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

Percentage Accurate: 85.4% → 91.7%

Time: 10.9s

Alternatives: 12

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+107} \lor \neg \left(z \leq 2.7 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.1e+107) (not (<= z 2.7e+135)))
   (/ (- 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 <= -2.1e+107) || !(z <= 2.7e+135)) {
		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 <= (-2.1d+107)) .or. (.not. (z <= 2.7d+135))) 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 <= -2.1e+107) || !(z <= 2.7e+135)) {
		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 <= -2.1e+107) or not (z <= 2.7e+135):
		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 <= -2.1e+107) || !(z <= 2.7e+135))
		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 <= -2.1e+107) || ~((z <= 2.7e+135)))
		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, -2.1e+107], N[Not[LessEqual[z, 2.7e+135]], $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 < -2.1e107 or 2.69999999999999985e135 < z

   1. Initial program 57.2%

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

      1. *-commutative 57.2%

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

   3. Simplified 57.2%

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

   5. Taylor expanded in t around 0 48.2%

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

      1. associate-*r/ 48.2%

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

      2. *-commutative 48.2%

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

      3. associate-/r* 66.0%

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

      4. associate-*r/ 66.0%

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

      5. mul-1-neg 66.0%

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

      6. div-sub 66.0%

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

      7. associate-/l* 85.6%

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

      8. *-inverses 85.6%

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

   7. Simplified 85.6%

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

   8. Taylor expanded in x around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. mul-1-neg 82.4%

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

      3. sub-neg 82.4%

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

      4. associate-/l/ 85.6%

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

      5. div-sub 85.6%

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

   10. Simplified 85.6%

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

   if -2.1e107 < z < 2.69999999999999985e135

   1. Initial program 97.5%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+107} \lor \neg \left(z \leq 2.7 \cdot 10^{+135}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t} - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y (/ x z)) a)))
   (if (<= z -9e+29)
     t_1
     (if (<= z -3.5e-27)
       (/ (- x (* z y)) t)
       (if (<= z -2e-84)
         t_1
         (if (<= z 1.7e-7)
           (/ x (- t (* z a)))
           (if (<= z 5.6e+77) (* z (- (/ x (* z t)) (/ y t))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -9e+29) {
		tmp = t_1;
	} else if (z <= -3.5e-27) {
		tmp = (x - (z * y)) / t;
	} else if (z <= -2e-84) {
		tmp = t_1;
	} else if (z <= 1.7e-7) {
		tmp = x / (t - (z * a));
	} else if (z <= 5.6e+77) {
		tmp = z * ((x / (z * t)) - (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y - (x / z)) / a
    if (z <= (-9d+29)) then
        tmp = t_1
    else if (z <= (-3.5d-27)) then
        tmp = (x - (z * y)) / t
    else if (z <= (-2d-84)) then
        tmp = t_1
    else if (z <= 1.7d-7) then
        tmp = x / (t - (z * a))
    else if (z <= 5.6d+77) then
        tmp = z * ((x / (z * t)) - (y / t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y - (x / z)) / a;
	double tmp;
	if (z <= -9e+29) {
		tmp = t_1;
	} else if (z <= -3.5e-27) {
		tmp = (x - (z * y)) / t;
	} else if (z <= -2e-84) {
		tmp = t_1;
	} else if (z <= 1.7e-7) {
		tmp = x / (t - (z * a));
	} else if (z <= 5.6e+77) {
		tmp = z * ((x / (z * t)) - (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y - (x / z)) / a
	tmp = 0
	if z <= -9e+29:
		tmp = t_1
	elif z <= -3.5e-27:
		tmp = (x - (z * y)) / t
	elif z <= -2e-84:
		tmp = t_1
	elif z <= 1.7e-7:
		tmp = x / (t - (z * a))
	elif z <= 5.6e+77:
		tmp = z * ((x / (z * t)) - (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -9e+29)
		tmp = t_1;
	elseif (z <= -3.5e-27)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= -2e-84)
		tmp = t_1;
	elseif (z <= 1.7e-7)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 5.6e+77)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t)) - Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -9e+29)
		tmp = t_1;
	elseif (z <= -3.5e-27)
		tmp = (x - (z * y)) / t;
	elseif (z <= -2e-84)
		tmp = t_1;
	elseif (z <= 1.7e-7)
		tmp = x / (t - (z * a));
	elseif (z <= 5.6e+77)
		tmp = z * ((x / (z * t)) - (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -9e+29], t$95$1, If[LessEqual[z, -3.5e-27], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, -2e-84], t$95$1, If[LessEqual[z, 1.7e-7], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+77], N[(z * N[(N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision] - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.0000000000000005e29 or -3.5000000000000001e-27 < z < -2.0000000000000001e-84 or 5.60000000000000001e77 < z

