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

Percentage Accurate: 85.5% → 90.3%

Time: 9.8s

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: 90.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+207}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.9e+207)
   (- (/ y a) (/ (/ x a) z))
   (if (<= z 7.2e+155) (/ (- x (* z y)) (- t (* z a))) (/ (- y (/ x z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+207) {
		tmp = (y / a) - ((x / a) / z);
	} else if (z <= 7.2e+155) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.9d+207)) then
        tmp = (y / a) - ((x / a) / z)
    else if (z <= 7.2d+155) then
        tmp = (x - (z * y)) / (t - (z * a))
    else
        tmp = (y - (x / z)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.9e+207) {
		tmp = (y / a) - ((x / a) / z);
	} else if (z <= 7.2e+155) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = (y - (x / z)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.9e+207:
		tmp = (y / a) - ((x / a) / z)
	elif z <= 7.2e+155:
		tmp = (x - (z * y)) / (t - (z * a))
	else:
		tmp = (y - (x / z)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.9e+207)
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	elseif (z <= 7.2e+155)
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.9e+207)
		tmp = (y / a) - ((x / a) / z);
	elseif (z <= 7.2e+155)
		tmp = (x - (z * y)) / (t - (z * a));
	else
		tmp = (y - (x / z)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.9e+207], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+155], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.89999999999999993e207

   1. Initial program 39.1%

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

      1. *-commutative 39.1%

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

   3. Simplified 39.1%

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

   4. Taylor expanded in z around inf 60.6%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 60.6%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 60.6%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 84.0%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 84.0%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 84.0%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 84.0%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 84.0%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 84.0%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 84.0%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 84.0%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 84.0%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 92.3%

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

   7. Taylor expanded in x around inf 100.0%

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

   if -1.89999999999999993e207 < z < 7.20000000000000015e155

   1. Initial program 94.8%

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

   if 7.20000000000000015e155 < z

   1. Initial program 56.8%

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

      1. *-commutative 56.8%

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

   3. Simplified 56.8%

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

   4. Taylor expanded in z around inf 64.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 64.2%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 64.2%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 67.0%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 67.0%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 64.2%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 64.2%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 64.2%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 64.2%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 64.2%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 64.2%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 64.2%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 79.1%

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

   7. Taylor expanded in a around inf 85.1%

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

4. Final simplification 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+207}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+155}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 2: 64.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+156}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+80} \lor \neg \left(a \leq 6 \cdot 10^{-63}\right) \land \left(a \leq 8.5 \cdot 10^{+62} \lor \neg \left(a \leq 2.25 \cdot 10^{+105}\right)\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.3e+156)
   (/ x (- t (* z a)))
   (if (or (<= a -1.05e+80)
           (and (not (<= a 6e-63)) (or (<= a 8.5e+62) (not (<= a 2.25e+105)))))
     (/ (- y (/ x z)) a)
     (/ (- x (* z y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.3e+156) {
		tmp = x / (t - (z * a));
	} else if ((a <= -1.05e+80) || (!(a <= 6e-63) && ((a <= 8.5e+62) || !(a <= 2.25e+105)))) {
		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 (a <= (-5.3d+156)) then
        tmp = x / (t - (z * a))
    else if ((a <= (-1.05d+80)) .or. (.not. (a <= 6d-63)) .and. (a <= 8.5d+62) .or. (.not. (a <= 2.25d+105))) 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 (a <= -5.3e+156) {
		tmp = x / (t - (z * a));
	} else if ((a <= -1.05e+80) || (!(a <= 6e-63) && ((a <= 8.5e+62) || !(a <= 2.25e+105)))) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.3e+156:
		tmp = x / (t - (z * a))
	elif (a <= -1.05e+80) or (not (a <= 6e-63) and ((a <= 8.5e+62) or not (a <= 2.25e+105))):
		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 (a <= -5.3e+156)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif ((a <= -1.05e+80) || (!(a <= 6e-63) && ((a <= 8.5e+62) || !(a <= 2.25e+105))))
		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 (a <= -5.3e+156)
		tmp = x / (t - (z * a));
	elseif ((a <= -1.05e+80) || (~((a <= 6e-63)) && ((a <= 8.5e+62) || ~((a <= 2.25e+105)))))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.3e+156], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -1.05e+80], And[N[Not[LessEqual[a, 6e-63]], $MachinePrecision], Or[LessEqual[a, 8.5e+62], N[Not[LessEqual[a, 2.25e+105]], $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 3 regimes

