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

Percentage Accurate: 86.1% → 91.6%

Time: 14.1s

Alternatives: 10

Speedup: 0.5×

• could not determine a ground truth

  1. x = -5.453064344492791e-102
  2. y = 1.23485057791917e-233
  3. z = 1.8591605742092392e+253
  4. t = 8.153518615070953e+154
  5. a = -4.717192531236068e-140

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: 86.1% 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: 91.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+184} \lor \neg \left(z \leq 1.15 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+184) (not (<= z 1.15e+147)))
   (/ (- 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 <= -9.5e+184) || !(z <= 1.15e+147)) {
		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 <= (-9.5d+184)) .or. (.not. (z <= 1.15d+147))) 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 <= -9.5e+184) || !(z <= 1.15e+147)) {
		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 <= -9.5e+184) or not (z <= 1.15e+147):
		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 <= -9.5e+184) || !(z <= 1.15e+147))
		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 <= -9.5e+184) || ~((z <= 1.15e+147)))
		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, -9.5e+184], N[Not[LessEqual[z, 1.15e+147]], $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 < -9.4999999999999995e184 or 1.15e147 < z

   1. Initial program 55.4%

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

      1. *-commutative 55.4%

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

   3. Simplified 55.4%

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

   5. Taylor expanded in t around 0 48.5%

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

      1. mul-1-neg 48.5%

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

      2. *-commutative 48.5%

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

      3. distribute-neg-frac2 48.5%

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

      4. *-commutative 48.5%

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

      5. distribute-rgt-neg-in 48.5%

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

   7. Simplified 48.5%

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

   8. Taylor expanded in x around 0 81.8%

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

      1. +-commutative 81.8%

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

      2. mul-1-neg 81.8%

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

      3. unsub-neg 81.8%

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

      4. *-commutative 81.8%

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

   10. Simplified 81.8%

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

   11. Taylor expanded in y around 0 81.8%

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

       1. +-commutative 81.8%

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

       2. metadata-eval 81.8%

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

       3. *-commutative 81.8%

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

       4. cancel-sign-sub-inv 81.8%

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

       5. *-lft-identity 81.8%

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

       6. associate-/r* 88.2%

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

       7. div-sub 88.2%

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

   13. Simplified 88.2%

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

   if -9.4999999999999995e184 < z < 1.15e147

   1. Initial program 95.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+184} \lor \neg \left(z \leq 1.15 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{z \cdot a - t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- (* z a) t)))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -4.6e+98)
     t_2
     (if (<= z -5.3e-9)
       t_1
       (if (<= z -5e-57)
         (/ x (- t (* z a)))
         (if (<= z -2.15e-108)
           t_1
           (if (<= z 3.3e-31) (/ (- x (* z y)) t) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / ((z * a) - t));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -4.6e+98) {
		tmp = t_2;
	} else if (z <= -5.3e-9) {
		tmp = t_1;
	} else if (z <= -5e-57) {
		tmp = x / (t - (z * a));
	} else if (z <= -2.15e-108) {
		tmp = t_1;
	} else if (z <= 3.3e-31) {
		tmp = (x - (z * y)) / t;
	} 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 = z * (y / ((z * a) - t))
    t_2 = (y - (x / z)) / a
    if (z <= (-4.6d+98)) then
        tmp = t_2
    else if (z <= (-5.3d-9)) then
        tmp = t_1
    else if (z <= (-5d-57)) then
        tmp = x / (t - (z * a))
    else if (z <= (-2.15d-108)) then
        tmp = t_1
    else if (z <= 3.3d-31) then
        tmp = (x - (z * y)) / t
    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 = z * (y / ((z * a) - t));
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -4.6e+98) {
		tmp = t_2;
	} else if (z <= -5.3e-9) {
		tmp = t_1;
	} else if (z <= -5e-57) {
		tmp = x / (t - (z * a));
	} else if (z <= -2.15e-108) {
		tmp = t_1;
	} else if (z <= 3.3e-31) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / ((z * a) - t))
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -4.6e+98:
		tmp = t_2
	elif z <= -5.3e-9:
		tmp = t_1
	elif z <= -5e-57:
		tmp = x / (t - (z * a))
	elif z <= -2.15e-108:
		tmp = t_1
	elif z <= 3.3e-31:
		tmp = (x - (z * y)) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(Float64(z * a) - t)))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -4.6e+98)
		tmp = t_2;
	elseif (z <= -5.3e-9)
		tmp = t_1;
	elseif (z <= -5e-57)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= -2.15e-108)
		tmp = t_1;
	elseif (z <= 3.3e-31)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / ((z * a) - t));
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -4.6e+98)
		tmp = t_2;
	elseif (z <= -5.3e-9)
		tmp = t_1;
	elseif (z <= -5e-57)
		tmp = x / (t - (z * a));
	elseif (z <= -2.15e-108)
		tmp = t_1;
	elseif (z <= 3.3e-31)
		tmp = (x - (z * y)) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -4.6e+98], t$95$2, If[LessEqual[z, -5.3e-9], t$95$1, If[LessEqual[z, -5e-57], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-108], t$95$1, If[LessEqual[z, 3.3e-31], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.60000000000000026e98 or 3.2999999999999999e-31 < z

