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

Percentage Accurate: 85.5% → 90.7%

Time: 13.0s

Alternatives: 11

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.5% 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: 90.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+108} \lor \neg \left(z \leq 9.8 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.2e+108) (not (<= z 9.8e+175)))
   (/ (- 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 <= -9.2e+108) || !(z <= 9.8e+175)) {
		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 <= (-9.2d+108)) .or. (.not. (z <= 9.8d+175))) 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 <= -9.2e+108) || !(z <= 9.8e+175)) {
		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 <= -9.2e+108) or not (z <= 9.8e+175):
		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 <= -9.2e+108) || !(z <= 9.8e+175))
		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 <= -9.2e+108) || ~((z <= 9.8e+175)))
		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, -9.2e+108], N[Not[LessEqual[z, 9.8e+175]], $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 < -9.1999999999999996e108 or 9.80000000000000002e175 < z

   1. Initial program 60.3%

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

      1. *-commutative 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in x around 0 60.3%

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

   5. Taylor expanded in a around inf 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

   7. Simplified 89.4%

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

   if -9.1999999999999996e108 < z < 9.80000000000000002e175

   1. Initial program 97.9%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+108} \lor \neg \left(z \leq 9.8 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]

Alternative 2: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-199}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-167}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-66}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7e+73)
   (/ y a)
   (if (<= z -7e-82)
     (/ (/ (- x) a) z)
     (if (<= z 8e-199)
       (/ x t)
       (if (<= z 3.05e-167)
         (/ (* z (- y)) t)
         (if (<= z 3.7e-122)
           (/ x t)
           (if (<= z 7.7e-66)
             (/ (- x) (* z a))
             (if (<= z 2.45e+33) (/ x t) (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7e+73) {
		tmp = y / a;
	} else if (z <= -7e-82) {
		tmp = (-x / a) / z;
	} else if (z <= 8e-199) {
		tmp = x / t;
	} else if (z <= 3.05e-167) {
		tmp = (z * -y) / t;
	} else if (z <= 3.7e-122) {
		tmp = x / t;
	} else if (z <= 7.7e-66) {
		tmp = -x / (z * a);
	} else if (z <= 2.45e+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 <= (-7d+73)) then
        tmp = y / a
    else if (z <= (-7d-82)) then
        tmp = (-x / a) / z
    else if (z <= 8d-199) then
        tmp = x / t
    else if (z <= 3.05d-167) then
        tmp = (z * -y) / t
    else if (z <= 3.7d-122) then
        tmp = x / t
    else if (z <= 7.7d-66) then
        tmp = -x / (z * a)
    else if (z <= 2.45d+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 <= -7e+73) {
		tmp = y / a;
	} else if (z <= -7e-82) {
		tmp = (-x / a) / z;
	} else if (z <= 8e-199) {
		tmp = x / t;
	} else if (z <= 3.05e-167) {
		tmp = (z * -y) / t;
	} else if (z <= 3.7e-122) {
		tmp = x / t;
	} else if (z <= 7.7e-66) {
		tmp = -x / (z * a);
	} else if (z <= 2.45e+33) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7e+73:
		tmp = y / a
	elif z <= -7e-82:
		tmp = (-x / a) / z
	elif z <= 8e-199:
		tmp = x / t
	elif z <= 3.05e-167:
		tmp = (z * -y) / t
	elif z <= 3.7e-122:
		tmp = x / t
	elif z <= 7.7e-66:
		tmp = -x / (z * a)
	elif z <= 2.45e+33:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7e+73)
		tmp = Float64(y / a);
	elseif (z <= -7e-82)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 8e-199)
		tmp = Float64(x / t);
	elseif (z <= 3.05e-167)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif (z <= 3.7e-122)
		tmp = Float64(x / t);
	elseif (z <= 7.7e-66)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 2.45e+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 <= -7e+73)
		tmp = y / a;
	elseif (z <= -7e-82)
		tmp = (-x / a) / z;
	elseif (z <= 8e-199)
		tmp = x / t;
	elseif (z <= 3.05e-167)
		tmp = (z * -y) / t;
	elseif (z <= 3.7e-122)
		tmp = x / t;
	elseif (z <= 7.7e-66)
		tmp = -x / (z * a);
	elseif (z <= 2.45e+33)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7e+73], N[(y / a), $MachinePrecision], If[LessEqual[z, -7e-82], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 8e-199], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.05e-167], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.7e-122], N[(x / t), $MachinePrecision], If[LessEqual[z, 7.7e-66], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.45e+33], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -7.00000000000000004e73 or 2.45000000000000007e33 < z

