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

Percentage Accurate: 95.7% → 99.4%

Time: 7.2s

Alternatives: 7

Speedup: 1.0×

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: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;t \cdot z \leq -2 \cdot 10^{+210}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{\left(t \cdot t\right) \cdot z}, \frac{x}{t}\right)}{-z}\\ \mathbf{elif}\;t \cdot z \leq 10^{+259}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{-z}{x} \cdot t}\\ \end{array} \end{array} \]

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 (<= (* t z) -2e+210)
   (/ (fma x (/ y (* (* t t) z)) (/ x t)) (- z))
   (if (<= (* t z) 1e+259) (/ x (fma (- z) t y)) (/ 1.0 (* (/ (- z) x) t)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if ((t * z) <= -2e+210) {
		tmp = fma(x, (y / ((t * t) * z)), (x / t)) / -z;
	} else if ((t * z) <= 1e+259) {
		tmp = x / fma(-z, t, y);
	} else {
		tmp = 1.0 / ((-z / x) * t);
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (Float64(t * z) <= -2e+210)
		tmp = Float64(fma(x, Float64(y / Float64(Float64(t * t) * z)), Float64(x / t)) / Float64(-z));
	elseif (Float64(t * z) <= 1e+259)
		tmp = Float64(x / fma(Float64(-z), t, y));
	else
		tmp = Float64(1.0 / Float64(Float64(Float64(-z) / x) * t));
	end
	return 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[(t * z), $MachinePrecision], -2e+210], N[(N[(x * N[(y / N[(N[(t * t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[N[(t * z), $MachinePrecision], 1e+259], N[(x / N[((-z) * t + y), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[((-z) / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.99999999999999985e210

   1. Initial program 80.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. flip-- N/A

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

      4. associate-/r/ N/A

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

      5. associate-*l/ N/A

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

      6. frac-2neg N/A

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

      7. lower-/.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. +-commutative N/A

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

      12. lift-*.f64 N/A

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

      13. *-commutative N/A

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

      14. lower-fma.f64 N/A

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

      15. difference-of-squares N/A

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

      16. lift--.f64 N/A

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

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

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

      18. lower-*.f64 N/A

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

   4. Applied rewrites 22.1%

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

   5. Taylor expanded in z around inf

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

      1. distribute-lft-out N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-frac2 N/A

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

      5. mul-1-neg N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. mul-1-neg N/A

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

      16. lower-neg.f64 99.8

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

   7. Applied rewrites 99.8%

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

   if -1.99999999999999985e210 < (*.f64 z t) < 9.999999999999999e258

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

   if 9.999999999999999e258 < (*.f64 z t)

   1. Initial program 56.9%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 56.9

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 56.9

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

   4. Applied rewrites 56.9%

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

   5. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 99.8

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

   7. Applied rewrites 99.8%

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

   9. Applied rewrites 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -2 \cdot 10^{+210}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, \frac{y}{\left(t \cdot t\right) \cdot z}, \frac{x}{t}\right)}{-z}\\ \mathbf{elif}\;t \cdot z \leq 10^{+259}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{-z}{x} \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{1}{\frac{-z}{x} \cdot t}\\ \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+252}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 10^{+259}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 1.0 (* (/ (- z) x) t))))
   (if (<= (* t z) -5e+252)
     t_1
     (if (<= (* t z) 1e+259) (/ x (fma (- z) t y)) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = 1.0 / ((-z / x) * t);
	double tmp;
	if ((t * z) <= -5e+252) {
		tmp = t_1;
	} else if ((t * z) <= 1e+259) {
		tmp = x / fma(-z, t, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(1.0 / Float64(Float64(Float64(-z) / x) * t))
	tmp = 0.0
	if (Float64(t * z) <= -5e+252)
		tmp = t_1;
	elseif (Float64(t * z) <= 1e+259)
		tmp = Float64(x / fma(Float64(-z), t, y));
	else
		tmp = t_1;
	end
	return 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[(1.0 / N[(N[((-z) / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -5e+252], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 1e+259], N[(x / N[((-z) * t + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.9999999999999997e252 or 9.999999999999999e258 < (*.f64 z t)