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in t around 0 53.8%

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

      1. associate-*r/ 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-/r* 68.2%

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

      4. associate-*r/ 68.2%

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

      5. mul-1-neg 68.2%

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

      6. div-sub 68.2%

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

      7. associate-/l* 82.4%

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

      8. *-inverses 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in x around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. mul-1-neg 78.7%

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

      3. sub-neg 78.7%

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

      4. associate-/l/ 82.4%

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

      5. div-sub 82.4%

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

   10. Simplified 82.4%

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

   if -9.0000000000000005e29 < z < -3.5000000000000001e-27

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 90.2%

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

   if -2.0000000000000001e-84 < z < 1.69999999999999987e-7

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 82.6%

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

      1. *-commutative 82.6%

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

   7. Simplified 82.6%

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

   if 1.69999999999999987e-7 < z < 5.60000000000000001e77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 73.7%

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

   6. Taylor expanded in z around inf 73.7%

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

      1. +-commutative 73.7%

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

      2. mul-1-neg 73.7%

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

      3. unsub-neg 73.7%

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

      4. *-commutative 73.7%

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

   8. Simplified 73.7%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+29}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-27}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t} - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 53.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-a\right)}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (* z (- a)))))
   (if (<= z -6.6e+106)
     (/ y a)
     (if (<= z -5.8e+39)
       t_1
       (if (<= z -3.6e+20)
         (/ y a)
         (if (<= z -1.36e-18)
           (* y (/ z (- t)))
           (if (<= z -4.1e-109) t_1 (if (<= z 8.8e+77) (/ 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 <= -6.6e+106) {
		tmp = y / a;
	} else if (z <= -5.8e+39) {
		tmp = t_1;
	} else if (z <= -3.6e+20) {
		tmp = y / a;
	} else if (z <= -1.36e-18) {
		tmp = y * (z / -t);
	} else if (z <= -4.1e-109) {
		tmp = t_1;
	} else if (z <= 8.8e+77) {
		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 <= (-6.6d+106)) then
        tmp = y / a
    else if (z <= (-5.8d+39)) then
        tmp = t_1
    else if (z <= (-3.6d+20)) then
        tmp = y / a
    else if (z <= (-1.36d-18)) then
        tmp = y * (z / -t)
    else if (z <= (-4.1d-109)) then
        tmp = t_1
    else if (z <= 8.8d+77) 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 <= -6.6e+106) {
		tmp = y / a;
	} else if (z <= -5.8e+39) {
		tmp = t_1;
	} else if (z <= -3.6e+20) {
		tmp = y / a;
	} else if (z <= -1.36e-18) {
		tmp = y * (z / -t);
	} else if (z <= -4.1e-109) {
		tmp = t_1;
	} else if (z <= 8.8e+77) {
		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 <= -6.6e+106:
		tmp = y / a
	elif z <= -5.8e+39:
		tmp = t_1
	elif z <= -3.6e+20:
		tmp = y / a
	elif z <= -1.36e-18:
		tmp = y * (z / -t)
	elif z <= -4.1e-109:
		tmp = t_1
	elif z <= 8.8e+77:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z * Float64(-a)))
	tmp = 0.0
	if (z <= -6.6e+106)
		tmp = Float64(y / a);
	elseif (z <= -5.8e+39)
		tmp = t_1;
	elseif (z <= -3.6e+20)
		tmp = Float64(y / a);
	elseif (z <= -1.36e-18)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= -4.1e-109)
		tmp = t_1;
	elseif (z <= 8.8e+77)
		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 <= -6.6e+106)
		tmp = y / a;
	elseif (z <= -5.8e+39)
		tmp = t_1;
	elseif (z <= -3.6e+20)
		tmp = y / a;
	elseif (z <= -1.36e-18)
		tmp = y * (z / -t);
	elseif (z <= -4.1e-109)
		tmp = t_1;
	elseif (z <= 8.8e+77)
		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, -6.6e+106], N[(y / a), $MachinePrecision], If[LessEqual[z, -5.8e+39], t$95$1, If[LessEqual[z, -3.6e+20], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.36e-18], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.1e-109], t$95$1, If[LessEqual[z, 8.8e+77], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.60000000000000015e106 or -5.80000000000000059e39 < z < -3.6e20 or 8.8000000000000002e77 < z

