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

Percentage Accurate: 85.2% → 92.0%

Time: 11.9s

Alternatives: 11

Speedup: 0.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 92.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - y \cdot z}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t_1}{-z}}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-311} \lor \neg \left(t_2 \leq 0\right) \land t_2 \leq 5 \cdot 10^{+293}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* y z)) t_1)))
   (if (<= t_2 (- INFINITY))
     (/ y (/ t_1 (- z)))
     (if (or (<= t_2 -2e-311) (and (not (<= t_2 0.0)) (<= t_2 5e+293)))
       t_2
       (- (/ y a) (/ (/ x a) z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = y / (t_1 / -z);
	} else if ((t_2 <= -2e-311) || (!(t_2 <= 0.0) && (t_2 <= 5e+293))) {
		tmp = t_2;
	} else {
		tmp = (y / a) - ((x / a) / z);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (y * z)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = y / (t_1 / -z);
	} else if ((t_2 <= -2e-311) || (!(t_2 <= 0.0) && (t_2 <= 5e+293))) {
		tmp = t_2;
	} else {
		tmp = (y / a) - ((x / a) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (x - (y * z)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = y / (t_1 / -z)
	elif (t_2 <= -2e-311) or (not (t_2 <= 0.0) and (t_2 <= 5e+293)):
		tmp = t_2
	else:
		tmp = (y / a) - ((x / a) / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(y * z)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(y / Float64(t_1 / Float64(-z)));
	elseif ((t_2 <= -2e-311) || (!(t_2 <= 0.0) && (t_2 <= 5e+293)))
		tmp = t_2;
	else
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (x - (y * z)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = y / (t_1 / -z);
	elseif ((t_2 <= -2e-311) || (~((t_2 <= 0.0)) && (t_2 <= 5e+293)))
		tmp = t_2;
	else
		tmp = (y / a) - ((x / a) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(y / N[(t$95$1 / (-z)), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -2e-311], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 5e+293]]], t$95$2, N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -inf.0

   1. Initial program 41.3%

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

      1. *-commutative 41.3%

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

   3. Simplified 41.3%

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

   4. Taylor expanded in x around 0 33.6%

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

      1. associate-*r/ 33.6%

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

      2. mul-1-neg 33.6%

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

      3. distribute-rgt-neg-out 33.6%

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

      4. associate-/l* 92.0%

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

      5. *-commutative 92.0%

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

   6. Simplified 92.0%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -1.9999999999999e-311 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 5.00000000000000033e293

   1. Initial program 99.7%

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

   if -1.9999999999999e-311 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0 or 5.00000000000000033e293 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 39.9%

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

      1. *-commutative 39.9%

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

   3. Simplified 39.9%

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

   4. Taylor expanded in z around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. associate--l+ 63.2%

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

      3. associate-/r* 73.3%

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

      4. associate-*r/ 73.3%

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

      5. associate-/r* 73.4%

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

      6. associate-*r/ 73.4%

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

      7. div-sub 73.4%

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

      8. distribute-lft-out-- 73.4%

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

      9. associate-*r/ 73.4%

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

      10. mul-1-neg 73.4%

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

      11. unsub-neg 73.4%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in x around inf 75.8%

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

      1. associate-/r* 85.9%

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

   9. Simplified 85.9%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{t - z \cdot a}{-z}}\\ \mathbf{elif}\;\frac{x - y \cdot z}{t - z \cdot a} \leq -2 \cdot 10^{-311} \lor \neg \left(\frac{x - y \cdot z}{t - z \cdot a} \leq 0\right) \land \frac{x - y \cdot z}{t - z \cdot a} \leq 5 \cdot 10^{+293}:\\ \;\;\;\;\frac{x - y \cdot z}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \end{array} \]

