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

Percentage Accurate: 84.9% → 89.9%

Time: 10.7s

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: 84.9% 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: 89.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x}{z}\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+196}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ x z))))
   (if (<= z -9.5e+84)
     (/ t_1 a)
     (if (<= z 1.32e+196)
       (+ (/ (* z y) (- (* z a) t)) (/ x (- t (* z a))))
       (* t_1 (/ 1.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x / z);
	double tmp;
	if (z <= -9.5e+84) {
		tmp = t_1 / a;
	} else if (z <= 1.32e+196) {
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)));
	} else {
		tmp = t_1 * (1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = y - (x / z)
    if (z <= (-9.5d+84)) then
        tmp = t_1 / a
    else if (z <= 1.32d+196) then
        tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)))
    else
        tmp = t_1 * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x / z);
	double tmp;
	if (z <= -9.5e+84) {
		tmp = t_1 / a;
	} else if (z <= 1.32e+196) {
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)));
	} else {
		tmp = t_1 * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x / z)
	tmp = 0
	if z <= -9.5e+84:
		tmp = t_1 / a
	elif z <= 1.32e+196:
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)))
	else:
		tmp = t_1 * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x / z))
	tmp = 0.0
	if (z <= -9.5e+84)
		tmp = Float64(t_1 / a);
	elseif (z <= 1.32e+196)
		tmp = Float64(Float64(Float64(z * y) / Float64(Float64(z * a) - t)) + Float64(x / Float64(t - Float64(z * a))));
	else
		tmp = Float64(t_1 * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x / z);
	tmp = 0.0;
	if (z <= -9.5e+84)
		tmp = t_1 / a;
	elseif (z <= 1.32e+196)
		tmp = ((z * y) / ((z * a) - t)) + (x / (t - (z * a)));
	else
		tmp = t_1 * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+84], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[z, 1.32e+196], N[(N[(N[(z * y), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision] + N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999979e84

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in x around 0 58.3%

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

   6. Taylor expanded in a around inf 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

   8. Simplified 89.4%

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

   if -9.49999999999999979e84 < z < 1.32e196

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around 0 95.8%

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

   if 1.32e196 < z

   1. Initial program 36.0%

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

      1. *-commutative 36.0%

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

   3. Simplified 36.0%

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

   5. Taylor expanded in x around 0 36.0%

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

   6. Taylor expanded in a around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

   8. Simplified 88.2%

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

      1. div-inv 88.3%

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

   10. Applied egg-rr 88.3%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+84}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+196}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t} + \frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - \frac{x}{z}\right) \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 53.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5200000000.0)
   (/ y a)
   (if (<= z -2.8e-105)
     (/ x t)
     (if (<= z -1.52e-136)
       (/ x (* z (- a)))
       (if (<= z 9.4e-117)
         (/ x t)
         (if (<= z 4e-82)
           (* y (/ z (- t)))
           (if (<= z 7.2e-44) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5200000000.0) {
		tmp = y / a;
	} else if (z <= -2.8e-105) {
		tmp = x / t;
	} else if (z <= -1.52e-136) {
		tmp = x / (z * -a);
	} else if (z <= 9.4e-117) {
		tmp = x / t;
	} else if (z <= 4e-82) {
		tmp = y * (z / -t);
	} else if (z <= 7.2e-44) {
		tmp = x / 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 <= (-5200000000.0d0)) then
        tmp = y / a
    else if (z <= (-2.8d-105)) then
        tmp = x / t
    else if (z <= (-1.52d-136)) then
        tmp = x / (z * -a)
    else if (z <= 9.4d-117) then
        tmp = x / t
    else if (z <= 4d-82) then
        tmp = y * (z / -t)
    else if (z <= 7.2d-44) then
        tmp = x / 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 <= -5200000000.0) {
		tmp = y / a;
	} else if (z <= -2.8e-105) {
		tmp = x / t;
	} else if (z <= -1.52e-136) {
		tmp = x / (z * -a);
	} else if (z <= 9.4e-117) {
		tmp = x / t;
	} else if (z <= 4e-82) {
		tmp = y * (z / -t);
	} else if (z <= 7.2e-44) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5200000000.0:
		tmp = y / a
	elif z <= -2.8e-105:
		tmp = x / t
	elif z <= -1.52e-136:
		tmp = x / (z * -a)
	elif z <= 9.4e-117:
		tmp = x / t
	elif z <= 4e-82:
		tmp = y * (z / -t)
	elif z <= 7.2e-44:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5200000000.0)
		tmp = Float64(y / a);
	elseif (z <= -2.8e-105)
		tmp = Float64(x / t);
	elseif (z <= -1.52e-136)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 9.4e-117)
		tmp = Float64(x / t);
	elseif (z <= 4e-82)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= 7.2e-44)
		tmp = Float64(x / 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 <= -5200000000.0)
		tmp = y / a;
	elseif (z <= -2.8e-105)
		tmp = x / t;
	elseif (z <= -1.52e-136)
		tmp = x / (z * -a);
	elseif (z <= 9.4e-117)
		tmp = x / t;
	elseif (z <= 4e-82)
		tmp = y * (z / -t);
	elseif (z <= 7.2e-44)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5200000000.0], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.8e-105], N[(x / t), $MachinePrecision], If[LessEqual[z, -1.52e-136], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.4e-117], N[(x / t), $MachinePrecision], If[LessEqual[z, 4e-82], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-44], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.2e9 or 7.1999999999999998e-44 < z

