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

Percentage Accurate: 85.2% → 96.9%

Time: 12.2s

Alternatives: 12

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = (x - (y * z)) / (t - (a * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := t - z \cdot a\\ t_3 := \frac{x - y \cdot z}{t\_2}\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(\frac{z}{t\_1} + \frac{x}{y \cdot t\_2}\right)\\ \mathbf{elif}\;t\_3 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;t\_3 \leq 10^{+286}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} - \frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (- t (* z a))) (t_3 (/ (- x (* y z)) t_2)))
   (if (<= t_3 -2e+275)
     (* y (+ (/ z t_1) (/ x (* y t_2))))
     (if (<= t_3 -4e-316)
       t_3
       (if (<= t_3 0.0)
         (/ -1.0 (* z (/ (- (/ t z) a) (- (* y z) x))))
         (if (<= t_3 1e+286)
           (- (/ (* y z) t_1) (/ x t_1))
           (/ y (- a (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -2e+275) {
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	} else if (t_3 <= -4e-316) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_3 <= 1e+286) {
		tmp = ((y * z) / t_1) - (x / t_1);
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z * a) - t
    t_2 = t - (z * a)
    t_3 = (x - (y * z)) / t_2
    if (t_3 <= (-2d+275)) then
        tmp = y * ((z / t_1) + (x / (y * t_2)))
    else if (t_3 <= (-4d-316)) then
        tmp = t_3
    else if (t_3 <= 0.0d0) then
        tmp = (-1.0d0) / (z * (((t / z) - a) / ((y * z) - x)))
    else if (t_3 <= 1d+286) then
        tmp = ((y * z) / t_1) - (x / t_1)
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = t - (z * a);
	double t_3 = (x - (y * z)) / t_2;
	double tmp;
	if (t_3 <= -2e+275) {
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	} else if (t_3 <= -4e-316) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_3 <= 1e+286) {
		tmp = ((y * z) / t_1) - (x / t_1);
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = t - (z * a)
	t_3 = (x - (y * z)) / t_2
	tmp = 0
	if t_3 <= -2e+275:
		tmp = y * ((z / t_1) + (x / (y * t_2)))
	elif t_3 <= -4e-316:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)))
	elif t_3 <= 1e+286:
		tmp = ((y * z) / t_1) - (x / t_1)
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(t - Float64(z * a))
	t_3 = Float64(Float64(x - Float64(y * z)) / t_2)
	tmp = 0.0
	if (t_3 <= -2e+275)
		tmp = Float64(y * Float64(Float64(z / t_1) + Float64(x / Float64(y * t_2))));
	elseif (t_3 <= -4e-316)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(-1.0 / Float64(z * Float64(Float64(Float64(t / z) - a) / Float64(Float64(y * z) - x))));
	elseif (t_3 <= 1e+286)
		tmp = Float64(Float64(Float64(y * z) / t_1) - Float64(x / t_1));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = t - (z * a);
	t_3 = (x - (y * z)) / t_2;
	tmp = 0.0;
	if (t_3 <= -2e+275)
		tmp = y * ((z / t_1) + (x / (y * t_2)));
	elseif (t_3 <= -4e-316)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	elseif (t_3 <= 1e+286)
		tmp = ((y * z) / t_1) - (x / t_1);
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, -2e+275], N[(y * N[(N[(z / t$95$1), $MachinePrecision] + N[(x / N[(y * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -4e-316], t$95$3, If[LessEqual[t$95$3, 0.0], N[(-1.0 / N[(z * N[(N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+286], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.99999999999999992e275

   1. Initial program 64.9%

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

      1. *-commutative 64.9%

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

   3. Simplified 64.9%

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

   5. Taylor expanded in y around inf 99.8%

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

   if -1.99999999999999992e275 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.999999984e-316

   1. Initial program 99.6%

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

   if -3.999999984e-316 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. clear-num 48.8%

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

      2. inv-pow 48.8%

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

   7. Applied egg-rr 48.8%

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

      1. unpow-1 48.8%

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

      2. associate-/l* 98.3%

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

   9. Simplified 98.3%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000003e286

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

   if 1.00000000000000003e286 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 31.7%