Alternative 2: 63.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{t - z \cdot a}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+125}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (- t (* z a)))))
   (if (<= z -1.35e+125)
     (/ y a)
     (if (<= z 5.6e-61)
       t_1
       (if (<= z 1.4e+22)
         (/ (* y (- z)) t)
         (if (<= z 3.5e+66) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (t - (z * a));
	double tmp;
	if (z <= -1.35e+125) {
		tmp = y / a;
	} else if (z <= 5.6e-61) {
		tmp = t_1;
	} else if (z <= 1.4e+22) {
		tmp = (y * -z) / t;
	} else if (z <= 3.5e+66) {
		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 / (t - (z * a))
    if (z <= (-1.35d+125)) then
        tmp = y / a
    else if (z <= 5.6d-61) then
        tmp = t_1
    else if (z <= 1.4d+22) then
        tmp = (y * -z) / t
    else if (z <= 3.5d+66) 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 / (t - (z * a));
	double tmp;
	if (z <= -1.35e+125) {
		tmp = y / a;
	} else if (z <= 5.6e-61) {
		tmp = t_1;
	} else if (z <= 1.4e+22) {
		tmp = (y * -z) / t;
	} else if (z <= 3.5e+66) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x / (t - (z * a))
	tmp = 0
	if z <= -1.35e+125:
		tmp = y / a
	elif z <= 5.6e-61:
		tmp = t_1
	elif z <= 1.4e+22:
		tmp = (y * -z) / t
	elif z <= 3.5e+66:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(t - Float64(z * a)))
	tmp = 0.0
	if (z <= -1.35e+125)
		tmp = Float64(y / a);
	elseif (z <= 5.6e-61)
		tmp = t_1;
	elseif (z <= 1.4e+22)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	elseif (z <= 3.5e+66)
		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 / (t - (z * a));
	tmp = 0.0;
	if (z <= -1.35e+125)
		tmp = y / a;
	elseif (z <= 5.6e-61)
		tmp = t_1;
	elseif (z <= 1.4e+22)
		tmp = (y * -z) / t;
	elseif (z <= 3.5e+66)
		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[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+125], N[(y / a), $MachinePrecision], If[LessEqual[z, 5.6e-61], t$95$1, If[LessEqual[z, 1.4e+22], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.5e+66], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3499999999999999e125 or 3.4999999999999997e66 < z

   1. Initial program 60.5%

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

      1. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   4. Taylor expanded in z around inf 69.0%

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

   if -1.3499999999999999e125 < z < 5.6000000000000002e-61 or 1.4e22 < z < 3.4999999999999997e66

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in x around inf 73.7%

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

      1. *-commutative 73.7%

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

   6. Simplified 73.7%

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

   if 5.6000000000000002e-61 < z < 1.4e22

   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. Taylor expanded in t around inf 70.8%

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

   5. Taylor expanded in x around 0 54.6%

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

      1. associate-*r* 54.6%

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

      2. neg-mul-1 54.6%

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

   7. Simplified 54.6%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+125}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 3: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - y \cdot z}{t}\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* y z)) t)))
   (if (<= z -2.7e+73)
     (/ y a)
     (if (<= z -1.3e-227)
       t_1
       (if (<= z 5.2e-62)
         (/ x (- t (* z a)))
         (if (<= z 1.02e+60) t_1 (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (y * z)) / t;
	double tmp;
	if (z <= -2.7e+73) {
		tmp = y / a;
	} else if (z <= -1.3e-227) {
		tmp = t_1;
	} else if (z <= 5.2e-62) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.02e+60) {
		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 - (y * z)) / t
    if (z <= (-2.7d+73)) then
        tmp = y / a
    else if (z <= (-1.3d-227)) then
        tmp = t_1
    else if (z <= 5.2d-62) then
        tmp = x / (t - (z * a))
    else if (z <= 1.02d+60) 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 - (y * z)) / t;
	double tmp;
	if (z <= -2.7e+73) {
		tmp = y / a;
	} else if (z <= -1.3e-227) {
		tmp = t_1;
	} else if (z <= 5.2e-62) {
		tmp = x / (t - (z * a));
	} else if (z <= 1.02e+60) {
		tmp = t_1;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (y * z)) / t
	tmp = 0
	if z <= -2.7e+73:
		tmp = y / a
	elif z <= -1.3e-227:
		tmp = t_1
	elif z <= 5.2e-62:
		tmp = x / (t - (z * a))
	elif z <= 1.02e+60:
		tmp = t_1
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(y * z)) / t)
	tmp = 0.0
	if (z <= -2.7e+73)
		tmp = Float64(y / a);
	elseif (z <= -1.3e-227)
		tmp = t_1;
	elseif (z <= 5.2e-62)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 1.02e+60)
		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 - (y * z)) / t;
	tmp = 0.0;
	if (z <= -2.7e+73)
		tmp = y / a;
	elseif (z <= -1.3e-227)
		tmp = t_1;
	elseif (z <= 5.2e-62)
		tmp = x / (t - (z * a));
	elseif (z <= 1.02e+60)
		tmp = t_1;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -2.7e+73], N[(y / a), $MachinePrecision], If[LessEqual[z, -1.3e-227], t$95$1, If[LessEqual[z, 5.2e-62], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.02e+60], t$95$1, N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6999999999999999e73 or 1.0200000000000001e60 < z

