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

Percentage Accurate: 85.2% → 88.7%

Time: 12.0s

Alternatives: 10

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: 85.2% 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: 88.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - \frac{x}{z \cdot y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.6e+42)
   (- (/ y a) (/ x (* z a)))
   (if (<= z 1.8e+150)
     (/ (- x (* z y)) (- t (* z a)))
     (* y (/ (- 1.0 (/ x (* z y))) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.6e+42) {
		tmp = (y / a) - (x / (z * a));
	} else if (z <= 1.8e+150) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = y * ((1.0 - (x / (z * 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 <= (-9.6d+42)) then
        tmp = (y / a) - (x / (z * a))
    else if (z <= 1.8d+150) then
        tmp = (x - (z * y)) / (t - (z * a))
    else
        tmp = y * ((1.0d0 - (x / (z * 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 <= -9.6e+42) {
		tmp = (y / a) - (x / (z * a));
	} else if (z <= 1.8e+150) {
		tmp = (x - (z * y)) / (t - (z * a));
	} else {
		tmp = y * ((1.0 - (x / (z * y))) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.6e+42:
		tmp = (y / a) - (x / (z * a))
	elif z <= 1.8e+150:
		tmp = (x - (z * y)) / (t - (z * a))
	else:
		tmp = y * ((1.0 - (x / (z * y))) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.6e+42)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	elseif (z <= 1.8e+150)
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	else
		tmp = Float64(y * Float64(Float64(1.0 - Float64(x / Float64(z * y))) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.6e+42)
		tmp = (y / a) - (x / (z * a));
	elseif (z <= 1.8e+150)
		tmp = (x - (z * y)) / (t - (z * a));
	else
		tmp = y * ((1.0 - (x / (z * y))) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.6e+42], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+150], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(1.0 - N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5999999999999994e42

