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

Percentage Accurate: 84.8% → 98.9%

Time: 13.5s

Alternatives: 13

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: 84.8% 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: 98.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a - \frac{t}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+64} \lor \neg \left(z \leq 3.3 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{y}{t\_1} - \frac{\frac{x}{z}}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- a (/ t z))))
   (if (or (<= z -1.8e+64) (not (<= z 3.3e-49)))
     (- (/ y t_1) (/ (/ x z) t_1))
     (/ (- x (* z y)) (- t (* z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a - (t / z);
	double tmp;
	if ((z <= -1.8e+64) || !(z <= 3.3e-49)) {
		tmp = (y / t_1) - ((x / z) / t_1);
	} else {
		tmp = (x - (z * y)) / (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) :: t_1
    real(8) :: tmp
    t_1 = a - (t / z)
    if ((z <= (-1.8d+64)) .or. (.not. (z <= 3.3d-49))) then
        tmp = (y / t_1) - ((x / z) / t_1)
    else
        tmp = (x - (z * y)) / (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 t_1 = a - (t / z);
	double tmp;
	if ((z <= -1.8e+64) || !(z <= 3.3e-49)) {
		tmp = (y / t_1) - ((x / z) / t_1);
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a - (t / z)
	tmp = 0
	if (z <= -1.8e+64) or not (z <= 3.3e-49):
		tmp = (y / t_1) - ((x / z) / t_1)
	else:
		tmp = (x - (z * y)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a - Float64(t / z))
	tmp = 0.0
	if ((z <= -1.8e+64) || !(z <= 3.3e-49))
		tmp = Float64(Float64(y / t_1) - Float64(Float64(x / z) / t_1));
	else
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a - (t / z);
	tmp = 0.0;
	if ((z <= -1.8e+64) || ~((z <= 3.3e-49)))
		tmp = (y / t_1) - ((x / z) / t_1);
	else
		tmp = (x - (z * y)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -1.8e+64], N[Not[LessEqual[z, 3.3e-49]], $MachinePrecision]], N[(N[(y / t$95$1), $MachinePrecision] - N[(N[(x / z), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.80000000000000007e64 or 3.3e-49 < z

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 68.3%

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

   6. Taylor expanded in x around 0 96.7%

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

      1. +-commutative 96.7%

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

      2. mul-1-neg 96.7%

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

      3. unsub-neg 96.7%

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

      4. associate-/r* 99.8%

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

   8. Simplified 99.8%

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

   if -1.80000000000000007e64 < z < 3.3e-49

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+64} \lor \neg \left(z \leq 3.3 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}} - \frac{\frac{x}{z}}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+131}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;\left(x - z \cdot y\right) \cdot \frac{\frac{-1}{a}}{z}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -2.9e+131)
     t_1
     (if (<= z -2e+56)
       (/ y (- a (/ t z)))
       (if (<= z -3.8e-16)
         (* (- x (* z y)) (/ (/ -1.0 a) z))
         (if (<= z -6.1e-80)
           (/ (* z y) (- (* z a) t))
           (if (<= z 6.2e+18) (/ x (- t (* z a))) 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 <= -2.9e+131) {
		tmp = t_1;
	} else if (z <= -2e+56) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.8e-16) {
		tmp = (x - (z * y)) * ((-1.0 / a) / z);
	} else if (z <= -6.1e-80) {
		tmp = (z * y) / ((z * a) - t);
	} else if (z <= 6.2e+18) {
		tmp = x / (t - (z * a));
	} 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 <= (-2.9d+131)) then
        tmp = t_1
    else if (z <= (-2d+56)) then
        tmp = y / (a - (t / z))
    else if (z <= (-3.8d-16)) then
        tmp = (x - (z * y)) * (((-1.0d0) / a) / z)
    else if (z <= (-6.1d-80)) then
        tmp = (z * y) / ((z * a) - t)
    else if (z <= 6.2d+18) then
        tmp = x / (t - (z * a))
    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 <= -2.9e+131) {
		tmp = t_1;
	} else if (z <= -2e+56) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.8e-16) {
		tmp = (x - (z * y)) * ((-1.0 / a) / z);
	} else if (z <= -6.1e-80) {
		tmp = (z * y) / ((z * a) - t);
	} else if (z <= 6.2e+18) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -2.9e+131:
		tmp = t_1
	elif z <= -2e+56:
		tmp = y / (a - (t / z))
	elif z <= -3.8e-16:
		tmp = (x - (z * y)) * ((-1.0 / a) / z)
	elif z <= -6.1e-80:
		tmp = (z * y) / ((z * a) - t)
	elif z <= 6.2e+18:
		tmp = x / (t - (z * a))
	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 <= -2.9e+131)
		tmp = t_1;
	elseif (z <= -2e+56)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -3.8e-16)
		tmp = Float64(Float64(x - Float64(z * y)) * Float64(Float64(-1.0 / a) / z));
	elseif (z <= -6.1e-80)
		tmp = Float64(Float64(z * y) / Float64(Float64(z * a) - t));
	elseif (z <= 6.2e+18)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	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 <= -2.9e+131)
		tmp = t_1;
	elseif (z <= -2e+56)
		tmp = y / (a - (t / z));
	elseif (z <= -3.8e-16)
		tmp = (x - (z * y)) * ((-1.0 / a) / z);
	elseif (z <= -6.1e-80)
		tmp = (z * y) / ((z * a) - t);
	elseif (z <= 6.2e+18)
		tmp = x / (t - (z * a));
	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, -2.9e+131], t$95$1, If[LessEqual[z, -2e+56], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.8e-16], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] * N[(N[(-1.0 / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.1e-80], N[(N[(z * y), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+18], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.9000000000000001e131 or 6.2e18 < z