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in z around inf 54.2%

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

   if -5.2e9 < z < -2.8e-105 or -1.51999999999999999e-136 < z < 9.40000000000000017e-117 or 4e-82 < z < 7.1999999999999998e-44

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 65.0%

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

   if -2.8e-105 < z < -1.51999999999999999e-136

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

   6. Taylor expanded in a around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. unsub-neg 33.8%

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

   8. Simplified 33.8%

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

   9. Taylor expanded in y around 0 57.2%

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

       1. associate-*r/ 57.2%

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

       2. neg-mul-1 57.2%

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

       3. *-commutative 57.2%

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

   11. Simplified 57.2%

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

   if 9.40000000000000017e-117 < z < 4e-82

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 72.8%

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

      1. div-sub 72.8%

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

   7. Applied egg-rr 72.8%

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

   8. Taylor expanded in x around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-*r/ 74.1%

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

      3. distribute-rgt-neg-in 74.1%

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

      4. distribute-neg-frac 74.1%

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

   10. Simplified 74.1%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5200000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1400000000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1400000000000.0)
   (/ y a)
   (if (<= z -2.8e-105)
     (/ x t)
     (if (<= z -1.52e-136)
       (/ x (* z (- a)))
       (if (<= z 7.2e-117)
         (/ x t)
         (if (<= z 1.4e-40) (/ (* z y) (- t)) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1400000000000.0) {
		tmp = y / a;
	} else if (z <= -2.8e-105) {
		tmp = x / t;
	} else if (z <= -1.52e-136) {
		tmp = x / (z * -a);
	} else if (z <= 7.2e-117) {
		tmp = x / t;
	} else if (z <= 1.4e-40) {
		tmp = (z * y) / -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 <= (-1400000000000.0d0)) then
        tmp = y / a
    else if (z <= (-2.8d-105)) then
        tmp = x / t
    else if (z <= (-1.52d-136)) then
        tmp = x / (z * -a)
    else if (z <= 7.2d-117) then
        tmp = x / t
    else if (z <= 1.4d-40) then
        tmp = (z * y) / -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 <= -1400000000000.0) {
		tmp = y / a;
	} else if (z <= -2.8e-105) {
		tmp = x / t;
	} else if (z <= -1.52e-136) {
		tmp = x / (z * -a);
	} else if (z <= 7.2e-117) {
		tmp = x / t;
	} else if (z <= 1.4e-40) {
		tmp = (z * y) / -t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1400000000000.0:
		tmp = y / a
	elif z <= -2.8e-105:
		tmp = x / t
	elif z <= -1.52e-136:
		tmp = x / (z * -a)
	elif z <= 7.2e-117:
		tmp = x / t
	elif z <= 1.4e-40:
		tmp = (z * y) / -t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1400000000000.0)
		tmp = Float64(y / a);
	elseif (z <= -2.8e-105)
		tmp = Float64(x / t);
	elseif (z <= -1.52e-136)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 7.2e-117)
		tmp = Float64(x / t);
	elseif (z <= 1.4e-40)
		tmp = Float64(Float64(z * y) / 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 <= -1400000000000.0)
		tmp = y / a;
	elseif (z <= -2.8e-105)
		tmp = x / t;
	elseif (z <= -1.52e-136)
		tmp = x / (z * -a);
	elseif (z <= 7.2e-117)
		tmp = x / t;
	elseif (z <= 1.4e-40)
		tmp = (z * y) / -t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1400000000000.0], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.8e-105], N[(x / t), $MachinePrecision], If[LessEqual[z, -1.52e-136], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-117], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.4e-40], N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4e12 or 1.4e-40 < z