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -7.00000000000000004e73 < z < -6.9999999999999997e-82

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 63.0%

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

      1. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in t around 0 48.4%

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

      1. associate-*r/ 48.4%

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

      2. neg-mul-1 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-/r* 48.4%

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

      5. neg-mul-1 48.4%

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

      6. associate-*r/ 48.4%

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

      7. mul-1-neg 48.4%

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

   9. Simplified 48.4%

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

   10. Taylor expanded in x around 0 48.4%

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

       1. mul-1-neg 48.4%

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

       2. associate-/r* 51.2%

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

       3. distribute-neg-frac 51.2%

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

   12. Simplified 51.2%

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

   if -6.9999999999999997e-82 < z < 7.99999999999999986e-199 or 3.0499999999999999e-167 < z < 3.6999999999999997e-122 or 7.7000000000000001e-66 < z < 2.45000000000000007e33

   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. Taylor expanded in z around 0 58.3%

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

   if 7.99999999999999986e-199 < z < 3.0499999999999999e-167

   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. Taylor expanded in t around inf 54.9%

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

   5. Taylor expanded in x around 0 49.5%

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

      1. associate-*r/ 49.5%

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

      2. associate-*r* 49.5%

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

      3. mul-1-neg 49.5%

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

   7. Simplified 49.5%

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

   if 3.6999999999999997e-122 < z < 7.7000000000000001e-66

   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. Taylor expanded in x around inf 62.2%

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

      1. *-commutative 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in t around 0 61.4%

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

      1. associate-*r/ 61.4%

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

      2. neg-mul-1 61.4%

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

      3. *-commutative 61.4%

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

   9. Simplified 61.4%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-199}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-167}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-122}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-66}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 3: 70.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+53} \lor \neg \left(t \leq -44000 \lor \neg \left(t \leq -3.3 \cdot 10^{-32}\right) \land t \leq 75000000000000\right):\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.8e+53)
         (not
          (or (<= t -44000.0)
              (and (not (<= t -3.3e-32)) (<= t 75000000000000.0)))))
   (- (/ x t) (* z (/ y t)))
   (/ (- y (/ x z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e+53) || !((t <= -44000.0) || (!(t <= -3.3e-32) && (t <= 75000000000000.0)))) {
		tmp = (x / t) - (z * (y / t));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.8d+53)) .or. (.not. (t <= (-44000.0d0)) .or. (.not. (t <= (-3.3d-32))) .and. (t <= 75000000000000.0d0))) then
        tmp = (x / t) - (z * (y / t))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.8e+53) || !((t <= -44000.0) || (!(t <= -3.3e-32) && (t <= 75000000000000.0)))) {
		tmp = (x / t) - (z * (y / t));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.8e+53) or not ((t <= -44000.0) or (not (t <= -3.3e-32) and (t <= 75000000000000.0))):
		tmp = (x / t) - (z * (y / t))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.8e+53) || !((t <= -44000.0) || (!(t <= -3.3e-32) && (t <= 75000000000000.0))))
		tmp = Float64(Float64(x / t) - Float64(z * Float64(y / t)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.8e+53) || ~(((t <= -44000.0) || (~((t <= -3.3e-32)) && (t <= 75000000000000.0)))))
		tmp = (x / t) - (z * (y / t));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.8e+53], N[Not[Or[LessEqual[t, -44000.0], And[N[Not[LessEqual[t, -3.3e-32]], $MachinePrecision], LessEqual[t, 75000000000000.0]]]], $MachinePrecision]], N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8e53 or -44000 < t < -3.30000000000000025e-32 or 7.5e13 < t