   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 y around inf 74.5%

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

      1. mul-1-neg 74.5%

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

      2. distribute-neg-frac2 74.5%

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

      3. cancel-sign-sub-inv 74.5%

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

      4. *-commutative 74.5%

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

      5. +-commutative 74.5%

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

      6. *-commutative 74.5%

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

      7. distribute-lft-neg-in 74.5%

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

      8. distribute-rgt-neg-in 74.5%

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

      9. fma-undefine 74.5%

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

      10. neg-sub0 74.5%

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

      11. fma-undefine 74.5%

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

      12. distribute-rgt-neg-in 74.5%

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

      13. distribute-lft-neg-in 74.5%

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

      14. *-commutative 74.5%

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

      15. associate--r+ 74.5%

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

      16. neg-sub0 74.5%

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

      17. distribute-rgt-neg-out 74.5%

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

      18. remove-double-neg 74.5%

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

   7. Simplified 74.5%

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

   8. Taylor expanded in a around inf 91.8%

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

      1. associate-/l* 89.5%

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

      2. mul-1-neg 89.5%

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

      3. unsub-neg 89.5%

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

      4. *-commutative 89.5%

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

   10. Simplified 89.5%

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

   11. Taylor expanded in y around 0 91.8%

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

       1. +-commutative 91.8%

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

       2. mul-1-neg 91.8%

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

       3. unsub-neg 91.8%

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

   13. Simplified 91.8%

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

   if -9.5999999999999994e42 < z < 1.79999999999999993e150

   1. Initial program 97.2%

      \[\frac{x - y \cdot z}{t - a \cdot z} \]
   2. Add Preprocessing

   if 1.79999999999999993e150 < z

   1. Initial program 50.7%

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

      1. *-commutative 50.7%

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

   3. Simplified 50.7%

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

   5. Taylor expanded in y around inf 58.2%

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

      1. mul-1-neg 58.2%

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

      2. distribute-neg-frac2 58.2%

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

      3. cancel-sign-sub-inv 58.2%

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

      4. *-commutative 58.2%

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

      5. +-commutative 58.2%

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

      6. *-commutative 58.2%

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

      7. distribute-lft-neg-in 58.2%

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

      8. distribute-rgt-neg-in 58.2%

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

      9. fma-undefine 58.2%

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

      10. neg-sub0 58.2%

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

      11. fma-undefine 58.2%

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

      12. distribute-rgt-neg-in 58.2%

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

      13. distribute-lft-neg-in 58.2%

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

      14. *-commutative 58.2%

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

      15. associate--r+ 58.2%

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

      16. neg-sub0 58.2%

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

      17. distribute-rgt-neg-out 58.2%

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

      18. remove-double-neg 58.2%

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

   7. Simplified 58.2%

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

   8. Taylor expanded in a around inf 86.3%

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

      1. associate-/l* 82.6%

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

      2. mul-1-neg 82.6%

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

      3. unsub-neg 82.6%

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

      4. *-commutative 82.6%

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

   10. Simplified 82.6%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+42}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+150}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - \frac{x}{z \cdot y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;z \leq -5.3 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - \frac{x}{z \cdot y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ (- x (* z y)) t)))
   (if (<= z -5.3e+47)
     (- (/ y a) (/ x (* z a)))
     (if (<= z -1.15e-16)
       (* z (/ y (- (* z a) t)))
       (if (<= z -2.5e-95)
         t_1
         (if (<= z -1.35e-174)
           t_2
           (if (<= z 7.5e-275)
             t_1
             (if (<= z 1.1e+56) t_2 (* y (/ (- 1.0 (/ x (* z y))) a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (z <= -5.3e+47) {
		tmp = (y / a) - (x / (z * a));
	} else if (z <= -1.15e-16) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -1.35e-174) {
		tmp = t_2;
	} else if (z <= 7.5e-275) {
		tmp = t_1;
	} else if (z <= 1.1e+56) {
		tmp = t_2;
	} else {
		tmp = y * ((1.0 - (x / (z * 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 / (t - (z * a))
    t_2 = (x - (z * y)) / t
    if (z <= (-5.3d+47)) then
        tmp = (y / a) - (x / (z * a))
    else if (z <= (-1.15d-16)) then
        tmp = z * (y / ((z * a) - t))
    else if (z <= (-2.5d-95)) then
        tmp = t_1
    else if (z <= (-1.35d-174)) then
        tmp = t_2
    else if (z <= 7.5d-275) then
        tmp = t_1
    else if (z <= 1.1d+56) then
        tmp = t_2
    else
        tmp = y * ((1.0d0 - (x / (z * y))) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (z <= -5.3e+47) {
		tmp = (y / a) - (x / (z * a));
	} else if (z <= -1.15e-16) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -1.35e-174) {
		tmp = t_2;
	} else if (z <= 7.5e-275) {
		tmp = t_1;
	} else if (z <= 1.1e+56) {
		tmp = t_2;
	} else {
		tmp = y * ((1.0 - (x / (z * y))) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (x - (z * y)) / t
	tmp = 0
	if z <= -5.3e+47:
		tmp = (y / a) - (x / (z * a))
	elif z <= -1.15e-16:
		tmp = z * (y / ((z * a) - t))
	elif z <= -2.5e-95:
		tmp = t_1
	elif z <= -1.35e-174:
		tmp = t_2
	elif z <= 7.5e-275:
		tmp = t_1
	elif z <= 1.1e+56:
		tmp = t_2
	else:
		tmp = y * ((1.0 - (x / (z * y))) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (z <= -5.3e+47)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	elseif (z <= -1.15e-16)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -1.35e-174)
		tmp = t_2;
	elseif (z <= 7.5e-275)
		tmp = t_1;
	elseif (z <= 1.1e+56)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(1.0 - Float64(x / Float64(z * y))) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (x - (z * y)) / t;
	tmp = 0.0;
	if (z <= -5.3e+47)
		tmp = (y / a) - (x / (z * a));
	elseif (z <= -1.15e-16)
		tmp = z * (y / ((z * a) - t));
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -1.35e-174)
		tmp = t_2;
	elseif (z <= 7.5e-275)
		tmp = t_1;
	elseif (z <= 1.1e+56)
		tmp = t_2;
	else
		tmp = y * ((1.0 - (x / (z * y))) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -5.3e+47], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-16], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-95], t$95$1, If[LessEqual[z, -1.35e-174], t$95$2, If[LessEqual[z, 7.5e-275], t$95$1, If[LessEqual[z, 1.1e+56], t$95$2, N[(y * N[(N[(1.0 - N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.3e47

   1. Initial program 68.4%

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

      1. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in y around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. distribute-neg-frac2 73.4%