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around inf 54.6%

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

   if -1.4e12 < z < -2.8e-105 or -1.51999999999999999e-136 < z < 7.2000000000000001e-117

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 66.8%

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

   if -2.8e-105 < z < -1.51999999999999999e-136

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.9%

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

   6. Taylor expanded in a around inf 33.8%

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

      1. mul-1-neg 33.8%

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

      2. unsub-neg 33.8%

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

   8. Simplified 33.8%

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

   9. Taylor expanded in y around 0 57.2%

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

       1. associate-*r/ 57.2%

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

       2. neg-mul-1 57.2%

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

       3. *-commutative 57.2%

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

   11. Simplified 57.2%

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

   if 7.2000000000000001e-117 < z < 1.4e-40

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 67.7%

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

   6. Taylor expanded in x around 0 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-neg-frac2 49.3%

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

   8. Simplified 49.3%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1400000000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-136}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-40}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+151}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-40}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9e+151)
   (/ y a)
   (if (<= z -7.8e+118)
     (/ (/ x a) (- z))
     (if (<= z -1.02e+15)
       (/ y a)
       (if (<= z 4.4e-117)
         (/ x t)
         (if (<= z 1.35e-40) (/ (* z y) (- t)) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9e+151) {
		tmp = y / a;
	} else if (z <= -7.8e+118) {
		tmp = (x / a) / -z;
	} else if (z <= -1.02e+15) {
		tmp = y / a;
	} else if (z <= 4.4e-117) {
		tmp = x / t;
	} else if (z <= 1.35e-40) {
		tmp = (z * y) / -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 <= (-9d+151)) then
        tmp = y / a
    else if (z <= (-7.8d+118)) then
        tmp = (x / a) / -z
    else if (z <= (-1.02d+15)) then
        tmp = y / a
    else if (z <= 4.4d-117) then
        tmp = x / t
    else if (z <= 1.35d-40) then
        tmp = (z * y) / -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 <= -9e+151) {
		tmp = y / a;
	} else if (z <= -7.8e+118) {
		tmp = (x / a) / -z;
	} else if (z <= -1.02e+15) {
		tmp = y / a;
	} else if (z <= 4.4e-117) {
		tmp = x / t;
	} else if (z <= 1.35e-40) {
		tmp = (z * y) / -t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9e+151:
		tmp = y / a
	elif z <= -7.8e+118:
		tmp = (x / a) / -z
	elif z <= -1.02e+15:
		tmp = y / a
	elif z <= 4.4e-117:
		tmp = x / t
	elif z <= 1.35e-40:
		tmp = (z * y) / -t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9e+151)
		tmp = Float64(y / a);
	elseif (z <= -7.8e+118)
		tmp = Float64(Float64(x / a) / Float64(-z));
	elseif (z <= -1.02e+15)
		tmp = Float64(y / a);
	elseif (z <= 4.4e-117)
		tmp = Float64(x / t);
	elseif (z <= 1.35e-40)
		tmp = Float64(Float64(z * y) / 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 <= -9e+151)
		tmp = y / a;
	elseif (z <= -7.8e+118)
		tmp = (x / a) / -z;
	elseif (z <= -1.02e+15)
		tmp = y / a;
	elseif (z <= 4.4e-117)
		tmp = x / t;
	elseif (z <= 1.35e-40)
		tmp = (z * y) / -t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9e+151], N[(y / a), $MachinePrecision], If[LessEqual[z, -7.8e+118], N[(N[(x / a), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, -1.02e+15], N[(y / a), $MachinePrecision], If[LessEqual[z, 4.4e-117], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.35e-40], N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.9999999999999997e151 or -7.8e118 < z < -1.02e15 or 1.35e-40 < z