   1. Initial program 71.4%

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

      1. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. distribute-neg-frac2 50.6%

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

      4. *-commutative 50.6%

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

      5. distribute-rgt-neg-in 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in x around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. *-commutative 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in y around 0 71.4%

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

       1. +-commutative 71.4%

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

       2. metadata-eval 71.4%

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

       3. *-commutative 71.4%

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

       4. cancel-sign-sub-inv 71.4%

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

       5. *-lft-identity 71.4%

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

       6. associate-/r* 75.2%

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

       7. div-sub 75.2%

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

   13. Simplified 75.2%

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

   if -4.60000000000000026e98 < z < -5.30000000000000031e-9 or -5.0000000000000002e-57 < z < -2.15e-108

   1. Initial program 97.3%

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

      1. *-commutative 97.3%

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

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t - z \cdot a}} \]
   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. mul-1-neg 74.3%

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

      2. distribute-neg-frac2 74.3%

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

      3. sub-neg 74.3%

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

      4. +-commutative 74.3%

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

      5. distribute-neg-in 74.3%

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

      6. unsub-neg 74.3%

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

      7. *-commutative 74.3%

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

      8. 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. Taylor expanded in y around 0 74.3%

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

      1. *-commutative 74.3%

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

      2. associate-*r/ 76.8%

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

      3. *-commutative 76.8%

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

   10. Simplified 76.8%

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

   if -5.30000000000000031e-9 < z < -5.0000000000000002e-57

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 89.6%

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

      1. *-commutative 89.6%

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

   7. Simplified 89.6%

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

   if -2.15e-108 < z < 3.2999999999999999e-31

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 85.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+98}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -5.3 \cdot 10^{-9}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-57}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \frac{y}{t\_1}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-108}:\\ \;\;\;\;\frac{z \cdot y}{t\_1}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -2.6e+101)
     t_2
     (if (<= z -6.6e-7)
       (* z (/ y t_1))
       (if (<= z -3.1e-61)
         (/ x (- t (* z a)))
