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

Percentage Accurate: 85.6% → 97.7%

Time: 14.6s

Alternatives: 14

Speedup: 0.6×

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: 85.6% 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: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ \mathbf{if}\;z \leq -2 \cdot 10^{-44} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\frac{x}{t_1} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))))
   (if (or (<= z -2e-44) (not (<= z 90000000.0)))
     (- (/ x t_1) (/ y (- (/ t z) a)))
     (/ (- x (* z y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double tmp;
	if ((z <= -2e-44) || !(z <= 90000000.0)) {
		tmp = (x / t_1) - (y / ((t / z) - a));
	} else {
		tmp = (x - (z * y)) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t - (z * a)
    if ((z <= (-2d-44)) .or. (.not. (z <= 90000000.0d0))) then
        tmp = (x / t_1) - (y / ((t / z) - a))
    else
        tmp = (x - (z * y)) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double tmp;
	if ((z <= -2e-44) || !(z <= 90000000.0)) {
		tmp = (x / t_1) - (y / ((t / z) - a));
	} else {
		tmp = (x - (z * y)) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	tmp = 0
	if (z <= -2e-44) or not (z <= 90000000.0):
		tmp = (x / t_1) - (y / ((t / z) - a))
	else:
		tmp = (x - (z * y)) / t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	tmp = 0.0
	if ((z <= -2e-44) || !(z <= 90000000.0))
		tmp = Float64(Float64(x / t_1) - Float64(y / Float64(Float64(t / z) - a)));
	else
		tmp = Float64(Float64(x - Float64(z * y)) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	tmp = 0.0;
	if ((z <= -2e-44) || ~((z <= 90000000.0)))
		tmp = (x / t_1) - (y / ((t / z) - a));
	else
		tmp = (x - (z * y)) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -2e-44], N[Not[LessEqual[z, 90000000.0]], $MachinePrecision]], N[(N[(x / t$95$1), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.99999999999999991e-44 or 9e7 < z

   1. Initial program 69.1%

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

      1. *-commutative 69.1%

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

   3. Simplified 69.1%

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

      1. clear-num 68.5%

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

      2. associate-/r/ 69.1%

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

      3. sub-neg 69.1%

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

      4. +-commutative 69.1%

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

      5. *-commutative 69.1%

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

      6. distribute-rgt-neg-in 69.1%

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

      7. fma-def 69.1%

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

   5. Applied egg-rr 69.1%

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

   6. Taylor expanded in x around 0 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. mul-1-neg 69.1%

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

      5. sub-neg 69.1%

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

      6. *-commutative 69.1%

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

      7. associate-/l* 81.7%

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

      8. mul-1-neg 81.7%

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

      9. sub-neg 81.7%

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

      10. *-commutative 81.7%

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

      11. div-sub 81.7%

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

      12. *-commutative 81.7%

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

      13. associate-*l/ 86.3%

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

      14. associate-/r/ 95.8%

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

      15. *-inverses 95.8%

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

      16. /-rgt-identity 95.8%

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

   8. Simplified 95.8%

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

   if -1.99999999999999991e-44 < z < 9e7

   1. Initial program 99.9%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-44} \lor \neg \left(z \leq 90000000\right):\\ \;\;\;\;\frac{x}{t - z \cdot a} - \frac{y}{\frac{t}{z} - a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \end{array} \]