   1. Initial program 66.2%

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

      1. *-commutative 66.2%

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

   3. Simplified 66.2%

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

      1. clear-num 66.0%

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

      2. associate-/r/ 66.1%

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

      3. sub-neg 66.1%

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

      4. +-commutative 66.1%

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

      5. distribute-rgt-neg-in 66.1%

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

      6. fma-define 66.2%

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

   6. Applied egg-rr 66.2%

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

   7. Taylor expanded in z around inf 52.2%

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

      1. associate-/r* 52.4%

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

   9. Simplified 52.4%

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

   10. Taylor expanded in z around inf 80.0%

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

       1. +-commutative 80.0%

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

       2. associate-*r/ 80.0%

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

       3. neg-mul-1 80.0%

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

       4. *-commutative 80.0%

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

   12. Simplified 80.0%

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

   13. Taylor expanded in y around 0 80.0%

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

       1. mul-1-neg 80.0%

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

       2. associate-/l/ 84.0%

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

       3. +-commutative 84.0%

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

       4. sub-neg 84.0%

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

       5. div-sub 84.0%

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

   15. Simplified 84.0%

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

   if -2.9000000000000001e131 < z < -2.00000000000000018e56

   1. Initial program 68.2%

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

      1. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in z around inf 68.2%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

   8. Simplified 83.9%

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

   if -2.00000000000000018e56 < z < -3.80000000000000012e-16

   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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-rgt-neg-in 99.8%

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

      6. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in z around inf 72.8%

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

      1. associate-/r* 72.9%

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

   9. Simplified 72.9%

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

   if -3.80000000000000012e-16 < z < -6.1000000000000002e-80

   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 79.4%

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

      1. associate-/l* 71.6%

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

      2. cancel-sign-sub-inv 71.6%

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

      3. *-commutative 71.6%

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

      4. +-commutative 71.6%

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

      5. fma-define 71.6%

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

      6. neg-mul-1 71.6%

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

      7. associate-*r/ 79.4%

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

      8. distribute-frac-neg2 79.4%

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

      9. neg-sub0 79.4%

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

      10. fma-define 79.4%

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

      11. associate--r+ 79.4%

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

      12. neg-sub0 79.4%

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

      13. distribute-rgt-neg-out 79.4%

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

      14. remove-double-neg 79.4%

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

   7. Simplified 79.4%

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

   if -6.1000000000000002e-80 < z < 6.2e18

   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 x around inf 80.6%

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

      1. *-commutative 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+131}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-16}:\\ \;\;\;\;\left(x - z \cdot y\right) \cdot \frac{\frac{-1}{a}}{z}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -9e+132)
     t_1
     (if (<= z -6.4e+63)
       (/ y (- a (/ t z)))
       (if (<= z -2.3e-16)
         t_1
         (if (<= z -1.4e-80)
           (/ (* z y) (- (* z a) t))
           (if (<= z 1.05e+19) (/ x (- t (* z a))) 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 <= -9e+132) {
		tmp = t_1;
	} else if (z <= -6.4e+63) {
		tmp = y / (a - (t / z));
	} else if (z <= -2.3e-16) {
		tmp = t_1;
	} else if (z <= -1.4e-80) {
		tmp = (z * y) / ((z * a) - t);
	} else if (z <= 1.05e+19) {
		tmp = x / (t - (z * a));
	} 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 <= (-9d+132)) then
        tmp = t_1
    else if (z <= (-6.4d+63)) then
        tmp = y / (a - (t / z))
    else if (z <= (-2.3d-16)) then
        tmp = t_1
    else if (z <= (-1.4d-80)) then
        tmp = (z * y) / ((z * a) - t)
    else if (z <= 1.05d+19) then
        tmp = x / (t - (z * a))
    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 <= -9e+132) {
		tmp = t_1;
	} else if (z <= -6.4e+63) {
		tmp = y / (a - (t / z));
	} else if (z <= -2.3e-16) {
		tmp = t_1;
	} else if (z <= -1.4e-80) {
		tmp = (z * y) / ((z * a) - t);
	} else if (z <= 1.05e+19) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -9e+132:
		tmp = t_1
	elif z <= -6.4e+63:
		tmp = y / (a - (t / z))
	elif z <= -2.3e-16:
		tmp = t_1
	elif z <= -1.4e-80:
		tmp = (z * y) / ((z * a) - t)
	elif z <= 1.05e+19:
		tmp = x / (t - (z * a))
	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 <= -9e+132)
		tmp = t_1;
	elseif (z <= -6.4e+63)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -2.3e-16)
		tmp = t_1;
	elseif (z <= -1.4e-80)
		tmp = Float64(Float64(z * y) / Float64(Float64(z * a) - t));
	elseif (z <= 1.05e+19)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	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 <= -9e+132)
		tmp = t_1;
	elseif (z <= -6.4e+63)
		tmp = y / (a - (t / z));
	elseif (z <= -2.3e-16)
		tmp = t_1;
	elseif (z <= -1.4e-80)
		tmp = (z * y) / ((z * a) - t);
	elseif (z <= 1.05e+19)
		tmp = x / (t - (z * a));
	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, -9e+132], t$95$1, If[LessEqual[z, -6.4e+63], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.3e-16], t$95$1, If[LessEqual[z, -1.4e-80], N[(N[(z * y), $MachinePrecision] / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e+19], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.99999999999999944e132 or -6.40000000000000022e63 < z < -2.2999999999999999e-16 or 1.05e19 < z