         (if (<= z -2.15e-108)
           (/ (* z y) t_1)
           (if (<= z 2.5e-31) (/ (- x (* z y)) t) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -2.6e+101) {
		tmp = t_2;
	} else if (z <= -6.6e-7) {
		tmp = z * (y / t_1);
	} else if (z <= -3.1e-61) {
		tmp = x / (t - (z * a));
	} else if (z <= -2.15e-108) {
		tmp = (z * y) / t_1;
	} else if (z <= 2.5e-31) {
		tmp = (x - (z * y)) / t;
	} 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 = (z * a) - t
    t_2 = (y - (x / z)) / a
    if (z <= (-2.6d+101)) then
        tmp = t_2
    else if (z <= (-6.6d-7)) then
        tmp = z * (y / t_1)
    else if (z <= (-3.1d-61)) then
        tmp = x / (t - (z * a))
    else if (z <= (-2.15d-108)) then
        tmp = (z * y) / t_1
    else if (z <= 2.5d-31) then
        tmp = (x - (z * y)) / t
    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 = (z * a) - t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -2.6e+101) {
		tmp = t_2;
	} else if (z <= -6.6e-7) {
		tmp = z * (y / t_1);
	} else if (z <= -3.1e-61) {
		tmp = x / (t - (z * a));
	} else if (z <= -2.15e-108) {
		tmp = (z * y) / t_1;
	} else if (z <= 2.5e-31) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -2.6e+101:
		tmp = t_2
	elif z <= -6.6e-7:
		tmp = z * (y / t_1)
	elif z <= -3.1e-61:
		tmp = x / (t - (z * a))
	elif z <= -2.15e-108:
		tmp = (z * y) / t_1
	elif z <= 2.5e-31:
		tmp = (x - (z * y)) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -2.6e+101)
		tmp = t_2;
	elseif (z <= -6.6e-7)
		tmp = Float64(z * Float64(y / t_1));
	elseif (z <= -3.1e-61)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= -2.15e-108)
		tmp = Float64(Float64(z * y) / t_1);
	elseif (z <= 2.5e-31)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -2.6e+101)
		tmp = t_2;
	elseif (z <= -6.6e-7)
		tmp = z * (y / t_1);
	elseif (z <= -3.1e-61)
		tmp = x / (t - (z * a));
	elseif (z <= -2.15e-108)
		tmp = (z * y) / t_1;
	elseif (z <= 2.5e-31)
		tmp = (x - (z * y)) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -2.6e+101], t$95$2, If[LessEqual[z, -6.6e-7], N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.1e-61], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-108], N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.5e-31], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.6e101 or 2.5e-31 < z

   1. Initial program 71.4%

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

      1. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. distribute-neg-frac2 50.6%

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

      4. *-commutative 50.6%

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

      5. distribute-rgt-neg-in 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in x around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. *-commutative 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in y around 0 71.4%

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

       1. +-commutative 71.4%

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

       2. metadata-eval 71.4%

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

       3. *-commutative 71.4%

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

       4. cancel-sign-sub-inv 71.4%

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

       5. *-lft-identity 71.4%

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

       6. associate-/r* 75.2%

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

       7. div-sub 75.2%

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

   13. Simplified 75.2%

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

   if -2.6e101 < z < -6.6000000000000003e-7

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. distribute-neg-frac2 76.6%

