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

Percentage Accurate: 84.7% → 90.8%

Time: 14.7s

Alternatives: 12

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+143} \lor \neg \left(z \leq 4.2 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e+143) (not (<= z 4.2e+124)))
   (/ (- y (/ x z)) a)
   (/ (- x (* z y)) (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+143) || !(z <= 4.2e+124)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.95d+143)) .or. (.not. (z <= 4.2d+124))) then
        tmp = (y - (x / z)) / a
    else
        tmp = (x - (z * y)) / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e+143) || !(z <= 4.2e+124)) {
		tmp = (y - (x / z)) / a;
	} else {
		tmp = (x - (z * y)) / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e+143) or not (z <= 4.2e+124):
		tmp = (y - (x / z)) / a
	else:
		tmp = (x - (z * y)) / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e+143) || !(z <= 4.2e+124))
		tmp = Float64(Float64(y - Float64(x / z)) / a);
	else
		tmp = Float64(Float64(x - Float64(z * y)) / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.95e+143) || ~((z <= 4.2e+124)))
		tmp = (y - (x / z)) / a;
	else
		tmp = (x - (z * y)) / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e+143], N[Not[LessEqual[z, 4.2e+124]], $MachinePrecision]], N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e143 or 4.20000000000000023e124 < z

   1. Initial program 59.7%

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

      1. *-commutative 59.7%

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

   3. Simplified 59.7%

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

   5. Taylor expanded in z around inf 59.7%

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

   6. Taylor expanded in t around 0 89.5%

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

      1. associate-*r/ 89.5%

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

      2. mul-1-neg 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in x around 0 81.8%

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

       1. +-commutative 81.8%

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

       2. mul-1-neg 81.8%

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

       3. sub-neg 81.8%

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

       4. associate-/l/ 89.5%

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

       5. div-sub 89.5%

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

   11. Simplified 89.5%

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

   if -1.9499999999999999e143 < z < 4.20000000000000023e124

   1. Initial program 97.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+143} \lor \neg \left(z \leq 4.2 \cdot 10^{+124}\right):\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 52.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-a\right)}\\ t_2 := z \cdot \frac{-y}{t}\\ \mathbf{if}\;z \leq -9 \cdot 10^{+149}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-114}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (* z (- a)))) (t_2 (* z (/ (- y) t))))
   (if (<= z -9e+149)
     (/ y a)
     (if (<= z -2.05e+135)
       (/ (/ x a) (- z))
       (if (<= z -5.2e+99)
         (/ y a)
         (if (<= z -4.6e-98)
           (/ x t)
           (if (<= z -3e-114)
             t_2
             (if (<= z 3.1e-116)
               (/ x t)
               (if (<= z 1.15e-37)
                 t_1
                 (if (<= z 6e+44)
                   t_2
                   (if (<= z 1.5e+107) t_1 (/ y a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z * -a);
	double t_2 = z * (-y / t);
	double tmp;
	if (z <= -9e+149) {
		tmp = y / a;
	} else if (z <= -2.05e+135) {
		tmp = (x / a) / -z;
	} else if (z <= -5.2e+99) {
		tmp = y / a;
	} else if (z <= -4.6e-98) {
		tmp = x / t;
	} else if (z <= -3e-114) {
		tmp = t_2;
	} else if (z <= 3.1e-116) {
		tmp = x / t;
	} else if (z <= 1.15e-37) {
		tmp = t_1;
	} else if (z <= 6e+44) {
		tmp = t_2;
	} else if (z <= 1.5e+107) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (z * -a)
    t_2 = z * (-y / t)
    if (z <= (-9d+149)) then
        tmp = y / a
    else if (z <= (-2.05d+135)) then
        tmp = (x / a) / -z
    else if (z <= (-5.2d+99)) then
        tmp = y / a
    else if (z <= (-4.6d-98)) then
        tmp = x / t
    else if (z <= (-3d-114)) then
        tmp = t_2
    else if (z <= 3.1d-116) then
        tmp = x / t
    else if (z <= 1.15d-37) then
        tmp = t_1
    else if (z <= 6d+44) then
        tmp = t_2
    else if (z <= 1.5d+107) 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 * -a);
	double t_2 = z * (-y / t);
	double tmp;
	if (z <= -9e+149) {
		tmp = y / a;
	} else if (z <= -2.05e+135) {
		tmp = (x / a) / -z;
	} else if (z <= -5.2e+99) {
		tmp = y / a;
	} else if (z <= -4.6e-98) {
		tmp = x / t;
	} else if (z <= -3e-114) {
		tmp = t_2;
	} else if (z <= 3.1e-116) {
		tmp = x / t;
	} else if (z <= 1.15e-37) {
		tmp = t_1;
	} else if (z <= 6e+44) {
		tmp = t_2;
	} else if (z <= 1.5e+107) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z * -a)
	t_2 = z * (-y / t)
	tmp = 0
	if z <= -9e+149:
		tmp = y / a
	elif z <= -2.05e+135:
		tmp = (x / a) / -z
	elif z <= -5.2e+99:
		tmp = y / a
	elif z <= -4.6e-98:
		tmp = x / t
	elif z <= -3e-114:
		tmp = t_2
	elif z <= 3.1e-116:
		tmp = x / t
	elif z <= 1.15e-37:
		tmp = t_1
	elif z <= 6e+44:
		tmp = t_2
	elif z <= 1.5e+107:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z * Float64(-a)))
	t_2 = Float64(z * Float64(Float64(-y) / t))
	tmp = 0.0
	if (z <= -9e+149)
		tmp = Float64(y / a);
	elseif (z <= -2.05e+135)
		tmp = Float64(Float64(x / a) / Float64(-z));
	elseif (z <= -5.2e+99)
		tmp = Float64(y / a);
	elseif (z <= -4.6e-98)
		tmp = Float64(x / t);
	elseif (z <= -3e-114)
		tmp = t_2;
	elseif (z <= 3.1e-116)
		tmp = Float64(x / t);
	elseif (z <= 1.15e-37)
		tmp = t_1;
	elseif (z <= 6e+44)
		tmp = t_2;
	elseif (z <= 1.5e+107)
		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 * -a);
	t_2 = z * (-y / t);
	tmp = 0.0;
	if (z <= -9e+149)
		tmp = y / a;
	elseif (z <= -2.05e+135)
		tmp = (x / a) / -z;
	elseif (z <= -5.2e+99)
		tmp = y / a;
	elseif (z <= -4.6e-98)
		tmp = x / t;
	elseif (z <= -3e-114)
		tmp = t_2;
	elseif (z <= 3.1e-116)
		tmp = x / t;
	elseif (z <= 1.15e-37)
		tmp = t_1;
	elseif (z <= 6e+44)
		tmp = t_2;
	elseif (z <= 1.5e+107)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9e+149], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.05e+135], N[(N[(x / a), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, -5.2e+99], N[(y / a), $MachinePrecision], If[LessEqual[z, -4.6e-98], N[(x / t), $MachinePrecision], If[LessEqual[z, -3e-114], t$95$2, If[LessEqual[z, 3.1e-116], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.15e-37], t$95$1, If[LessEqual[z, 6e+44], t$95$2, If[LessEqual[z, 1.5e+107], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -8.99999999999999965e149 or -2.05e135 < z < -5.1999999999999999e99 or 1.50000000000000012e107 < z