   1. Initial program 70.3%

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

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. sub-neg 70.2%

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

      4. +-commutative 70.2%

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

      5. distribute-rgt-neg-in 70.2%

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

      6. fma-define 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in z around inf 54.7%

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

      1. associate-/r* 54.9%

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

   9. Simplified 54.9%

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

   10. Taylor expanded in z around inf 78.3%

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

       1. +-commutative 78.3%

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

       2. associate-*r/ 78.3%

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

       3. neg-mul-1 78.3%

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

       4. *-commutative 78.3%

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

   12. Simplified 78.3%

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

   13. Taylor expanded in y around 0 78.3%

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

       1. mul-1-neg 78.3%

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

       2. associate-/l/ 81.7%

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

       3. +-commutative 81.7%

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

       4. sub-neg 81.7%

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

       5. div-sub 82.6%

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

   15. Simplified 82.6%

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

   if -8.99999999999999944e132 < z < -6.40000000000000022e63

   1. Initial program 68.2%

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

      1. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in z around inf 68.2%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

   8. Simplified 83.9%

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

   if -2.2999999999999999e-16 < z < -1.39999999999999995e-80

   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 79.4%

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

      1. associate-/l* 71.6%

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

      2. cancel-sign-sub-inv 71.6%

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

      3. *-commutative 71.6%

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

      4. +-commutative 71.6%

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

      5. fma-define 71.6%

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

      6. neg-mul-1 71.6%

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

      7. associate-*r/ 79.4%

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

      8. distribute-frac-neg2 79.4%

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

      9. neg-sub0 79.4%

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

      10. fma-define 79.4%

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

      11. associate--r+ 79.4%

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

      12. neg-sub0 79.4%

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

      13. distribute-rgt-neg-out 79.4%

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

      14. remove-double-neg 79.4%

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

   7. Simplified 79.4%

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

   if -1.39999999999999995e-80 < z < 1.05e19

   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 x around inf 80.6%

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

      1. *-commutative 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+132}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{\frac{z \cdot a - t}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -2.1e+129)
     t_1
     (if (<= z -3e+63)
       (/ y (- a (/ t z)))
       (if (<= z -3.6e-16)
         t_1
         (if (<= z -6.1e-80)
           (/ z (/ (- (* z a) t) y))
           (if (<= z 1.6e+21) (/ x (- t (* z a))) 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 <= -2.1e+129) {
		tmp = t_1;
	} else if (z <= -3e+63) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.6e-16) {
		tmp = t_1;
	} else if (z <= -6.1e-80) {
		tmp = z / (((z * a) - t) / y);
	} else if (z <= 1.6e+21) {
		tmp = x / (t - (z * a));
	} 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 <= (-2.1d+129)) then
        tmp = t_1
    else if (z <= (-3d+63)) then
        tmp = y / (a - (t / z))
    else if (z <= (-3.6d-16)) then
        tmp = t_1
    else if (z <= (-6.1d-80)) then
        tmp = z / (((z * a) - t) / y)
    else if (z <= 1.6d+21) then
        tmp = x / (t - (z * a))
    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 <= -2.1e+129) {
		tmp = t_1;
	} else if (z <= -3e+63) {
		tmp = y / (a - (t / z));
	} else if (z <= -3.6e-16) {
		tmp = t_1;
	} else if (z <= -6.1e-80) {
		tmp = z / (((z * a) - t) / y);
	} else if (z <= 1.6e+21) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -2.1e+129:
		tmp = t_1
	elif z <= -3e+63:
		tmp = y / (a - (t / z))
	elif z <= -3.6e-16:
		tmp = t_1
	elif z <= -6.1e-80:
		tmp = z / (((z * a) - t) / y)
	elif z <= 1.6e+21:
		tmp = x / (t - (z * a))
	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 <= -2.1e+129)
		tmp = t_1;
	elseif (z <= -3e+63)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -3.6e-16)
		tmp = t_1;
	elseif (z <= -6.1e-80)
		tmp = Float64(z / Float64(Float64(Float64(z * a) - t) / y));
	elseif (z <= 1.6e+21)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	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 <= -2.1e+129)
		tmp = t_1;
	elseif (z <= -3e+63)
		tmp = y / (a - (t / z));
	elseif (z <= -3.6e-16)
		tmp = t_1;
	elseif (z <= -6.1e-80)
		tmp = z / (((z * a) - t) / y);
	elseif (z <= 1.6e+21)
		tmp = x / (t - (z * a));
	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, -2.1e+129], t$95$1, If[LessEqual[z, -3e+63], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.6e-16], t$95$1, If[LessEqual[z, -6.1e-80], N[(z / N[(N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+21], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.09999999999999997e129 or -2.99999999999999999e63 < z < -3.59999999999999983e-16 or 1.6e21 < z