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

      1. *-commutative 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

   6. Taylor expanded in x around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

   8. Simplified 95.7%

      \[\leadsto \color{blue}{\frac{-y}{\frac{t}{z} - a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{+275}:\\ \;\;\;\;y \cdot \left(\frac{z}{z \cdot a - t} + \frac{x}{y \cdot \left(t - z \cdot a\right)}\right)\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+286}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;t\_2 \leq 10^{+286}:\\ \;\;\;\;\frac{y \cdot z}{t\_1} - \frac{x}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_2 -4e-316)
     t_2
     (if (<= t_2 0.0)
       (/ -1.0 (* z (/ (- (/ t z) a) (- (* y z) x))))
       (if (<= t_2 1e+286)
         (- (/ (* y z) t_1) (/ x t_1))
         (/ y (- a (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_2 <= -4e-316) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_2 <= 1e+286) {
		tmp = ((y * z) / t_1) - (x / t_1);
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * a) - t
    t_2 = (x - (y * z)) / (t - (z * a))
    if (t_2 <= (-4d-316)) then
        tmp = t_2
    else if (t_2 <= 0.0d0) then
        tmp = (-1.0d0) / (z * (((t / z) - a) / ((y * z) - x)))
    else if (t_2 <= 1d+286) then
        tmp = ((y * z) / t_1) - (x / t_1)
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_2 <= -4e-316) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_2 <= 1e+286) {
		tmp = ((y * z) / t_1) - (x / t_1);
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_2 <= -4e-316:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)))
	elif t_2 <= 1e+286:
		tmp = ((y * z) / t_1) - (x / t_1)
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_2 <= -4e-316)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(-1.0 / Float64(z * Float64(Float64(Float64(t / z) - a) / Float64(Float64(y * z) - x))));
	elseif (t_2 <= 1e+286)
		tmp = Float64(Float64(Float64(y * z) / t_1) - Float64(x / t_1));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_2 <= -4e-316)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	elseif (t_2 <= 1e+286)
		tmp = ((y * z) / t_1) - (x / t_1);
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-316], t$95$2, If[LessEqual[t$95$2, 0.0], N[(-1.0 / N[(z * N[(N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+286], N[(N[(N[(y * z), $MachinePrecision] / t$95$1), $MachinePrecision] - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.999999984e-316

   1. Initial program 93.8%

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

   if -3.999999984e-316 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. clear-num 48.8%

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

      2. inv-pow 48.8%

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

   7. Applied egg-rr 48.8%

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

      1. unpow-1 48.8%

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

      2. associate-/l* 98.3%

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

   9. Simplified 98.3%

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

   if 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000003e286

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 99.6%

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

   if 1.00000000000000003e286 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 31.7%

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

      1. *-commutative 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

   6. Taylor expanded in x around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

   8. Simplified 95.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+286}:\\ \;\;\;\;\frac{y \cdot z}{z \cdot a - t} - \frac{x}{z \cdot a - t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-316}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;t\_1 \leq 10^{+286}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) (- t (* z a)))))
   (if (<= t_1 -4e-316)
     t_1
     (if (<= t_1 0.0)
       (/ -1.0 (* z (/ (- (/ t z) a) (- (* y z) x))))
       (if (<= t_1 1e+286) t_1 (/ y (- a (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_1 <= 1e+286) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y * z)) / (t - (z * a))
    if (t_1 <= (-4d-316)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = (-1.0d0) / (z * (((t / z) - a) / ((y * z) - x)))
    else if (t_1 <= 1d+286) then
        tmp = t_1
    else
        tmp = y / (a - (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / (t - (z * a));
	double tmp;
	if (t_1 <= -4e-316) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	} else if (t_1 <= 1e+286) {
		tmp = t_1;
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / (t - (z * a))
	tmp = 0
	if t_1 <= -4e-316:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)))
	elif t_1 <= 1e+286:
		tmp = t_1
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (t_1 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(-1.0 / Float64(z * Float64(Float64(Float64(t / z) - a) / Float64(Float64(y * z) - x))));
	elseif (t_1 <= 1e+286)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (y * z)) / (t - (z * a));
	tmp = 0.0;
	if (t_1 <= -4e-316)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = -1.0 / (z * (((t / z) - a) / ((y * z) - x)));
	elseif (t_1 <= 1e+286)
		tmp = t_1;
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-316], t$95$1, If[LessEqual[t$95$1, 0.0], N[(-1.0 / N[(z * N[(N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision] / N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+286], t$95$1, N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -3.999999984e-316 or 0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 1.00000000000000003e286