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around inf 70.7%

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

   if -8.99999999999999965e149 < z < -2.05e135

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. associate-/r* 87.4%

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

      3. sub-neg 87.4%

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

      4. distribute-rgt-neg-out 87.4%

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

      5. +-commutative 87.4%

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

      6. fma-define 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in y around 0 75.6%

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

      1. associate-/r* 87.4%

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

   10. Simplified 87.4%

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

   if -5.1999999999999999e99 < z < -4.60000000000000001e-98 or -3.00000000000000015e-114 < z < 3.10000000000000018e-116

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 60.1%

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

   if -4.60000000000000001e-98 < z < -3.00000000000000015e-114 or 1.15e-37 < z < 5.99999999999999974e44

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 60.9%

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

      3. distribute-rgt-neg-in 60.9%

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

      4. distribute-neg-frac2 60.9%

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

      5. cancel-sign-sub-inv 60.9%

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

      6. *-commutative 60.9%

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

      7. +-commutative 60.9%

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

      8. distribute-rgt-neg-out 60.9%

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

      9. distribute-lft-neg-in 60.9%

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

      10. *-commutative 60.9%

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

      11. fma-undefine 60.9%

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

      12. neg-sub0 60.9%

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

      13. fma-undefine 60.9%

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

      14. distribute-rgt-neg-in 60.9%

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

      15. mul-1-neg 60.9%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 60.9%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 60.9%

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

      18. *-commutative 60.9%

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

      19. associate--r+ 60.9%

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

      20. neg-sub0 60.9%

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

      21. distribute-rgt-neg-out 60.9%

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

      22. remove-double-neg 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in z around 0 51.7%

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

      1. associate-*r/ 51.7%

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

      2. mul-1-neg 51.7%

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

   10. Simplified 51.7%

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

   11. Taylor expanded in y around 0 61.9%

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

       1. associate-*r/ 61.9%

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

       2. neg-mul-1 61.9%

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

       3. distribute-lft-neg-in 61.9%

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

   13. Simplified 61.9%

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

   14. Taylor expanded in y around 0 61.9%

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

       1. mul-1-neg 61.9%

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

       2. associate-*r/ 51.7%

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

       3. *-commutative 51.7%

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

       4. associate-*l/ 61.9%

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

       5. associate-*r/ 61.9%

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

       6. distribute-rgt-neg-in 61.9%

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

       7. distribute-neg-frac2 61.9%

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

   16. Simplified 61.9%

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

   if 3.10000000000000018e-116 < z < 1.15e-37 or 5.99999999999999974e44 < z < 1.50000000000000012e107

   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 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. associate-/r* 63.5%