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

      3. sub-neg 76.6%

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

      4. +-commutative 76.6%

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

      5. distribute-neg-in 76.6%

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

      6. unsub-neg 76.6%

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

      7. *-commutative 76.6%

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

      8. remove-double-neg 76.6%

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

   7. Simplified 76.6%

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

   8. Taylor expanded in y around 0 76.6%

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

      1. *-commutative 76.6%

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

      2. associate-*r/ 80.6%

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

      3. *-commutative 80.6%

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

   10. Simplified 80.6%

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

   if -6.6000000000000003e-7 < z < -3.09999999999999995e-61

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 83.3%

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

      1. *-commutative 83.3%

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

   7. Simplified 83.3%

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

   if -3.09999999999999995e-61 < z < -2.15e-108

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 73.7%

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

      1. mul-1-neg 73.7%

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

      2. distribute-neg-frac2 73.7%

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

      3. sub-neg 73.7%

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

      4. +-commutative 73.7%

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

      5. distribute-neg-in 73.7%

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

      6. unsub-neg 73.7%

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

      7. *-commutative 73.7%

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

      8. remove-double-neg 73.7%

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

   7. Simplified 73.7%

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

   if -2.15e-108 < z < 2.5e-31

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 85.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+101}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-7}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-108}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot a - t\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-105}:\\ \;\;\;\;\frac{z \cdot y}{t\_1}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* z a) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -5.3e+98)
     t_2
     (if (<= z -1.42e-6)
       (* y (/ z t_1))
       (if (<= z -6.8e-62)
         (/ x (- t (* z a)))
         (if (<= z -1.95e-105)
           (/ (* z y) t_1)
           (if (<= z 2.3e-32) (/ (- x (* z y)) t) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * a) - t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5.3e+98) {
		tmp = t_2;
	} else if (z <= -1.42e-6) {
		tmp = y * (z / t_1);
	} else if (z <= -6.8e-62) {
		tmp = x / (t - (z * a));
	} else if (z <= -1.95e-105) {
		tmp = (z * y) / t_1;
	} else if (z <= 2.3e-32) {
		tmp = (x - (z * y)) / t;
	} 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 = (z * a) - t
    t_2 = (y - (x / z)) / a
    if (z <= (-5.3d+98)) then
        tmp = t_2
    else if (z <= (-1.42d-6)) then
        tmp = y * (z / t_1)
    else if (z <= (-6.8d-62)) then
        tmp = x / (t - (z * a))
    else if (z <= (-1.95d-105)) then
        tmp = (z * y) / t_1
    else if (z <= 2.3d-32) then
        tmp = (x - (z * y)) / t
    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 = (z * a) - t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -5.3e+98) {
		tmp = t_2;
	} else if (z <= -1.42e-6) {
		tmp = y * (z / t_1);
	} else if (z <= -6.8e-62) {
		tmp = x / (t - (z * a));
	} else if (z <= -1.95e-105) {
		tmp = (z * y) / t_1;
	} else if (z <= 2.3e-32) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * a) - t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -5.3e+98:
		tmp = t_2
	elif z <= -1.42e-6:
		tmp = y * (z / t_1)
	elif z <= -6.8e-62:
		tmp = x / (t - (z * a))
	elif z <= -1.95e-105:
		tmp = (z * y) / t_1
	elif z <= 2.3e-32:
		tmp = (x - (z * y)) / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * a) - t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -5.3e+98)
		tmp = t_2;
	elseif (z <= -1.42e-6)
		tmp = Float64(y * Float64(z / t_1));
	elseif (z <= -6.8e-62)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= -1.95e-105)
		tmp = Float64(Float64(z * y) / t_1);
	elseif (z <= 2.3e-32)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * a) - t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -5.3e+98)
		tmp = t_2;
	elseif (z <= -1.42e-6)
		tmp = y * (z / t_1);
	elseif (z <= -6.8e-62)
		tmp = x / (t - (z * a));
	elseif (z <= -1.95e-105)
		tmp = (z * y) / t_1;
	elseif (z <= 2.3e-32)
		tmp = (x - (z * y)) / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -5.3e+98], t$95$2, If[LessEqual[z, -1.42e-6], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-62], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-105], N[(N[(z * y), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 2.3e-32], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.29999999999999997e98 or 2.3000000000000001e-32 < z

   1. Initial program 71.4%

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

      1. *-commutative 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in t around 0 50.6%

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

      1. mul-1-neg 50.6%

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

      2. *-commutative 50.6%

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

      3. distribute-neg-frac2 50.6%

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

      4. *-commutative 50.6%

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

      5. distribute-rgt-neg-in 50.6%

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

   7. Simplified 50.6%

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

   8. Taylor expanded in x around 0 71.4%

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

      1. +-commutative 71.4%

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

      2. mul-1-neg 71.4%

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

      3. unsub-neg 71.4%

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

      4. *-commutative 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in y around 0 71.4%