   1. Initial program 69.6%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. lower-/.f64 N/A

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

      4. lower-/.f64 69.6

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 69.6

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

   4. Applied rewrites 69.6%

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

   5. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. lower-*.f64 N/A

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

      4. associate-*r/ N/A

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

      5. lower-/.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 99.8

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

   7. Applied rewrites 99.8%

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

   9. Applied rewrites 99.9%

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

   if -4.9999999999999997e252 < (*.f64 z t) < 9.999999999999999e258

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+252}:\\ \;\;\;\;\frac{1}{\frac{-z}{x} \cdot t}\\ \mathbf{elif}\;t \cdot z \leq 10^{+259}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{-z}{x} \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{\frac{x}{z}}{-t}\\ \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+240}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 10^{+259}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ x z) (- t))))
   (if (<= (* t z) -5e+240)
     t_1
     (if (<= (* t z) 1e+259) (/ x (fma (- z) t y)) t_1))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = (x / z) / -t;
	double tmp;
	if ((t * z) <= -5e+240) {
		tmp = t_1;
	} else if ((t * z) <= 1e+259) {
		tmp = x / fma(-z, t, y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(x / z) / Float64(-t))
	tmp = 0.0
	if (Float64(t * z) <= -5e+240)
		tmp = t_1;
	elseif (Float64(t * z) <= 1e+259)
		tmp = Float64(x / fma(Float64(-z), t, y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / z), $MachinePrecision] / (-t)), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -5e+240], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 1e+259], N[(x / N[((-z) * t + y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -5.0000000000000003e240 or 9.999999999999999e258 < (*.f64 z t)

   1. Initial program 70.9%

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

   3. Taylor expanded in t around inf

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

      1. distribute-lft-out N/A

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

      2. associate-*r/ N/A

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

      3. mul-1-neg N/A

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

      4. distribute-neg-frac2 N/A

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

      5. mul-1-neg N/A

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

      6. lower-/.f64 N/A

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

      7. +-commutative N/A

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

      8. *-commutative N/A

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

      9. times-frac N/A

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

      10. lower-fma.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. unpow2 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-/.f64 N/A

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

      15. lower-/.f64 N/A

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

      16. mul-1-neg N/A

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

      17. lower-neg.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 99.8%

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

   if -5.0000000000000003e240 < (*.f64 z t) < 9.999999999999999e258

   1. Initial program 99.9%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-*.f64 N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -5 \cdot 10^{+240}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \mathbf{elif}\;t \cdot z \leq 10^{+259}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(-z, t, y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{-t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\left(-t\right) \cdot z}\\ \mathbf{if}\;t \cdot z \leq -200:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \cdot z \leq 4 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

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 (<= (* t z) -200.0) t_1 (if (<= (* t z) 4e-86) (/ 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 ((t * z) <= -200.0) {
		tmp = t_1;
	} else if ((t * z) <= 4e-86) {
		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 ((t * z) <= (-200.0d0)) then
        tmp = t_1
    else if ((t * z) <= 4d-86) 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 ((t * z) <= -200.0) {
		tmp = t_1;
	} else if ((t * z) <= 4e-86) {
		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 (t * z) <= -200.0:
		tmp = t_1
	elif (t * z) <= 4e-86:
		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(x / Float64(Float64(-t) * z))
	tmp = 0.0
	if (Float64(t * z) <= -200.0)
		tmp = t_1;
	elseif (Float64(t * z) <= 4e-86)
		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 ((t * z) <= -200.0)
		tmp = t_1;
	elseif ((t * z) <= 4e-86)
		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[(x / N[((-t) * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t * z), $MachinePrecision], -200.0], t$95$1, If[LessEqual[N[(t * z), $MachinePrecision], 4e-86], N[(x / y), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -200 or 4.00000000000000034e-86 < (*.f64 z t)

   1. Initial program 90.6%

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

   3. Taylor expanded in t around inf

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

      1. associate-*r* N/A

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

      2. lower-*.f64 N/A

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

      3. mul-1-neg N/A

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

      4. lower-neg.f64 75.1

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

   5. Applied rewrites 75.1%

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

   if -200 < (*.f64 z t) < 4.00000000000000034e-86

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 86.7

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

   5. Applied rewrites 86.7%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \cdot z \leq -200:\\ \;\;\;\;\frac{x}{\left(-t\right) \cdot z}\\ \mathbf{elif}\;t \cdot z \leq 4 \cdot 10^{-86}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(-t\right) \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.7% accurate, 1.0× speedup

Math

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

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 (fma (- z) t y)))

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

   1. lift--.f64 N/A

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. distribute-lft-neg-in N/A

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

   6. lower-fma.f64 N/A

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

   7. lower-neg.f64 94.8

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

4. Applied rewrites 94.8%

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

Alternative 6: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x / (y - (t * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.8%

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

3. Final simplification 94.8%

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

Alternative 7: 54.2% accurate, 1.7× 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 94.8%

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

3. Taylor expanded in t around 0

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

   1. lower-/.f64 54.4

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

5. Applied rewrites 54.4%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
6. Add Preprocessing

Developer Target 1: 96.9% accurate, 0.4× 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 2024277 
(FPCore (x y z t)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -161819597360704900000000000000000000000000000000000) (/ 1 (- (/ y x) (* (/ z x) t))) (if (< x 213783064348764440000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (- y (* z t))) (/ 1 (- (/ y x) (* (/ z x) t))))))

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