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

      3. sub-neg 63.5%

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

      4. distribute-rgt-neg-out 63.5%

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

      5. +-commutative 63.5%

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

      6. fma-define 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 47.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+149}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-98}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+44}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-y}{t}\\ t_2 := \frac{\frac{x}{z}}{-a}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+107}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (- y) t))) (t_2 (/ (/ x z) (- a))))
   (if (<= z -1.7e+150)
     (/ y a)
     (if (<= z -2.1e+135)
       t_2
       (if (<= z -4e+99)
         (/ y a)
         (if (<= z -8e-101)
           (/ x t)
           (if (<= z -3.6e-114)
             t_1
             (if (<= z 3.1e-116)
               (/ x t)
               (if (<= z 2.9e-42)
                 (/ x (* z (- a)))
                 (if (<= z 9.2e+45)
                   t_1
                   (if (<= z 1.2e+107) t_2 (/ y a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (-y / t);
	double t_2 = (x / z) / -a;
	double tmp;
	if (z <= -1.7e+150) {
		tmp = y / a;
	} else if (z <= -2.1e+135) {
		tmp = t_2;
	} else if (z <= -4e+99) {
		tmp = y / a;
	} else if (z <= -8e-101) {
		tmp = x / t;
	} else if (z <= -3.6e-114) {
		tmp = t_1;
	} else if (z <= 3.1e-116) {
		tmp = x / t;
	} else if (z <= 2.9e-42) {
		tmp = x / (z * -a);
	} else if (z <= 9.2e+45) {
		tmp = t_1;
	} else if (z <= 1.2e+107) {
		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 = z * (-y / t)
    t_2 = (x / z) / -a
    if (z <= (-1.7d+150)) then
        tmp = y / a
    else if (z <= (-2.1d+135)) then
        tmp = t_2
    else if (z <= (-4d+99)) then
        tmp = y / a
    else if (z <= (-8d-101)) then
        tmp = x / t
    else if (z <= (-3.6d-114)) then
        tmp = t_1
    else if (z <= 3.1d-116) then
        tmp = x / t
    else if (z <= 2.9d-42) then
        tmp = x / (z * -a)
    else if (z <= 9.2d+45) then
        tmp = t_1
    else if (z <= 1.2d+107) 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 = z * (-y / t);
	double t_2 = (x / z) / -a;
	double tmp;
	if (z <= -1.7e+150) {
		tmp = y / a;
	} else if (z <= -2.1e+135) {
		tmp = t_2;
	} else if (z <= -4e+99) {
		tmp = y / a;
	} else if (z <= -8e-101) {
		tmp = x / t;
	} else if (z <= -3.6e-114) {
		tmp = t_1;
	} else if (z <= 3.1e-116) {
		tmp = x / t;
	} else if (z <= 2.9e-42) {
		tmp = x / (z * -a);
	} else if (z <= 9.2e+45) {
		tmp = t_1;
	} else if (z <= 1.2e+107) {
		tmp = t_2;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (-y / t)
	t_2 = (x / z) / -a
	tmp = 0
	if z <= -1.7e+150:
		tmp = y / a
	elif z <= -2.1e+135:
		tmp = t_2
	elif z <= -4e+99:
		tmp = y / a
	elif z <= -8e-101:
		tmp = x / t
	elif z <= -3.6e-114:
		tmp = t_1
	elif z <= 3.1e-116:
		tmp = x / t
	elif z <= 2.9e-42:
		tmp = x / (z * -a)
	elif z <= 9.2e+45:
		tmp = t_1
	elif z <= 1.2e+107:
		tmp = t_2
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(-y) / t))
	t_2 = Float64(Float64(x / z) / Float64(-a))
	tmp = 0.0
	if (z <= -1.7e+150)
		tmp = Float64(y / a);
	elseif (z <= -2.1e+135)
		tmp = t_2;
	elseif (z <= -4e+99)
		tmp = Float64(y / a);
	elseif (z <= -8e-101)
		tmp = Float64(x / t);
	elseif (z <= -3.6e-114)
		tmp = t_1;
	elseif (z <= 3.1e-116)
		tmp = Float64(x / t);
	elseif (z <= 2.9e-42)
		tmp = Float64(x / Float64(z * Float64(-a)));
	elseif (z <= 9.2e+45)
		tmp = t_1;
	elseif (z <= 1.2e+107)
		tmp = t_2;
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (-y / t);
	t_2 = (x / z) / -a;
	tmp = 0.0;
	if (z <= -1.7e+150)
		tmp = y / a;
	elseif (z <= -2.1e+135)
		tmp = t_2;
	elseif (z <= -4e+99)
		tmp = y / a;
	elseif (z <= -8e-101)
		tmp = x / t;
	elseif (z <= -3.6e-114)
		tmp = t_1;
	elseif (z <= 3.1e-116)
		tmp = x / t;
	elseif (z <= 2.9e-42)
		tmp = x / (z * -a);
	elseif (z <= 9.2e+45)
		tmp = t_1;
	elseif (z <= 1.2e+107)
		tmp = t_2;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / z), $MachinePrecision] / (-a)), $MachinePrecision]}, If[LessEqual[z, -1.7e+150], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.1e+135], t$95$2, If[LessEqual[z, -4e+99], N[(y / a), $MachinePrecision], If[LessEqual[z, -8e-101], N[(x / t), $MachinePrecision], If[LessEqual[z, -3.6e-114], t$95$1, If[LessEqual[z, 3.1e-116], N[(x / t), $MachinePrecision], If[LessEqual[z, 2.9e-42], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e+45], t$95$1, If[LessEqual[z, 1.2e+107], t$95$2, N[(y / a), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.69999999999999991e150 or -2.1000000000000001e135 < z < -3.9999999999999999e99 or 1.2e107 < z

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around inf 70.7%

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

   if -1.69999999999999991e150 < z < -2.1000000000000001e135 or 9.20000000000000049e45 < z < 1.2e107

   1. Initial program 96.3%

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

      1. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 96.3%

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

   6. Taylor expanded in t around 0 73.0%

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

      1. associate-*r/ 73.0%

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

      2. mul-1-neg 73.0%

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

   8. Simplified 73.0%

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

   9. Taylor expanded in x around inf 58.7%

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

   if -3.9999999999999999e99 < z < -8.00000000000000041e-101 or -3.60000000000000018e-114 < z < 3.10000000000000018e-116

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 60.1%

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

   if -8.00000000000000041e-101 < z < -3.60000000000000018e-114 or 2.9000000000000003e-42 < z < 9.20000000000000049e45

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in x around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. associate-/l* 60.9%

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

      3. distribute-rgt-neg-in 60.9%

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

      4. distribute-neg-frac2 60.9%

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

      5. cancel-sign-sub-inv 60.9%

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

      6. *-commutative 60.9%

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

      7. +-commutative 60.9%

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

      8. distribute-rgt-neg-out 60.9%

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

      9. distribute-lft-neg-in 60.9%

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

      10. *-commutative 60.9%

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

      11. fma-undefine 60.9%

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

      12. neg-sub0 60.9%

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

      13. fma-undefine 60.9%

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

      14. distribute-rgt-neg-in 60.9%

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

      15. mul-1-neg 60.9%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 60.9%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 60.9%