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

      3. cancel-sign-sub-inv 73.4%

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

      4. *-commutative 73.4%

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

      5. +-commutative 73.4%

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

      6. *-commutative 73.4%

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

      7. distribute-lft-neg-in 73.4%

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

      8. distribute-rgt-neg-in 73.4%

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

      9. fma-undefine 73.4%

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

      10. neg-sub0 73.4%

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

      11. fma-undefine 73.4%

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

      12. distribute-rgt-neg-in 73.4%

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

      13. distribute-lft-neg-in 73.4%

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

      14. *-commutative 73.4%

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

      15. associate--r+ 73.4%

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

      16. neg-sub0 73.4%

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

      17. distribute-rgt-neg-out 73.4%

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

      18. remove-double-neg 73.4%

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

   7. Simplified 73.4%

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

   8. Taylor expanded in a around inf 91.5%

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

      1. associate-/l* 89.1%

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

      2. mul-1-neg 89.1%

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

      3. unsub-neg 89.1%

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

      4. *-commutative 89.1%

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

   10. Simplified 89.1%

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

   11. Taylor expanded in y around 0 91.5%

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

       1. +-commutative 91.5%

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

       2. mul-1-neg 91.5%

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

       3. unsub-neg 91.5%

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

   13. Simplified 91.5%

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

   if -5.3e47 < z < -1.15e-16

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 92.6%

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

      1. mul-1-neg 92.6%

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

      2. distribute-neg-frac2 92.6%

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

      3. cancel-sign-sub-inv 92.6%

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

      4. *-commutative 92.6%

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

      5. +-commutative 92.6%

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

      6. *-commutative 92.6%

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

      7. distribute-lft-neg-in 92.6%

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

      8. distribute-rgt-neg-in 92.6%

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

      9. fma-undefine 92.6%

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

      10. neg-sub0 92.6%

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

      11. fma-undefine 92.6%

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

      12. distribute-rgt-neg-in 92.6%

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

      13. distribute-lft-neg-in 92.6%

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

      14. *-commutative 92.6%

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

      15. associate--r+ 92.6%

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

      16. neg-sub0 92.6%

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

      17. distribute-rgt-neg-out 92.6%

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

      18. remove-double-neg 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in y around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-/l* 75.2%

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

      3. *-commutative 75.2%

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

   10. Applied egg-rr 75.2%

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

   if -1.15e-16 < z < -2.4999999999999999e-95 or -1.34999999999999994e-174 < z < 7.49999999999999943e-275

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.4%

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

      1. *-commutative 86.4%

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

   7. Simplified 86.4%

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

   if -2.4999999999999999e-95 < z < -1.34999999999999994e-174 or 7.49999999999999943e-275 < z < 1.10000000000000008e56

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 77.9%

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

   if 1.10000000000000008e56 < z

   1. Initial program 60.1%

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

      1. *-commutative 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in y around inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. distribute-neg-frac2 71.2%

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

      3. cancel-sign-sub-inv 71.2%

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

      4. *-commutative 71.2%

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

      5. +-commutative 71.2%

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

      6. *-commutative 71.2%

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

      7. distribute-lft-neg-in 71.2%

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

      8. distribute-rgt-neg-in 71.2%

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

      9. fma-undefine 71.2%

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

      10. neg-sub0 71.2%

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

      11. fma-undefine 71.2%

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

      12. distribute-rgt-neg-in 71.2%

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

      13. distribute-lft-neg-in 71.2%

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

      14. *-commutative 71.2%

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

      15. associate--r+ 71.2%

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

      16. neg-sub0 71.2%

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

      17. distribute-rgt-neg-out 71.2%

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

      18. remove-double-neg 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in a around inf 77.7%