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in x around 0 88.8%

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

   5. Taylor expanded in a around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. neg-mul-1 80.2%

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

      3. sub-neg 80.2%

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

      4. associate-/l* 75.8%

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

   7. Simplified 75.8%

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

      1. associate-/r/ 82.0%

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

   9. Applied egg-rr 82.0%

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

   if -1.8e53 < t < -44000 or -3.30000000000000025e-32 < t < 7.5e13

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 90.2%

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

   5. Taylor expanded in a around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+53} \lor \neg \left(t \leq -44000 \lor \neg \left(t \leq -3.3 \cdot 10^{-32}\right) \land t \leq 75000000000000\right):\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 4: 70.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1650000:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-32} \lor \neg \left(t \leq 8 \cdot 10^{+17}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (/ x t) (* z (/ y t)))))
   (if (<= t -6.8e+49)
     t_1
     (if (<= t -1650000.0)
       (/ (- y (/ x z)) a)
       (if (or (<= t -2.25e-32) (not (<= t 8e+17)))
         t_1
         (- (/ y a) (/ x (* z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / t) - (z * (y / t));
	double tmp;
	if (t <= -6.8e+49) {
		tmp = t_1;
	} else if (t <= -1650000.0) {
		tmp = (y - (x / z)) / a;
	} else if ((t <= -2.25e-32) || !(t <= 8e+17)) {
		tmp = t_1;
	} else {
		tmp = (y / a) - (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) :: t_1
    real(8) :: tmp
    t_1 = (x / t) - (z * (y / t))
    if (t <= (-6.8d+49)) then
        tmp = t_1
    else if (t <= (-1650000.0d0)) then
        tmp = (y - (x / z)) / a
    else if ((t <= (-2.25d-32)) .or. (.not. (t <= 8d+17))) then
        tmp = t_1
    else
        tmp = (y / a) - (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 t_1 = (x / t) - (z * (y / t));
	double tmp;
	if (t <= -6.8e+49) {
		tmp = t_1;
	} else if (t <= -1650000.0) {
		tmp = (y - (x / z)) / a;
	} else if ((t <= -2.25e-32) || !(t <= 8e+17)) {
		tmp = t_1;
	} else {
		tmp = (y / a) - (x / (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / t) - (z * (y / t))
	tmp = 0
	if t <= -6.8e+49:
		tmp = t_1
	elif t <= -1650000.0:
		tmp = (y - (x / z)) / a
	elif (t <= -2.25e-32) or not (t <= 8e+17):
		tmp = t_1
	else:
		tmp = (y / a) - (x / (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / t) - Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -6.8e+49)
		tmp = t_1;
	elseif (t <= -1650000.0)
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	elseif ((t <= -2.25e-32) || !(t <= 8e+17))
		tmp = t_1;
	else
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x / t) - (z * (y / t));
	tmp = 0.0;
	if (t <= -6.8e+49)
		tmp = t_1;
	elseif (t <= -1650000.0)
		tmp = (y - (x / z)) / a;
	elseif ((t <= -2.25e-32) || ~((t <= 8e+17)))
		tmp = t_1;
	else
		tmp = (y / a) - (x / (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.8e+49], t$95$1, If[LessEqual[t, -1650000.0], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[Or[LessEqual[t, -2.25e-32], N[Not[LessEqual[t, 8e+17]], $MachinePrecision]], t$95$1, N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.8000000000000001e49 or -1.65e6 < t < -2.25000000000000002e-32 or 8e17 < t

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in x around 0 88.8%

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

   5. Taylor expanded in a around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. neg-mul-1 80.2%

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

      3. sub-neg 80.2%

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

      4. associate-/l* 75.8%

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

   7. Simplified 75.8%

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

      1. associate-/r/ 82.0%

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

   9. Applied egg-rr 82.0%

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

   if -6.8000000000000001e49 < t < -1.65e6

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in x around 0 77.8%

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

   5. Taylor expanded in a around inf 89.0%

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

      1. mul-1-neg 89.0%

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

      2. unsub-neg 89.0%

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

   7. Simplified 89.0%

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

   if -2.25000000000000002e-32 < t < 8e17

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in x around 0 91.0%

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

   5. Taylor expanded in t around 0 76.5%

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

      1. +-commutative 76.5%

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

      2. mul-1-neg 76.5%

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

      3. unsub-neg 76.5%

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

      4. *-commutative 76.5%

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

   7. Simplified 76.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+49}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;t \leq -1650000:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-32} \lor \neg \left(t \leq 8 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \end{array} \]