   1. Initial program 60.9%

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

      1. *-commutative 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 74.0%

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

   if -6.60000000000000015e106 < z < -5.80000000000000059e39 or -1.3600000000000001e-18 < z < -4.1000000000000002e-109

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in x around inf 62.1%

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

      1. *-commutative 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in t around 0 50.3%

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

      1. associate-*r/ 50.3%

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

      2. neg-mul-1 50.3%

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

   10. Simplified 50.3%

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

   if -3.6e20 < z < -1.3600000000000001e-18

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 98.8%

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

      2. associate-/r/ 99.5%

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

      3. sub-neg 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. distribute-rgt-neg-in 99.5%

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

      7. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in a around 0 90.0%

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

   8. Taylor expanded in x around 0 60.3%

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

      1. mul-1-neg 60.3%

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

      2. associate-/l* 60.3%

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

      3. distribute-rgt-neg-in 60.3%

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

      4. distribute-neg-frac2 60.3%

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

   10. Simplified 60.3%

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

   if -4.1000000000000002e-109 < z < 8.8000000000000002e77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ x (- t (* z a)))))
   (if (<= z -6.6e+106)
     (/ y a)
     (if (<= z -3.4e-109)
       t_2
       (if (<= z -2.2e-174)
         t_1
         (if (<= z 6e-16) t_2 (if (<= z 5.6e+77) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -6.6e+106) {
		tmp = y / a;
	} else if (z <= -3.4e-109) {
		tmp = t_2;
	} else if (z <= -2.2e-174) {
		tmp = t_1;
	} else if (z <= 6e-16) {
		tmp = t_2;
	} else if (z <= 5.6e+77) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (z * y)) / t
    t_2 = x / (t - (z * a))
    if (z <= (-6.6d+106)) then
        tmp = y / a
    else if (z <= (-3.4d-109)) then
        tmp = t_2
    else if (z <= (-2.2d-174)) then
        tmp = t_1
    else if (z <= 6d-16) then
        tmp = t_2
    else if (z <= 5.6d+77) then
        tmp = t_1
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = x / (t - (z * a));
	double tmp;
	if (z <= -6.6e+106) {
		tmp = y / a;
	} else if (z <= -3.4e-109) {
		tmp = t_2;
	} else if (z <= -2.2e-174) {
		tmp = t_1;
	} else if (z <= 6e-16) {
		tmp = t_2;
	} else if (z <= 5.6e+77) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = x / (t - (z * a))
	tmp = 0
	if z <= -6.6e+106:
		tmp = y / a
	elif z <= -3.4e-109:
		tmp = t_2
	elif z <= -2.2e-174:
		tmp = t_1
	elif z <= 6e-16:
		tmp = t_2
	elif z <= 5.6e+77:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -6.6e+106)
		tmp = Float64(y / a);
	elseif (z <= -3.4e-109)
		tmp = t_2;
	elseif (z <= -2.2e-174)
		tmp = t_1;
	elseif (z <= 6e-16)
		tmp = t_2;
	elseif (z <= 5.6e+77)
		tmp = t_1;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (z * y)) / t;
	t_2 = x / (t - (z * a));
	tmp = 0.0;
	if (z <= -6.6e+106)
		tmp = y / a;
	elseif (z <= -3.4e-109)
		tmp = t_2;
	elseif (z <= -2.2e-174)
		tmp = t_1;
	elseif (z <= 6e-16)
		tmp = t_2;
	elseif (z <= 5.6e+77)
		tmp = t_1;
	else
		tmp = y / a;
	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[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.6e+106], N[(y / a), $MachinePrecision], If[LessEqual[z, -3.4e-109], t$95$2, If[LessEqual[z, -2.2e-174], t$95$1, If[LessEqual[z, 6e-16], t$95$2, If[LessEqual[z, 5.6e+77], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.60000000000000015e106 or 5.60000000000000001e77 < z