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

      1. associate-/l* 75.4%

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

      2. mul-1-neg 75.4%

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

      3. unsub-neg 75.4%

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

      4. *-commutative 75.4%

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

   10. Simplified 75.4%

       \[\leadsto \color{blue}{y \cdot \frac{1 - \frac{x}{z \cdot y}}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-174}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+56}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - \frac{x}{z \cdot y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} - \frac{x}{z \cdot a}\\ t_2 := \frac{x}{t - z \cdot a}\\ t_3 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-95}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-172}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-274}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+48}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (/ y a) (/ x (* z a))))
        (t_2 (/ x (- t (* z a))))
        (t_3 (/ (- x (* z y)) t)))
   (if (<= z -1.4e+48)
     t_1
     (if (<= z -5.7e-15)
       (* z (/ y (- (* z a) t)))
       (if (<= z -2.45e-95)
         t_2
         (if (<= z -3.6e-172)
           t_3
           (if (<= z 5e-274) t_2 (if (<= z 8e+48) t_3 t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) - (x / (z * a));
	double t_2 = x / (t - (z * a));
	double t_3 = (x - (z * y)) / t;
	double tmp;
	if (z <= -1.4e+48) {
		tmp = t_1;
	} else if (z <= -5.7e-15) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= -2.45e-95) {
		tmp = t_2;
	} else if (z <= -3.6e-172) {
		tmp = t_3;
	} else if (z <= 5e-274) {
		tmp = t_2;
	} else if (z <= 8e+48) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = (y / a) - (x / (z * a))
    t_2 = x / (t - (z * a))
    t_3 = (x - (z * y)) / t
    if (z <= (-1.4d+48)) then
        tmp = t_1
    else if (z <= (-5.7d-15)) then
        tmp = z * (y / ((z * a) - t))
    else if (z <= (-2.45d-95)) then
        tmp = t_2
    else if (z <= (-3.6d-172)) then
        tmp = t_3
    else if (z <= 5d-274) then
        tmp = t_2
    else if (z <= 8d+48) then
        tmp = t_3
    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 / a) - (x / (z * a));
	double t_2 = x / (t - (z * a));
	double t_3 = (x - (z * y)) / t;
	double tmp;
	if (z <= -1.4e+48) {
		tmp = t_1;
	} else if (z <= -5.7e-15) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= -2.45e-95) {
		tmp = t_2;
	} else if (z <= -3.6e-172) {
		tmp = t_3;
	} else if (z <= 5e-274) {
		tmp = t_2;
	} else if (z <= 8e+48) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) - (x / (z * a))
	t_2 = x / (t - (z * a))
	t_3 = (x - (z * y)) / t
	tmp = 0
	if z <= -1.4e+48:
		tmp = t_1
	elif z <= -5.7e-15:
		tmp = z * (y / ((z * a) - t))
	elif z <= -2.45e-95:
		tmp = t_2
	elif z <= -3.6e-172:
		tmp = t_3
	elif z <= 5e-274:
		tmp = t_2
	elif z <= 8e+48:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) - Float64(x / Float64(z * a)))
	t_2 = Float64(x / Float64(t - Float64(z * a)))
	t_3 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (z <= -1.4e+48)
		tmp = t_1;
	elseif (z <= -5.7e-15)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	elseif (z <= -2.45e-95)
		tmp = t_2;
	elseif (z <= -3.6e-172)
		tmp = t_3;
	elseif (z <= 5e-274)
		tmp = t_2;
	elseif (z <= 8e+48)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) - (x / (z * a));
	t_2 = x / (t - (z * a));
	t_3 = (x - (z * y)) / t;
	tmp = 0.0;
	if (z <= -1.4e+48)
		tmp = t_1;
	elseif (z <= -5.7e-15)
		tmp = z * (y / ((z * a) - t));
	elseif (z <= -2.45e-95)
		tmp = t_2;
	elseif (z <= -3.6e-172)
		tmp = t_3;
	elseif (z <= 5e-274)
		tmp = t_2;
	elseif (z <= 8e+48)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -1.4e+48], t$95$1, If[LessEqual[z, -5.7e-15], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.45e-95], t$95$2, If[LessEqual[z, -3.6e-172], t$95$3, If[LessEqual[z, 5e-274], t$95$2, If[LessEqual[z, 8e+48], t$95$3, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.40000000000000006e48 or 8.00000000000000035e48 < z

   1. Initial program 64.4%

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

      1. *-commutative 64.4%

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

   3. Simplified 64.4%

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

   5. Taylor expanded in y around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-neg-frac2 72.3%

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

      3. cancel-sign-sub-inv 72.3%

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

      4. *-commutative 72.3%

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

      5. +-commutative 72.3%

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

      6. *-commutative 72.3%

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

      7. distribute-lft-neg-in 72.3%

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

      8. distribute-rgt-neg-in 72.3%

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

      9. fma-undefine 72.3%

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

      10. neg-sub0 72.3%

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

      11. fma-undefine 72.3%

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

      12. distribute-rgt-neg-in 72.3%

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

      13. distribute-lft-neg-in 72.3%

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

      14. *-commutative 72.3%

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

      15. associate--r+ 72.3%

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

      16. neg-sub0 72.3%

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

      17. distribute-rgt-neg-out 72.3%

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

      18. remove-double-neg 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in a around inf 84.8%

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

      1. associate-/l* 82.4%

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

      2. mul-1-neg 82.4%

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

      3. unsub-neg 82.4%

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

      4. *-commutative 82.4%

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

   10. Simplified 82.4%

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

   11. Taylor expanded in y around 0 83.5%

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

       1. +-commutative 83.5%

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

       2. mul-1-neg 83.5%

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

       3. unsub-neg 83.5%

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

   13. Simplified 83.5%

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

   if -1.40000000000000006e48 < z < -5.7000000000000003e-15

   1. Initial program 90.7%

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

      1. *-commutative 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around inf 92.6%