2. if a < -5.2999999999999998e156

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in x around inf 71.6%

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

      1. *-commutative 71.6%

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

   6. Simplified 71.6%

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

   if -5.2999999999999998e156 < a < -1.05000000000000001e80 or 5.99999999999999959e-63 < a < 8.4999999999999997e62 or 2.2500000000000001e105 < a

   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 69.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 69.0%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 75.8%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 75.8%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 74.7%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 74.7%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 74.7%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 74.7%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 74.7%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 74.7%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 74.7%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 79.0%

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

   7. Taylor expanded in a around inf 78.0%

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

   if -1.05000000000000001e80 < a < 5.99999999999999959e-63 or 8.4999999999999997e62 < a < 2.2500000000000001e105

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 81.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.3 \cdot 10^{+156}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+80} \lor \neg \left(a \leq 6 \cdot 10^{-63}\right) \land \left(a \leq 8.5 \cdot 10^{+62} \lor \neg \left(a \leq 2.25 \cdot 10^{+105}\right)\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]

Alternative 3: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;a \leq -1.38 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+261}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-1}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= a -1.38e+48)
     t_1
     (if (<= a 2.8e-74)
       (/ (- x (* z y)) t)
       (if (<= a 1.9e+109)
         t_1
         (if (<= a 4.5e+158)
           (/ y a)
           (if (<= a 1.65e+261) t_1 (* (/ x a) (/ -1.0 z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (a <= -1.38e+48) {
		tmp = t_1;
	} else if (a <= 2.8e-74) {
		tmp = (x - (z * y)) / t;
	} else if (a <= 1.9e+109) {
		tmp = t_1;
	} else if (a <= 4.5e+158) {
		tmp = y / a;
	} else if (a <= 1.65e+261) {
		tmp = t_1;
	} else {
		tmp = (x / a) * (-1.0 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (t - (z * a))
    if (a <= (-1.38d+48)) then
        tmp = t_1
    else if (a <= 2.8d-74) then
        tmp = (x - (z * y)) / t
    else if (a <= 1.9d+109) then
        tmp = t_1
    else if (a <= 4.5d+158) then
        tmp = y / a
    else if (a <= 1.65d+261) then
        tmp = t_1
    else
        tmp = (x / a) * ((-1.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (a <= -1.38e+48) {
		tmp = t_1;
	} else if (a <= 2.8e-74) {
		tmp = (x - (z * y)) / t;
	} else if (a <= 1.9e+109) {
		tmp = t_1;
	} else if (a <= 4.5e+158) {
		tmp = y / a;
	} else if (a <= 1.65e+261) {
		tmp = t_1;
	} else {
		tmp = (x / a) * (-1.0 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if a <= -1.38e+48:
		tmp = t_1
	elif a <= 2.8e-74:
		tmp = (x - (z * y)) / t
	elif a <= 1.9e+109:
		tmp = t_1
	elif a <= 4.5e+158:
		tmp = y / a
	elif a <= 1.65e+261:
		tmp = t_1
	else:
		tmp = (x / a) * (-1.0 / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (a <= -1.38e+48)
		tmp = t_1;
	elseif (a <= 2.8e-74)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (a <= 1.9e+109)
		tmp = t_1;
	elseif (a <= 4.5e+158)
		tmp = Float64(y / a);
	elseif (a <= 1.65e+261)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / a) * Float64(-1.0 / z));
	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 <= -1.38e+48)
		tmp = t_1;
	elseif (a <= 2.8e-74)
		tmp = (x - (z * y)) / t;
	elseif (a <= 1.9e+109)
		tmp = t_1;
	elseif (a <= 4.5e+158)
		tmp = y / a;
	elseif (a <= 1.65e+261)
		tmp = t_1;
	else
		tmp = (x / a) * (-1.0 / z);
	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, -1.38e+48], t$95$1, If[LessEqual[a, 2.8e-74], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 1.9e+109], t$95$1, If[LessEqual[a, 4.5e+158], N[(y / a), $MachinePrecision], If[LessEqual[a, 1.65e+261], t$95$1, N[(N[(x / a), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.3800000000000001e48 or 2.79999999999999988e-74 < a < 1.90000000000000019e109 or 4.50000000000000046e158 < a < 1.65e261