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in z around inf 73.8%

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

   if -6.60000000000000015e106 < z < -3.40000000000000012e-109 or -2.20000000000000022e-174 < z < 5.99999999999999987e-16

   1. Initial program 97.4%

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

      1. *-commutative 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf 76.7%

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

      1. *-commutative 76.7%

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

   7. Simplified 76.7%

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

   if -3.40000000000000012e-109 < z < -2.20000000000000022e-174 or 5.99999999999999987e-16 < z < 5.60000000000000001e77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 82.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-109}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.92 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+77}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -2.5e+34)
     t_2
     (if (<= z -1.92e-19)
       t_1
       (if (<= z -2e-84)
         t_2
         (if (<= z 6.8e-16)
           (/ x (- t (* z a)))
           (if (<= z 4.3e+77) 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 - (x / z)) / a;
	double tmp;
	if (z <= -2.5e+34) {
		tmp = t_2;
	} else if (z <= -1.92e-19) {
		tmp = t_1;
	} else if (z <= -2e-84) {
		tmp = t_2;
	} else if (z <= 6.8e-16) {
		tmp = x / (t - (z * a));
	} else if (z <= 4.3e+77) {
		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 - (x / z)) / a
    if (z <= (-2.5d+34)) then
        tmp = t_2
    else if (z <= (-1.92d-19)) then
        tmp = t_1
    else if (z <= (-2d-84)) then
        tmp = t_2
    else if (z <= 6.8d-16) then
        tmp = x / (t - (z * a))
    else if (z <= 4.3d+77) 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 - (x / z)) / a;
	double tmp;
	if (z <= -2.5e+34) {
		tmp = t_2;
	} else if (z <= -1.92e-19) {
		tmp = t_1;
	} else if (z <= -2e-84) {
		tmp = t_2;
	} else if (z <= 6.8e-16) {
		tmp = x / (t - (z * a));
	} else if (z <= 4.3e+77) {
		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 - (x / z)) / a
	tmp = 0
	if z <= -2.5e+34:
		tmp = t_2
	elif z <= -1.92e-19:
		tmp = t_1
	elif z <= -2e-84:
		tmp = t_2
	elif z <= 6.8e-16:
		tmp = x / (t - (z * a))
	elif z <= 4.3e+77:
		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 - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -2.5e+34)
		tmp = t_2;
	elseif (z <= -1.92e-19)
		tmp = t_1;
	elseif (z <= -2e-84)
		tmp = t_2;
	elseif (z <= 6.8e-16)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 4.3e+77)
		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 - (x / z)) / a;
	tmp = 0.0;
	if (z <= -2.5e+34)
		tmp = t_2;
	elseif (z <= -1.92e-19)
		tmp = t_1;
	elseif (z <= -2e-84)
		tmp = t_2;
	elseif (z <= 6.8e-16)
		tmp = x / (t - (z * a));
	elseif (z <= 4.3e+77)
		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 - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -2.5e+34], t$95$2, If[LessEqual[z, -1.92e-19], t$95$1, If[LessEqual[z, -2e-84], t$95$2, If[LessEqual[z, 6.8e-16], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.3e+77], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4999999999999999e34 or -1.91999999999999994e-19 < z < -2.0000000000000001e-84 or 4.29999999999999991e77 < z

   1. Initial program 67.7%

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

      1. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   5. Taylor expanded in t around 0 53.8%

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

      1. associate-*r/ 53.8%

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

      2. *-commutative 53.8%

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

      3. associate-/r* 68.2%

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

      4. associate-*r/ 68.2%

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

      5. mul-1-neg 68.2%

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

      6. div-sub 68.2%

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

      7. associate-/l* 82.4%

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

      8. *-inverses 82.4%

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

   7. Simplified 82.4%

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

   8. Taylor expanded in x around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. mul-1-neg 78.7%

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

      3. sub-neg 78.7%

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

      4. associate-/l/ 82.4%

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

      5. div-sub 82.4%

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

   10. Simplified 82.4%

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

   if -2.4999999999999999e34 < z < -1.91999999999999994e-19 or 6.8e-16 < z < 4.29999999999999991e77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 80.5%