   1. Initial program 62.5%

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

      1. *-commutative 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in z around inf 66.4%

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

   if -2.6999999999999999e73 < z < -1.30000000000000006e-227 or 5.1999999999999999e-62 < z < 1.0200000000000001e60

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 70.4%

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

   if -1.30000000000000006e-227 < z < 5.1999999999999999e-62

   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. Taylor expanded in x around inf 86.8%

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

      1. *-commutative 86.8%

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

   6. Simplified 86.8%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-227}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+60}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 4: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.5e+73)
   (/ y a)
   (if (<= z -7e-165)
     (- (/ x t) (* z (/ y t)))
     (if (<= z 3e-62)
       (/ x (- t (* z a)))
       (if (<= z 2.1e+63) (/ (- x (* y z)) t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+73) {
		tmp = y / a;
	} else if (z <= -7e-165) {
		tmp = (x / t) - (z * (y / t));
	} else if (z <= 3e-62) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.1e+63) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-7.5d+73)) then
        tmp = y / a
    else if (z <= (-7d-165)) then
        tmp = (x / t) - (z * (y / t))
    else if (z <= 3d-62) then
        tmp = x / (t - (z * a))
    else if (z <= 2.1d+63) then
        tmp = (x - (y * z)) / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.5e+73) {
		tmp = y / a;
	} else if (z <= -7e-165) {
		tmp = (x / t) - (z * (y / t));
	} else if (z <= 3e-62) {
		tmp = x / (t - (z * a));
	} else if (z <= 2.1e+63) {
		tmp = (x - (y * z)) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.5e+73:
		tmp = y / a
	elif z <= -7e-165:
		tmp = (x / t) - (z * (y / t))
	elif z <= 3e-62:
		tmp = x / (t - (z * a))
	elif z <= 2.1e+63:
		tmp = (x - (y * z)) / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.5e+73)
		tmp = Float64(y / a);
	elseif (z <= -7e-165)
		tmp = Float64(Float64(x / t) - Float64(z * Float64(y / t)));
	elseif (z <= 3e-62)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 2.1e+63)
		tmp = Float64(Float64(x - Float64(y * z)) / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.5e+73)
		tmp = y / a;
	elseif (z <= -7e-165)
		tmp = (x / t) - (z * (y / t));
	elseif (z <= 3e-62)
		tmp = x / (t - (z * a));
	elseif (z <= 2.1e+63)
		tmp = (x - (y * z)) / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.5e+73], N[(y / a), $MachinePrecision], If[LessEqual[z, -7e-165], N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3e-62], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+63], N[(N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.5e73 or 2.1000000000000002e63 < z

   1. Initial program 62.5%

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

      1. *-commutative 62.5%

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

   3. Simplified 62.5%

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

   4. Taylor expanded in z around inf 66.4%

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

   if -7.5e73 < z < -7.0000000000000003e-165

   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. Taylor expanded in t around inf 71.2%