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

      1. mul-1-neg 92.6%

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

      2. distribute-neg-frac2 92.6%

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

      3. cancel-sign-sub-inv 92.6%

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

      4. *-commutative 92.6%

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

      5. +-commutative 92.6%

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

      6. *-commutative 92.6%

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

      7. distribute-lft-neg-in 92.6%

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

      8. distribute-rgt-neg-in 92.6%

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

      9. fma-undefine 92.6%

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

      10. neg-sub0 92.6%

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

      11. fma-undefine 92.6%

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

      12. distribute-rgt-neg-in 92.6%

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

      13. distribute-lft-neg-in 92.6%

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

      14. *-commutative 92.6%

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

      15. associate--r+ 92.6%

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

      16. neg-sub0 92.6%

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

      17. distribute-rgt-neg-out 92.6%

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

      18. remove-double-neg 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in y around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-/l* 75.2%

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

      3. *-commutative 75.2%

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

   10. Applied egg-rr 75.2%

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

   if -5.7000000000000003e-15 < z < -2.45e-95 or -3.60000000000000015e-172 < z < 5e-274

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.4%

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

      1. *-commutative 86.4%

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

   7. Simplified 86.4%

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

   if -2.45e-95 < z < -3.60000000000000015e-172 or 5e-274 < z < 8.00000000000000035e48

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 77.9%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-15}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-172}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+48}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-275}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 10^{+54}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ (- x (* z y)) t)))
   (if (<= z -2.7e+105)
     (/ y a)
     (if (<= z -2e-15)
       (* y (/ z (- (* z a) t)))
       (if (<= z -2.5e-95)
         t_1
         (if (<= z -1.15e-174)
           t_2
           (if (<= z 4.4e-275) t_1 (if (<= z 1e+54) t_2 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (z <= -2.7e+105) {
		tmp = y / a;
	} else if (z <= -2e-15) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -1.15e-174) {
		tmp = t_2;
	} else if (z <= 4.4e-275) {
		tmp = t_1;
	} else if (z <= 1e+54) {
		tmp = t_2;
	} 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 / (t - (z * a))
    t_2 = (x - (z * y)) / t
    if (z <= (-2.7d+105)) then
        tmp = y / a
    else if (z <= (-2d-15)) then
        tmp = y * (z / ((z * a) - t))
    else if (z <= (-2.5d-95)) then
        tmp = t_1
    else if (z <= (-1.15d-174)) then
        tmp = t_2
    else if (z <= 4.4d-275) then
        tmp = t_1
    else if (z <= 1d+54) then
        tmp = t_2
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (z <= -2.7e+105) {
		tmp = y / a;
	} else if (z <= -2e-15) {
		tmp = y * (z / ((z * a) - t));
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -1.15e-174) {
		tmp = t_2;
	} else if (z <= 4.4e-275) {
		tmp = t_1;
	} else if (z <= 1e+54) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (x - (z * y)) / t
	tmp = 0
	if z <= -2.7e+105:
		tmp = y / a
	elif z <= -2e-15:
		tmp = y * (z / ((z * a) - t))
	elif z <= -2.5e-95:
		tmp = t_1
	elif z <= -1.15e-174:
		tmp = t_2
	elif z <= 4.4e-275:
		tmp = t_1
	elif z <= 1e+54:
		tmp = t_2
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (z <= -2.7e+105)
		tmp = Float64(y / a);
	elseif (z <= -2e-15)
		tmp = Float64(y * Float64(z / Float64(Float64(z * a) - t)));
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -1.15e-174)
		tmp = t_2;
	elseif (z <= 4.4e-275)
		tmp = t_1;
	elseif (z <= 1e+54)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (x - (z * y)) / t;
	tmp = 0.0;
	if (z <= -2.7e+105)
		tmp = y / a;
	elseif (z <= -2e-15)
		tmp = y * (z / ((z * a) - t));
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -1.15e-174)
		tmp = t_2;
	elseif (z <= 4.4e-275)
		tmp = t_1;
	elseif (z <= 1e+54)
		tmp = t_2;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.7e+105], N[(y / a), $MachinePrecision], If[LessEqual[z, -2e-15], N[(y * N[(z / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-95], t$95$1, If[LessEqual[z, -1.15e-174], t$95$2, If[LessEqual[z, 4.4e-275], t$95$1, If[LessEqual[z, 1e+54], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.70000000000000016e105 or 1.0000000000000001e54 < z

   1. Initial program 61.6%

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

      1. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   5. Taylor expanded in z around inf 72.5%

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

   if -2.70000000000000016e105 < z < -2.0000000000000002e-15

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in x around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. associate-/l* 79.3%