   1. Initial program 70.3%

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

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. sub-neg 70.2%

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

      4. +-commutative 70.2%

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

      5. distribute-rgt-neg-in 70.2%

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

      6. fma-define 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in z around inf 54.7%

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

      1. associate-/r* 54.9%

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

   9. Simplified 54.9%

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

   10. Taylor expanded in z around inf 78.3%

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

       1. +-commutative 78.3%

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

       2. associate-*r/ 78.3%

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

       3. neg-mul-1 78.3%

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

       4. *-commutative 78.3%

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

   12. Simplified 78.3%

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

   13. Taylor expanded in y around 0 78.3%

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

       1. mul-1-neg 78.3%

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

       2. associate-/l/ 81.7%

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

       3. +-commutative 81.7%

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

       4. sub-neg 81.7%

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

       5. div-sub 82.6%

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

   15. Simplified 82.6%

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

   if -2.09999999999999997e129 < z < -2.99999999999999999e63

   1. Initial program 68.2%

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

      1. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in z around inf 68.2%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

   8. Simplified 83.9%

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

   if -3.59999999999999983e-16 < z < -6.1000000000000002e-80

   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 79.4%

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

      1. associate-/l* 71.6%

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

      2. cancel-sign-sub-inv 71.6%

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

      3. *-commutative 71.6%

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

      4. +-commutative 71.6%

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

      5. fma-define 71.6%

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

      6. neg-mul-1 71.6%

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

      7. associate-*r/ 79.4%

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

      8. distribute-frac-neg2 79.4%

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

      9. neg-sub0 79.4%

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

      10. fma-define 79.4%

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

      11. associate--r+ 79.4%

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

      12. neg-sub0 79.4%

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

      13. distribute-rgt-neg-out 79.4%

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

      14. remove-double-neg 79.4%

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

   7. Simplified 79.4%

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

      1. *-commutative 79.4%

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

      2. associate-/l* 79.2%

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

   9. Applied egg-rr 79.2%

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

       1. clear-num 79.2%

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

       2. un-div-inv 79.3%

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

   11. Applied egg-rr 79.3%

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

   if -6.1000000000000002e-80 < z < 1.6e21

   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 x around inf 80.6%

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

      1. *-commutative 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+129}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-80}:\\ \;\;\;\;\frac{z}{\frac{z \cdot a - t}{y}}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -2.75e+132)
     t_1
     (if (<= z -5.5e+63)
       (/ y (- a (/ t z)))
       (if (<= z -1.95e-16)
         t_1
         (if (<= z -2.1e-69)
           (* z (/ y (- (* z a) t)))
           (if (<= z 1.7e+23) (/ x (- t (* z a))) 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 <= -2.75e+132) {
		tmp = t_1;
	} else if (z <= -5.5e+63) {
		tmp = y / (a - (t / z));
	} else if (z <= -1.95e-16) {
		tmp = t_1;
	} else if (z <= -2.1e-69) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= 1.7e+23) {
		tmp = x / (t - (z * a));
	} 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 <= (-2.75d+132)) then
        tmp = t_1
    else if (z <= (-5.5d+63)) then
        tmp = y / (a - (t / z))
    else if (z <= (-1.95d-16)) then
        tmp = t_1
    else if (z <= (-2.1d-69)) then
        tmp = z * (y / ((z * a) - t))
    else if (z <= 1.7d+23) then
        tmp = x / (t - (z * a))
    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 <= -2.75e+132) {
		tmp = t_1;
	} else if (z <= -5.5e+63) {
		tmp = y / (a - (t / z));
	} else if (z <= -1.95e-16) {
		tmp = t_1;
	} else if (z <= -2.1e-69) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= 1.7e+23) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -2.75e+132:
		tmp = t_1
	elif z <= -5.5e+63:
		tmp = y / (a - (t / z))
	elif z <= -1.95e-16:
		tmp = t_1
	elif z <= -2.1e-69:
		tmp = z * (y / ((z * a) - t))
	elif z <= 1.7e+23:
		tmp = x / (t - (z * a))
	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 <= -2.75e+132)
		tmp = t_1;
	elseif (z <= -5.5e+63)
		tmp = Float64(y / Float64(a - Float64(t / z)));
	elseif (z <= -1.95e-16)
		tmp = t_1;
	elseif (z <= -2.1e-69)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	elseif (z <= 1.7e+23)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	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 <= -2.75e+132)
		tmp = t_1;
	elseif (z <= -5.5e+63)
		tmp = y / (a - (t / z));
	elseif (z <= -1.95e-16)
		tmp = t_1;
	elseif (z <= -2.1e-69)
		tmp = z * (y / ((z * a) - t));
	elseif (z <= 1.7e+23)
		tmp = x / (t - (z * a));
	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, -2.75e+132], t$95$1, If[LessEqual[z, -5.5e+63], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-16], t$95$1, If[LessEqual[z, -2.1e-69], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+23], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.75e132 or -5.50000000000000004e63 < z < -1.94999999999999989e-16 or 1.69999999999999996e23 < z