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

   if -2.0000000000000001e-84 < z < 6.8e-16

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 82.4%

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

      1. *-commutative 82.4%

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

   7. Simplified 82.4%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+34}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -1.92 \cdot 10^{-19}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-84}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{+77}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 53.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -960000:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.6e+106)
   (/ y a)
   (if (<= z -960000.0)
     (/ (/ x a) (- z))
     (if (<= z -3.4e-21)
       (* z (/ y (- t)))
       (if (<= z -2.25e-108)
         (/ x (* z (- a)))
         (if (<= z 5.6e+77) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.6e+106) {
		tmp = y / a;
	} else if (z <= -960000.0) {
		tmp = (x / a) / -z;
	} else if (z <= -3.4e-21) {
		tmp = z * (y / -t);
	} else if (z <= -2.25e-108) {
		tmp = x / (z * -a);
	} else if (z <= 5.6e+77) {
		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 <= (-6.6d+106)) then
        tmp = y / a
    else if (z <= (-960000.0d0)) then
        tmp = (x / a) / -z
    else if (z <= (-3.4d-21)) then
        tmp = z * (y / -t)
    else if (z <= (-2.25d-108)) then
        tmp = x / (z * -a)
    else if (z <= 5.6d+77) 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 <= -6.6e+106) {
		tmp = y / a;
	} else if (z <= -960000.0) {
		tmp = (x / a) / -z;
	} else if (z <= -3.4e-21) {
		tmp = z * (y / -t);
	} else if (z <= -2.25e-108) {
		tmp = x / (z * -a);
	} else if (z <= 5.6e+77) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.6e+106:
		tmp = y / a
	elif z <= -960000.0:
		tmp = (x / a) / -z
	elif z <= -3.4e-21:
		tmp = z * (y / -t)
	elif z <= -2.25e-108:
		tmp = x / (z * -a)
	elif z <= 5.6e+77:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.6e+106)
		tmp = Float64(y / a);
	elseif (z <= -960000.0)
		tmp = Float64(Float64(x / a) / Float64(-z));
	elseif (z <= -3.4e-21)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif (z <= -2.25e-108)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 5.6e+77)
		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 <= -6.6e+106)
		tmp = y / a;
	elseif (z <= -960000.0)
		tmp = (x / a) / -z;
	elseif (z <= -3.4e-21)
		tmp = z * (y / -t);
	elseif (z <= -2.25e-108)
		tmp = x / (z * -a);
	elseif (z <= 5.6e+77)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.6e+106], N[(y / a), $MachinePrecision], If[LessEqual[z, -960000.0], N[(N[(x / a), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, -3.4e-21], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-108], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.6e+77], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.60000000000000015e106 or 5.60000000000000001e77 < z

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in z around inf 73.8%

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

   if -6.60000000000000015e106 < z < -9.6e5

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in a around inf 77.0%

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

   6. Taylor expanded in x around inf 59.3%

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

      1. associate-/r* 50.6%

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

   8. Simplified 50.6%

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

   9. Taylor expanded in t around 0 45.7%

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

       1. mul-1-neg 45.7%

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

   11. Simplified 45.7%

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

   if -9.6e5 < z < -3.4e-21

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 98.4%

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

      2. associate-/r/ 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 99.8%

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

   8. Taylor expanded in x around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-/l* 71.4%

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

      3. distribute-rgt-neg-in 71.4%

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

      4. distribute-neg-frac2 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in y around 0 71.4%

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

       1. mul-1-neg 71.4%

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

       2. associate-*r/ 71.4%

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

       3. *-commutative 71.4%

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

       4. associate-*l/ 71.4%

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

       5. associate-*r/ 71.6%

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

       6. distribute-rgt-neg-in 71.6%

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

       7. distribute-neg-frac2 71.6%

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

   13. Simplified 71.6%

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

   if -3.4e-21 < z < -2.24999999999999985e-108

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 63.3%

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

      1. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in t around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   10. Simplified 57.1%