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

      1. div-sub 71.2%

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

      2. *-commutative 71.2%

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

   6. Applied egg-rr 71.2%

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

      1. clear-num 71.3%

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

      2. inv-pow 71.3%

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

      3. *-commutative 71.3%

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

      4. associate-/r* 73.6%

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

   8. Applied egg-rr 73.6%

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

      1. unpow-1 73.6%

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

   10. Simplified 73.6%

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

       1. associate-/r/ 73.5%

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

       2. clear-num 73.6%

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

   12. Applied egg-rr 73.6%

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

   if -7.0000000000000003e-165 < z < 3.0000000000000001e-62

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 84.1%

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

      1. *-commutative 84.1%

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

   6. Simplified 84.1%

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

   if 3.0000000000000001e-62 < z < 2.1000000000000002e63

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 66.5%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+73}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{x - y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 69.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-10} \lor \neg \left(a \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} + \frac{-1}{\frac{\frac{t}{y}}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.15e-10) (not (<= a 6.5e+33)))
   (- (/ y a) (/ (/ x a) z))
   (+ (/ x t) (/ -1.0 (/ (/ t y) z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e-10) || !(a <= 6.5e+33)) {
		tmp = (y / a) - ((x / a) / z);
	} else {
		tmp = (x / t) + (-1.0 / ((t / y) / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.15d-10)) .or. (.not. (a <= 6.5d+33))) then
        tmp = (y / a) - ((x / a) / z)
    else
        tmp = (x / t) + ((-1.0d0) / ((t / y) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.15e-10) || !(a <= 6.5e+33)) {
		tmp = (y / a) - ((x / a) / z);
	} else {
		tmp = (x / t) + (-1.0 / ((t / y) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.15e-10) or not (a <= 6.5e+33):
		tmp = (y / a) - ((x / a) / z)
	else:
		tmp = (x / t) + (-1.0 / ((t / y) / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.15e-10) || !(a <= 6.5e+33))
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	else
		tmp = Float64(Float64(x / t) + Float64(-1.0 / Float64(Float64(t / y) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.15e-10) || ~((a <= 6.5e+33)))
		tmp = (y / a) - ((x / a) / z);
	else
		tmp = (x / t) + (-1.0 / ((t / y) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.15e-10], N[Not[LessEqual[a, 6.5e+33]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] + N[(-1.0 / N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.15000000000000004e-10 or 6.49999999999999993e33 < a

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. associate--l+ 66.8%

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

      3. associate-/r* 69.7%

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

      4. associate-*r/ 69.7%

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

      5. associate-/r* 69.7%

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

      6. associate-*r/ 69.7%

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

      7. div-sub 69.7%

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

      8. distribute-lft-out-- 69.7%

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

      9. associate-*r/ 69.7%

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

      10. mul-1-neg 69.7%

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

      11. unsub-neg 69.7%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in x around inf 70.3%

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

      1. associate-/r* 73.2%

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

   9. Simplified 73.2%

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

   if -1.15000000000000004e-10 < a < 6.49999999999999993e33

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 75.0%

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

      1. div-sub 75.0%

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

      2. *-commutative 75.0%

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

   6. Applied egg-rr 75.0%

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

      1. clear-num 74.4%

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

      2. inv-pow 74.4%

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

      3. *-commutative 74.4%

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

      4. associate-/r* 76.4%

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

   8. Applied egg-rr 76.4%

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

      1. unpow-1 76.4%

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

   10. Simplified 76.4%

       \[\leadsto \frac{x}{t} - \color{blue}{\frac{1}{\frac{\frac{t}{y}}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{-10} \lor \neg \left(a \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} + \frac{-1}{\frac{\frac{t}{y}}{z}}\\ \end{array} \]