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

      3. distribute-rgt-neg-in 79.3%

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

      4. distribute-neg-frac2 79.3%

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

      5. cancel-sign-sub-inv 79.3%

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

      6. *-commutative 79.3%

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

      7. +-commutative 79.3%

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

      8. *-commutative 79.3%

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

      9. distribute-lft-neg-in 79.3%

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

      10. distribute-rgt-neg-in 79.3%

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

      11. fma-undefine 79.3%

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

      12. neg-sub0 79.3%

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

      13. fma-undefine 79.3%

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

      14. distribute-rgt-neg-in 79.3%

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

      15. distribute-lft-neg-in 79.3%

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

      16. *-commutative 79.3%

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

      17. associate--r+ 79.3%

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

      18. neg-sub0 79.3%

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

      19. distribute-rgt-neg-out 79.3%

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

      20. remove-double-neg 79.3%

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

   7. Simplified 79.3%

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

   if -2.0000000000000002e-15 < z < -2.4999999999999999e-95 or -1.1499999999999999e-174 < z < 4.39999999999999977e-275

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.4%

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

      1. *-commutative 86.4%

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

   7. Simplified 86.4%

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

   if -2.4999999999999999e-95 < z < -1.1499999999999999e-174 or 4.39999999999999977e-275 < z < 1.0000000000000001e54

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 77.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+105}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-174}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-275}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 10^{+54}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ t_2 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;z \leq -1.04 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-172}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 4.55 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))) (t_2 (/ (- x (* z y)) t)))
   (if (<= z -1.04e+102)
     (/ y a)
     (if (<= z -1.3e-16)
       (* z (/ y (- (* z a) t)))
       (if (<= z -2.5e-95)
         t_1
         (if (<= z -8.5e-172)
           t_2
           (if (<= z 4.55e-274) t_1 (if (<= z 1.55e+66) t_2 (/ y a)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (z <= -1.04e+102) {
		tmp = y / a;
	} else if (z <= -1.3e-16) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -8.5e-172) {
		tmp = t_2;
	} else if (z <= 4.55e-274) {
		tmp = t_1;
	} else if (z <= 1.55e+66) {
		tmp = t_2;
	} 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 / (t - (z * a))
    t_2 = (x - (z * y)) / t
    if (z <= (-1.04d+102)) then
        tmp = y / a
    else if (z <= (-1.3d-16)) then
        tmp = z * (y / ((z * a) - t))
    else if (z <= (-2.5d-95)) then
        tmp = t_1
    else if (z <= (-8.5d-172)) then
        tmp = t_2
    else if (z <= 4.55d-274) then
        tmp = t_1
    else if (z <= 1.55d+66) then
        tmp = t_2
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double t_2 = (x - (z * y)) / t;
	double tmp;
	if (z <= -1.04e+102) {
		tmp = y / a;
	} else if (z <= -1.3e-16) {
		tmp = z * (y / ((z * a) - t));
	} else if (z <= -2.5e-95) {
		tmp = t_1;
	} else if (z <= -8.5e-172) {
		tmp = t_2;
	} else if (z <= 4.55e-274) {
		tmp = t_1;
	} else if (z <= 1.55e+66) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	t_2 = (x - (z * y)) / t
	tmp = 0
	if z <= -1.04e+102:
		tmp = y / a
	elif z <= -1.3e-16:
		tmp = z * (y / ((z * a) - t))
	elif z <= -2.5e-95:
		tmp = t_1
	elif z <= -8.5e-172:
		tmp = t_2
	elif z <= 4.55e-274:
		tmp = t_1
	elif z <= 1.55e+66:
		tmp = t_2
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	t_2 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (z <= -1.04e+102)
		tmp = Float64(y / a);
	elseif (z <= -1.3e-16)
		tmp = Float64(z * Float64(y / Float64(Float64(z * a) - t)));
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -8.5e-172)
		tmp = t_2;
	elseif (z <= 4.55e-274)
		tmp = t_1;
	elseif (z <= 1.55e+66)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (t - (z * a));
	t_2 = (x - (z * y)) / t;
	tmp = 0.0;
	if (z <= -1.04e+102)
		tmp = y / a;
	elseif (z <= -1.3e-16)
		tmp = z * (y / ((z * a) - t));
	elseif (z <= -2.5e-95)
		tmp = t_1;
	elseif (z <= -8.5e-172)
		tmp = t_2;
	elseif (z <= 4.55e-274)
		tmp = t_1;
	elseif (z <= 1.55e+66)
		tmp = t_2;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -1.04e+102], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.3e-16], N[(z * N[(y / N[(N[(z * a), $MachinePrecision] - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-95], t$95$1, If[LessEqual[z, -8.5e-172], t$95$2, If[LessEqual[z, 4.55e-274], t$95$1, If[LessEqual[z, 1.55e+66], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.04e102 or 1.55000000000000009e66 < z