   1. Initial program 70.3%

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

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. sub-neg 70.2%

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

      4. +-commutative 70.2%

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

      5. distribute-rgt-neg-in 70.2%

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

      6. fma-define 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in z around inf 54.7%

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

      1. associate-/r* 54.9%

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

   9. Simplified 54.9%

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

   10. Taylor expanded in z around inf 78.3%

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

       1. +-commutative 78.3%

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

       2. associate-*r/ 78.3%

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

       3. neg-mul-1 78.3%

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

       4. *-commutative 78.3%

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

   12. Simplified 78.3%

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

   13. Taylor expanded in y around 0 78.3%

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

       1. mul-1-neg 78.3%

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

       2. associate-/l/ 81.7%

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

       3. +-commutative 81.7%

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

       4. sub-neg 81.7%

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

       5. div-sub 82.6%

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

   15. Simplified 82.6%

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

   if -2.75e132 < z < -5.50000000000000004e63

   1. Initial program 68.2%

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

      1. *-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in z around inf 68.2%

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

   6. Taylor expanded in x around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. neg-mul-1 83.9%

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

   8. Simplified 83.9%

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

   if -1.94999999999999989e-16 < z < -2.1e-69

   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 84.0%

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

      1. associate-/l* 82.8%

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

      2. cancel-sign-sub-inv 82.8%

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

      3. *-commutative 82.8%

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

      4. +-commutative 82.8%

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

      5. fma-define 82.8%

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

      6. neg-mul-1 82.8%

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

      7. associate-*r/ 84.0%

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

      8. distribute-frac-neg2 84.0%

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

      9. neg-sub0 84.0%

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

      10. fma-define 84.0%

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

      11. associate--r+ 84.0%

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

      12. neg-sub0 84.0%

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

      13. distribute-rgt-neg-out 84.0%

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

      14. remove-double-neg 84.0%

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

   7. Simplified 84.0%

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

      1. *-commutative 84.0%

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

      2. associate-/l* 83.9%

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

   9. Applied egg-rr 83.9%

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

   if -2.1e-69 < z < 1.69999999999999996e23

   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 x around inf 80.1%

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

      1. *-commutative 80.1%

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

   7. Simplified 80.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+132}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-69}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - \frac{t}{z}}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+128}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+62}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a (/ t z)))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -5e+128)
     t_2
     (if (<= z -1.5e+62)
       t_1
       (if (<= z -1.6e-16)
         t_2
         (if (<= z -1.12e-69)
           t_1
           (if (<= z 2.05e+20) (/ x (- t (* z a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - (t / z));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5e+128) {
		tmp = t_2;
	} else if (z <= -1.5e+62) {
		tmp = t_1;
	} else if (z <= -1.6e-16) {
		tmp = t_2;
	} else if (z <= -1.12e-69) {
		tmp = t_1;
	} else if (z <= 2.05e+20) {
		tmp = x / (t - (z * a));
	} 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 = y / (a - (t / z))
    t_2 = (y - (x / z)) / a
    if (z <= (-5d+128)) then
        tmp = t_2
    else if (z <= (-1.5d+62)) then
        tmp = t_1
    else if (z <= (-1.6d-16)) then
        tmp = t_2
    else if (z <= (-1.12d-69)) then
        tmp = t_1
    else if (z <= 2.05d+20) then
        tmp = x / (t - (z * a))
    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 = y / (a - (t / z));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5e+128) {
		tmp = t_2;
	} else if (z <= -1.5e+62) {
		tmp = t_1;
	} else if (z <= -1.6e-16) {
		tmp = t_2;
	} else if (z <= -1.12e-69) {
		tmp = t_1;
	} else if (z <= 2.05e+20) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - (t / z))
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -5e+128:
		tmp = t_2
	elif z <= -1.5e+62:
		tmp = t_1
	elif z <= -1.6e-16:
		tmp = t_2
	elif z <= -1.12e-69:
		tmp = t_1
	elif z <= 2.05e+20:
		tmp = x / (t - (z * a))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - Float64(t / z)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -5e+128)
		tmp = t_2;
	elseif (z <= -1.5e+62)
		tmp = t_1;
	elseif (z <= -1.6e-16)
		tmp = t_2;
	elseif (z <= -1.12e-69)
		tmp = t_1;
	elseif (z <= 2.05e+20)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - (t / z));
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -5e+128)
		tmp = t_2;
	elseif (z <= -1.5e+62)
		tmp = t_1;
	elseif (z <= -1.6e-16)
		tmp = t_2;
	elseif (z <= -1.12e-69)
		tmp = t_1;
	elseif (z <= 2.05e+20)
		tmp = x / (t - (z * a));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -5e+128], t$95$2, If[LessEqual[z, -1.5e+62], t$95$1, If[LessEqual[z, -1.6e-16], t$95$2, If[LessEqual[z, -1.12e-69], t$95$1, If[LessEqual[z, 2.05e+20], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5e128 or -1.5e62 < z < -1.60000000000000011e-16 or 2.05e20 < z