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

   if -2.24999999999999985e-108 < z < 5.60000000000000001e77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.4%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+106}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -960000:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -750000:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.35e+107)
   (/ y a)
   (if (<= z -750000.0)
     (/ (/ x z) (- a))
     (if (<= z -6.6e-29)
       (* z (/ y (- t)))
       (if (<= z -2.5e-108)
         (/ x (* z (- a)))
         (if (<= z 6e+77) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.35e+107) {
		tmp = y / a;
	} else if (z <= -750000.0) {
		tmp = (x / z) / -a;
	} else if (z <= -6.6e-29) {
		tmp = z * (y / -t);
	} else if (z <= -2.5e-108) {
		tmp = x / (z * -a);
	} else if (z <= 6e+77) {
		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 <= (-1.35d+107)) then
        tmp = y / a
    else if (z <= (-750000.0d0)) then
        tmp = (x / z) / -a
    else if (z <= (-6.6d-29)) then
        tmp = z * (y / -t)
    else if (z <= (-2.5d-108)) then
        tmp = x / (z * -a)
    else if (z <= 6d+77) 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 <= -1.35e+107) {
		tmp = y / a;
	} else if (z <= -750000.0) {
		tmp = (x / z) / -a;
	} else if (z <= -6.6e-29) {
		tmp = z * (y / -t);
	} else if (z <= -2.5e-108) {
		tmp = x / (z * -a);
	} else if (z <= 6e+77) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.35e+107:
		tmp = y / a
	elif z <= -750000.0:
		tmp = (x / z) / -a
	elif z <= -6.6e-29:
		tmp = z * (y / -t)
	elif z <= -2.5e-108:
		tmp = x / (z * -a)
	elif z <= 6e+77:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.35e+107)
		tmp = Float64(y / a);
	elseif (z <= -750000.0)
		tmp = Float64(Float64(x / z) / Float64(-a));
	elseif (z <= -6.6e-29)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif (z <= -2.5e-108)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 6e+77)
		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 <= -1.35e+107)
		tmp = y / a;
	elseif (z <= -750000.0)
		tmp = (x / z) / -a;
	elseif (z <= -6.6e-29)
		tmp = z * (y / -t);
	elseif (z <= -2.5e-108)
		tmp = x / (z * -a);
	elseif (z <= 6e+77)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.35e+107], N[(y / a), $MachinePrecision], If[LessEqual[z, -750000.0], N[(N[(x / z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[z, -6.6e-29], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-108], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+77], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.3500000000000001e107 or 5.9999999999999996e77 < z

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in z around inf 73.8%

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

   if -1.3500000000000001e107 < z < -7.5e5

   1. Initial program 86.0%

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

      1. *-commutative 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around inf 59.3%

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

      1. *-commutative 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in t around 0 40.7%

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

      1. mul-1-neg 40.7%

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

      2. associate-/l/ 49.9%

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

      3. distribute-neg-frac 49.9%

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

      4. distribute-neg-frac2 49.9%

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

   10. Simplified 49.9%

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

   if -7.5e5 < z < -6.60000000000000055e-29

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 98.4%

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

      2. associate-/r/ 99.8%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

      7. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in a around 0 99.8%

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

   8. Taylor expanded in x around 0 71.4%

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

      1. mul-1-neg 71.4%

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

      2. associate-/l* 71.4%

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

      3. distribute-rgt-neg-in 71.4%

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

      4. distribute-neg-frac2 71.4%

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

   10. Simplified 71.4%

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

   11. Taylor expanded in y around 0 71.4%

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

       1. mul-1-neg 71.4%

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

       2. associate-*r/ 71.4%

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

       3. *-commutative 71.4%

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

       4. associate-*l/ 71.4%

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

       5. associate-*r/ 71.6%

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

       6. distribute-rgt-neg-in 71.6%

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

       7. distribute-neg-frac2 71.6%

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

   13. Simplified 71.6%

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

   if -6.60000000000000055e-29 < z < -2.5e-108

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 63.3%

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

      1. *-commutative 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in t around 0 57.1%

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

      1. associate-*r/ 57.1%

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

      2. neg-mul-1 57.1%

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

   10. Simplified 57.1%

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

   if -2.5e-108 < z < 5.9999999999999996e77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.4%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -750000:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-29}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e+71)
   (/ y a)
   (if (<= z -7e-110) (* y (/ z (- t))) (if (<= z 2.3e+78) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e+71) {
		tmp = y / a;
	} else if (z <= -7e-110) {
		tmp = y * (z / -t);
	} else if (z <= 2.3e+78) {
		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 <= (-1.4d+71)) then
        tmp = y / a
    else if (z <= (-7d-110)) then
        tmp = y * (z / -t)
    else if (z <= 2.3d+78) 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 <= -1.4e+71) {
		tmp = y / a;
	} else if (z <= -7e-110) {
		tmp = y * (z / -t);
	} else if (z <= 2.3e+78) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e+71:
		tmp = y / a
	elif z <= -7e-110:
		tmp = y * (z / -t)
	elif z <= 2.3e+78:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e+71)
		tmp = Float64(y / a);
	elseif (z <= -7e-110)
		tmp = Float64(y * Float64(z / Float64(-t)));
	elseif (z <= 2.3e+78)
		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 <= -1.4e+71)
		tmp = y / a;
	elseif (z <= -7e-110)
		tmp = y * (z / -t);
	elseif (z <= 2.3e+78)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e+71], N[(y / a), $MachinePrecision], If[LessEqual[z, -7e-110], N[(y * N[(z / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.3e+78], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.40000000000000001e71 or 2.3000000000000002e78 < z