Alternative 2: 93.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - z \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{-y}{t_1}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-305} \lor \neg \left(t_2 \leq 0\right) \land t_2 \leq 10^{+291}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z} - \frac{y}{\frac{t}{z} - a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* z y)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* z (/ (- y) t_1))
     (if (or (<= t_2 -1e-305) (and (not (<= t_2 0.0)) (<= t_2 1e+291)))
       t_2
       (- (/ (/ (- x) a) z) (/ y (- (/ t z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (z * y)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (-y / t_1);
	} else if ((t_2 <= -1e-305) || (!(t_2 <= 0.0) && (t_2 <= 1e+291))) {
		tmp = t_2;
	} else {
		tmp = ((-x / a) / z) - (y / ((t / z) - a));
	}
	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 - (z * y)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (-y / t_1);
	} else if ((t_2 <= -1e-305) || (!(t_2 <= 0.0) && (t_2 <= 1e+291))) {
		tmp = t_2;
	} else {
		tmp = ((-x / a) / z) - (y / ((t / z) - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (x - (z * y)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * (-y / t_1)
	elif (t_2 <= -1e-305) or (not (t_2 <= 0.0) and (t_2 <= 1e+291)):
		tmp = t_2
	else:
		tmp = ((-x / a) / z) - (y / ((t / z) - a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(z * y)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(-y) / t_1));
	elseif ((t_2 <= -1e-305) || (!(t_2 <= 0.0) && (t_2 <= 1e+291)))
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(Float64(-x) / a) / z) - Float64(y / Float64(Float64(t / z) - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (x - (z * y)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * (-y / t_1);
	elseif ((t_2 <= -1e-305) || (~((t_2 <= 0.0)) && (t_2 <= 1e+291)))
		tmp = t_2;
	else
		tmp = ((-x / a) / z) - (y / ((t / z) - a));
	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[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[((-y) / t$95$1), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, -1e-305], And[N[Not[LessEqual[t$95$2, 0.0]], $MachinePrecision], LessEqual[t$95$2, 1e+291]]], t$95$2, N[(N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision] - N[(y / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $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 48.7%

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

      1. *-commutative 48.7%

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

   3. Simplified 48.7%

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

   4. Taylor expanded in x around 0 21.9%

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

      1. mul-1-neg 21.9%

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

      2. associate-/l* 73.0%

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

      3. associate-/r/ 77.1%

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

      4. cancel-sign-sub-inv 77.1%

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

      5. +-commutative 77.1%

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

      6. distribute-lft-neg-in 77.1%

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

      7. distribute-rgt-neg-in 77.1%

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

      8. fma-udef 77.1%

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

      9. distribute-rgt-neg-in 77.1%

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

      10. fma-udef 77.1%

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

      11. distribute-rgt-neg-in 77.1%

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

      12. distribute-lft-neg-in 77.1%

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

      13. +-commutative 77.1%

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

      14. cancel-sign-sub-inv 77.1%

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

      15. *-commutative 77.1%

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

   6. Simplified 77.1%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -9.99999999999999996e-306 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 9.9999999999999996e290

   1. Initial program 99.7%

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

   if -9.99999999999999996e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0 or 9.9999999999999996e290 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 46.0%

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

      1. *-commutative 46.0%

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

   3. Simplified 46.0%

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

      1. clear-num 45.0%

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

      2. associate-/r/ 46.0%

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

      3. sub-neg 46.0%

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

      4. +-commutative 46.0%

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

      5. *-commutative 46.0%

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

      6. distribute-rgt-neg-in 46.0%

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

      7. fma-def 46.0%

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

   5. Applied egg-rr 46.0%

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

   6. Taylor expanded in x around 0 44.4%

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

      1. +-commutative 44.4%

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

      2. mul-1-neg 44.4%

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

      3. unsub-neg 44.4%

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

      4. mul-1-neg 44.4%

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

      5. sub-neg 44.4%

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

      6. *-commutative 44.4%

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

      7. associate-/l* 55.8%

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

      8. mul-1-neg 55.8%

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

      9. sub-neg 55.8%

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

      10. *-commutative 55.8%

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

      11. div-sub 55.8%

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

      12. *-commutative 55.8%

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

      13. associate-*l/ 85.6%

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

      14. associate-/r/ 88.9%

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

      15. *-inverses 88.9%

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

      16. /-rgt-identity 88.9%

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

   8. Simplified 88.9%

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

   9. Taylor expanded in t around 0 77.9%

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

       1. mul-1-neg 34.4%

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

       2. associate-/r* 46.5%

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

   11. Simplified 88.9%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - z \cdot y}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;z \cdot \frac{-y}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - z \cdot y}{t - z \cdot a} \leq -1 \cdot 10^{-305} \lor \neg \left(\frac{x - z \cdot y}{t - z \cdot a} \leq 0\right) \land \frac{x - z \cdot y}{t - z \cdot a} \leq 10^{+291}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z} - \frac{y}{\frac{t}{z} - a}\\ \end{array} \]