Alternative 6: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-62}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.12e+33)
   (/ y a)
   (if (<= z 3.4e-92)
     (/ x t)
     (if (<= z 5.6e-62)
       (/ (- x) (* z a))
       (if (<= z 6.8e+35)
         (* z (/ (- y) t))
         (if (<= z 3.7e+66) (/ x t) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+33) {
		tmp = y / a;
	} else if (z <= 3.4e-92) {
		tmp = x / t;
	} else if (z <= 5.6e-62) {
		tmp = -x / (z * a);
	} else if (z <= 6.8e+35) {
		tmp = z * (-y / t);
	} else if (z <= 3.7e+66) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.12d+33)) then
        tmp = y / a
    else if (z <= 3.4d-92) then
        tmp = x / t
    else if (z <= 5.6d-62) then
        tmp = -x / (z * a)
    else if (z <= 6.8d+35) then
        tmp = z * (-y / t)
    else if (z <= 3.7d+66) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+33) {
		tmp = y / a;
	} else if (z <= 3.4e-92) {
		tmp = x / t;
	} else if (z <= 5.6e-62) {
		tmp = -x / (z * a);
	} else if (z <= 6.8e+35) {
		tmp = z * (-y / t);
	} else if (z <= 3.7e+66) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.12e+33:
		tmp = y / a
	elif z <= 3.4e-92:
		tmp = x / t
	elif z <= 5.6e-62:
		tmp = -x / (z * a)
	elif z <= 6.8e+35:
		tmp = z * (-y / t)
	elif z <= 3.7e+66:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.12e+33)
		tmp = Float64(y / a);
	elseif (z <= 3.4e-92)
		tmp = Float64(x / t);
	elseif (z <= 5.6e-62)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 6.8e+35)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 3.7e+66)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.12e+33)
		tmp = y / a;
	elseif (z <= 3.4e-92)
		tmp = x / t;
	elseif (z <= 5.6e-62)
		tmp = -x / (z * a);
	elseif (z <= 6.8e+35)
		tmp = z * (-y / t);
	elseif (z <= 3.7e+66)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.12e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, 3.4e-92], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.6e-62], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.8e+35], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+66], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.12e33 or 3.7e66 < z

   1. Initial program 63.7%

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

      1. *-commutative 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around inf 63.1%

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

   if -1.12e33 < z < 3.4000000000000003e-92 or 6.8000000000000002e35 < z < 3.7e66

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 61.5%

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

   if 3.4000000000000003e-92 < z < 5.60000000000000005e-62

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 87.4%

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

      1. *-commutative 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in t around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. neg-mul-1 75.6%

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

      3. *-commutative 75.6%

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

   9. Simplified 75.6%

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

   if 5.60000000000000005e-62 < z < 6.8000000000000002e35

   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. Taylor expanded in t around inf 68.4%

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

      1. div-sub 68.4%

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

      2. *-commutative 68.4%

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

   6. Applied egg-rr 68.4%

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

      1. clear-num 68.4%

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

      2. inv-pow 68.4%

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

      3. *-commutative 68.4%

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

      4. associate-/r* 66.7%

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

   8. Applied egg-rr 66.7%

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

      1. unpow-1 66.7%

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

   10. Simplified 66.7%

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

   11. Taylor expanded in x around 0 53.8%

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

       1. associate-*l/ 49.3%

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

       2. *-commutative 49.3%

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

       3. neg-mul-1 49.3%

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

       4. distribute-rgt-neg-in 49.3%

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

   13. Simplified 49.3%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-62}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 7: 54.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-71}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+33)
   (/ y a)
   (if (<= z 5.2e-92)
     (/ x t)
     (if (<= z 1.95e-71)
       (/ (- x) (* z a))
       (if (<= z 4.2e+30) (/ (* y (- z)) t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+33) {
		tmp = y / a;
	} else if (z <= 5.2e-92) {
		tmp = x / t;
	} else if (z <= 1.95e-71) {
		tmp = -x / (z * a);
	} else if (z <= 4.2e+30) {
		tmp = (y * -z) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1d+33)) then
        tmp = y / a
    else if (z <= 5.2d-92) then
        tmp = x / t
    else if (z <= 1.95d-71) then
        tmp = -x / (z * a)
    else if (z <= 4.2d+30) then
        tmp = (y * -z) / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+33) {
		tmp = y / a;
	} else if (z <= 5.2e-92) {
		tmp = x / t;
	} else if (z <= 1.95e-71) {
		tmp = -x / (z * a);
	} else if (z <= 4.2e+30) {
		tmp = (y * -z) / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+33:
		tmp = y / a
	elif z <= 5.2e-92:
		tmp = x / t
	elif z <= 1.95e-71:
		tmp = -x / (z * a)
	elif z <= 4.2e+30:
		tmp = (y * -z) / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+33)
		tmp = Float64(y / a);
	elseif (z <= 5.2e-92)
		tmp = Float64(x / t);
	elseif (z <= 1.95e-71)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 4.2e+30)
		tmp = Float64(Float64(y * Float64(-z)) / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+33)
		tmp = y / a;
	elseif (z <= 5.2e-92)
		tmp = x / t;
	elseif (z <= 1.95e-71)
		tmp = -x / (z * a);
	elseif (z <= 4.2e+30)
		tmp = (y * -z) / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, 5.2e-92], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.95e-71], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+30], N[(N[(y * (-z)), $MachinePrecision] / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.9999999999999995e32 or 4.2e30 < z