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

   3. Simplified 80.9%

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

   4. Taylor expanded in x around inf 61.7%

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

      1. *-commutative 61.7%

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

   6. Simplified 61.7%

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

   if -1.3800000000000001e48 < a < 2.79999999999999988e-74

   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 t around inf 82.0%

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

   if 1.90000000000000019e109 < a < 4.50000000000000046e158

   1. Initial program 56.1%

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

      1. *-commutative 56.1%

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

   3. Simplified 56.1%

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

   4. Taylor expanded in z around inf 81.1%

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

   if 1.65e261 < a

   1. Initial program 62.5%

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

      1. *-commutative 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in z around inf 71.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 71.7%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 71.7%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 99.8%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 99.8%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 99.8%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 99.8%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 99.8%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 99.8%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 99.8%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 99.8%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 99.8%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 99.8%

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

   7. Taylor expanded in y around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. mul-1-neg 53.5%

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

      3. *-commutative 53.5%

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

   9. Simplified 53.5%

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

       1. neg-mul-1 53.5%

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

       2. times-frac 81.8%

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

   11. Applied egg-rr 81.8%

       \[\leadsto \color{blue}{\frac{-1}{z} \cdot \frac{x}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.38 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+158}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{+261}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-1}{z}\\ \end{array} \]

Alternative 4: 64.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ t_2 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;a \leq -8.8 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)) (t_2 (/ (- x (* z y)) t)))
   (if (<= a -8.8e+157)
     (/ x (- t (* z a)))
     (if (<= a -8e+78)
       t_1
       (if (<= a 6e-63)
         t_2
         (if (<= a 2.5e+62)
           (- (/ y a) (/ x (* z a)))
           (if (<= a 2.8e+105) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (a <= -8.8e+157) {
		tmp = x / (t - (z * a));
	} else if (a <= -8e+78) {
		tmp = t_1;
	} else if (a <= 6e-63) {
		tmp = t_2;
	} else if (a <= 2.5e+62) {
		tmp = (y / a) - (x / (z * a));
	} else if (a <= 2.8e+105) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    t_2 = (x - (z * y)) / t
    if (a <= (-8.8d+157)) then
        tmp = x / (t - (z * a))
    else if (a <= (-8d+78)) then
        tmp = t_1
    else if (a <= 6d-63) then
        tmp = t_2
    else if (a <= 2.5d+62) then
        tmp = (y / a) - (x / (z * a))
    else if (a <= 2.8d+105) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (a <= -8.8e+157) {
		tmp = x / (t - (z * a));
	} else if (a <= -8e+78) {
		tmp = t_1;
	} else if (a <= 6e-63) {
		tmp = t_2;
	} else if (a <= 2.5e+62) {
		tmp = (y / a) - (x / (z * a));
	} else if (a <= 2.8e+105) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	t_2 = (x - (z * y)) / t
	tmp = 0
	if a <= -8.8e+157:
		tmp = x / (t - (z * a))
	elif a <= -8e+78:
		tmp = t_1
	elif a <= 6e-63:
		tmp = t_2
	elif a <= 2.5e+62:
		tmp = (y / a) - (x / (z * a))
	elif a <= 2.8e+105:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	t_2 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (a <= -8.8e+157)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (a <= -8e+78)
		tmp = t_1;
	elseif (a <= 6e-63)
		tmp = t_2;
	elseif (a <= 2.5e+62)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	elseif (a <= 2.8e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	t_2 = (x - (z * y)) / t;
	tmp = 0.0;
	if (a <= -8.8e+157)
		tmp = x / (t - (z * a));
	elseif (a <= -8e+78)
		tmp = t_1;
	elseif (a <= 6e-63)
		tmp = t_2;
	elseif (a <= 2.5e+62)
		tmp = (y / a) - (x / (z * a));
	elseif (a <= 2.8e+105)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[a, -8.8e+157], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8e+78], t$95$1, If[LessEqual[a, 6e-63], t$95$2, If[LessEqual[a, 2.5e+62], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.8e+105], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.8000000000000005e157