   1. Initial program 70.3%

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

      1. *-commutative 70.3%

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

   3. Simplified 70.3%

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

      1. clear-num 70.1%

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

      2. associate-/r/ 70.2%

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

      3. sub-neg 70.2%

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

      4. +-commutative 70.2%

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

      5. distribute-rgt-neg-in 70.2%

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

      6. fma-define 70.3%

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

   6. Applied egg-rr 70.3%

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

   7. Taylor expanded in z around inf 54.7%

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

      1. associate-/r* 54.9%

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

   9. Simplified 54.9%

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

   10. Taylor expanded in z around inf 78.3%

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

       1. +-commutative 78.3%

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

       2. associate-*r/ 78.3%

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

       3. neg-mul-1 78.3%

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

       4. *-commutative 78.3%

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

   12. Simplified 78.3%

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

   13. Taylor expanded in y around 0 78.3%

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

       1. mul-1-neg 78.3%

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

       2. associate-/l/ 81.7%

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

       3. +-commutative 81.7%

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

       4. sub-neg 81.7%

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

       5. div-sub 82.6%

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

   15. Simplified 82.6%

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

   if -5e128 < z < -1.5e62 or -1.60000000000000011e-16 < z < -1.12e-69

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

   3. Simplified 80.8%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   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 80.8%

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

      1. associate-*r/ 80.8%

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

      2. neg-mul-1 80.8%

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

   8. Simplified 80.8%

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

   if -1.12e-69 < z < 2.05e20

   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 x around inf 80.1%

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

      1. *-commutative 80.1%

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

   7. Simplified 80.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+128}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-16}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 5.5 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.75e-14)
   (/ y a)
   (if (<= z -5.1e-80)
     (* z (/ y (- t)))
     (if (<= z 6.8e+18)
       (/ x t)
       (if (or (<= z 1.02e+197) (not (<= z 5.5e+237)))
         (/ y a)
         (/ (/ x (- z)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.75e-14) {
		tmp = y / a;
	} else if (z <= -5.1e-80) {
		tmp = z * (y / -t);
	} else if (z <= 6.8e+18) {
		tmp = x / t;
	} else if ((z <= 1.02e+197) || !(z <= 5.5e+237)) {
		tmp = y / a;
	} else {
		tmp = (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 <= (-2.75d-14)) then
        tmp = y / a
    else if (z <= (-5.1d-80)) then
        tmp = z * (y / -t)
    else if (z <= 6.8d+18) then
        tmp = x / t
    else if ((z <= 1.02d+197) .or. (.not. (z <= 5.5d+237))) then
        tmp = y / a
    else
        tmp = (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 <= -2.75e-14) {
		tmp = y / a;
	} else if (z <= -5.1e-80) {
		tmp = z * (y / -t);
	} else if (z <= 6.8e+18) {
		tmp = x / t;
	} else if ((z <= 1.02e+197) || !(z <= 5.5e+237)) {
		tmp = y / a;
	} else {
		tmp = (x / -z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.75e-14:
		tmp = y / a
	elif z <= -5.1e-80:
		tmp = z * (y / -t)
	elif z <= 6.8e+18:
		tmp = x / t
	elif (z <= 1.02e+197) or not (z <= 5.5e+237):
		tmp = y / a
	else:
		tmp = (x / -z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.75e-14)
		tmp = Float64(y / a);
	elseif (z <= -5.1e-80)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif (z <= 6.8e+18)
		tmp = Float64(x / t);
	elseif ((z <= 1.02e+197) || !(z <= 5.5e+237))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(x / Float64(-z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.75e-14)
		tmp = y / a;
	elseif (z <= -5.1e-80)
		tmp = z * (y / -t);
	elseif (z <= 6.8e+18)
		tmp = x / t;
	elseif ((z <= 1.02e+197) || ~((z <= 5.5e+237)))
		tmp = y / a;
	else
		tmp = (x / -z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.75e-14], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.1e-80], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+18], N[(x / t), $MachinePrecision], If[Or[LessEqual[z, 1.02e+197], N[Not[LessEqual[z, 5.5e+237]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.74999999999999996e-14 or 6.8e18 < z < 1.02000000000000008e197 or 5.5000000000000001e237 < z

   1. Initial program 68.3%

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

      1. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   5. Taylor expanded in z around inf 57.4%

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

   if -2.74999999999999996e-14 < z < -5.10000000000000008e-80

   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 74.3%

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

      1. associate-/l* 66.9%

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

      2. cancel-sign-sub-inv 66.9%

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

      3. *-commutative 66.9%

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

      4. +-commutative 66.9%

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

      5. fma-define 66.9%

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

      6. neg-mul-1 66.9%

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

      7. associate-*r/ 74.3%

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

      8. distribute-frac-neg2 74.3%

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

      9. neg-sub0 74.3%

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

      10. fma-define 74.3%

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

      11. associate--r+ 74.3%

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

      12. neg-sub0 74.3%

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

      13. distribute-rgt-neg-out 74.3%

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

      14. remove-double-neg 74.3%

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

   7. Simplified 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 74.0%

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

   9. Applied egg-rr 74.0%

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

   10. Taylor expanded in z around 0 61.7%

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

       1. associate-*r/ 61.7%

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

       2. neg-mul-1 61.7%

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

   12. Simplified 61.7%

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

   if -5.10000000000000008e-80 < z < 6.8e18

   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 61.1%

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

   if 1.02000000000000008e197 < z < 5.5000000000000001e237

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in t around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. neg-mul-1 67.2%