   1. Initial program 71.9%

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

      1. *-commutative 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in z around inf 57.1%

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

   if -8.9999999999999997e151 < z < -7.8e118

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   5. Taylor expanded in x around 0 88.0%

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

   6. Taylor expanded in a around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

   8. Simplified 77.4%

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

   9. Taylor expanded in y around 0 63.9%

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

       1. associate-*r/ 63.9%

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

       2. neg-mul-1 63.9%

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

       3. *-commutative 63.9%

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

   11. Simplified 63.9%

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

   12. Taylor expanded in x around 0 63.9%

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

       1. mul-1-neg 63.9%

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

       2. associate-/r* 75.4%

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

       3. distribute-neg-frac2 75.4%

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

   14. Simplified 75.4%

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

   if -1.02e15 < z < 4.4000000000000002e-117

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 62.1%

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

   if 4.4000000000000002e-117 < z < 1.35e-40

   1. Initial program 99.1%

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

      1. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around inf 67.7%

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

   6. Taylor expanded in x around 0 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-neg-frac2 49.3%

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

   8. Simplified 49.3%

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

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+151}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-40}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+138}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -4.5e+153)
     (/ y a)
     (if (<= z 9.4e-117)
       t_1
       (if (<= z 3e-91) (* y (/ z (- t))) (if (<= z 2.7e+138) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -4.5e+153) {
		tmp = y / a;
	} else if (z <= 9.4e-117) {
		tmp = t_1;
	} else if (z <= 3e-91) {
		tmp = y * (z / -t);
	} else if (z <= 2.7e+138) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    if (z <= (-4.5d+153)) then
        tmp = y / a
    else if (z <= 9.4d-117) then
        tmp = t_1
    else if (z <= 3d-91) then
        tmp = y * (z / -t)
    else if (z <= 2.7d+138) then
        tmp = t_1
    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 t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -4.5e+153) {
		tmp = y / a;
	} else if (z <= 9.4e-117) {
		tmp = t_1;
	} else if (z <= 3e-91) {
		tmp = y * (z / -t);
	} else if (z <= 2.7e+138) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if z <= -4.5e+153:
		tmp = y / a
	elif z <= 9.4e-117:
		tmp = t_1
	elif z <= 3e-91:
		tmp = y * (z / -t)
	elif z <= 2.7e+138:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -4.5e+153)
		tmp = Float64(y / a);
	elseif (z <= 9.4e-117)
		tmp = t_1;
	elseif (z <= 3e-91)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= 2.7e+138)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -4.5e+153)
		tmp = y / a;
	elseif (z <= 9.4e-117)
		tmp = t_1;
	elseif (z <= 3e-91)
		tmp = y * (z / -t);
	elseif (z <= 2.7e+138)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+153], N[(y / a), $MachinePrecision], If[LessEqual[z, 9.4e-117], t$95$1, If[LessEqual[z, 3e-91], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e+138], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.5000000000000001e153 or 2.70000000000000009e138 < z

   1. Initial program 55.8%

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

      1. *-commutative 55.8%

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

   3. Simplified 55.8%

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

   5. Taylor expanded in z around inf 71.5%

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

   if -4.5000000000000001e153 < z < 9.40000000000000017e-117 or 3.0000000000000002e-91 < z < 2.70000000000000009e138