   1. Initial program 61.7%

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

      1. *-commutative 61.7%

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

   3. Simplified 61.7%

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

   5. Taylor expanded in z around inf 70.0%

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

   if -1.40000000000000001e71 < z < -6.99999999999999947e-110

   1. Initial program 97.0%

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

      1. *-commutative 97.0%

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

   3. Simplified 97.0%

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

      1. clear-num 96.8%

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

      2. associate-/r/ 96.8%

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

      3. sub-neg 96.8%

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

      4. +-commutative 96.8%

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

      5. *-commutative 96.8%

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

      6. distribute-rgt-neg-in 96.8%

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

      7. fma-define 96.8%

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

   6. Applied egg-rr 96.8%

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

   7. Taylor expanded in a around 0 49.8%

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

   8. Taylor expanded in x around 0 36.8%

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

      1. mul-1-neg 36.8%

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

      2. associate-/l* 36.9%

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

      3. distribute-rgt-neg-in 36.9%

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

      4. distribute-neg-frac2 36.9%

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

   10. Simplified 36.9%

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

   if -6.99999999999999947e-110 < z < 2.3000000000000002e78

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.9%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{z}{-t}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 53.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-110}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e+61)
   (/ y a)
   (if (<= z -7.2e-110)
     (* z (/ y (- t)))
     (if (<= z 3.7e+77) (/ x t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+61) {
		tmp = y / a;
	} else if (z <= -7.2e-110) {
		tmp = z * (y / -t);
	} else if (z <= 3.7e+77) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.4d+61)) then
        tmp = y / a
    else if (z <= (-7.2d-110)) then
        tmp = z * (y / -t)
    else if (z <= 3.7d+77) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e+61) {
		tmp = y / a;
	} else if (z <= -7.2e-110) {
		tmp = z * (y / -t);
	} else if (z <= 3.7e+77) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e+61:
		tmp = y / a
	elif z <= -7.2e-110:
		tmp = z * (y / -t)
	elif z <= 3.7e+77:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e+61)
		tmp = Float64(y / a);
	elseif (z <= -7.2e-110)
		tmp = Float64(z * Float64(y / Float64(-t)));
	elseif (z <= 3.7e+77)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e+61)
		tmp = y / a;
	elseif (z <= -7.2e-110)
		tmp = z * (y / -t);
	elseif (z <= 3.7e+77)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e+61], N[(y / a), $MachinePrecision], If[LessEqual[z, -7.2e-110], N[(z * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+77], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999999e61 or 3.69999999999999995e77 < z

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in z around inf 68.5%

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

   if -2.3999999999999999e61 < z < -7.1999999999999999e-110

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

   3. Simplified 96.7%

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

      1. clear-num 96.4%

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

      2. associate-/r/ 96.6%

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

      3. sub-neg 96.6%

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

      4. +-commutative 96.6%

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

      5. *-commutative 96.6%

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

      6. distribute-rgt-neg-in 96.6%

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

      7. fma-define 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in a around 0 49.7%