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

       1. +-commutative 71.4%

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

       2. metadata-eval 71.4%

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

       3. *-commutative 71.4%

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

       4. cancel-sign-sub-inv 71.4%

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

       5. *-lft-identity 71.4%

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

       6. associate-/r* 75.2%

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

       7. div-sub 75.2%

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

   13. Simplified 75.2%

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

   if -5.29999999999999997e98 < z < -1.42e-6

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around 0 76.6%

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

      1. associate-/l* 80.7%

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

      2. associate-*r* 80.7%

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

      3. neg-mul-1 80.7%

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

      4. *-commutative 80.7%

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

   7. Simplified 80.7%

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

   if -1.42e-6 < z < -6.79999999999999975e-62

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 83.3%

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

      1. *-commutative 83.3%

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

   7. Simplified 83.3%

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

   if -6.79999999999999975e-62 < z < -1.95e-105

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 73.7%

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

      1. mul-1-neg 73.7%

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

      2. distribute-neg-frac2 73.7%

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

      3. sub-neg 73.7%

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

      4. +-commutative 73.7%

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

      5. distribute-neg-in 73.7%

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

      6. unsub-neg 73.7%

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

      7. *-commutative 73.7%

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

      8. remove-double-neg 73.7%

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

   7. Simplified 73.7%

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

   if -1.95e-105 < z < 2.3000000000000001e-32

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 85.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+98}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.42 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-105}:\\ \;\;\;\;\frac{z \cdot y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-32}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+70} \lor \neg \left(z \leq 1.5 \cdot 10^{+56}\right) \land \left(z \leq 1.75 \cdot 10^{+117} \lor \neg \left(z \leq 8.5 \cdot 10^{+131}\right)\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.7e+70)
         (and (not (<= z 1.5e+56))
              (or (<= z 1.75e+117) (not (<= z 8.5e+131)))))
   (/ y a)
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+70) || (!(z <= 1.5e+56) && ((z <= 1.75e+117) || !(z <= 8.5e+131)))) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.7d+70)) .or. (.not. (z <= 1.5d+56)) .and. (z <= 1.75d+117) .or. (.not. (z <= 8.5d+131))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.7e+70) || (!(z <= 1.5e+56) && ((z <= 1.75e+117) || !(z <= 8.5e+131)))) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.7e+70) or (not (z <= 1.5e+56) and ((z <= 1.75e+117) or not (z <= 8.5e+131))):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.7e+70) || (!(z <= 1.5e+56) && ((z <= 1.75e+117) || !(z <= 8.5e+131))))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.7e+70) || (~((z <= 1.5e+56)) && ((z <= 1.75e+117) || ~((z <= 8.5e+131)))))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.7e+70], And[N[Not[LessEqual[z, 1.5e+56]], $MachinePrecision], Or[LessEqual[z, 1.75e+117], N[Not[LessEqual[z, 8.5e+131]], $MachinePrecision]]]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e70 or 1.50000000000000003e56 < z < 1.74999999999999991e117 or 8.50000000000000063e131 < z

   1. Initial program 64.6%

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

      1. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in z around inf 63.7%

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

   if -1.7e70 < z < 1.50000000000000003e56 or 1.74999999999999991e117 < z < 8.50000000000000063e131