   1. Initial program 96.2%

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

   if -3.999999984e-316 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 0.0

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. clear-num 48.8%

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

      2. inv-pow 48.8%

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

   7. Applied egg-rr 48.8%

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

      1. unpow-1 48.8%

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

      2. associate-/l* 98.3%

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

   9. Simplified 98.3%

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

   if 1.00000000000000003e286 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 31.7%

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

      1. *-commutative 31.7%

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

   3. Simplified 31.7%

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

   5. Taylor expanded in z around inf 31.7%

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

   6. Taylor expanded in x around 0 95.7%

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

      1. associate-*r/ 95.7%

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

      2. mul-1-neg 95.7%

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

   8. Simplified 95.7%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -4 \cdot 10^{-316}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{-1}{z \cdot \frac{\frac{t}{z} - a}{y \cdot z - x}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq 10^{+286}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8e+35)
   (/ y (- a (/ t z)))
   (if (<= z -1.4e-47)
     (/ x (- t (* z a)))
     (if (<= z 1.3e+27) (/ (- x (* y z)) t) (/ (- y (/ x z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+35) {
		tmp = y / (a - (t / z));
	} else if (z <= -1.4e-47) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.3e+27) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-8d+35)) then
        tmp = y / (a - (t / z))
    else if (z <= (-1.4d-47)) then
        tmp = x / (t - (z * a))
    else if (z <= 1.3d+27) then
        tmp = (x - (y * z)) / t
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8e+35) {
		tmp = y / (a - (t / z));
	} else if (z <= -1.4e-47) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.3e+27) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8e+35:
		tmp = y / (a - (t / z))
	elif z <= -1.4e-47:
		tmp = x / (t - (z * a))
	elif z <= 1.3e+27:
		tmp = (x - (y * z)) / t
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8e+35)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -1.4e-47)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.3e+27)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8e+35)
		tmp = y / (a - (t / z));
	elseif (z <= -1.4e-47)
		tmp = x / (t - (z * a));
	elseif (z <= 1.3e+27)
		tmp = (x - (y * z)) / t;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8e+35], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.4e-47], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e+27], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.9999999999999997e35

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in z around inf 60.7%

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

   6. Taylor expanded in x around 0 85.1%

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

      1. associate-*r/ 85.1%

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

      2. mul-1-neg 85.1%

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

   8. Simplified 85.1%

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

   if -7.9999999999999997e35 < z < -1.39999999999999996e-47

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 82.2%

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

   if -1.39999999999999996e-47 < z < 1.30000000000000004e27

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 76.3%

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

      1. *-commutative 76.3%

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

   7. Simplified 76.3%

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

   if 1.30000000000000004e27 < z

   1. Initial program 65.5%

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

      1. *-commutative 65.5%

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

   3. Simplified 65.5%

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

   5. Taylor expanded in x around 0 65.5%

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

   6. Taylor expanded in a around inf 78.9%

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

      1. associate-*r/ 78.9%

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

      2. neg-mul-1 78.9%

         \[\leadsto \frac{y + \frac{\color{blue}{-x}}{z}}{a} \]

   8. Simplified 78.9%

      \[\leadsto \color{blue}{\frac{y + \frac{-x}{z}}{a}} \]

