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

Percentage Accurate: 95.8% → 96.9%

Time: 8.9s

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: 96.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+160}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1e+160) (/ -1.0 (* t (/ z x))) (/ x (- y (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+160) {
		tmp = -1.0 / (t * (z / x));
	} else {
		tmp = x / (y - (z * t));
	}
	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) :: tmp
    if ((z * t) <= (-1d+160)) then
        tmp = (-1.0d0) / (t * (z / x))
    else
        tmp = x / (y - (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+160) {
		tmp = -1.0 / (t * (z / x));
	} else {
		tmp = x / (y - (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1e+160:
		tmp = -1.0 / (t * (z / x))
	else:
		tmp = x / (y - (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+160)
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	else
		tmp = Float64(x / Float64(y - Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1e+160)
		tmp = -1.0 / (t * (z / x));
	else
		tmp = x / (y - (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+160], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y - N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -1.00000000000000001e160

   1. Initial program 84.4%

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

      1. clear-num 84.5%

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

      2. associate-/r/ 84.5%

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

   4. Applied egg-rr 84.5%

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

      1. associate-/r/ 84.5%

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

      2. clear-num 84.4%

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

      3. sub-neg 84.4%

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

      4. +-commutative 84.4%

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

      5. distribute-lft-neg-in 84.4%

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

      6. add-sqr-sqrt 49.0%

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

      7. associate-*r* 49.0%

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

      8. fma-udef 49.0%

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

      9. frac-2neg 49.0%

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

      10. neg-mul-1 49.0%

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

      11. associate-/l* 49.0%

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

      12. add-sqr-sqrt 24.6%

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

      13. sqrt-unprod 38.2%

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

      14. sqr-neg 38.2%

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

      15. sqrt-unprod 16.6%

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

      16. add-sqr-sqrt 35.9%

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

      17. frac-2neg 35.9%

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

   6. Applied egg-rr 84.5%

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

   7. Taylor expanded in y around 0 84.5%

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

      1. associate-*r/ 99.9%

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

   9. Simplified 99.9%

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

   if -1.00000000000000001e160 < (*.f64 z t)

   1. Initial program 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+160}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y - z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+184}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-90} \lor \neg \left(z \cdot t \leq 100000000\right):\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -1e+184)
   (/ (/ x (- t)) z)
   (if (or (<= (* z t) -4e-90) (not (<= (* z t) 100000000.0)))
     (- (/ x (* z t)))
     (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+184) {
		tmp = (x / -t) / z;
	} else if (((z * t) <= -4e-90) || !((z * t) <= 100000000.0)) {
		tmp = -(x / (z * t));
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if ((z * t) <= (-1d+184)) then
        tmp = (x / -t) / z
    else if (((z * t) <= (-4d-90)) .or. (.not. ((z * t) <= 100000000.0d0))) then
        tmp = -(x / (z * t))
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -1e+184) {
		tmp = (x / -t) / z;
	} else if (((z * t) <= -4e-90) || !((z * t) <= 100000000.0)) {
		tmp = -(x / (z * t));
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -1e+184:
		tmp = (x / -t) / z
	elif ((z * t) <= -4e-90) or not ((z * t) <= 100000000.0):
		tmp = -(x / (z * t))
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -1e+184)
		tmp = Float64(Float64(x / Float64(-t)) / z);
	elseif ((Float64(z * t) <= -4e-90) || !(Float64(z * t) <= 100000000.0))
		tmp = Float64(-Float64(x / Float64(z * t)));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -1e+184)
		tmp = (x / -t) / z;
	elseif (((z * t) <= -4e-90) || ~(((z * t) <= 100000000.0)))
		tmp = -(x / (z * t));
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -1e+184], N[(N[(x / (-t)), $MachinePrecision] / z), $MachinePrecision], If[Or[LessEqual[N[(z * t), $MachinePrecision], -4e-90], N[Not[LessEqual[N[(z * t), $MachinePrecision], 100000000.0]], $MachinePrecision]], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -1.00000000000000002e184

   1. Initial program 83.1%

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

   3. Taylor expanded in y around 0 83.1%

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

      1. associate-*r/ 83.1%

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

      2. neg-mul-1 83.1%

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

      3. *-commutative 83.1%

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

      4. associate-/r* 99.8%

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

   5. Simplified 99.8%

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

      1. associate-/l/ 83.1%

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

      2. neg-mul-1 83.1%

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

      3. times-frac 99.8%

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

   7. Applied egg-rr 99.8%

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

      1. associate-*r/ 99.6%

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

      2. frac-2neg 99.6%

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

      3. metadata-eval 99.6%

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

      4. associate-*l/ 99.7%

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

      5. *-un-lft-identity 99.7%

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

   9. Applied egg-rr 99.7%

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

   if -1.00000000000000002e184 < (*.f64 z t) < -3.99999999999999998e-90 or 1e8 < (*.f64 z t)