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

      18. *-commutative 60.9%

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

      19. associate--r+ 60.9%

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

      20. neg-sub0 60.9%

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

      21. distribute-rgt-neg-out 60.9%

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

      22. remove-double-neg 60.9%

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

   7. Simplified 60.9%

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

   8. Taylor expanded in z around 0 51.7%

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

      1. associate-*r/ 51.7%

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

      2. mul-1-neg 51.7%

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

   10. Simplified 51.7%

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

   11. Taylor expanded in y around 0 61.9%

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

       1. associate-*r/ 61.9%

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

       2. neg-mul-1 61.9%

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

       3. distribute-lft-neg-in 61.9%

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

   13. Simplified 61.9%

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

   14. Taylor expanded in y around 0 61.9%

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

       1. mul-1-neg 61.9%

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

       2. associate-*r/ 51.7%

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

       3. *-commutative 51.7%

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

       4. associate-*l/ 61.9%

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

       5. associate-*r/ 61.9%

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

       6. distribute-rgt-neg-in 61.9%

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

       7. distribute-neg-frac2 61.9%

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

   16. Simplified 61.9%

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

   if 3.10000000000000018e-116 < z < 2.9000000000000003e-42

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. associate-/r* 59.5%

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

      3. sub-neg 59.5%

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

      4. distribute-rgt-neg-out 59.5%

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

      5. +-commutative 59.5%

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

      6. fma-define 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in y around 0 47.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-114}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+45}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 52.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \left(-y\right)}{t}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* z (- y)) t)))
   (if (<= z -1.1e+150)
     (/ y a)
     (if (<= z -2.1e+135)
       (/ (/ x z) (- a))
       (if (<= z -2.9e+100)
         (/ y a)
         (if (<= z -7.4e-101)
           (/ x t)
           (if (<= z -1.06e-114)
             t_1
             (if (<= z 7.1e-84)
               (/ x t)
               (if (<= z 5.4e+72)
                 t_1
                 (if (<= z 1.42e+107) (/ x (* z (- a))) (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * -y) / t;
	double tmp;
	if (z <= -1.1e+150) {
		tmp = y / a;
	} else if (z <= -2.1e+135) {
		tmp = (x / z) / -a;
	} else if (z <= -2.9e+100) {
		tmp = y / a;
	} else if (z <= -7.4e-101) {
		tmp = x / t;
	} else if (z <= -1.06e-114) {
		tmp = t_1;
	} else if (z <= 7.1e-84) {
		tmp = x / t;
	} else if (z <= 5.4e+72) {
		tmp = t_1;
	} else if (z <= 1.42e+107) {
		tmp = x / (z * -a);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * -y) / t
    if (z <= (-1.1d+150)) then
        tmp = y / a
    else if (z <= (-2.1d+135)) then
        tmp = (x / z) / -a
    else if (z <= (-2.9d+100)) then
        tmp = y / a
    else if (z <= (-7.4d-101)) then
        tmp = x / t
    else if (z <= (-1.06d-114)) then
        tmp = t_1
    else if (z <= 7.1d-84) then
        tmp = x / t
    else if (z <= 5.4d+72) then
        tmp = t_1
    else if (z <= 1.42d+107) then
        tmp = x / (z * -a)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z * -y) / t;
	double tmp;
	if (z <= -1.1e+150) {
		tmp = y / a;
	} else if (z <= -2.1e+135) {
		tmp = (x / z) / -a;
	} else if (z <= -2.9e+100) {
		tmp = y / a;
	} else if (z <= -7.4e-101) {
		tmp = x / t;
	} else if (z <= -1.06e-114) {
		tmp = t_1;
	} else if (z <= 7.1e-84) {
		tmp = x / t;
	} else if (z <= 5.4e+72) {
		tmp = t_1;
	} else if (z <= 1.42e+107) {
		tmp = x / (z * -a);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z * -y) / t
	tmp = 0
	if z <= -1.1e+150:
		tmp = y / a
	elif z <= -2.1e+135:
		tmp = (x / z) / -a
	elif z <= -2.9e+100:
		tmp = y / a
	elif z <= -7.4e-101:
		tmp = x / t
	elif z <= -1.06e-114:
		tmp = t_1
	elif z <= 7.1e-84:
		tmp = x / t
	elif z <= 5.4e+72:
		tmp = t_1
	elif z <= 1.42e+107:
		tmp = x / (z * -a)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z * Float64(-y)) / t)
	tmp = 0.0
	if (z <= -1.1e+150)
		tmp = Float64(y / a);
	elseif (z <= -2.1e+135)
		tmp = Float64(Float64(x / z) / Float64(-a));
	elseif (z <= -2.9e+100)
		tmp = Float64(y / a);
	elseif (z <= -7.4e-101)
		tmp = Float64(x / t);
	elseif (z <= -1.06e-114)
		tmp = t_1;
	elseif (z <= 7.1e-84)
		tmp = Float64(x / t);
	elseif (z <= 5.4e+72)
		tmp = t_1;
	elseif (z <= 1.42e+107)
		tmp = Float64(x / Float64(z * Float64(-a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z * -y) / t;
	tmp = 0.0;
	if (z <= -1.1e+150)
		tmp = y / a;
	elseif (z <= -2.1e+135)
		tmp = (x / z) / -a;
	elseif (z <= -2.9e+100)
		tmp = y / a;
	elseif (z <= -7.4e-101)
		tmp = x / t;
	elseif (z <= -1.06e-114)
		tmp = t_1;
	elseif (z <= 7.1e-84)
		tmp = x / t;
	elseif (z <= 5.4e+72)
		tmp = t_1;
	elseif (z <= 1.42e+107)
		tmp = x / (z * -a);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -1.1e+150], N[(y / a), $MachinePrecision], If[LessEqual[z, -2.1e+135], N[(N[(x / z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[z, -2.9e+100], N[(y / a), $MachinePrecision], If[LessEqual[z, -7.4e-101], N[(x / t), $MachinePrecision], If[LessEqual[z, -1.06e-114], t$95$1, If[LessEqual[z, 7.1e-84], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.4e+72], t$95$1, If[LessEqual[z, 1.42e+107], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.1e150 or -2.1000000000000001e135 < z < -2.9e100 or 1.42000000000000006e107 < z

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around inf 70.7%

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

   if -1.1e150 < z < -2.1000000000000001e135

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in z around inf 87.9%

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

   6. Taylor expanded in t around 0 87.6%

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

      1. associate-*r/ 87.6%

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

      2. mul-1-neg 87.6%

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

   8. Simplified 87.6%

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

   9. Taylor expanded in x around inf 87.6%

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

   if -2.9e100 < z < -7.4000000000000001e-101 or -1.06e-114 < z < 7.0999999999999997e-84

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 58.8%

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

   if -7.4000000000000001e-101 < z < -1.06e-114 or 7.0999999999999997e-84 < z < 5.4000000000000001e72