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in z around inf 60.8%

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

   if -9.9999999999999995e32 < z < 5.2e-92

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 62.0%

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

   if 5.2e-92 < z < 1.9500000000000001e-71

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 87.4%

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

      1. *-commutative 87.4%

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

   6. Simplified 87.4%

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

   7. Taylor expanded in t around 0 75.6%

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

      1. associate-*r/ 75.6%

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

      2. neg-mul-1 75.6%

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

      3. *-commutative 75.6%

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

   9. Simplified 75.6%

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

   if 1.9500000000000001e-71 < z < 4.2e30

   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. Taylor expanded in t around inf 68.4%

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

   5. Taylor expanded in x around 0 53.8%

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

      1. associate-*r* 53.8%

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

      2. neg-mul-1 53.8%

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

   7. Simplified 53.8%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-71}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+30}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 8: 69.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-11} \lor \neg \left(a \leq 2.45 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.5e-11) (not (<= a 2.45e+33)))
   (- (/ y a) (/ (/ x a) z))
   (- (/ x t) (* z (/ y t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e-11) || !(a <= 2.45e+33)) {
		tmp = (y / a) - ((x / a) / z);
	} else {
		tmp = (x / t) - (z * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-7.5d-11)) .or. (.not. (a <= 2.45d+33))) then
        tmp = (y / a) - ((x / a) / z)
    else
        tmp = (x / t) - (z * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e-11) || !(a <= 2.45e+33)) {
		tmp = (y / a) - ((x / a) / z);
	} else {
		tmp = (x / t) - (z * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.5e-11) or not (a <= 2.45e+33):
		tmp = (y / a) - ((x / a) / z)
	else:
		tmp = (x / t) - (z * (y / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.5e-11) || !(a <= 2.45e+33))
		tmp = Float64(Float64(y / a) - Float64(Float64(x / a) / z));
	else
		tmp = Float64(Float64(x / t) - Float64(z * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.5e-11) || ~((a <= 2.45e+33)))
		tmp = (y / a) - ((x / a) / z);
	else
		tmp = (x / t) - (z * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.5e-11], N[Not[LessEqual[a, 2.45e+33]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / t), $MachinePrecision] - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.5e-11 or 2.45000000000000007e33 < a

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   4. Taylor expanded in z around inf 66.8%