   1. Initial program 81.3%

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

      1. *-commutative 81.3%

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

   3. Simplified 81.3%

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

   4. Taylor expanded in x around inf 71.6%

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

      1. *-commutative 71.6%

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

   6. Simplified 71.6%

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

   if -8.8000000000000005e157 < a < -8.00000000000000007e78 or 2.8000000000000001e105 < a

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

   3. Simplified 72.0%

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

   4. Taylor expanded in z around inf 68.2%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 68.2%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 68.2%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 77.9%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 77.9%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 77.9%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 77.9%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 77.9%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 77.9%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 77.9%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 77.9%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 77.9%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 82.5%

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

   7. Taylor expanded in a around inf 77.7%

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

   if -8.00000000000000007e78 < a < 5.99999999999999959e-63 or 2.50000000000000014e62 < a < 2.8000000000000001e105

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 81.5%

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

   if 5.99999999999999959e-63 < a < 2.50000000000000014e62

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 71.0%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 71.0%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 71.0%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 71.0%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 67.3%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 67.3%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 67.3%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 67.3%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 67.3%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 67.3%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 67.3%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 71.1%

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

   7. Taylor expanded in t around 0 78.6%

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

      1. *-commutative 78.6%

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

   9. Simplified 78.6%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+78}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 5: 68.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{if}\;a \leq -6 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (- (/ y a) (/ (/ x a) z))))
   (if (<= a -6e+80)
     t_2
     (if (<= a 6e-63)
       t_1
       (if (<= a 1.2e+63)
         (- (/ y a) (/ x (* z a)))
         (if (<= a 4e+105) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y / a) - ((x / a) / z);
	double tmp;
	if (a <= -6e+80) {
		tmp = t_2;
	} else if (a <= 6e-63) {
		tmp = t_1;
	} else if (a <= 1.2e+63) {
		tmp = (y / a) - (x / (z * a));
	} else if (a <= 4e+105) {
		tmp = 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 = (x - (z * y)) / t
    t_2 = (y / a) - ((x / a) / z)
    if (a <= (-6d+80)) then
        tmp = t_2
    else if (a <= 6d-63) then
        tmp = t_1
    else if (a <= 1.2d+63) then
        tmp = (y / a) - (x / (z * a))
    else if (a <= 4d+105) then
        tmp = 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 = (x - (z * y)) / t;
	double t_2 = (y / a) - ((x / a) / z);
	double tmp;
	if (a <= -6e+80) {
		tmp = t_2;
	} else if (a <= 6e-63) {
		tmp = t_1;
	} else if (a <= 1.2e+63) {
		tmp = (y / a) - (x / (z * a));
	} else if (a <= 4e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = (y / a) - ((x / a) / z)
	tmp = 0
	if a <= -6e+80:
		tmp = t_2
	elif a <= 6e-63:
		tmp = t_1
	elif a <= 1.2e+63:
		tmp = (y / a) - (x / (z * a))
	elif a <= 4e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(Float64(y / a) - Float64(Float64(x / a) / z))
	tmp = 0.0
	if (a <= -6e+80)
		tmp = t_2;
	elseif (a <= 6e-63)
		tmp = t_1;
	elseif (a <= 1.2e+63)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	elseif (a <= 4e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (z * y)) / t;
	t_2 = (y / a) - ((x / a) / z);
	tmp = 0.0;
	if (a <= -6e+80)
		tmp = t_2;
	elseif (a <= 6e-63)
		tmp = t_1;
	elseif (a <= 1.2e+63)
		tmp = (y / a) - (x / (z * a));
	elseif (a <= 4e+105)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6e+80], t$95$2, If[LessEqual[a, 6e-63], t$95$1, If[LessEqual[a, 1.2e+63], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4e+105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.99999999999999974e80 or 3.9999999999999998e105 < a

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in z around inf 64.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 64.1%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 64.1%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 71.7%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 71.7%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 71.7%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 71.7%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 71.7%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 71.7%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 71.7%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 71.7%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 71.7%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 75.9%

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

   7. Taylor expanded in x around inf 76.3%

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

   if -5.99999999999999974e80 < a < 5.99999999999999959e-63 or 1.2e63 < a < 3.9999999999999998e105

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 81.5%

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

   if 5.99999999999999959e-63 < a < 1.2e63

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 71.0%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 71.0%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 71.0%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 71.0%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 67.3%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 67.3%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 67.3%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 67.3%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 67.3%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 67.3%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 67.3%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 71.1%