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

      3. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   11. Taylor expanded in x around 0 67.2%

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

       1. mul-1-neg 67.2%

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

       2. associate-/l/ 79.8%

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

       3. distribute-frac-neg2 79.8%

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

   13. Simplified 79.8%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 5.5 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 5.5 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.15e+56)
   (/ y a)
   (if (<= z 1.36e+57)
     (/ x (- t (* z a)))
     (if (or (<= z 1.02e+197) (not (<= z 5.5e+237)))
       (/ y a)
       (/ (/ x (- z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.15e+56) {
		tmp = y / a;
	} else if (z <= 1.36e+57) {
		tmp = x / (t - (z * a));
	} else if ((z <= 1.02e+197) || !(z <= 5.5e+237)) {
		tmp = y / a;
	} else {
		tmp = (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 <= (-1.15d+56)) then
        tmp = y / a
    else if (z <= 1.36d+57) then
        tmp = x / (t - (z * a))
    else if ((z <= 1.02d+197) .or. (.not. (z <= 5.5d+237))) then
        tmp = y / a
    else
        tmp = (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 <= -1.15e+56) {
		tmp = y / a;
	} else if (z <= 1.36e+57) {
		tmp = x / (t - (z * a));
	} else if ((z <= 1.02e+197) || !(z <= 5.5e+237)) {
		tmp = y / a;
	} else {
		tmp = (x / -z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.15e+56:
		tmp = y / a
	elif z <= 1.36e+57:
		tmp = x / (t - (z * a))
	elif (z <= 1.02e+197) or not (z <= 5.5e+237):
		tmp = y / a
	else:
		tmp = (x / -z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.15e+56)
		tmp = Float64(y / a);
	elseif (z <= 1.36e+57)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif ((z <= 1.02e+197) || !(z <= 5.5e+237))
		tmp = Float64(y / a);
	else
		tmp = Float64(Float64(x / Float64(-z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.15e+56)
		tmp = y / a;
	elseif (z <= 1.36e+57)
		tmp = x / (t - (z * a));
	elseif ((z <= 1.02e+197) || ~((z <= 5.5e+237)))
		tmp = y / a;
	else
		tmp = (x / -z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.15e+56], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.36e+57], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 1.02e+197], N[Not[LessEqual[z, 5.5e+237]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(N[(x / (-z)), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000007e56 or 1.36e57 < z < 1.02000000000000008e197 or 5.5000000000000001e237 < z

   1. Initial program 61.1%

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

      1. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in z around inf 62.0%

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

   if -1.15000000000000007e56 < z < 1.36e57

   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 x around inf 73.9%

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

      1. *-commutative 73.9%

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

   7. Simplified 73.9%

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

   if 1.02000000000000008e197 < z < 5.5000000000000001e237

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in t around 0 67.2%

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

      1. associate-*r/ 67.2%

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

      2. neg-mul-1 67.2%

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

      3. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   11. Taylor expanded in x around 0 67.2%

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

       1. mul-1-neg 67.2%

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

       2. associate-/l/ 79.8%

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

       3. distribute-frac-neg2 79.8%

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

   13. Simplified 79.8%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{+57}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+197} \lor \neg \left(z \leq 5.5 \cdot 10^{+237}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{-z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+123} \lor \neg \left(z \leq 4.5 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e+123) (not (<= z 4.5e+80)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.85e+123) || !(z <= 4.5e+80)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (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 <= (-1.85d+123)) .or. (.not. (z <= 4.5d+80))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / (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 <= -1.85e+123) || !(z <= 4.5e+80)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.85e+123) or not (z <= 4.5e+80):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.85e+123) || !(z <= 4.5e+80))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.85e+123) || ~((z <= 4.5e+80)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.85e+123], N[Not[LessEqual[z, 4.5e+80]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.84999999999999998e123 or 4.50000000000000007e80 < z