   1. Initial program 97.1%

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

   3. Taylor expanded in y around 0 75.4%

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

      1. associate-*r/ 75.4%

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

      2. neg-mul-1 75.4%

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

   5. Simplified 75.4%

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

   if -3.99999999999999998e-90 < (*.f64 z t) < 1e8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.8%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -1 \cdot 10^{+184}:\\ \;\;\;\;\frac{\frac{x}{-t}}{z}\\ \mathbf{elif}\;z \cdot t \leq -4 \cdot 10^{-90} \lor \neg \left(z \cdot t \leq 100000000\right):\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-90} \lor \neg \left(z \cdot t \leq 100000000\right):\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -4e-90) (not (<= (* z t) 100000000.0)))
   (- (/ x (* z t)))
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -4e-90) || !((z * t) <= 100000000.0)) {
		tmp = -(x / (z * t));
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-4d-90)) .or. (.not. ((z * t) <= 100000000.0d0))) then
        tmp = -(x / (z * t))
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -4e-90) || !((z * t) <= 100000000.0)) {
		tmp = -(x / (z * t));
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -4e-90) or not ((z * t) <= 100000000.0):
		tmp = -(x / (z * t))
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -4e-90) || !(Float64(z * t) <= 100000000.0))
		tmp = Float64(-Float64(x / Float64(z * t)));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -4e-90) || ~(((z * t) <= 100000000.0)))
		tmp = -(x / (z * t));
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -4e-90], N[Not[LessEqual[N[(z * t), $MachinePrecision], 100000000.0]], $MachinePrecision]], (-N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -3.99999999999999998e-90 or 1e8 < (*.f64 z t)

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. neg-mul-1 77.2%

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

   5. Simplified 77.2%

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

   if -3.99999999999999998e-90 < (*.f64 z t) < 1e8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-90} \lor \neg \left(z \cdot t \leq 100000000\right):\\ \;\;\;\;-\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-90} \lor \neg \left(z \cdot t \leq 100000000\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z t) -4e-90) (not (<= (* z t) 100000000.0)))
   (/ (/ (- x) z) t)
   (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -4e-90) || !((z * t) <= 100000000.0)) {
		tmp = (-x / z) / t;
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if (((z * t) <= (-4d-90)) .or. (.not. ((z * t) <= 100000000.0d0))) then
        tmp = (-x / z) / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * t) <= -4e-90) || !((z * t) <= 100000000.0)) {
		tmp = (-x / z) / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * t) <= -4e-90) or not ((z * t) <= 100000000.0):
		tmp = (-x / z) / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * t) <= -4e-90) || !(Float64(z * t) <= 100000000.0))
		tmp = Float64(Float64(Float64(-x) / z) / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * t) <= -4e-90) || ~(((z * t) <= 100000000.0)))
		tmp = (-x / z) / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -4e-90], N[Not[LessEqual[N[(z * t), $MachinePrecision], 100000000.0]], $MachinePrecision]], N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -3.99999999999999998e-90 or 1e8 < (*.f64 z t)

   1. Initial program 93.8%

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

   3. Taylor expanded in y around 0 77.2%

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

      1. associate-*r/ 77.2%

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

      2. neg-mul-1 77.2%

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

      3. *-commutative 77.2%

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

      4. associate-/r* 79.9%

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

   5. Simplified 79.9%

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

   if -3.99999999999999998e-90 < (*.f64 z t) < 1e8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-90} \lor \neg \left(z \cdot t \leq 100000000\right):\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-90}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 100000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z t) -4e-90)
   (/ -1.0 (* t (/ z x)))
   (if (<= (* z t) 100000000.0) (/ x y) (/ (/ (- x) z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -4e-90) {
		tmp = -1.0 / (t * (z / x));
	} else if ((z * t) <= 100000000.0) {
		tmp = x / y;
	} else {
		tmp = (-x / z) / t;
	}
	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) :: tmp
    if ((z * t) <= (-4d-90)) then
        tmp = (-1.0d0) / (t * (z / x))
    else if ((z * t) <= 100000000.0d0) then
        tmp = x / y
    else
        tmp = (-x / z) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * t) <= -4e-90) {
		tmp = -1.0 / (t * (z / x));
	} else if ((z * t) <= 100000000.0) {
		tmp = x / y;
	} else {
		tmp = (-x / z) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * t) <= -4e-90:
		tmp = -1.0 / (t * (z / x))
	elif (z * t) <= 100000000.0:
		tmp = x / y
	else:
		tmp = (-x / z) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * t) <= -4e-90)
		tmp = Float64(-1.0 / Float64(t * Float64(z / x)));
	elseif (Float64(z * t) <= 100000000.0)
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(Float64(-x) / z) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * t) <= -4e-90)
		tmp = -1.0 / (t * (z / x));
	elseif ((z * t) <= 100000000.0)
		tmp = x / y;
	else
		tmp = (-x / z) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * t), $MachinePrecision], -4e-90], N[(-1.0 / N[(t * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 100000000.0], N[(x / y), $MachinePrecision], N[(N[((-x) / z), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -3.99999999999999998e-90