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. associate-/l* 59.0%

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

      3. distribute-rgt-neg-in 59.0%

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

      4. distribute-neg-frac2 59.0%

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

      5. cancel-sign-sub-inv 59.0%

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

      6. *-commutative 59.0%

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

      7. +-commutative 59.0%

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

      8. distribute-rgt-neg-out 59.0%

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

      9. distribute-lft-neg-in 59.0%

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

      10. *-commutative 59.0%

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

      11. fma-undefine 59.0%

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

      12. neg-sub0 59.0%

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

      13. fma-undefine 59.0%

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

      14. distribute-rgt-neg-in 59.0%

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

      15. mul-1-neg 59.0%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 59.0%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 59.0%

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

      18. *-commutative 59.0%

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

      19. associate--r+ 59.0%

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

      20. neg-sub0 59.0%

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

      21. distribute-rgt-neg-out 59.0%

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

      22. remove-double-neg 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in z around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. mul-1-neg 53.5%

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

      3. distribute-lft-neg-out 53.5%

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

      4. *-commutative 53.5%

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

   10. Simplified 53.5%

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

   if 5.4000000000000001e72 < z < 1.42000000000000006e107

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. associate-/r* 69.0%

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

      3. sub-neg 69.0%

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

      4. distribute-rgt-neg-out 69.0%

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

      5. +-commutative 69.0%

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

      6. fma-define 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in y around 0 55.5%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{z}}{-a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq -1.06 \cdot 10^{-114}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 7.1 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+72}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{z \cdot \left(-a\right)}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (* z (- a)))))
   (if (<= z -4.5e+149)
     (/ y a)
     (if (<= z -1.7e+135)
       (/ (/ x a) (- z))
       (if (<= z -4.5e+99)
         (/ y a)
         (if (<= z 2.6e-116)
           (/ x t)
           (if (<= z 3.4e-43)
             t_1
             (if (<= z 8.5e+47)
               (* y (/ (- z) t))
               (if (<= z 1.25e+107) t_1 (/ y a))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (z * -a);
	double tmp;
	if (z <= -4.5e+149) {
		tmp = y / a;
	} else if (z <= -1.7e+135) {
		tmp = (x / a) / -z;
	} else if (z <= -4.5e+99) {
		tmp = y / a;
	} else if (z <= 2.6e-116) {
		tmp = x / t;
	} else if (z <= 3.4e-43) {
		tmp = t_1;
	} else if (z <= 8.5e+47) {
		tmp = y * (-z / t);
	} else if (z <= 1.25e+107) {
		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 * -a)
    if (z <= (-4.5d+149)) then
        tmp = y / a
    else if (z <= (-1.7d+135)) then
        tmp = (x / a) / -z
    else if (z <= (-4.5d+99)) then
        tmp = y / a
    else if (z <= 2.6d-116) then
        tmp = x / t
    else if (z <= 3.4d-43) then
        tmp = t_1
    else if (z <= 8.5d+47) then
        tmp = y * (-z / t)
    else if (z <= 1.25d+107) 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 * -a);
	double tmp;
	if (z <= -4.5e+149) {
		tmp = y / a;
	} else if (z <= -1.7e+135) {
		tmp = (x / a) / -z;
	} else if (z <= -4.5e+99) {
		tmp = y / a;
	} else if (z <= 2.6e-116) {
		tmp = x / t;
	} else if (z <= 3.4e-43) {
		tmp = t_1;
	} else if (z <= 8.5e+47) {
		tmp = y * (-z / t);
	} else if (z <= 1.25e+107) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (z * -a)
	tmp = 0
	if z <= -4.5e+149:
		tmp = y / a
	elif z <= -1.7e+135:
		tmp = (x / a) / -z
	elif z <= -4.5e+99:
		tmp = y / a
	elif z <= 2.6e-116:
		tmp = x / t
	elif z <= 3.4e-43:
		tmp = t_1
	elif z <= 8.5e+47:
		tmp = y * (-z / t)
	elif z <= 1.25e+107:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(z * Float64(-a)))
	tmp = 0.0
	if (z <= -4.5e+149)
		tmp = Float64(y / a);
	elseif (z <= -1.7e+135)
		tmp = Float64(Float64(x / a) / Float64(-z));
	elseif (z <= -4.5e+99)
		tmp = Float64(y / a);
	elseif (z <= 2.6e-116)
		tmp = Float64(x / t);
	elseif (z <= 3.4e-43)
		tmp = t_1;
	elseif (z <= 8.5e+47)
		tmp = Float64(y * Float64(Float64(-z) / t));
	elseif (z <= 1.25e+107)
		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 * -a);
	tmp = 0.0;
	if (z <= -4.5e+149)
		tmp = y / a;
	elseif (z <= -1.7e+135)
		tmp = (x / a) / -z;
	elseif (z <= -4.5e+99)
		tmp = y / a;
	elseif (z <= 2.6e-116)
		tmp = x / t;
	elseif (z <= 3.4e-43)
		tmp = t_1;
	elseif (z <= 8.5e+47)
		tmp = y * (-z / t);
	elseif (z <= 1.25e+107)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+149], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.7e+135], N[(N[(x / a), $MachinePrecision] / (-z)), $MachinePrecision], If[LessEqual[z, -4.5e+99], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.6e-116], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.4e-43], t$95$1, If[LessEqual[z, 8.5e+47], N[(y * N[((-z) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+107], t$95$1, N[(y / a), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.49999999999999982e149 or -1.70000000000000005e135 < z < -4.5e99 or 1.25e107 < z

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around inf 70.7%

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

   if -4.49999999999999982e149 < z < -1.70000000000000005e135

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in t around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. associate-/r* 87.4%

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

      3. sub-neg 87.4%

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

      4. distribute-rgt-neg-out 87.4%

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

      5. +-commutative 87.4%

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

      6. fma-define 87.4%

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

   7. Simplified 87.4%

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

   8. Taylor expanded in y around 0 75.6%

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

      1. associate-/r* 87.4%

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

   10. Simplified 87.4%

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

   if -4.5e99 < z < 2.6e-116

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 58.0%

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

   if 2.6e-116 < z < 3.4000000000000001e-43 or 8.5000000000000008e47 < z < 1.25e107

   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 0 65.0%

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

      1. mul-1-neg 65.0%

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

      2. associate-/r* 63.5%

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

      3. sub-neg 63.5%

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

      4. distribute-rgt-neg-out 63.5%

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

      5. +-commutative 63.5%

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

      6. fma-define 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in y around 0 47.5%