Alternative 5: 69.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+49} \lor \neg \left(t \leq -48000000 \lor \neg \left(t \leq -2.4 \cdot 10^{-32}\right) \land t \leq 8 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.5e+49)
         (not
          (or (<= t -48000000.0) (and (not (<= t -2.4e-32)) (<= t 8e+15)))))
   (/ (- x (* z y)) t)
   (/ (- y (/ x z)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+49) || !((t <= -48000000.0) || (!(t <= -2.4e-32) && (t <= 8e+15)))) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.5d+49)) .or. (.not. (t <= (-48000000.0d0)) .or. (.not. (t <= (-2.4d-32))) .and. (t <= 8d+15))) then
        tmp = (x - (z * y)) / t
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.5e+49) || !((t <= -48000000.0) || (!(t <= -2.4e-32) && (t <= 8e+15)))) {
		tmp = (x - (z * y)) / t;
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.5e+49) or not ((t <= -48000000.0) or (not (t <= -2.4e-32) and (t <= 8e+15))):
		tmp = (x - (z * y)) / t
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.5e+49) || !((t <= -48000000.0) || (!(t <= -2.4e-32) && (t <= 8e+15))))
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.5e+49) || ~(((t <= -48000000.0) || (~((t <= -2.4e-32)) && (t <= 8e+15)))))
		tmp = (x - (z * y)) / t;
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.5e+49], N[Not[Or[LessEqual[t, -48000000.0], And[N[Not[LessEqual[t, -2.4e-32]], $MachinePrecision], LessEqual[t, 8e+15]]]], $MachinePrecision]], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.4999999999999996e49 or -4.8e7 < t < -2.4000000000000001e-32 or 8e15 < t

   1. Initial program 88.8%

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

      1. *-commutative 88.8%

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

   3. Simplified 88.8%

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

   4. Taylor expanded in t around inf 80.2%

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

   if -8.4999999999999996e49 < t < -4.8e7 or -2.4000000000000001e-32 < t < 8e15

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in x around 0 90.2%

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

   5. Taylor expanded in a around inf 75.4%

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

      1. mul-1-neg 75.4%

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

      2. unsub-neg 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{+49} \lor \neg \left(t \leq -48000000 \lor \neg \left(t \leq -2.4 \cdot 10^{-32}\right) \land t \leq 8 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 6: 53.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-x}{z \cdot a}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x) (* z a))))
   (if (<= z -5.8e+72)
     (/ y a)
     (if (<= z -1.6e-82)
       t_1
       (if (<= z 3e-120)
         (/ x t)
         (if (<= z 5e-66) t_1 (if (<= z 2.45e+33) (/ x t) (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -x / (z * a);
	double tmp;
	if (z <= -5.8e+72) {
		tmp = y / a;
	} else if (z <= -1.6e-82) {
		tmp = t_1;
	} else if (z <= 3e-120) {
		tmp = x / t;
	} else if (z <= 5e-66) {
		tmp = t_1;
	} else if (z <= 2.45e+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) :: t_1
    real(8) :: tmp
    t_1 = -x / (z * a)
    if (z <= (-5.8d+72)) then
        tmp = y / a
    else if (z <= (-1.6d-82)) then
        tmp = t_1
    else if (z <= 3d-120) then
        tmp = x / t
    else if (z <= 5d-66) then
        tmp = t_1
    else if (z <= 2.45d+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 t_1 = -x / (z * a);
	double tmp;
	if (z <= -5.8e+72) {
		tmp = y / a;
	} else if (z <= -1.6e-82) {
		tmp = t_1;
	} else if (z <= 3e-120) {
		tmp = x / t;
	} else if (z <= 5e-66) {
		tmp = t_1;
	} else if (z <= 2.45e+33) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -x / (z * a)
	tmp = 0
	if z <= -5.8e+72:
		tmp = y / a
	elif z <= -1.6e-82:
		tmp = t_1
	elif z <= 3e-120:
		tmp = x / t
	elif z <= 5e-66:
		tmp = t_1
	elif z <= 2.45e+33:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-x) / Float64(z * a))
	tmp = 0.0
	if (z <= -5.8e+72)
		tmp = Float64(y / a);
	elseif (z <= -1.6e-82)
		tmp = t_1;
	elseif (z <= 3e-120)
		tmp = Float64(x / t);
	elseif (z <= 5e-66)
		tmp = t_1;
	elseif (z <= 2.45e+33)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -x / (z * a);
	tmp = 0.0;
	if (z <= -5.8e+72)
		tmp = y / a;
	elseif (z <= -1.6e-82)
		tmp = t_1;
	elseif (z <= 3e-120)
		tmp = x / t;
	elseif (z <= 5e-66)
		tmp = t_1;
	elseif (z <= 2.45e+33)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+72], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.6e-82], t$95$1, If[LessEqual[z, 3e-120], N[(x / t), $MachinePrecision], If[LessEqual[z, 5e-66], t$95$1, If[LessEqual[z, 2.45e+33], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.80000000000000034e72 or 2.45000000000000007e33 < z