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

   7. Taylor expanded in t around 0 78.6%

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

      1. *-commutative 78.6%

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

   9. Simplified 78.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \end{array} \]

Alternative 6: 68.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{if}\;a \leq -7.2 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{a} + \frac{-1}{\frac{a}{\frac{x}{z}}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (- (/ y a) (/ (/ x a) z))))
   (if (<= a -7.2e+78)
     t_2
     (if (<= a 6e-63)
       t_1
       (if (<= a 7.6e+62)
         (+ (/ y a) (/ -1.0 (/ a (/ x z))))
         (if (<= a 2.25e+105) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y / a) - ((x / a) / z);
	double tmp;
	if (a <= -7.2e+78) {
		tmp = t_2;
	} else if (a <= 6e-63) {
		tmp = t_1;
	} else if (a <= 7.6e+62) {
		tmp = (y / a) + (-1.0 / (a / (x / z)));
	} else if (a <= 2.25e+105) {
		tmp = 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 = (x - (z * y)) / t
    t_2 = (y / a) - ((x / a) / z)
    if (a <= (-7.2d+78)) then
        tmp = t_2
    else if (a <= 6d-63) then
        tmp = t_1
    else if (a <= 7.6d+62) then
        tmp = (y / a) + ((-1.0d0) / (a / (x / z)))
    else if (a <= 2.25d+105) then
        tmp = 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 = (x - (z * y)) / t;
	double t_2 = (y / a) - ((x / a) / z);
	double tmp;
	if (a <= -7.2e+78) {
		tmp = t_2;
	} else if (a <= 6e-63) {
		tmp = t_1;
	} else if (a <= 7.6e+62) {
		tmp = (y / a) + (-1.0 / (a / (x / z)));
	} else if (a <= 2.25e+105) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = (y / a) - ((x / a) / z)
	tmp = 0
	if a <= -7.2e+78:
		tmp = t_2
	elif a <= 6e-63:
		tmp = t_1
	elif a <= 7.6e+62:
		tmp = (y / a) + (-1.0 / (a / (x / z)))
	elif a <= 2.25e+105:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(Float64(y / a) - Float64(Float64(x / a) / z))
	tmp = 0.0
	if (a <= -7.2e+78)
		tmp = t_2;
	elseif (a <= 6e-63)
		tmp = t_1;
	elseif (a <= 7.6e+62)
		tmp = Float64(Float64(y / a) + Float64(-1.0 / Float64(a / Float64(x / z))));
	elseif (a <= 2.25e+105)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (z * y)) / t;
	t_2 = (y / a) - ((x / a) / z);
	tmp = 0.0;
	if (a <= -7.2e+78)
		tmp = t_2;
	elseif (a <= 6e-63)
		tmp = t_1;
	elseif (a <= 7.6e+62)
		tmp = (y / a) + (-1.0 / (a / (x / z)));
	elseif (a <= 2.25e+105)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7.2e+78], t$95$2, If[LessEqual[a, 6e-63], t$95$1, If[LessEqual[a, 7.6e+62], N[(N[(y / a), $MachinePrecision] + N[(-1.0 / N[(a / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.25e+105], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -7.20000000000000039e78 or 2.2500000000000001e105 < a

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in z around inf 64.1%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 64.1%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 64.1%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 71.7%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 71.7%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 71.7%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 71.7%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 71.7%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 71.7%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 71.7%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 71.7%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 71.7%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 75.9%

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

   7. Taylor expanded in x around inf 76.3%

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

   if -7.20000000000000039e78 < a < 5.99999999999999959e-63 or 7.59999999999999967e62 < a < 2.2500000000000001e105

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 81.5%

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

   if 5.99999999999999959e-63 < a < 7.59999999999999967e62

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{a \cdot z} + \frac{y}{a}\right) - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}} \]
   5. Step-by-step derivation

      1. +-commutative 71.0%

         \[\leadsto \color{blue}{\left(\frac{y}{a} + -1 \cdot \frac{x}{a \cdot z}\right)} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z} \]

      2. associate--l+ 71.0%

         \[\leadsto \color{blue}{\frac{y}{a} + \left(-1 \cdot \frac{x}{a \cdot z} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right)} \]