   9. Taylor expanded in a around 0 78.9%

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

       1. neg-mul-1 78.9%

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

       2. sub-neg 78.9%

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

   11. Simplified 78.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+35}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+27}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e-22)
   (/ y a)
   (if (<= z 4.6e-98) (/ x t) (if (<= z 2.3e+32) (/ (* y z) (- t)) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e-22) {
		tmp = y / a;
	} else if (z <= 4.6e-98) {
		tmp = x / t;
	} else if (z <= 2.3e+32) {
		tmp = (y * z) / -t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.8d-22)) then
        tmp = y / a
    else if (z <= 4.6d-98) then
        tmp = x / t
    else if (z <= 2.3d+32) then
        tmp = (y * z) / -t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e-22) {
		tmp = y / a;
	} else if (z <= 4.6e-98) {
		tmp = x / t;
	} else if (z <= 2.3e+32) {
		tmp = (y * z) / -t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e-22:
		tmp = y / a
	elif z <= 4.6e-98:
		tmp = x / t
	elif z <= 2.3e+32:
		tmp = (y * z) / -t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e-22)
		tmp = Float64(y / a);
	elseif (z <= 4.6e-98)
		tmp = Float64(x / t);
	elseif (z <= 2.3e+32)
		tmp = Float64(Float64(y * z) / Float64(-t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e-22)
		tmp = y / a;
	elseif (z <= 4.6e-98)
		tmp = x / t;
	elseif (z <= 2.3e+32)
		tmp = (y * z) / -t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e-22], N[(y / a), $MachinePrecision], If[LessEqual[z, 4.6e-98], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.3e+32], N[(N[(y * z), $MachinePrecision] / (-t)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e-22 or 2.3e32 < z

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in z around inf 59.4%

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

   if -1.7999999999999999e-22 < z < 4.60000000000000001e-98

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 59.6%

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

   if 4.60000000000000001e-98 < z < 2.3e32

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 62.5%

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

      1. mul-1-neg 62.5%

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

      2. associate-/l* 59.3%

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

      3. distribute-rgt-neg-in 59.3%

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

      4. sub-neg 59.3%

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

      5. mul-1-neg 59.3%

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

      6. +-commutative 59.3%

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

      7. mul-1-neg 59.3%

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

      8. distribute-rgt-neg-in 59.3%

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

      9. fma-undefine 59.3%

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

      10. distribute-neg-frac2 59.3%

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

      11. neg-sub0 59.3%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      12. fma-undefine 59.3%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      13. distribute-rgt-neg-in 59.3%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      14. distribute-lft-neg-in 59.3%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      15. *-commutative 59.3%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      16. associate--r+ 59.3%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      17. neg-sub0 59.3%

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

      18. distribute-rgt-neg-out 59.3%

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

      19. remove-double-neg 59.3%

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

      20. *-commutative 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in z around 0 43.6%

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

      1. associate-*r/ 43.6%

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

      2. neg-mul-1 43.6%

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

   10. Simplified 43.6%

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

   11. Taylor expanded in y around 0 50.3%

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

       1. associate-*r/ 50.3%

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

       2. *-commutative 50.3%

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

       3. neg-mul-1 50.3%

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

       4. distribute-lft-neg-in 50.3%

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

   13. Simplified 50.3%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+32}:\\ \;\;\;\;\frac{y \cdot z}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 56.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+28}:\\ \;\;\;\;\left(-y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5e-22)
   (/ y a)
   (if (<= z 2.8e-32) (/ x t) (if (<= z 6.9e+28) (* (- y) (/ z t)) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-22) {
		tmp = y / a;
	} else if (z <= 2.8e-32) {
		tmp = x / t;
	} else if (z <= 6.9e+28) {
		tmp = -y * (z / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5d-22)) then
        tmp = y / a
    else if (z <= 2.8d-32) then
        tmp = x / t
    else if (z <= 6.9d+28) then
        tmp = -y * (z / t)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e-22) {
		tmp = y / a;
	} else if (z <= 2.8e-32) {
		tmp = x / t;
	} else if (z <= 6.9e+28) {
		tmp = -y * (z / t);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e-22:
		tmp = y / a
	elif z <= 2.8e-32:
		tmp = x / t
	elif z <= 6.9e+28:
		tmp = -y * (z / t)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e-22)
		tmp = Float64(y / a);
	elseif (z <= 2.8e-32)
		tmp = Float64(x / t);
	elseif (z <= 6.9e+28)
		tmp = Float64(Float64(-y) * Float64(z / t));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e-22)
		tmp = y / a;
	elseif (z <= 2.8e-32)
		tmp = x / t;
	elseif (z <= 6.9e+28)
		tmp = -y * (z / t);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5e-22], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.8e-32], N[(x / t), $MachinePrecision], If[LessEqual[z, 6.9e+28], N[((-y) * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.99999999999999954e-22 or 6.9e28 < z

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   5. Taylor expanded in z around inf 59.4%