Alternative 3: 93.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t - z \cdot a\\ t_2 := \frac{x - z \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{-y}{t_1}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{elif}\;t_2 \leq 10^{+291}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(1 - \frac{x}{z \cdot y}\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- t (* z a))) (t_2 (/ (- x (* z y)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* z (/ (- y) t_1))
     (if (<= t_2 -1e-305)
       t_2
       (if (<= t_2 0.0)
         (/ (- y) (- (/ t z) a))
         (if (<= t_2 1e+291) t_2 (/ (* y (- 1.0 (/ x (* z y)))) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t - (z * a);
	double t_2 = (x - (z * y)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (-y / t_1);
	} else if (t_2 <= -1e-305) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -y / ((t / z) - a);
	} else if (t_2 <= 1e+291) {
		tmp = t_2;
	} else {
		tmp = (y * (1.0 - (x / (z * y)))) / a;
	}
	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 - (z * y)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (-y / t_1);
	} else if (t_2 <= -1e-305) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = -y / ((t / z) - a);
	} else if (t_2 <= 1e+291) {
		tmp = t_2;
	} else {
		tmp = (y * (1.0 - (x / (z * y)))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t - (z * a)
	t_2 = (x - (z * y)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * (-y / t_1)
	elif t_2 <= -1e-305:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = -y / ((t / z) - a)
	elif t_2 <= 1e+291:
		tmp = t_2
	else:
		tmp = (y * (1.0 - (x / (z * y)))) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t - Float64(z * a))
	t_2 = Float64(Float64(x - Float64(z * y)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(-y) / t_1));
	elseif (t_2 <= -1e-305)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(-y) / Float64(Float64(t / z) - a));
	elseif (t_2 <= 1e+291)
		tmp = t_2;
	else
		tmp = Float64(Float64(y * Float64(1.0 - Float64(x / Float64(z * y)))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t - (z * a);
	t_2 = (x - (z * y)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * (-y / t_1);
	elseif (t_2 <= -1e-305)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = -y / ((t / z) - a);
	elseif (t_2 <= 1e+291)
		tmp = t_2;
	else
		tmp = (y * (1.0 - (x / (z * y)))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[((-y) / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -1e-305], t$95$2, If[LessEqual[t$95$2, 0.0], N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+291], t$95$2, N[(N[(y * N[(1.0 - N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 48.7%

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

      1. *-commutative 48.7%

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

   3. Simplified 48.7%

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

   4. Taylor expanded in x around 0 21.9%

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

      1. mul-1-neg 21.9%

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

      2. associate-/l* 73.0%

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

      3. associate-/r/ 77.1%

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

      4. cancel-sign-sub-inv 77.1%

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

      5. +-commutative 77.1%

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

      6. distribute-lft-neg-in 77.1%

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

      7. distribute-rgt-neg-in 77.1%

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

      8. fma-udef 77.1%

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

      9. distribute-rgt-neg-in 77.1%

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

      10. fma-udef 77.1%

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

      11. distribute-rgt-neg-in 77.1%

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

      12. distribute-lft-neg-in 77.1%

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

      13. +-commutative 77.1%

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

      14. cancel-sign-sub-inv 77.1%

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

      15. *-commutative 77.1%

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

   6. Simplified 77.1%

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

   if -inf.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -9.99999999999999996e-306 or -0.0 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < 9.9999999999999996e290