   1. Initial program 61.6%

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

      1. *-commutative 61.6%

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

   3. Simplified 61.6%

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

   5. Taylor expanded in z around inf 72.5%

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

   if -1.04e102 < z < -1.2999999999999999e-16

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in y around inf 94.7%

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

      1. mul-1-neg 94.7%

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

      2. distribute-neg-frac2 94.7%

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

      3. cancel-sign-sub-inv 94.7%

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

      4. *-commutative 94.7%

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

      5. +-commutative 94.7%

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

      6. *-commutative 94.7%

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

      7. distribute-lft-neg-in 94.7%

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

      8. distribute-rgt-neg-in 94.7%

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

      9. fma-undefine 94.7%

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

      10. neg-sub0 94.7%

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

      11. fma-undefine 94.7%

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

      12. distribute-rgt-neg-in 94.7%

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

      13. distribute-lft-neg-in 94.7%

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

      14. *-commutative 94.7%

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

      15. associate--r+ 94.7%

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

      16. neg-sub0 94.7%

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

      17. distribute-rgt-neg-out 94.7%

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

      18. remove-double-neg 94.7%

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

   7. Simplified 94.7%

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

   8. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-/l* 79.3%

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

      3. *-commutative 79.3%

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

   10. Applied egg-rr 79.3%

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

   if -1.2999999999999999e-16 < z < -2.4999999999999999e-95 or -8.49999999999999963e-172 < z < 4.54999999999999992e-274

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 86.4%

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

      1. *-commutative 86.4%

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

   7. Simplified 86.4%

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

   if -2.4999999999999999e-95 < z < -8.49999999999999963e-172 or 4.54999999999999992e-274 < z < 1.55000000000000009e66

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 77.9%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.04 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot a - t}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-172}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 4.55 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+66}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)))
   (if (<= z -4.8e+33)
     (/ y a)
     (if (<= z -1.45e-16)
       t_1
       (if (<= z 1.14e-274)
         (/ x (- t (* z a)))
         (if (<= z 1.5e+55) 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 tmp;
	if (z <= -4.8e+33) {
		tmp = y / a;
	} else if (z <= -1.45e-16) {
		tmp = t_1;
	} else if (z <= 1.14e-274) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.5e+55) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (z * y)) / t
    if (z <= (-4.8d+33)) then
        tmp = y / a
    else if (z <= (-1.45d-16)) then
        tmp = t_1
    else if (z <= 1.14d-274) then
        tmp = x / (t - (z * a))
    else if (z <= 1.5d+55) 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 tmp;
	if (z <= -4.8e+33) {
		tmp = y / a;
	} else if (z <= -1.45e-16) {
		tmp = t_1;
	} else if (z <= 1.14e-274) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.5e+55) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	tmp = 0
	if z <= -4.8e+33:
		tmp = y / a
	elif z <= -1.45e-16:
		tmp = t_1
	elif z <= 1.14e-274:
		tmp = x / (t - (z * a))
	elif z <= 1.5e+55:
		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)
	tmp = 0.0
	if (z <= -4.8e+33)
		tmp = Float64(y / a);
	elseif (z <= -1.45e-16)
		tmp = t_1;
	elseif (z <= 1.14e-274)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.5e+55)
		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;
	tmp = 0.0;
	if (z <= -4.8e+33)
		tmp = y / a;
	elseif (z <= -1.45e-16)
		tmp = t_1;
	elseif (z <= 1.14e-274)
		tmp = x / (t - (z * a));
	elseif (z <= 1.5e+55)
		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]}, If[LessEqual[z, -4.8e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.45e-16], t$95$1, If[LessEqual[z, 1.14e-274], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e+55], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e33 or 1.50000000000000008e55 < z

   1. Initial program 64.6%

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

      1. *-commutative 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in z around inf 72.7%

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

   if -4.8e33 < z < -1.4499999999999999e-16 or 1.13999999999999998e-274 < z < 1.50000000000000008e55