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -5.80000000000000034e72 < z < -1.6000000000000001e-82 or 3.00000000000000011e-120 < z < 4.99999999999999962e-66

   1. Initial program 97.6%

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

      1. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 62.8%

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

      1. *-commutative 62.8%

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

   6. Simplified 62.8%

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

   7. Taylor expanded in t around 0 51.4%

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

      1. associate-*r/ 51.4%

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

      2. neg-mul-1 51.4%

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

      3. *-commutative 51.4%

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

   9. Simplified 51.4%

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

   if -1.6000000000000001e-82 < z < 3.00000000000000011e-120 or 4.99999999999999962e-66 < z < 2.45000000000000007e33

   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. Taylor expanded in z around 0 53.9%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-66}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7: 53.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-64}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.2e+80)
   (/ y a)
   (if (<= z -1.9e-82)
     (/ (/ (- x) a) z)
     (if (<= z 4.2e-120)
       (/ x t)
       (if (<= z 2.55e-64)
         (/ (- x) (* z a))
         (if (<= z 6.8e+33) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.2e+80) {
		tmp = y / a;
	} else if (z <= -1.9e-82) {
		tmp = (-x / a) / z;
	} else if (z <= 4.2e-120) {
		tmp = x / t;
	} else if (z <= 2.55e-64) {
		tmp = -x / (z * a);
	} else if (z <= 6.8e+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 <= (-8.2d+80)) then
        tmp = y / a
    else if (z <= (-1.9d-82)) then
        tmp = (-x / a) / z
    else if (z <= 4.2d-120) then
        tmp = x / t
    else if (z <= 2.55d-64) then
        tmp = -x / (z * a)
    else if (z <= 6.8d+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 <= -8.2e+80) {
		tmp = y / a;
	} else if (z <= -1.9e-82) {
		tmp = (-x / a) / z;
	} else if (z <= 4.2e-120) {
		tmp = x / t;
	} else if (z <= 2.55e-64) {
		tmp = -x / (z * a);
	} else if (z <= 6.8e+33) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.2e+80:
		tmp = y / a
	elif z <= -1.9e-82:
		tmp = (-x / a) / z
	elif z <= 4.2e-120:
		tmp = x / t
	elif z <= 2.55e-64:
		tmp = -x / (z * a)
	elif z <= 6.8e+33:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.2e+80)
		tmp = Float64(y / a);
	elseif (z <= -1.9e-82)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 4.2e-120)
		tmp = Float64(x / t);
	elseif (z <= 2.55e-64)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 6.8e+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 <= -8.2e+80)
		tmp = y / a;
	elseif (z <= -1.9e-82)
		tmp = (-x / a) / z;
	elseif (z <= 4.2e-120)
		tmp = x / t;
	elseif (z <= 2.55e-64)
		tmp = -x / (z * a);
	elseif (z <= 6.8e+33)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.2e+80], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.9e-82], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.2e-120], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.55e-64], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+33], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.20000000000000003e80 or 6.7999999999999999e33 < z

   1. Initial program 72.7%

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

      1. *-commutative 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in z around inf 62.7%

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

   if -8.20000000000000003e80 < z < -1.9000000000000001e-82

   1. Initial program 96.9%

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

      1. *-commutative 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in x around inf 63.0%

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

      1. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   7. Taylor expanded in t around 0 48.4%

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

      1. associate-*r/ 48.4%

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

      2. neg-mul-1 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-/r* 48.4%

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

      5. neg-mul-1 48.4%

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

      6. associate-*r/ 48.4%

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

      7. mul-1-neg 48.4%

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

   9. Simplified 48.4%

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

   10. Taylor expanded in x around 0 48.4%

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

       1. mul-1-neg 48.4%

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

       2. associate-/r* 51.2%

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

       3. distribute-neg-frac 51.2%

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

   12. Simplified 51.2%

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

   if -1.9000000000000001e-82 < z < 4.2000000000000001e-120 or 2.54999999999999992e-64 < z < 6.7999999999999999e33

   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. Taylor expanded in z around 0 53.9%

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

   if 4.2000000000000001e-120 < z < 2.54999999999999992e-64

   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. Taylor expanded in x around inf 62.2%