   1. Initial program 93.1%

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

      1. clear-num 93.1%

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

      2. associate-/r/ 93.1%

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

   4. Applied egg-rr 93.1%

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

      1. associate-/r/ 93.1%

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

      2. clear-num 93.1%

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

      3. sub-neg 93.1%

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

      4. +-commutative 93.1%

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

      5. distribute-lft-neg-in 93.1%

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

      6. add-sqr-sqrt 46.5%

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

      7. associate-*r* 46.6%

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

      8. fma-udef 46.6%

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

      9. frac-2neg 46.6%

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

      10. neg-mul-1 46.6%

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

      11. associate-/l* 46.6%

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

      12. add-sqr-sqrt 24.4%

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

      13. sqrt-unprod 27.4%

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

      14. sqr-neg 27.4%

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

      15. sqrt-unprod 8.5%

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

      16. add-sqr-sqrt 17.3%

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

      17. frac-2neg 17.3%

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

   6. Applied egg-rr 74.9%

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

   7. Taylor expanded in y around 0 72.9%

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

      1. associate-*r/ 76.2%

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

   9. Simplified 76.2%

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

   if -3.99999999999999998e-90 < (*.f64 z t) < 1e8

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 82.8%

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

   if 1e8 < (*.f64 z t)

   1. Initial program 94.9%

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

   3. Taylor expanded in y around 0 83.7%

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

      1. associate-*r/ 83.7%

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

      2. neg-mul-1 83.7%

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

      3. *-commutative 83.7%

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

      4. associate-/r* 84.5%

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

   5. Simplified 84.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{-90}:\\ \;\;\;\;\frac{-1}{t \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \cdot t \leq 100000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+189} \lor \neg \left(z \leq 2.3 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.8e+189) (not (<= z 2.3e+63))) (/ x (* z t)) (/ x y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+189) || !(z <= 2.3e+63)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	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) :: tmp
    if ((z <= (-1.8d+189)) .or. (.not. (z <= 2.3d+63))) then
        tmp = x / (z * t)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.8e+189) || !(z <= 2.3e+63)) {
		tmp = x / (z * t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.8e+189) or not (z <= 2.3e+63):
		tmp = x / (z * t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.8e+189) || !(z <= 2.3e+63))
		tmp = Float64(x / Float64(z * t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.8e+189) || ~((z <= 2.3e+63)))
		tmp = x / (z * t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.8e+189], N[Not[LessEqual[z, 2.3e+63]], $MachinePrecision]], N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000004e189 or 2.29999999999999993e63 < z

   1. Initial program 93.0%

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

   3. Taylor expanded in y around 0 77.5%

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

      1. associate-*r/ 77.5%

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

      2. neg-mul-1 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-/r* 84.9%

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

   5. Simplified 84.9%

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

      1. expm1-log1p-u 76.9%

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

      2. expm1-udef 58.9%

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

      3. associate-/r* 58.9%

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

      4. add-sqr-sqrt 26.5%

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

      5. sqrt-unprod 50.4%

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

      6. sqr-neg 50.4%

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

      7. sqrt-unprod 25.6%

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

      8. add-sqr-sqrt 49.4%

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

   7. Applied egg-rr 49.4%

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

      1. expm1-def 45.0%

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

      2. expm1-log1p 45.4%

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

      3. *-commutative 45.4%

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

   9. Simplified 45.4%

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

   if -1.80000000000000004e189 < z < 2.29999999999999993e63

   1. Initial program 97.8%

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

   3. Taylor expanded in y around inf 60.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+189} \lor \neg \left(z \leq 2.3 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{x}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ 1.0 (/ y x)))

C

double code(double x, double y, double z, double t) {
	return 1.0 / (y / x);
}

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 = 1.0d0 / (y / x)
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 / (y / x);
}

Python

def code(x, y, z, t):
	return 1.0 / (y / x)

Julia

function code(x, y, z, t)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 / (y / x);
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.5%

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

   1. clear-num 96.3%

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

   2. associate-/r/ 96.3%

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

4. Applied egg-rr 96.3%

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

5. Taylor expanded in y around inf 50.0%

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

   1. associate-*l/ 50.2%

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

   2. associate-/l* 50.3%

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

7. Applied egg-rr 50.3%

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

8. Final simplification 50.3%

   \[\leadsto \frac{1}{\frac{y}{x}} \]
9. Add Preprocessing

Alternative 8: 54.4% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in y around inf 50.2%

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

4. Final simplification 50.2%

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

Developer target: 96.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 / ((y / x) - ((z / x) * t))
    if (x < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (x < 2.1378306434876444d+131) then
        tmp = x / (y - (z * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024020 
(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))))