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

   if 3.4000000000000001e-43 < z < 8.5000000000000008e47

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around 0 59.2%

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

      1. mul-1-neg 59.2%

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

      2. associate-/l* 64.5%

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

      3. distribute-rgt-neg-in 64.5%

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

      4. distribute-neg-frac2 64.5%

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

      5. cancel-sign-sub-inv 64.5%

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

      6. *-commutative 64.5%

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

      7. +-commutative 64.5%

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

      8. distribute-rgt-neg-out 64.5%

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

      9. distribute-lft-neg-in 64.5%

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

      10. *-commutative 64.5%

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

      11. fma-undefine 64.5%

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

      12. neg-sub0 64.5%

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

      13. fma-undefine 64.5%

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

      14. distribute-rgt-neg-in 64.5%

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

      15. mul-1-neg 64.5%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 64.5%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 64.5%

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

      18. *-commutative 64.5%

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

      19. associate--r+ 64.5%

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

      20. neg-sub0 64.5%

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

      21. distribute-rgt-neg-out 64.5%

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

      22. remove-double-neg 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in z around 0 51.1%

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

      1. associate-*r/ 51.1%

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

      2. mul-1-neg 51.1%

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

   10. Simplified 51.1%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+149}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \frac{-z}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{-z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+135}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+110}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (/ x a) (- z))))
   (if (<= z -7e+150)
     (/ y a)
     (if (<= z -1.8e+135)
       t_1
       (if (<= z -4e+99)
         (/ y a)
         (if (<= z 9.5e-117) (/ x t) (if (<= z 2e+110) t_1 (/ y a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x / a) / -z;
	double tmp;
	if (z <= -7e+150) {
		tmp = y / a;
	} else if (z <= -1.8e+135) {
		tmp = t_1;
	} else if (z <= -4e+99) {
		tmp = y / a;
	} else if (z <= 9.5e-117) {
		tmp = x / t;
	} else if (z <= 2e+110) {
		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 / a) / -z
    if (z <= (-7d+150)) then
        tmp = y / a
    else if (z <= (-1.8d+135)) then
        tmp = t_1
    else if (z <= (-4d+99)) then
        tmp = y / a
    else if (z <= 9.5d-117) then
        tmp = x / t
    else if (z <= 2d+110) 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 / a) / -z;
	double tmp;
	if (z <= -7e+150) {
		tmp = y / a;
	} else if (z <= -1.8e+135) {
		tmp = t_1;
	} else if (z <= -4e+99) {
		tmp = y / a;
	} else if (z <= 9.5e-117) {
		tmp = x / t;
	} else if (z <= 2e+110) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x / a) / -z
	tmp = 0
	if z <= -7e+150:
		tmp = y / a
	elif z <= -1.8e+135:
		tmp = t_1
	elif z <= -4e+99:
		tmp = y / a
	elif z <= 9.5e-117:
		tmp = x / t
	elif z <= 2e+110:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x / a) / Float64(-z))
	tmp = 0.0
	if (z <= -7e+150)
		tmp = Float64(y / a);
	elseif (z <= -1.8e+135)
		tmp = t_1;
	elseif (z <= -4e+99)
		tmp = Float64(y / a);
	elseif (z <= 9.5e-117)
		tmp = Float64(x / t);
	elseif (z <= 2e+110)
		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 / a) / -z;
	tmp = 0.0;
	if (z <= -7e+150)
		tmp = y / a;
	elseif (z <= -1.8e+135)
		tmp = t_1;
	elseif (z <= -4e+99)
		tmp = y / a;
	elseif (z <= 9.5e-117)
		tmp = x / t;
	elseif (z <= 2e+110)
		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 / a), $MachinePrecision] / (-z)), $MachinePrecision]}, If[LessEqual[z, -7e+150], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.8e+135], t$95$1, If[LessEqual[z, -4e+99], N[(y / a), $MachinePrecision], If[LessEqual[z, 9.5e-117], N[(x / t), $MachinePrecision], If[LessEqual[z, 2e+110], t$95$1, N[(y / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.99999999999999968e150 or -1.7999999999999999e135 < z < -3.9999999999999999e99 or 2e110 < z

   1. Initial program 61.5%

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

      1. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around inf 70.7%

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

   if -6.99999999999999968e150 < z < -1.7999999999999999e135 or 9.5000000000000004e-117 < z < 2e110

   1. Initial program 96.7%

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

      1. *-commutative 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 58.3%

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

      1. mul-1-neg 58.3%

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

      2. associate-/r* 59.0%

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

      3. sub-neg 59.0%

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

      4. distribute-rgt-neg-out 59.0%

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

      5. +-commutative 59.0%

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

      6. fma-define 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in y around 0 44.1%

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

      1. associate-/r* 45.7%

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

   10. Simplified 45.7%

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

   if -3.9999999999999999e99 < z < 9.5000000000000004e-117

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 58.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+135}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\frac{\frac{x}{a}}{-z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 56.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+40} \lor \neg \left(y \leq 3.9 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.6e+95)
   (/ (* z (- y)) t)
   (if (or (<= y -3.2e+40) (not (<= y 3.9e+83))) (/ y a) (/ x (- t (* z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.6e+95) {
		tmp = (z * -y) / t;
	} else if ((y <= -3.2e+40) || !(y <= 3.9e+83)) {
		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 (y <= (-2.6d+95)) then
        tmp = (z * -y) / t
    else if ((y <= (-3.2d+40)) .or. (.not. (y <= 3.9d+83))) 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 (y <= -2.6e+95) {
		tmp = (z * -y) / t;
	} else if ((y <= -3.2e+40) || !(y <= 3.9e+83)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.6e+95:
		tmp = (z * -y) / t
	elif (y <= -3.2e+40) or not (y <= 3.9e+83):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.6e+95)
		tmp = Float64(Float64(z * Float64(-y)) / t);
	elseif ((y <= -3.2e+40) || !(y <= 3.9e+83))
		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 (y <= -2.6e+95)
		tmp = (z * -y) / t;
	elseif ((y <= -3.2e+40) || ~((y <= 3.9e+83)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.6e+95], N[(N[(z * (-y)), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[y, -3.2e+40], N[Not[LessEqual[y, 3.9e+83]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5999999999999999e95