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

      1. *-commutative 62.2%

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

   6. Simplified 62.2%

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

   7. Taylor expanded in t around 0 61.4%

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

      1. associate-*r/ 61.4%

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

      2. neg-mul-1 61.4%

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

      3. *-commutative 61.4%

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

   9. Simplified 61.4%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-82}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-64}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)))
   (if (<= y -4.6e+142)
     t_1
     (if (<= y -3.3e+109)
       (/ y a)
       (if (<= y 6.3e-21) (/ x (- t (* z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double tmp;
	if (y <= -4.6e+142) {
		tmp = t_1;
	} else if (y <= -3.3e+109) {
		tmp = y / a;
	} else if (y <= 6.3e-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 = (x - (z * y)) / t
    if (y <= (-4.6d+142)) then
        tmp = t_1
    else if (y <= (-3.3d+109)) then
        tmp = y / a
    else if (y <= 6.3d-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 = (x - (z * y)) / t;
	double tmp;
	if (y <= -4.6e+142) {
		tmp = t_1;
	} else if (y <= -3.3e+109) {
		tmp = y / a;
	} else if (y <= 6.3e-21) {
		tmp = x / (t - (z * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	tmp = 0
	if y <= -4.6e+142:
		tmp = t_1
	elif y <= -3.3e+109:
		tmp = y / a
	elif y <= 6.3e-21:
		tmp = x / (t - (z * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (y <= -4.6e+142)
		tmp = t_1;
	elseif (y <= -3.3e+109)
		tmp = Float64(y / a);
	elseif (y <= 6.3e-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 = (x - (z * y)) / t;
	tmp = 0.0;
	if (y <= -4.6e+142)
		tmp = t_1;
	elseif (y <= -3.3e+109)
		tmp = y / a;
	elseif (y <= 6.3e-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[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[y, -4.6e+142], t$95$1, If[LessEqual[y, -3.3e+109], N[(y / a), $MachinePrecision], If[LessEqual[y, 6.3e-21], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.60000000000000004e142 or 6.3e-21 < y

   1. Initial program 86.8%

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

      1. *-commutative 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in t around inf 58.1%

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

   if -4.60000000000000004e142 < y < -3.2999999999999999e109

   1. Initial program 50.4%

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

      1. *-commutative 50.4%

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

   3. Simplified 50.4%

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

   4. Taylor expanded in z around inf 88.7%

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

   if -3.2999999999999999e109 < y < 6.3e-21

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 73.3%

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

      1. *-commutative 73.3%

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

   6. Simplified 73.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+142}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;y \leq 6.3 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]

Alternative 9: 65.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+82} \lor \neg \left(z \leq 1.08 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.2e+82) (not (<= z 1.08e+43))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.2e+82) || !(z <= 1.08e+43)) {
		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 <= (-1.2d+82)) .or. (.not. (z <= 1.08d+43))) 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 <= -1.2e+82) || !(z <= 1.08e+43)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.2e+82) or not (z <= 1.08e+43):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.2e+82) || !(z <= 1.08e+43))
		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 <= -1.2e+82) || ~((z <= 1.08e+43)))
		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, -1.2e+82], N[Not[LessEqual[z, 1.08e+43]], $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 < -1.19999999999999999e82 or 1.08e43 < z

   1. Initial program 72.4%

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

      1. *-commutative 72.4%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in z around inf 63.4%

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

   if -1.19999999999999999e82 < z < 1.08e43

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around inf 67.3%

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

      1. *-commutative 67.3%

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

   6. Simplified 67.3%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+82} \lor \neg \left(z \leq 1.08 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 10: 54.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2800000000 \lor \neg \left(z \leq 4.5 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2800000000.0) (not (<= z 4.5e+36))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2800000000.0) || !(z <= 4.5e+36)) {
		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 <= (-2800000000.0d0)) .or. (.not. (z <= 4.5d+36))) 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 <= -2800000000.0) || !(z <= 4.5e+36)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2800000000.0) or not (z <= 4.5e+36):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2800000000.0) || !(z <= 4.5e+36))
		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 <= -2800000000.0) || ~((z <= 4.5e+36)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2800000000.0], N[Not[LessEqual[z, 4.5e+36]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.8e9 or 4.49999999999999997e36 < 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. Taylor expanded in z around inf 57.7%

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

   if -2.8e9 < z < 4.49999999999999997e36

   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. Taylor expanded in z around 0 48.2%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2800000000 \lor \neg \left(z \leq 4.5 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 11: 35.8% 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 89.7%

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

   1. *-commutative 89.7%

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

3. Simplified 89.7%

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

4. Taylor expanded in z around 0 32.2%

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

5. Final simplification 32.2%

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

Developer target: 97.4% accurate, 0.6× 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 2023320 
(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))))