      3. associate-/r* 71.0%

         \[\leadsto \frac{y}{a} + \left(-1 \cdot \color{blue}{\frac{\frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      4. associate-*r/ 71.0%

         \[\leadsto \frac{y}{a} + \left(\color{blue}{\frac{-1 \cdot \frac{x}{a}}{z}} - -1 \cdot \frac{t \cdot y}{{a}^{2} \cdot z}\right) \]

      5. associate-/r* 67.3%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - -1 \cdot \color{blue}{\frac{\frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      6. associate-*r/ 67.3%

         \[\leadsto \frac{y}{a} + \left(\frac{-1 \cdot \frac{x}{a}}{z} - \color{blue}{\frac{-1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}}\right) \]

      7. div-sub 67.3%

         \[\leadsto \frac{y}{a} + \color{blue}{\frac{-1 \cdot \frac{x}{a} - -1 \cdot \frac{t \cdot y}{{a}^{2}}}{z}} \]

      8. distribute-lft-out-- 67.3%

         \[\leadsto \frac{y}{a} + \frac{\color{blue}{-1 \cdot \left(\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}\right)}}{z} \]

      9. associate-*r/ 67.3%

         \[\leadsto \frac{y}{a} + \color{blue}{-1 \cdot \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

      10. mul-1-neg 67.3%

          \[\leadsto \frac{y}{a} + \color{blue}{\left(-\frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}\right)} \]

      11. unsub-neg 67.3%

          \[\leadsto \color{blue}{\frac{y}{a} - \frac{\frac{x}{a} - \frac{t \cdot y}{{a}^{2}}}{z}} \]

   6. Simplified 71.1%

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

   7. Taylor expanded in t around 0 78.6%

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

      1. *-commutative 78.6%

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

   9. Simplified 78.6%

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

       1. clear-num 78.6%

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

       2. inv-pow 78.6%

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

   11. Applied egg-rr 78.6%

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

       1. unpow-1 78.6%

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

       2. *-commutative 78.6%

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

       3. associate-/l* 78.6%

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

   13. Simplified 78.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-63}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{+62}:\\ \;\;\;\;\frac{y}{a} + \frac{-1}{\frac{a}{\frac{x}{z}}}\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+105}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \end{array} \]

Alternative 7: 65.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+99)
   (/ y a)
   (if (<= z 3.15e+153) (/ x (- t (* z a))) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+99) {
		tmp = y / a;
	} else if (z <= 3.15e+153) {
		tmp = x / (t - (z * a));
	} 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 <= (-3.8d+99)) then
        tmp = y / a
    else if (z <= 3.15d+153) then
        tmp = x / (t - (z * a))
    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 <= -3.8e+99) {
		tmp = y / a;
	} else if (z <= 3.15e+153) {
		tmp = x / (t - (z * a));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+99:
		tmp = y / a
	elif z <= 3.15e+153:
		tmp = x / (t - (z * a))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+99)
		tmp = Float64(y / a);
	elseif (z <= 3.15e+153)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.8e+99)
		tmp = y / a;
	elseif (z <= 3.15e+153)
		tmp = x / (t - (z * a));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+99], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.15e+153], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.8e99 or 3.1500000000000001e153 < z

   1. Initial program 60.2%

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

      1. *-commutative 60.2%

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

   3. Simplified 60.2%

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

   4. Taylor expanded in z around inf 60.1%

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

   if -3.8e99 < z < 3.1500000000000001e153

   1. Initial program 97.7%

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

      1. *-commutative 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 69.5%

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

      1. *-commutative 69.5%

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

   6. Simplified 69.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 12000000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.5e+88)
   (/ y a)
   (if (<= z -2.8e-53)
     (/ (* z (- y)) t)
     (if (<= z 12000000000.0) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.5e+88) {
		tmp = y / a;
	} else if (z <= -2.8e-53) {
		tmp = (z * -y) / t;
	} else if (z <= 12000000000.0) {
		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 <= (-6.5d+88)) then
        tmp = y / a
    else if (z <= (-2.8d-53)) then
        tmp = (z * -y) / t
    else if (z <= 12000000000.0d0) 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 <= -6.5e+88) {
		tmp = y / a;
	} else if (z <= -2.8e-53) {
		tmp = (z * -y) / t;
	} else if (z <= 12000000000.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.5e+88:
		tmp = y / a
	elif z <= -2.8e-53:
		tmp = (z * -y) / t
	elif z <= 12000000000.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.5e+88)
		tmp = Float64(y / a);
	elseif (z <= -2.8e-53)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif (z <= 12000000000.0)
		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 <= -6.5e+88)
		tmp = y / a;
	elseif (z <= -2.8e-53)
		tmp = (z * -y) / t;
	elseif (z <= 12000000000.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.5e+88], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.8e-53], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 12000000000.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.5000000000000002e88 or 1.2e10 < z