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 77.1%

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

   if -1.4499999999999999e-16 < z < 1.13999999999999998e-274

   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 79.1%

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

      1. *-commutative 79.1%

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

   7. Simplified 79.1%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.14 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-43}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+31)
   (/ y a)
   (if (<= z 7.2e-129)
     (/ x t)
     (if (<= z 6e-43) (/ (* z y) (- t)) (if (<= z 7.6e+48) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+31) {
		tmp = y / a;
	} else if (z <= 7.2e-129) {
		tmp = x / t;
	} else if (z <= 6e-43) {
		tmp = (z * y) / -t;
	} else if (z <= 7.6e+48) {
		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 <= (-1.2d+31)) then
        tmp = y / a
    else if (z <= 7.2d-129) then
        tmp = x / t
    else if (z <= 6d-43) then
        tmp = (z * y) / -t
    else if (z <= 7.6d+48) 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 <= -1.2e+31) {
		tmp = y / a;
	} else if (z <= 7.2e-129) {
		tmp = x / t;
	} else if (z <= 6e-43) {
		tmp = (z * y) / -t;
	} else if (z <= 7.6e+48) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+31:
		tmp = y / a
	elif z <= 7.2e-129:
		tmp = x / t
	elif z <= 6e-43:
		tmp = (z * y) / -t
	elif z <= 7.6e+48:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+31)
		tmp = Float64(y / a);
	elseif (z <= 7.2e-129)
		tmp = Float64(x / t);
	elseif (z <= 6e-43)
		tmp = Float64(Float64(z * y) / Float64(-t));
	elseif (z <= 7.6e+48)
		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 <= -1.2e+31)
		tmp = y / a;
	elseif (z <= 7.2e-129)
		tmp = x / t;
	elseif (z <= 6e-43)
		tmp = (z * y) / -t;
	elseif (z <= 7.6e+48)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+31], N[(y / a), $MachinePrecision], If[LessEqual[z, 7.2e-129], N[(x / t), $MachinePrecision], If[LessEqual[z, 6e-43], N[(N[(z * y), $MachinePrecision] / (-t)), $MachinePrecision], If[LessEqual[z, 7.6e+48], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.19999999999999991e31 or 7.60000000000000001e48 < z

   1. Initial program 65.7%

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

      1. *-commutative 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -1.19999999999999991e31 < z < 7.2e-129 or 6.00000000000000007e-43 < z < 7.60000000000000001e48

   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 56.4%

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

   if 7.2e-129 < z < 6.00000000000000007e-43

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around inf 72.9%

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

   6. Taylor expanded in x around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. distribute-rgt-neg-out 58.5%

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

   8. Simplified 58.5%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-43}:\\ \;\;\;\;\frac{z \cdot y}{-t}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+31} \lor \neg \left(z \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.1e+31) (not (<= z 5e+120))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.1e+31) || !(z <= 5e+120)) {
		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 <= (-3.1d+31)) .or. (.not. (z <= 5d+120))) 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 <= -3.1e+31) || !(z <= 5e+120)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.1e+31) or not (z <= 5e+120):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.1e+31) || !(z <= 5e+120))
		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 <= -3.1e+31) || ~((z <= 5e+120)))
		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, -3.1e+31], N[Not[LessEqual[z, 5e+120]], $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 < -3.1000000000000002e31 or 5.00000000000000019e120 < z

   1. Initial program 64.0%

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

      1. *-commutative 64.0%

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

   3. Simplified 64.0%

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

   5. Taylor expanded in z around inf 74.8%

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

   if -3.1000000000000002e31 < z < 5.00000000000000019e120

   1. Initial program 98.6%

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

      1. *-commutative 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around inf 68.2%

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

      1. *-commutative 68.2%

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

   7. Simplified 68.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+31} \lor \neg \left(z \leq 5 \cdot 10^{+120}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+32} \lor \neg \left(z \leq 1.05 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+32) (not (<= z 1.05e+49))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+32) || !(z <= 1.05e+49)) {
		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 <= (-2.6d+32)) .or. (.not. (z <= 1.05d+49))) 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 <= -2.6e+32) || !(z <= 1.05e+49)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+32) or not (z <= 1.05e+49):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+32) || !(z <= 1.05e+49))
		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 <= -2.6e+32) || ~((z <= 1.05e+49)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+32], N[Not[LessEqual[z, 1.05e+49]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000002e32 or 1.05000000000000005e49 < z

   1. Initial program 65.7%

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

      1. *-commutative 65.7%

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

   3. Simplified 65.7%

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

   5. Taylor expanded in z around inf 71.6%

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

   if -2.6000000000000002e32 < z < 1.05000000000000005e49

   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 53.8%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+32} \lor \neg \left(z \leq 1.05 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.0% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

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

   1. *-commutative 86.6%

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

3. Simplified 86.6%

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

5. Taylor expanded in z around 0 37.4%

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

6. Final simplification 37.4%

   \[\leadsto \frac{x}{t} \]
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 2024115 
(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))))