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

      1. +-commutative 66.8%

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

      2. associate--l+ 66.8%

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

      3. associate-/r* 69.7%

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

      4. associate-*r/ 69.7%

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

      5. associate-/r* 69.7%

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

      6. associate-*r/ 69.7%

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

      7. div-sub 69.7%

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

      8. distribute-lft-out-- 69.7%

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

      9. associate-*r/ 69.7%

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

      10. mul-1-neg 69.7%

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

      11. unsub-neg 69.7%

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

   6. Simplified 72.4%

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

   7. Taylor expanded in x around inf 70.3%

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

      1. associate-/r* 73.2%

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

   9. Simplified 73.2%

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

   if -7.5e-11 < a < 2.45000000000000007e33

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 75.0%

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

      1. div-sub 75.0%

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

      2. *-commutative 75.0%

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

   6. Applied egg-rr 75.0%

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

      1. clear-num 74.4%

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

      2. inv-pow 74.4%

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

      3. *-commutative 74.4%

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

      4. associate-/r* 76.4%

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

   8. Applied egg-rr 76.4%

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

      1. unpow-1 76.4%

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

   10. Simplified 76.4%

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

       1. associate-/r/ 75.2%

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

       2. clear-num 75.9%

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

   12. Applied egg-rr 75.9%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{-11} \lor \neg \left(a \leq 2.45 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{y}{a} - \frac{\frac{x}{a}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t} - z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 9: 53.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.12e+33)
   (/ y a)
   (if (<= z 6.5e-92)
     (/ x t)
     (if (<= z 1.5e+31)
       (* z (/ (- y) t))
       (if (<= z 6.5e+59) (/ x t) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+33) {
		tmp = y / a;
	} else if (z <= 6.5e-92) {
		tmp = x / t;
	} else if (z <= 1.5e+31) {
		tmp = z * (-y / t);
	} else if (z <= 6.5e+59) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.12d+33)) then
        tmp = y / a
    else if (z <= 6.5d-92) then
        tmp = x / t
    else if (z <= 1.5d+31) then
        tmp = z * (-y / t)
    else if (z <= 6.5d+59) then
        tmp = x / t
    else
        tmp = y / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.12e+33) {
		tmp = y / a;
	} else if (z <= 6.5e-92) {
		tmp = x / t;
	} else if (z <= 1.5e+31) {
		tmp = z * (-y / t);
	} else if (z <= 6.5e+59) {
		tmp = x / t;
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.12e+33:
		tmp = y / a
	elif z <= 6.5e-92:
		tmp = x / t
	elif z <= 1.5e+31:
		tmp = z * (-y / t)
	elif z <= 6.5e+59:
		tmp = x / t
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.12e+33)
		tmp = Float64(y / a);
	elseif (z <= 6.5e-92)
		tmp = Float64(x / t);
	elseif (z <= 1.5e+31)
		tmp = Float64(z * Float64(Float64(-y) / t));
	elseif (z <= 6.5e+59)
		tmp = Float64(x / t);
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.12e+33)
		tmp = y / a;
	elseif (z <= 6.5e-92)
		tmp = x / t;
	elseif (z <= 1.5e+31)
		tmp = z * (-y / t);
	elseif (z <= 6.5e+59)
		tmp = x / t;
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.12e+33], N[(y / a), $MachinePrecision], If[LessEqual[z, 6.5e-92], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.5e+31], N[(z * N[((-y) / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e+59], N[(x / t), $MachinePrecision], N[(y / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12e33 or 6.50000000000000021e59 < z

   1. Initial program 64.1%

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

      1. *-commutative 64.1%

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

   3. Simplified 64.1%

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

   4. Taylor expanded in z around inf 63.4%

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

   if -1.12e33 < z < 6.50000000000000035e-92 or 1.49999999999999995e31 < z < 6.50000000000000021e59

   1. Initial program 99.0%

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

      1. *-commutative 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in z around 0 61.9%

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

   if 6.50000000000000035e-92 < z < 1.49999999999999995e31

   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. Taylor expanded in t around inf 56.7%

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

      1. div-sub 56.7%

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

      2. *-commutative 56.7%

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

   6. Applied egg-rr 56.7%

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

      1. clear-num 56.7%

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

      2. inv-pow 56.7%

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

      3. *-commutative 56.7%

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

      4. associate-/r* 55.4%

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

   8. Applied egg-rr 55.4%

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

      1. unpow-1 55.4%

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

   10. Simplified 55.4%

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

   11. Taylor expanded in x around 0 42.8%

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

       1. associate-*l/ 39.6%

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

       2. *-commutative 39.6%

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

       3. neg-mul-1 39.6%

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

       4. distribute-rgt-neg-in 39.6%

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

   13. Simplified 39.6%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-92}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{-y}{t}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 10: 54.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+33} \lor \neg \left(z \leq 10.5\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+33) (not (<= z 10.5))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+33) || !(z <= 10.5)) {
		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 <= (-1.15d+33)) .or. (.not. (z <= 10.5d0))) 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 <= -1.15e+33) || !(z <= 10.5)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+33) or not (z <= 10.5):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+33) || !(z <= 10.5))
		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 <= -1.15e+33) || ~((z <= 10.5)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+33], N[Not[LessEqual[z, 10.5]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15000000000000005e33 or 10.5 < z

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in z around inf 59.6%

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

   if -1.15000000000000005e33 < z < 10.5

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 55.9%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+33} \lor \neg \left(z \leq 10.5\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 11: 35.5% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.6%

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

   1. *-commutative 83.6%

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

3. Simplified 83.6%

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

4. Taylor expanded in z around 0 34.0%

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

5. Final simplification 34.0%

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

Developer target: 97.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023307 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Tridiagonal:solveTriDiagonal from diagrams-solve-0.1, A"
  :precision binary64

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

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