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

   if -4.99999999999999954e-22 < z < 2.7999999999999999e-32

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 57.1%

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

   if 2.7999999999999999e-32 < z < 6.9e28

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. associate-/l* 74.2%

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

      3. distribute-rgt-neg-in 74.2%

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

      4. sub-neg 74.2%

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

      5. mul-1-neg 74.2%

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

      6. +-commutative 74.2%

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

      7. mul-1-neg 74.2%

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

      8. distribute-rgt-neg-in 74.2%

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

      9. fma-undefine 74.2%

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

      10. distribute-neg-frac2 74.2%

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

      11. neg-sub0 74.2%

          \[\leadsto y \cdot \frac{z}{\color{blue}{0 - \mathsf{fma}\left(a, -z, t\right)}} \]

      12. fma-undefine 74.2%

          \[\leadsto y \cdot \frac{z}{0 - \color{blue}{\left(a \cdot \left(-z\right) + t\right)}} \]

      13. distribute-rgt-neg-in 74.2%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a \cdot z\right)} + t\right)} \]

      14. distribute-lft-neg-in 74.2%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-a\right) \cdot z} + t\right)} \]

      15. *-commutative 74.2%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{z \cdot \left(-a\right)} + t\right)} \]

      16. associate--r+ 74.2%

          \[\leadsto y \cdot \frac{z}{\color{blue}{\left(0 - z \cdot \left(-a\right)\right) - t}} \]

      17. neg-sub0 74.2%

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

      18. distribute-rgt-neg-out 74.2%

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

      19. remove-double-neg 74.2%

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

      20. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   8. Taylor expanded in z around 0 64.7%

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

      1. associate-*r/ 64.7%

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

      2. neg-mul-1 64.7%

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

   10. Simplified 64.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+28}:\\ \;\;\;\;\left(-y\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.8e+136)
   (/ y (- a (/ t z)))
   (if (<= z 4.5e+144) (/ (- x (* y z)) (- t (* z a))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+136) {
		tmp = y / (a - (t / z));
	} else if (z <= 4.5e+144) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-6.8d+136)) then
        tmp = y / (a - (t / z))
    else if (z <= 4.5d+144) then
        tmp = (x - (y * z)) / (t - (z * a))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.8e+136) {
		tmp = y / (a - (t / z));
	} else if (z <= 4.5e+144) {
		tmp = (x - (y * z)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.8e+136:
		tmp = y / (a - (t / z))
	elif z <= 4.5e+144:
		tmp = (x - (y * z)) / (t - (z * a))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.8e+136)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= 4.5e+144)
		tmp = Float64(Float64(x - Float64(y * z)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.8e+136)
		tmp = y / (a - (t / z));
	elseif (z <= 4.5e+144)
		tmp = (x - (y * z)) / (t - (z * a));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.8e+136], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e+144], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.79999999999999993e136

   1. Initial program 48.8%

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

      1. *-commutative 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 48.7%

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

   6. Taylor expanded in x around 0 89.4%

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

      1. associate-*r/ 89.4%

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

      2. mul-1-neg 89.4%

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

   8. Simplified 89.4%

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

   if -6.79999999999999993e136 < z < 4.49999999999999967e144

   1. Initial program 95.5%

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

   if 4.49999999999999967e144 < z

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   5. Taylor expanded in x around 0 60.9%

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

   6. Taylor expanded in a around inf 87.1%

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

      1. associate-*r/ 87.1%

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

      2. neg-mul-1 87.1%

         \[\leadsto \frac{y + \frac{\color{blue}{-x}}{z}}{a} \]

   8. Simplified 87.1%

      \[\leadsto \color{blue}{\frac{y + \frac{-x}{z}}{a}} \]

   9. Taylor expanded in a around 0 87.1%

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

       1. neg-mul-1 87.1%

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

       2. sub-neg 87.1%

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

   11. Simplified 87.1%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+136}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+144}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+76} \lor \neg \left(z \leq 1.4 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+76) (not (<= z 1.4e+33)))
   (/ (- y (/ x z)) a)
   (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+76) || !(z <= 1.4e+33)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+76)) .or. (.not. (z <= 1.4d+33))) then
        tmp = (y - (x / z)) / a
    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 a) {
	double tmp;
	if ((z <= -9.5e+76) || !(z <= 1.4e+33)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+76) or not (z <= 1.4e+33):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+76) || !(z <= 1.4e+33))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+76) || ~((z <= 1.4e+33)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+76], N[Not[LessEqual[z, 1.4e+33]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.5000000000000003e76 or 1.4e33 < z