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 68.8%

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

      1. *-commutative 68.8%

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

   7. Simplified 68.8%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+70} \lor \neg \left(z \leq 1.5 \cdot 10^{+56}\right) \land \left(z \leq 1.75 \cdot 10^{+117} \lor \neg \left(z \leq 8.5 \cdot 10^{+131}\right)\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;a \leq -8 \cdot 10^{+217}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-32}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+197}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= a -8e+217)
     (/ y a)
     (if (<= a -5.2e-52)
       t_1
       (if (<= a 2.35e-32)
         (/ (- x (* z y)) t)
         (if (<= a 1.5e+197) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (a <= -8e+217) {
		tmp = y / a;
	} else if (a <= -5.2e-52) {
		tmp = t_1;
	} else if (a <= 2.35e-32) {
		tmp = (x - (z * y)) / t;
	} else if (a <= 1.5e+197) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    if (a <= (-8d+217)) then
        tmp = y / a
    else if (a <= (-5.2d-52)) then
        tmp = t_1
    else if (a <= 2.35d-32) then
        tmp = (x - (z * y)) / t
    else if (a <= 1.5d+197) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (a <= -8e+217) {
		tmp = y / a;
	} else if (a <= -5.2e-52) {
		tmp = t_1;
	} else if (a <= 2.35e-32) {
		tmp = (x - (z * y)) / t;
	} else if (a <= 1.5e+197) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if a <= -8e+217:
		tmp = y / a
	elif a <= -5.2e-52:
		tmp = t_1
	elif a <= 2.35e-32:
		tmp = (x - (z * y)) / t
	elif a <= 1.5e+197:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (a <= -8e+217)
		tmp = Float64(y / a);
	elseif (a <= -5.2e-52)
		tmp = t_1;
	elseif (a <= 2.35e-32)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (a <= 1.5e+197)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	tmp = 0.0;
	if (a <= -8e+217)
		tmp = y / a;
	elseif (a <= -5.2e-52)
		tmp = t_1;
	elseif (a <= 2.35e-32)
		tmp = (x - (z * y)) / t;
	elseif (a <= 1.5e+197)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -8e+217], N[(y / a), $MachinePrecision], If[LessEqual[a, -5.2e-52], t$95$1, If[LessEqual[a, 2.35e-32], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.5e+197], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.99999999999999968e217 or 1.5000000000000001e197 < a

   1. Initial program 65.6%

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

      1. *-commutative 65.6%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in z around inf 72.6%

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

   if -7.99999999999999968e217 < a < -5.1999999999999997e-52 or 2.3500000000000001e-32 < a < 1.5000000000000001e197

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around inf 61.6%

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

      1. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   if -5.1999999999999997e-52 < a < 2.3500000000000001e-32

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in t around inf 74.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+217}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{-32}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.25e-6)
   (/ y a)
   (if (<= z 3.7e-118)
     (/ x t)
     (if (<= z 9.5e-80)
       (/ (* z y) (- t))
       (if (<= z 4.4e+33) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.25e-6) {
		tmp = y / a;
	} else if (z <= 3.7e-118) {
		tmp = x / t;
	} else if (z <= 9.5e-80) {
		tmp = (z * y) / -t;
	} else if (z <= 4.4e+33) {
		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 <= (-2.25d-6)) then
        tmp = y / a
    else if (z <= 3.7d-118) then
        tmp = x / t
    else if (z <= 9.5d-80) then
        tmp = (z * y) / -t
    else if (z <= 4.4d+33) 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 <= -2.25e-6) {
		tmp = y / a;
	} else if (z <= 3.7e-118) {
		tmp = x / t;
	} else if (z <= 9.5e-80) {
		tmp = (z * y) / -t;
	} else if (z <= 4.4e+33) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.25e-6:
		tmp = y / a
	elif z <= 3.7e-118:
		tmp = x / t
	elif z <= 9.5e-80:
		tmp = (z * y) / -t
	elif z <= 4.4e+33:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.25e-6)
		tmp = Float64(y / a);
	elseif (z <= 3.7e-118)
		tmp = Float64(x / t);
	elseif (z <= 9.5e-80)
		tmp = Float64(Float64(z * y) / Float64(-t));
	elseif (z <= 4.4e+33)
		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 <= -2.25e-6)
		tmp = y / a;
	elseif (z <= 3.7e-118)
		tmp = x / t;
	elseif (z <= 9.5e-80)
		tmp = (z * y) / -t;
	elseif (z <= 4.4e+33)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.25e-6], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.7e-118], N[(x / t), $MachinePrecision], If[LessEqual[z, 9.5e-80], N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 4.4e+33], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25000000000000006e-6 or 4.39999999999999988e33 < z