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

      1. clear-num 61.3%

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

      2. associate-/r/ 61.5%

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

      3. sub-neg 61.5%

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

      4. +-commutative 61.5%

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

      5. distribute-rgt-neg-in 61.5%

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

      6. fma-define 61.5%

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

   6. Applied egg-rr 61.5%

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

   7. Taylor expanded in z around inf 49.2%

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

      1. associate-/r* 49.3%

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

   9. Simplified 49.3%

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

   10. Taylor expanded in z around inf 80.0%

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

       1. +-commutative 80.0%

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

       2. associate-*r/ 80.0%

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

       3. neg-mul-1 80.0%

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

       4. *-commutative 80.0%

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

   12. Simplified 80.0%

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

   13. Taylor expanded in y around 0 80.0%

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

       1. mul-1-neg 80.0%

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

       2. associate-/l/ 84.4%

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

       3. +-commutative 84.4%

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

       4. sub-neg 84.4%

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

       5. div-sub 84.4%

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

   15. Simplified 84.4%

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

   if -1.84999999999999998e123 < z < 4.50000000000000007e80

   1. Initial program 96.9%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+123} \lor \neg \left(z \leq 4.5 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.2e-15)
   (/ y a)
   (if (<= z -6.5e-80) (* z (/ y (- t))) (if (<= z 1.6e+23) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e-15) {
		tmp = y / a;
	} else if (z <= -6.5e-80) {
		tmp = z * (y / -t);
	} else if (z <= 1.6e+23) {
		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 <= (-5.2d-15)) then
        tmp = y / a
    else if (z <= (-6.5d-80)) then
        tmp = z * (y / -t)
    else if (z <= 1.6d+23) 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 <= -5.2e-15) {
		tmp = y / a;
	} else if (z <= -6.5e-80) {
		tmp = z * (y / -t);
	} else if (z <= 1.6e+23) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.2e-15:
		tmp = y / a
	elif z <= -6.5e-80:
		tmp = z * (y / -t)
	elif z <= 1.6e+23:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.2e-15)
		tmp = Float64(y / a);
	elseif (z <= -6.5e-80)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif (z <= 1.6e+23)
		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 <= -5.2e-15)
		tmp = y / a;
	elseif (z <= -6.5e-80)
		tmp = z * (y / -t);
	elseif (z <= 1.6e+23)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.2e-15], N[(y / a), $MachinePrecision], If[LessEqual[z, -6.5e-80], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.6e+23], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.20000000000000009e-15 or 1.6e23 < z

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

   3. Simplified 69.8%

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

   5. Taylor expanded in z around inf 55.6%

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

   if -5.20000000000000009e-15 < z < -6.49999999999999984e-80

   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 74.3%

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

      1. associate-/l* 66.9%

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

      2. cancel-sign-sub-inv 66.9%

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

      3. *-commutative 66.9%

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

      4. +-commutative 66.9%

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

      5. fma-define 66.9%

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

      6. neg-mul-1 66.9%

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

      7. associate-*r/ 74.3%

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

      8. distribute-frac-neg2 74.3%

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

      9. neg-sub0 74.3%

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

      10. fma-define 74.3%

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

      11. associate--r+ 74.3%

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

      12. neg-sub0 74.3%

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

      13. distribute-rgt-neg-out 74.3%

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

      14. remove-double-neg 74.3%

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

   7. Simplified 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-/l* 74.0%

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

   9. Applied egg-rr 74.0%

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

   10. Taylor expanded in z around 0 61.7%

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

       1. associate-*r/ 61.7%

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

       2. neg-mul-1 61.7%

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

   12. Simplified 61.7%

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

   if -6.49999999999999984e-80 < z < 1.6e23

   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 61.1%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-15}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 70.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-16} \lor \neg \left(z \leq 1.05 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e-16) (not (<= z 1.05e-80)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e-16) || !(z <= 1.05e-80)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / 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 <= (-1.6d-16)) .or. (.not. (z <= 1.05d-80))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / 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 <= -1.6e-16) || !(z <= 1.05e-80)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e-16) or not (z <= 1.05e-80):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e-16) || !(z <= 1.05e-80))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e-16) || ~((z <= 1.05e-80)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e-16], N[Not[LessEqual[z, 1.05e-80]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.60000000000000011e-16 or 1.05000000000000001e-80 < z

   1. Initial program 72.8%

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

      1. *-commutative 72.8%

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

   3. Simplified 72.8%

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

      1. clear-num 72.7%

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

      2. associate-/r/ 72.8%

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

      3. sub-neg 72.8%

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

      4. +-commutative 72.8%

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

      5. distribute-rgt-neg-in 72.8%

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

      6. fma-define 72.8%

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

   6. Applied egg-rr 72.8%

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

   7. Taylor expanded in z around inf 53.3%

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

      1. associate-/r* 53.8%

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

   9. Simplified 53.8%

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

   10. Taylor expanded in z around inf 74.3%

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

       1. +-commutative 74.3%

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

       2. associate-*r/ 74.3%

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

       3. neg-mul-1 74.3%

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

       4. *-commutative 74.3%

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

   12. Simplified 74.3%

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

   13. Taylor expanded in y around 0 74.3%

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

       1. mul-1-neg 74.3%

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

       2. associate-/l/ 77.0%

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

       3. +-commutative 77.0%

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

       4. sub-neg 77.0%

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

       5. div-sub 77.7%

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

   15. Simplified 77.7%

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

   if -1.60000000000000011e-16 < z < 1.05000000000000001e-80

   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 t around inf 77.7%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-16} \lor \neg \left(z \leq 1.05 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-45} \lor \neg \left(z \leq 4.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7e-45) (not (<= z 4.4e+18))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7e-45) || !(z <= 4.4e+18)) {
		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 <= (-7d-45)) .or. (.not. (z <= 4.4d+18))) 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 <= -7e-45) || !(z <= 4.4e+18)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7e-45) or not (z <= 4.4e+18):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7e-45) || !(z <= 4.4e+18))
		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 <= -7e-45) || ~((z <= 4.4e+18)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7e-45], N[Not[LessEqual[z, 4.4e+18]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7e-45 or 4.4e18 < z

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

   3. Simplified 71.7%

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

   5. Taylor expanded in z around inf 53.6%

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

   if -7e-45 < z < 4.4e18

   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 58.0%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-45} \lor \neg \left(z \leq 4.4 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.9% 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 84.3%

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

   1. *-commutative 84.3%

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

3. Simplified 84.3%

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

5. Taylor expanded in z around 0 32.8%

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

Developer target: 97.2% 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 2024096 
(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))))