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x around inf 69.9%

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

      1. *-commutative 69.9%

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

   7. Simplified 69.9%

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

   if 9.40000000000000017e-117 < z < 3.0000000000000002e-91

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 84.2%

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

      1. div-sub 84.2%

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

   7. Applied egg-rr 84.2%

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

   8. Taylor expanded in x around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. associate-*r/ 85.0%

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

      3. distribute-rgt-neg-in 85.0%

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

      4. distribute-neg-frac 85.0%

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

   10. Simplified 85.0%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-91}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+138}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -3.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-40}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+130}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -3.9e+152)
     (/ y a)
     (if (<= z 7.5e-233)
       t_1
       (if (<= z 1.22e-40)
         (/ (- x (* z y)) t)
         (if (<= z 3.2e+130) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -3.9e+152) {
		tmp = y / a;
	} else if (z <= 7.5e-233) {
		tmp = t_1;
	} else if (z <= 1.22e-40) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.2e+130) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    if (z <= (-3.9d+152)) then
        tmp = y / a
    else if (z <= 7.5d-233) then
        tmp = t_1
    else if (z <= 1.22d-40) then
        tmp = (x - (z * y)) / t
    else if (z <= 3.2d+130) then
        tmp = t_1
    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 t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -3.9e+152) {
		tmp = y / a;
	} else if (z <= 7.5e-233) {
		tmp = t_1;
	} else if (z <= 1.22e-40) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.2e+130) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if z <= -3.9e+152:
		tmp = y / a
	elif z <= 7.5e-233:
		tmp = t_1
	elif z <= 1.22e-40:
		tmp = (x - (z * y)) / t
	elif z <= 3.2e+130:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -3.9e+152)
		tmp = Float64(y / a);
	elseif (z <= 7.5e-233)
		tmp = t_1;
	elseif (z <= 1.22e-40)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 3.2e+130)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -3.9e+152)
		tmp = y / a;
	elseif (z <= 7.5e-233)
		tmp = t_1;
	elseif (z <= 1.22e-40)
		tmp = (x - (z * y)) / t;
	elseif (z <= 3.2e+130)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.9e+152], N[(y / a), $MachinePrecision], If[LessEqual[z, 7.5e-233], t$95$1, If[LessEqual[z, 1.22e-40], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.2e+130], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.90000000000000011e152 or 3.2e130 < z

   1. Initial program 55.8%

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

      1. *-commutative 55.8%

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

   3. Simplified 55.8%

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

   5. Taylor expanded in z around inf 71.5%

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

   if -3.90000000000000011e152 < z < 7.49999999999999974e-233 or 1.22e-40 < z < 3.2e130

   1. Initial program 94.6%

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

      1. *-commutative 94.6%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 69.5%

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

      1. *-commutative 69.5%

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

   7. Simplified 69.5%

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

   if 7.49999999999999974e-233 < z < 1.22e-40

   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 t around inf 77.5%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-40}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2700000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2700000000.0)
   (/ y a)
   (if (<= z 9.4e-117)
     (/ x t)
     (if (<= z 5e-82) (* y (/ z (- t))) (if (<= z 1.8e-41) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2700000000.0) {
		tmp = y / a;
	} else if (z <= 9.4e-117) {
		tmp = x / t;
	} else if (z <= 5e-82) {
		tmp = y * (z / -t);
	} else if (z <= 1.8e-41) {
		tmp = x / 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 <= (-2700000000.0d0)) then
        tmp = y / a
    else if (z <= 9.4d-117) then
        tmp = x / t
    else if (z <= 5d-82) then
        tmp = y * (z / -t)
    else if (z <= 1.8d-41) then
        tmp = x / 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 <= -2700000000.0) {
		tmp = y / a;
	} else if (z <= 9.4e-117) {
		tmp = x / t;
	} else if (z <= 5e-82) {
		tmp = y * (z / -t);
	} else if (z <= 1.8e-41) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2700000000.0:
		tmp = y / a
	elif z <= 9.4e-117:
		tmp = x / t
	elif z <= 5e-82:
		tmp = y * (z / -t)
	elif z <= 1.8e-41:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2700000000.0)
		tmp = Float64(y / a);
	elseif (z <= 9.4e-117)
		tmp = Float64(x / t);
	elseif (z <= 5e-82)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= 1.8e-41)
		tmp = Float64(x / 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 <= -2700000000.0)
		tmp = y / a;
	elseif (z <= 9.4e-117)
		tmp = x / t;
	elseif (z <= 5e-82)
		tmp = y * (z / -t);
	elseif (z <= 1.8e-41)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2700000000.0], N[(y / a), $MachinePrecision], If[LessEqual[z, 9.4e-117], N[(x / t), $MachinePrecision], If[LessEqual[z, 5e-82], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-41], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7e9 or 1.8e-41 < z