   1. Initial program 99.7%

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

   if -9.99999999999999996e-306 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z))) < -0.0

   1. Initial program 63.2%

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

      1. *-commutative 63.2%

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

   3. Simplified 63.2%

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

      1. clear-num 61.4%

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

      2. associate-/r/ 63.2%

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

      3. sub-neg 63.2%

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

      4. +-commutative 63.2%

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

      5. *-commutative 63.2%

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

      6. distribute-rgt-neg-in 63.2%

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

      7. fma-def 63.2%

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

   5. Applied egg-rr 63.2%

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

   6. Taylor expanded in x around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-/l* 63.2%

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

      3. distribute-neg-frac 63.2%

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

      4. mul-1-neg 63.2%

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

      5. sub-neg 63.2%

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

      6. *-commutative 63.2%

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

      7. div-sub 63.2%

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

      8. *-commutative 63.2%

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

      9. associate-*l/ 80.3%

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

      10. associate-/r/ 83.2%

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

      11. *-inverses 83.2%

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

      12. /-rgt-identity 83.2%

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

   8. Simplified 83.2%

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

   if 9.9999999999999996e290 < (/.f64 (-.f64 x (*.f64 y z)) (-.f64 t (*.f64 a z)))

   1. Initial program 23.7%

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

      1. *-commutative 23.7%

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

   3. Simplified 23.7%

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

   4. Taylor expanded in t around 0 23.6%

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

      1. associate-*r* 23.6%

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

      2. neg-mul-1 23.6%

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

      3. *-commutative 23.6%

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

   6. Simplified 23.6%

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

   7. Taylor expanded in x around 0 81.9%

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

      1. +-commutative 81.9%

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

      2. mul-1-neg 81.9%

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

      3. unsub-neg 81.9%

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

      4. *-commutative 81.9%

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

   9. Simplified 81.9%

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

       1. clear-num 81.7%

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

       2. associate-/r* 81.7%

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

       3. frac-sub 64.1%

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

       4. *-un-lft-identity 64.1%

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

   11. Applied egg-rr 64.1%

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

   12. Taylor expanded in a around 0 89.3%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - z \cdot y}{t - z \cdot a} \leq -\infty:\\ \;\;\;\;z \cdot \frac{-y}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - z \cdot y}{t - z \cdot a} \leq -1 \cdot 10^{-305}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{elif}\;\frac{x - z \cdot y}{t - z \cdot a} \leq 0:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{elif}\;\frac{x - z \cdot y}{t - z \cdot a} \leq 10^{+291}:\\ \;\;\;\;\frac{x - z \cdot y}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(1 - \frac{x}{z \cdot y}\right)}{a}\\ \end{array} \]