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

   8. Taylor expanded in x around 0 37.9%

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

      1. mul-1-neg 37.9%

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

      2. associate-/l* 37.9%

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

      3. distribute-rgt-neg-in 37.9%

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

      4. distribute-neg-frac2 37.9%

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

   10. Simplified 37.9%

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

   11. Taylor expanded in y around 0 37.9%

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

       1. mul-1-neg 37.9%

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

       2. associate-*r/ 37.9%

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

       3. *-commutative 37.9%

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

       4. associate-*l/ 37.9%

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

       5. associate-*r/ 40.7%

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

       6. distribute-rgt-neg-in 40.7%

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

       7. distribute-neg-frac2 40.7%

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

   13. Simplified 40.7%

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

   if -7.1999999999999999e-110 < z < 3.69999999999999995e77

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 57.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+61}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-110}:\\ \;\;\;\;z \cdot \frac{y}{-t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+106} \lor \neg \left(z \leq 3.6 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+106) (not (<= z 3.6e+77))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+106) || !(z <= 3.6e+77)) {
		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 <= (-6.8d+106)) .or. (.not. (z <= 3.6d+77))) 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 <= -6.8e+106) || !(z <= 3.6e+77)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+106) or not (z <= 3.6e+77):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+106) || !(z <= 3.6e+77))
		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 <= -6.8e+106) || ~((z <= 3.6e+77)))
		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, -6.8e+106], N[Not[LessEqual[z, 3.6e+77]], $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 < -6.79999999999999989e106 or 3.5999999999999998e77 < z

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   5. Taylor expanded in z around inf 73.8%

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

   if -6.79999999999999989e106 < z < 3.5999999999999998e77

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around inf 71.9%

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

      1. *-commutative 71.9%

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

   7. Simplified 71.9%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+106} \lor \neg \left(z \leq 3.6 \cdot 10^{+77}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+36} \lor \neg \left(z \leq 2.3 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+36) (not (<= z 2.3e+78))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+36) || !(z <= 2.3e+78)) {
		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 <= (-4.2d+36)) .or. (.not. (z <= 2.3d+78))) 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 <= -4.2e+36) || !(z <= 2.3e+78)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+36) or not (z <= 2.3e+78):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+36) || !(z <= 2.3e+78))
		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 <= -4.2e+36) || ~((z <= 2.3e+78)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+36], N[Not[LessEqual[z, 2.3e+78]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.20000000000000009e36 or 2.3000000000000002e78 < z

   1. Initial program 64.1%

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

      1. *-commutative 64.1%

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

   3. Simplified 64.1%

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

   5. Taylor expanded in z around inf 65.9%

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

   if -4.20000000000000009e36 < z < 2.3000000000000002e78

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 50.8%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+36} \lor \neg \left(z \leq 2.3 \cdot 10^{+78}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.7% 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 83.6%

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

   1. *-commutative 83.6%

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

3. Simplified 83.6%

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

5. Taylor expanded in z around 0 33.7%

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

6. Final simplification 33.7%

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

Developer target: 97.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - a \cdot z\\ t_2 := \frac{x}{t\_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{if}\;z < -32113435955957344:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z < 3.5139522372978296 \cdot 10^{-86}:\\ \;\;\;\;\left(x - y \cdot z\right) \cdot \frac{1}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* a z))) (t_2 (- (/ x t_1) (/ y (- (/ t z) a)))))
   (if (< z -32113435955957344.0)
     t_2
     (if (< z 3.5139522372978296e-86) (* (- x (* y z)) (/ 1.0 t_1)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t - (a * z)
    t_2 = (x / t_1) - (y / ((t / z) - a))
    if (z < (-32113435955957344.0d0)) then
        tmp = t_2
    else if (z < 3.5139522372978296d-86) then
        tmp = (x - (y * z)) * (1.0d0 / t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (a * z);
	double t_2 = (x / t_1) - (y / ((t / z) - a));
	double tmp;
	if (z < -32113435955957344.0) {
		tmp = t_2;
	} else if (z < 3.5139522372978296e-86) {
		tmp = (x - (y * z)) * (1.0 / t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (a * z)
	t_2 = (x / t_1) - (y / ((t / z) - a))
	tmp = 0
	if z < -32113435955957344.0:
		tmp = t_2
	elif z < 3.5139522372978296e-86:
		tmp = (x - (y * z)) * (1.0 / t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(a * z))
	t_2 = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)))
	tmp = 0.0
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = Float64(Float64(x - Float64(y * z)) * Float64(1.0 / t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (a * z);
	t_2 = (x / t_1) - (y / ((t / z) - a));
	tmp = 0.0;
	if (z < -32113435955957344.0)
		tmp = t_2;
	elseif (z < 3.5139522372978296e-86)
		tmp = (x - (y * z)) * (1.0 / t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(a * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -32113435955957344.0], t$95$2, If[Less[z, 3.5139522372978296e-86], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024080 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

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

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