   1. Initial program 72.6%

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

      1. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in z around inf 56.8%

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

   if -2.25000000000000006e-6 < z < 3.70000000000000014e-118 or 9.5000000000000003e-80 < z < 4.39999999999999988e33

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 55.5%

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

   if 3.70000000000000014e-118 < z < 9.5000000000000003e-80

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-neg-frac2 63.2%

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

      3. sub-neg 63.2%

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

      4. +-commutative 63.2%

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

      5. distribute-neg-in 63.2%

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

      6. unsub-neg 63.2%

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

      7. *-commutative 63.2%

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

      8. remove-double-neg 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in z around 0 62.7%

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

      1. associate-*r/ 62.7%

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

      2. *-commutative 62.7%

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

      3. neg-mul-1 62.7%

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

      4. *-commutative 62.7%

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

      5. distribute-rgt-neg-in 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-80}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-10} \lor \neg \left(z \leq 1.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.85e-10) (not (<= z 1.2e-31)))
   (/ (- 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 <= -1.85e-10) || !(z <= 1.2e-31)) {
		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 <= (-1.85d-10)) .or. (.not. (z <= 1.2d-31))) 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 <= -1.85e-10) || !(z <= 1.2e-31)) {
		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 <= -1.85e-10) or not (z <= 1.2e-31):
		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 <= -1.85e-10) || !(z <= 1.2e-31))
		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 <= -1.85e-10) || ~((z <= 1.2e-31)))
		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, -1.85e-10], N[Not[LessEqual[z, 1.2e-31]], $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 < -1.85000000000000007e-10 or 1.2e-31 < z

   1. Initial program 75.4%

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

      1. *-commutative 75.4%

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

   3. Simplified 75.4%

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

   5. Taylor expanded in t around 0 51.5%

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

      1. mul-1-neg 51.5%

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

      2. *-commutative 51.5%

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

      3. distribute-neg-frac2 51.5%

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

      4. *-commutative 51.5%

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

      5. distribute-rgt-neg-in 51.5%

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

   7. Simplified 51.5%

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

   8. Taylor expanded in x around 0 68.8%

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

      1. +-commutative 68.8%

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

      2. mul-1-neg 68.8%

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

      3. unsub-neg 68.8%

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

      4. *-commutative 68.8%

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

   10. Simplified 68.8%

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

   11. Taylor expanded in y around 0 68.8%

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

       1. +-commutative 68.8%

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

       2. metadata-eval 68.8%

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

       3. *-commutative 68.8%

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

       4. cancel-sign-sub-inv 68.8%

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

       5. *-lft-identity 68.8%

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

       6. associate-/r* 72.0%

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

       7. div-sub 72.2%

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

   13. Simplified 72.2%

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

   if -1.85000000000000007e-10 < z < 1.2e-31

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 78.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{-10} \lor \neg \left(z \leq 1.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-8} \lor \neg \left(z \leq 4.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.4e-8) (not (<= z 4.5e+33))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.4e-8) || !(z <= 4.5e+33)) {
		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 <= (-2.4d-8)) .or. (.not. (z <= 4.5d+33))) 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 <= -2.4e-8) || !(z <= 4.5e+33)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.4e-8) or not (z <= 4.5e+33):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.4e-8) || !(z <= 4.5e+33))
		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 <= -2.4e-8) || ~((z <= 4.5e+33)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.4e-8], N[Not[LessEqual[z, 4.5e+33]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.39999999999999998e-8 or 4.5e33 < z

   1. Initial program 72.6%

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

      1. *-commutative 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in z around inf 56.8%

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

   if -2.39999999999999998e-8 < z < 4.5e33

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 52.3%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-8} \lor \neg \left(z \leq 4.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.0% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.0%

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

   1. *-commutative 86.0%

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

3. Simplified 86.0%

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

5. Taylor expanded in z around 0 33.7%

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

6. Final simplification 33.7%

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

Developer target: 97.4% 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 2024045 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (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))))