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. associate-/l* 56.5%

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

      3. distribute-rgt-neg-in 56.5%

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

      4. distribute-neg-frac2 56.5%

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

      5. cancel-sign-sub-inv 56.5%

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

      6. *-commutative 56.5%

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

      7. +-commutative 56.5%

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

      8. distribute-rgt-neg-out 56.5%

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

      9. distribute-lft-neg-in 56.5%

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

      10. *-commutative 56.5%

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

      11. fma-undefine 56.5%

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

      12. neg-sub0 56.5%

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

      13. fma-undefine 56.5%

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

      14. distribute-rgt-neg-in 56.5%

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

      15. mul-1-neg 56.5%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 56.5%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 56.5%

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

      18. *-commutative 56.5%

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

      19. associate--r+ 56.5%

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

      20. neg-sub0 56.5%

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

      21. distribute-rgt-neg-out 56.5%

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

      22. remove-double-neg 56.5%

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

   7. Simplified 56.5%

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

   8. Taylor expanded in z around 0 48.7%

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

      1. associate-*r/ 48.7%

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

      2. mul-1-neg 48.7%

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

      3. distribute-lft-neg-out 48.7%

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

      4. *-commutative 48.7%

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

   10. Simplified 48.7%

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

   if -2.5999999999999999e95 < y < -3.19999999999999981e40 or 3.9000000000000002e83 < y

   1. Initial program 72.9%

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

      1. *-commutative 72.9%

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

   3. Simplified 72.9%

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

   5. Taylor expanded in z around inf 63.8%

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

   if -3.19999999999999981e40 < y < 3.9000000000000002e83

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in x around inf 79.9%

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

      1. *-commutative 79.9%

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

   7. Simplified 79.9%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+95}:\\ \;\;\;\;\frac{z \cdot \left(-y\right)}{t}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+40} \lor \neg \left(y \leq 3.9 \cdot 10^{+83}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+31} \lor \neg \left(y \leq 1.25 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.4e+105)
   (/ (- x (* z y)) t)
   (if (or (<= y -1.7e+31) (not (<= y 1.25e-52)))
     (/ y (- a (/ t z)))
     (/ x (- t (* z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.4e+105) {
		tmp = (x - (z * y)) / t;
	} else if ((y <= -1.7e+31) || !(y <= 1.25e-52)) {
		tmp = y / (a - (t / z));
	} 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 (y <= (-2.4d+105)) then
        tmp = (x - (z * y)) / t
    else if ((y <= (-1.7d+31)) .or. (.not. (y <= 1.25d-52))) then
        tmp = y / (a - (t / z))
    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 (y <= -2.4e+105) {
		tmp = (x - (z * y)) / t;
	} else if ((y <= -1.7e+31) || !(y <= 1.25e-52)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.4e+105:
		tmp = (x - (z * y)) / t
	elif (y <= -1.7e+31) or not (y <= 1.25e-52):
		tmp = y / (a - (t / z))
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.4e+105)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif ((y <= -1.7e+31) || !(y <= 1.25e-52))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	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 (y <= -2.4e+105)
		tmp = (x - (z * y)) / t;
	elseif ((y <= -1.7e+31) || ~((y <= 1.25e-52)))
		tmp = y / (a - (t / z));
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.4e+105], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[y, -1.7e+31], N[Not[LessEqual[y, 1.25e-52]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999975e105

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around inf 71.4%

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

   if -2.39999999999999975e105 < y < -1.6999999999999999e31 or 1.25e-52 < y

   1. Initial program 77.6%

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

      1. *-commutative 77.6%

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

   3. Simplified 77.6%

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

   5. Taylor expanded in x around 0 57.0%

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

      1. mul-1-neg 57.0%

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

      2. associate-/l* 62.7%

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

      3. distribute-rgt-neg-in 62.7%

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

      4. distribute-neg-frac2 62.7%

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

      5. cancel-sign-sub-inv 62.7%

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

      6. *-commutative 62.7%

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

      7. +-commutative 62.7%

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

      8. distribute-rgt-neg-out 62.7%

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

      9. distribute-lft-neg-in 62.7%

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

      10. *-commutative 62.7%

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

      11. fma-undefine 62.8%

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

      12. neg-sub0 62.8%

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

      13. fma-undefine 62.7%

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

      14. distribute-rgt-neg-in 62.7%

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

      15. mul-1-neg 62.7%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 62.7%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 62.7%

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

      18. *-commutative 62.7%

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

      19. associate--r+ 62.7%

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

      20. neg-sub0 62.7%

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

      21. distribute-rgt-neg-out 62.7%

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

      22. remove-double-neg 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in z around inf 61.6%