   1. Initial program 61.4%

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

      1. *-commutative 61.4%

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

   3. Simplified 61.4%

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

   5. Taylor expanded in x around 0 61.5%

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

   6. Taylor expanded in a around inf 80.5%

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

      1. associate-*r/ 80.5%

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

      2. neg-mul-1 80.5%

         \[\leadsto \frac{y + \frac{\color{blue}{-x}}{z}}{a} \]

   8. Simplified 80.5%

      \[\leadsto \color{blue}{\frac{y + \frac{-x}{z}}{a}} \]

   9. Taylor expanded in a around 0 80.5%

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

       1. neg-mul-1 80.5%

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

       2. sub-neg 80.5%

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

   11. Simplified 80.5%

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

   if -9.5000000000000003e76 < z < 1.4e33

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 74.0%

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

      1. *-commutative 74.0%

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

   7. Simplified 74.0%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+76} \lor \neg \left(z \leq 1.4 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+77} \lor \neg \left(z \leq 1.9 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+77) (not (<= z 1.9e+92))) (/ y a) (/ (- x (* y z)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+77) || !(z <= 1.9e+92)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.4d+77)) .or. (.not. (z <= 1.9d+92))) then
        tmp = y / a
    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 a) {
	double tmp;
	if ((z <= -1.4e+77) || !(z <= 1.9e+92)) {
		tmp = y / a;
	} else {
		tmp = (x - (y * z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+77) or not (z <= 1.9e+92):
		tmp = y / a
	else:
		tmp = (x - (y * z)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+77) || !(z <= 1.9e+92))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.4e+77) || ~((z <= 1.9e+92)))
		tmp = y / a;
	else
		tmp = (x - (y * z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+77], N[Not[LessEqual[z, 1.9e+92]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e77 or 1.9e92 < z

   1. Initial program 59.9%

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

      1. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in z around inf 65.6%

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

   if -1.4e77 < z < 1.9e92

   1. Initial program 97.9%

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

      1. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around inf 72.4%

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

      1. *-commutative 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+77} \lor \neg \left(z \leq 1.9 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+39} \lor \neg \left(z \leq 5.7 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+39) (not (<= z 5.7e+23))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+39) || !(z <= 5.7e+23)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d+39)) .or. (.not. (z <= 5.7d+23))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+39) || !(z <= 5.7e+23)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+39) or not (z <= 5.7e+23):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+39) || !(z <= 5.7e+23))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+39) || ~((z <= 5.7e+23)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+39], N[Not[LessEqual[z, 5.7e+23]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e39 or 5.7e23 < z

   1. Initial program 63.0%

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

      1. *-commutative 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in z around inf 62.6%

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

   if -1.95e39 < z < 5.7e23

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 71.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+39} \lor \neg \left(z \leq 5.7 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-24} \lor \neg \left(z \leq 3.2 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.6e-24) (not (<= z 3.2e+22))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e-24) || !(z <= 3.2e+22)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.6d-24)) .or. (.not. (z <= 3.2d+22))) then
        tmp = y / a
    else
        tmp = x / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.6e-24) || !(z <= 3.2e+22)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.6e-24) or not (z <= 3.2e+22):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.6e-24) || !(z <= 3.2e+22))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.6e-24) || ~((z <= 3.2e+22)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.6e-24], N[Not[LessEqual[z, 3.2e+22]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6000000000000001e-24 or 3.2e22 < z

   1. Initial program 65.7%

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

      1. *-commutative 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in z around inf 58.9%

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

   if -3.6000000000000001e-24 < z < 3.2e22

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 54.8%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-24} \lor \neg \left(z \leq 3.2 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 36.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

   1. *-commutative 83.8%

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

3. Simplified 83.8%

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

5. Taylor expanded in z around 0 35.4%

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

Developer Target 1: 97.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024123 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -32113435955957344) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 4392440296622287/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* (- x (* y z)) (/ 1 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))))))

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