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in z around inf 54.2%

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

   if -2.7e9 < z < 9.40000000000000017e-117 or 4.9999999999999998e-82 < z < 1.8e-41

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 60.8%

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

   if 9.40000000000000017e-117 < z < 4.9999999999999998e-82

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around inf 72.8%

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

      1. div-sub 72.8%

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

   7. Applied egg-rr 72.8%

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

   8. Taylor expanded in x around 0 73.4%

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

      1. mul-1-neg 73.4%

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

      2. associate-*r/ 74.1%

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

      3. distribute-rgt-neg-in 74.1%

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

      4. distribute-neg-frac 74.1%

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

   10. Simplified 74.1%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2700000000:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-40}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -1.25e+78)
     t_1
     (if (<= z 3.8e-228)
       (/ x (- t (* z a)))
       (if (<= z 1.65e-40) (/ (- x (* z y)) t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.25e+78) {
		tmp = t_1;
	} else if (z <= 3.8e-228) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.65e-40) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = t_1;
	}
	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 = (y - (x / z)) / a
    if (z <= (-1.25d+78)) then
        tmp = t_1
    else if (z <= 3.8d-228) then
        tmp = x / (t - (z * a))
    else if (z <= 1.65d-40) then
        tmp = (x - (z * y)) / 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 a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.25e+78) {
		tmp = t_1;
	} else if (z <= 3.8e-228) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.65e-40) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.25e+78:
		tmp = t_1
	elif z <= 3.8e-228:
		tmp = x / (t - (z * a))
	elif z <= 1.65e-40:
		tmp = (x - (z * y)) / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.25e+78)
		tmp = t_1;
	elseif (z <= 3.8e-228)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.65e-40)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.25e+78)
		tmp = t_1;
	elseif (z <= 3.8e-228)
		tmp = x / (t - (z * a));
	elseif (z <= 1.65e-40)
		tmp = (x - (z * y)) / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.25e+78], t$95$1, If[LessEqual[z, 3.8e-228], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e-40], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.24999999999999996e78 or 1.64999999999999996e-40 < z

   1. Initial program 70.2%

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

      1. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in x around 0 70.2%

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

   6. Taylor expanded in a around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

   8. Simplified 76.8%

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

   if -1.24999999999999996e78 < z < 3.7999999999999999e-228

   1. Initial program 98.9%

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

      1. *-commutative 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in x around inf 77.8%

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

      1. *-commutative 77.8%

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

   7. Simplified 77.8%

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

   if 3.7999999999999999e-228 < z < 1.64999999999999996e-40

   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 t around inf 77.5%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+78}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-40}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{x}{z}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+82}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+196}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (/ x z))))
   (if (<= z -2.9e+82)
     (/ t_1 a)
     (if (<= z 1.32e+196) (/ (- x (* z y)) (- t (* z a))) (* t_1 (/ 1.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x / z);
	double tmp;
	if (z <= -2.9e+82) {
		tmp = t_1 / a;
	} else if (z <= 1.32e+196) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = t_1 * (1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = y - (x / z)
    if (z <= (-2.9d+82)) then
        tmp = t_1 / a
    else if (z <= 1.32d+196) then
        tmp = (x - (z * y)) / (t - (z * a))
    else
        tmp = t_1 * (1.0d0 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (x / z);
	double tmp;
	if (z <= -2.9e+82) {
		tmp = t_1 / a;
	} else if (z <= 1.32e+196) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = t_1 * (1.0 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (x / z)
	tmp = 0
	if z <= -2.9e+82:
		tmp = t_1 / a
	elif z <= 1.32e+196:
		tmp = (x - (z * y)) / (t - (z * a))
	else:
		tmp = t_1 * (1.0 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(x / z))
	tmp = 0.0
	if (z <= -2.9e+82)
		tmp = Float64(t_1 / a);
	elseif (z <= 1.32e+196)
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(t_1 * Float64(1.0 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (x / z);
	tmp = 0.0;
	if (z <= -2.9e+82)
		tmp = t_1 / a;
	elseif (z <= 1.32e+196)
		tmp = (x - (z * y)) / (t - (z * a));
	else
		tmp = t_1 * (1.0 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+82], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[z, 1.32e+196], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9000000000000001e82