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in z around inf 55.6%

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

   if -6.5000000000000002e88 < z < -2.79999999999999985e-53

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in t around inf 49.5%

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

   5. Taylor expanded in x around 0 38.9%

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

      1. mul-1-neg 38.9%

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

   7. Simplified 38.9%

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

   if -2.79999999999999985e-53 < z < 1.2e10

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 59.6%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-53}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 12000000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 9: 55.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(-\frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 380000000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -8.5e+88)
   (/ y a)
   (if (<= z -1.9e-52)
     (* z (- (/ y t)))
     (if (<= z 380000000000.0) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.5e+88) {
		tmp = y / a;
	} else if (z <= -1.9e-52) {
		tmp = z * -(y / t);
	} else if (z <= 380000000000.0) {
		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 <= (-8.5d+88)) then
        tmp = y / a
    else if (z <= (-1.9d-52)) then
        tmp = z * -(y / t)
    else if (z <= 380000000000.0d0) 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 <= -8.5e+88) {
		tmp = y / a;
	} else if (z <= -1.9e-52) {
		tmp = z * -(y / t);
	} else if (z <= 380000000000.0) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.5e+88:
		tmp = y / a
	elif z <= -1.9e-52:
		tmp = z * -(y / t)
	elif z <= 380000000000.0:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.5e+88)
		tmp = Float64(y / a);
	elseif (z <= -1.9e-52)
		tmp = Float64(z * Float64(-Float64(y / t)));
	elseif (z <= 380000000000.0)
		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 <= -8.5e+88)
		tmp = y / a;
	elseif (z <= -1.9e-52)
		tmp = z * -(y / t);
	elseif (z <= 380000000000.0)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8.5e+88], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.9e-52], N[(z * (-N[(y / t), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 380000000000.0], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.5000000000000005e88 or 3.8e11 < z

   1. Initial program 67.8%

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

      1. *-commutative 67.8%

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

   3. Simplified 67.8%

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

   4. Taylor expanded in z around inf 55.6%

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

   if -8.5000000000000005e88 < z < -1.9000000000000002e-52

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in t around inf 49.5%

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

   5. Taylor expanded in x around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. associate-/l* 42.7%

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

      3. distribute-neg-frac 42.7%

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

   7. Simplified 42.7%

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

   8. Taylor expanded in y around 0 38.9%

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

      1. mul-1-neg 38.9%

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

      2. associate-*l/ 42.8%

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

      3. distribute-rgt-neg-in 42.8%

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

   10. Simplified 42.8%

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

   if -1.9000000000000002e-52 < z < 3.8e11

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 59.6%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(-\frac{y}{t}\right)\\ \mathbf{elif}\;z \leq 380000000000:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10: 56.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-51} \lor \neg \left(z \leq 105000000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.65e-51) (not (<= z 105000000000.0))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.65e-51) || !(z <= 105000000000.0)) {
		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 <= (-2.65d-51)) .or. (.not. (z <= 105000000000.0d0))) 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 <= -2.65e-51) || !(z <= 105000000000.0)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.65e-51) or not (z <= 105000000000.0):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.65e-51) || !(z <= 105000000000.0))
		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 <= -2.65e-51) || ~((z <= 105000000000.0)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.65e-51], N[Not[LessEqual[z, 105000000000.0]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.64999999999999987e-51 or 1.05e11 < z

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in z around inf 48.7%

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

   if -2.64999999999999987e-51 < z < 1.05e11

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 59.6%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-51} \lor \neg \left(z \leq 105000000000\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 11: 35.6% 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 87.3%

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

   1. *-commutative 87.3%

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

3. Simplified 87.3%

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

4. Taylor expanded in z around 0 39.4%

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

5. Final simplification 39.4%

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

Developer target: 97.5% 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 2023293 
(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))))