{\frac{-t}{-x}}}}{z}\right)} - 1 \]

      12. frac-2neg 58.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{1}{\color{blue}{\frac{t}{x}}}}{z}\right)} - 1 \]

      13. clear-num 58.2%

          \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{x}{t}}}{z}\right)} - 1 \]

   10. Applied egg-rr 58.2%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{x}{t}}{z}\right)} - 1} \]
   11. Step-by-step derivation

       1. expm1-def 55.1%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{x}{t}}{z}\right)\right)} \]

       2. expm1-log1p 55.3%

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

       3. associate-/l/ 55.4%

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

       4. associate-/r* 58.0%

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

   12. Simplified 58.0%

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

   if -2.79999999999999983e140 < z < 5.19999999999999963e80

   1. Initial program 98.7%

      \[\frac{x}{y - z \cdot t} \]

   2. Taylor expanded in y around inf 60.7%

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

   if 5.19999999999999963e80 < z

   1. Initial program 88.3%

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

      1. sub-neg 88.3%

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

      2. +-commutative 88.3%

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

      3. distribute-rgt-neg-in 88.3%

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

      4. fma-udef 88.3%

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

      5. clear-num 87.7%

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

      6. inv-pow 87.7%

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

      7. add-sqr-sqrt 48.8%

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

      8. sqrt-unprod 67.3%

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

      9. sqr-neg 67.3%

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

      10. sqrt-unprod 21.7%

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

      11. add-sqr-sqrt 50.9%

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

   3. Applied egg-rr 50.9%

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

   4. Taylor expanded in z around inf 31.8%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{\frac{x}{z}}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z \cdot t}\\ \end{array} \]

Alternative 8: 54.2% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: 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 z < t;
public static double code(double x, double y, double z, double t) {
	return x / y;
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: 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 95.8%

   \[\frac{x}{y - z \cdot t} \]

2. Taylor expanded in y around inf 50.1%

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

3. Final simplification 50.1%

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

Developer target: 96.6% accurate, 0.5× 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 2023293 
(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))))