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

      1. mul-1-neg 61.6%

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

      2. unsub-neg 61.6%

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

   10. Simplified 61.6%

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

   11. Taylor expanded in y around 0 75.6%

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

   if -1.6999999999999999e31 < y < 1.25e-52

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 85.2%

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

      1. *-commutative 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+105}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+31} \lor \neg \left(y \leq 1.25 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.4e+99)
   (/ y a)
   (if (<= z 9.5e-117)
     (/ x t)
     (if (<= z 9.8e+106) (/ x (* z (- a))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+99) {
		tmp = y / a;
	} else if (z <= 9.5e-117) {
		tmp = x / t;
	} else if (z <= 9.8e+106) {
		tmp = x / (z * -a);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-4.4d+99)) then
        tmp = y / a
    else if (z <= 9.5d-117) then
        tmp = x / t
    else if (z <= 9.8d+106) then
        tmp = x / (z * -a)
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.4e+99) {
		tmp = y / a;
	} else if (z <= 9.5e-117) {
		tmp = x / t;
	} else if (z <= 9.8e+106) {
		tmp = x / (z * -a);
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.4e+99:
		tmp = y / a
	elif z <= 9.5e-117:
		tmp = x / t
	elif z <= 9.8e+106:
		tmp = x / (z * -a)
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.4e+99)
		tmp = Float64(y / a);
	elseif (z <= 9.5e-117)
		tmp = Float64(x / t);
	elseif (z <= 9.8e+106)
		tmp = Float64(x / Float64(z * Float64(-a)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.4e+99)
		tmp = y / a;
	elseif (z <= 9.5e-117)
		tmp = x / t;
	elseif (z <= 9.8e+106)
		tmp = x / (z * -a);
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.4e+99], N[(y / a), $MachinePrecision], If[LessEqual[z, 9.5e-117], N[(x / t), $MachinePrecision], If[LessEqual[z, 9.8e+106], N[(x / N[(z * (-a)), $MachinePrecision]), $MachinePrecision], N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.39999999999999956e99 or 9.79999999999999996e106 < z

   1. Initial program 64.2%

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

      1. *-commutative 64.2%

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

   3. Simplified 64.2%

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

   5. Taylor expanded in z around inf 66.4%

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

   if -4.39999999999999956e99 < z < 9.5000000000000004e-117

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 58.0%

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

   if 9.5000000000000004e-117 < z < 9.79999999999999996e106

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t around 0 55.6%

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

      1. mul-1-neg 55.6%

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

      2. associate-/r* 54.6%

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

      3. sub-neg 54.6%

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

      4. distribute-rgt-neg-out 54.6%

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

      5. +-commutative 54.6%

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

      6. fma-define 54.6%

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

   7. Simplified 54.6%

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

   8. Taylor expanded in y around 0 39.2%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{+106}:\\ \;\;\;\;\frac{x}{z \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 70.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+31} \lor \neg \left(y \leq 2.45 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.3e+31) (not (<= y 2.45e-51)))
   (/ y (- a (/ t z)))
   (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.3e+31) || !(y <= 2.45e-51)) {
		tmp = y / (a - (t / z));
	} 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 ((y <= (-2.3d+31)) .or. (.not. (y <= 2.45d-51))) then
        tmp = y / (a - (t / z))
    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 ((y <= -2.3e+31) || !(y <= 2.45e-51)) {
		tmp = y / (a - (t / z));
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.3e+31) or not (y <= 2.45e-51):
		tmp = y / (a - (t / z))
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.3e+31) || !(y <= 2.45e-51))
		tmp = Float64(y / Float64(a - Float64(t / z)));
	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 ((y <= -2.3e+31) || ~((y <= 2.45e-51)))
		tmp = y / (a - (t / z));
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.3e+31], N[Not[LessEqual[y, 2.45e-51]], $MachinePrecision]], N[(y / N[(a - N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e31 or 2.44999999999999987e-51 < y

   1. Initial program 80.6%

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

      1. *-commutative 80.6%

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

   3. Simplified 80.6%

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

   5. Taylor expanded in x around 0 58.5%

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

      1. mul-1-neg 58.5%

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

      2. associate-/l* 60.1%

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

      3. distribute-rgt-neg-in 60.1%

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

      4. distribute-neg-frac2 60.1%

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

      5. cancel-sign-sub-inv 60.1%

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

      6. *-commutative 60.1%

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

      7. +-commutative 60.1%

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

      8. distribute-rgt-neg-out 60.1%

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

      9. distribute-lft-neg-in 60.1%

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

      10. *-commutative 60.1%

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

      11. fma-undefine 60.1%

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

      12. neg-sub0 60.1%

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

      13. fma-undefine 60.1%

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

      14. distribute-rgt-neg-in 60.1%

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

      15. mul-1-neg 60.1%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{-1 \cdot \left(a \cdot z\right)} + t\right)} \]

      16. associate-*r* 60.1%

          \[\leadsto y \cdot \frac{z}{0 - \left(\color{blue}{\left(-1 \cdot a\right) \cdot z} + t\right)} \]

      17. neg-mul-1 60.1%

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

      18. *-commutative 60.1%

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

      19. associate--r+ 60.1%

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

      20. neg-sub0 60.1%

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

      21. distribute-rgt-neg-out 60.1%

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

      22. remove-double-neg 60.1%

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

   7. Simplified 60.1%

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

   8. Taylor expanded in z around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. unsub-neg 59.3%

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

   10. Simplified 59.3%

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

   11. Taylor expanded in y around 0 70.6%

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

   if -2.3e31 < y < 2.44999999999999987e-51

   1. Initial program 95.0%

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

      1. *-commutative 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in x around inf 85.2%

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

      1. *-commutative 85.2%

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

   7. Simplified 85.2%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+31} \lor \neg \left(y \leq 2.45 \cdot 10^{-51}\right):\\ \;\;\;\;\frac{y}{a - \frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+99} \lor \neg \left(z \leq 1.35 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+99) (not (<= z 1.35e-6))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+99) || !(z <= 1.35e-6)) {
		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 <= (-4d+99)) .or. (.not. (z <= 1.35d-6))) 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 <= -4e+99) || !(z <= 1.35e-6)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+99) or not (z <= 1.35e-6):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+99) || !(z <= 1.35e-6))
		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 <= -4e+99) || ~((z <= 1.35e-6)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+99], N[Not[LessEqual[z, 1.35e-6]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9999999999999999e99 or 1.34999999999999999e-6 < z

   1. Initial program 72.2%

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

      1. *-commutative 72.2%

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

   3. Simplified 72.2%

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

   5. Taylor expanded in z around inf 57.2%

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

   if -3.9999999999999999e99 < z < 1.34999999999999999e-6

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 53.4%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+99} \lor \neg \left(z \leq 1.35 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 88.2%

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

   1. *-commutative 88.2%

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

3. Simplified 88.2%

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

5. Taylor expanded in z around 0 38.0%

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

6. Final simplification 38.0%

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

Developer target: 97.1% 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 2024067 
(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))))