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

   3. Simplified 58.3%

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

   5. Taylor expanded in x around 0 58.3%

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

   6. Taylor expanded in a around inf 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

   8. Simplified 89.4%

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

   if -2.9000000000000001e82 < z < 1.32e196

   1. Initial program 95.8%

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

   if 1.32e196 < z

   1. Initial program 36.0%

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

      1. *-commutative 36.0%

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

   3. Simplified 36.0%

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

   5. Taylor expanded in x around 0 36.0%

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

   6. Taylor expanded in a around inf 88.2%

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

      1. mul-1-neg 88.2%

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

      2. unsub-neg 88.2%

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

   8. Simplified 88.2%

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

      1. div-inv 88.3%

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

   10. Applied egg-rr 88.3%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+82}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+196}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\left(y - \frac{x}{z}\right) \cdot \frac{1}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 71.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-29} \lor \neg \left(x \leq 1.6 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -7.4e-29) (not (<= x 1.6e+21)))
   (/ x (- t (* z a)))
   (/ y (- a (/ t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -7.4e-29) || !(x <= 1.6e+21)) {
		tmp = x / (t - (z * a));
	} 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) :: tmp
    if ((x <= (-7.4d-29)) .or. (.not. (x <= 1.6d+21))) then
        tmp = x / (t - (z * a))
    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 tmp;
	if ((x <= -7.4e-29) || !(x <= 1.6e+21)) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / (a - (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -7.4e-29) or not (x <= 1.6e+21):
		tmp = x / (t - (z * a))
	else:
		tmp = y / (a - (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -7.4e-29) || !(x <= 1.6e+21))
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / Float64(a - Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -7.4e-29) || ~((x <= 1.6e+21)))
		tmp = x / (t - (z * a));
	else
		tmp = y / (a - (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -7.4e-29], N[Not[LessEqual[x, 1.6e+21]], $MachinePrecision]], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.3999999999999995e-29 or 1.6e21 < x

   1. Initial program 88.6%

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

      1. *-commutative 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in x around inf 77.1%

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

      1. *-commutative 77.1%

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

   7. Simplified 77.1%

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

   if -7.3999999999999995e-29 < x < 1.6e21

   1. Initial program 84.1%

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

      1. *-commutative 84.1%

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

   3. Simplified 84.1%

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

   5. Taylor expanded in z around inf 77.5%

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

   6. Taylor expanded in x around 0 79.3%

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

      1. associate-*r/ 79.3%

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

      2. neg-mul-1 79.3%

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

   8. Simplified 79.3%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{-29} \lor \neg \left(x \leq 1.6 \cdot 10^{+21}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 55.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -36000000000000 \lor \neg \left(z \leq 1.1 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -36000000000000.0) (not (<= z 1.1e-40))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -36000000000000.0) || !(z <= 1.1e-40)) {
		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 <= (-36000000000000.0d0)) .or. (.not. (z <= 1.1d-40))) 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 <= -36000000000000.0) || !(z <= 1.1e-40)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -36000000000000.0) or not (z <= 1.1e-40):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -36000000000000.0) || !(z <= 1.1e-40))
		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 <= -36000000000000.0) || ~((z <= 1.1e-40)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -36000000000000.0], N[Not[LessEqual[z, 1.1e-40]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e13 or 1.10000000000000004e-40 < z

   1. Initial program 73.2%

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

      1. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   5. Taylor expanded in z around inf 54.2%

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

   if -3.6e13 < z < 1.10000000000000004e-40

   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 57.6%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -36000000000000 \lor \neg \left(z \leq 1.1 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.2% 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 86.3%

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

   1. *-commutative 86.3%

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

3. Simplified 86.3%

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

5. Taylor expanded in z around 0 38.7%

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

6. Final simplification 38.7%

   \[\leadsto \frac{x}{t} \]
7. Add Preprocessing

Developer target: 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 2024077 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :alt
  (if (< z -32113435955957344.0) (- (/ x (- t (* a z))) (/ y (- (/ t z) a))) (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 (- t (* a z)))) (- (/ x (- t (* a z))) (/ y (- (/ t z) a)))))

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