Alternative 4: 49.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4800000:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+124}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+222}:\\ \;\;\;\;-\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.1e+152)
   (/ y a)
   (if (<= z -4800000.0)
     (/ (/ (- x) z) a)
     (if (<= z -2.9e-69)
       (/ y a)
       (if (<= z 5.2e-84)
         (/ x t)
         (if (<= z 1.05e+35)
           (/ (/ (- x) a) z)
           (if (<= z 5.3e+42)
             (/ x t)
             (if (<= z 6.2e+92)
               (/ y a)
               (if (<= z 1.75e+124)
                 (/ (- x) (* z a))
                 (if (<= z 3.6e+222) (- (/ y (/ t z))) (/ y a)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.1e+152) {
		tmp = y / a;
	} else if (z <= -4800000.0) {
		tmp = (-x / z) / a;
	} else if (z <= -2.9e-69) {
		tmp = y / a;
	} else if (z <= 5.2e-84) {
		tmp = x / t;
	} else if (z <= 1.05e+35) {
		tmp = (-x / a) / z;
	} else if (z <= 5.3e+42) {
		tmp = x / t;
	} else if (z <= 6.2e+92) {
		tmp = y / a;
	} else if (z <= 1.75e+124) {
		tmp = -x / (z * a);
	} else if (z <= 3.6e+222) {
		tmp = -(y / (t / z));
	} 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 <= (-1.1d+152)) then
        tmp = y / a
    else if (z <= (-4800000.0d0)) then
        tmp = (-x / z) / a
    else if (z <= (-2.9d-69)) then
        tmp = y / a
    else if (z <= 5.2d-84) then
        tmp = x / t
    else if (z <= 1.05d+35) then
        tmp = (-x / a) / z
    else if (z <= 5.3d+42) then
        tmp = x / t
    else if (z <= 6.2d+92) then
        tmp = y / a
    else if (z <= 1.75d+124) then
        tmp = -x / (z * a)
    else if (z <= 3.6d+222) then
        tmp = -(y / (t / z))
    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 <= -1.1e+152) {
		tmp = y / a;
	} else if (z <= -4800000.0) {
		tmp = (-x / z) / a;
	} else if (z <= -2.9e-69) {
		tmp = y / a;
	} else if (z <= 5.2e-84) {
		tmp = x / t;
	} else if (z <= 1.05e+35) {
		tmp = (-x / a) / z;
	} else if (z <= 5.3e+42) {
		tmp = x / t;
	} else if (z <= 6.2e+92) {
		tmp = y / a;
	} else if (z <= 1.75e+124) {
		tmp = -x / (z * a);
	} else if (z <= 3.6e+222) {
		tmp = -(y / (t / z));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.1e+152:
		tmp = y / a
	elif z <= -4800000.0:
		tmp = (-x / z) / a
	elif z <= -2.9e-69:
		tmp = y / a
	elif z <= 5.2e-84:
		tmp = x / t
	elif z <= 1.05e+35:
		tmp = (-x / a) / z
	elif z <= 5.3e+42:
		tmp = x / t
	elif z <= 6.2e+92:
		tmp = y / a
	elif z <= 1.75e+124:
		tmp = -x / (z * a)
	elif z <= 3.6e+222:
		tmp = -(y / (t / z))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.1e+152)
		tmp = Float64(y / a);
	elseif (z <= -4800000.0)
		tmp = Float64(Float64(Float64(-x) / z) / a);
	elseif (z <= -2.9e-69)
		tmp = Float64(y / a);
	elseif (z <= 5.2e-84)
		tmp = Float64(x / t);
	elseif (z <= 1.05e+35)
		tmp = Float64(Float64(Float64(-x) / a) / z);
	elseif (z <= 5.3e+42)
		tmp = Float64(x / t);
	elseif (z <= 6.2e+92)
		tmp = Float64(y / a);
	elseif (z <= 1.75e+124)
		tmp = Float64(Float64(-x) / Float64(z * a));
	elseif (z <= 3.6e+222)
		tmp = Float64(-Float64(y / Float64(t / z)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.1e+152)
		tmp = y / a;
	elseif (z <= -4800000.0)
		tmp = (-x / z) / a;
	elseif (z <= -2.9e-69)
		tmp = y / a;
	elseif (z <= 5.2e-84)
		tmp = x / t;
	elseif (z <= 1.05e+35)
		tmp = (-x / a) / z;
	elseif (z <= 5.3e+42)
		tmp = x / t;
	elseif (z <= 6.2e+92)
		tmp = y / a;
	elseif (z <= 1.75e+124)
		tmp = -x / (z * a);
	elseif (z <= 3.6e+222)
		tmp = -(y / (t / z));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.1e+152], N[(y / a), $MachinePrecision], If[LessEqual[z, -4800000.0], N[(N[((-x) / z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, -2.9e-69], N[(y / a), $MachinePrecision], If[LessEqual[z, 5.2e-84], N[(x / t), $MachinePrecision], If[LessEqual[z, 1.05e+35], N[(N[((-x) / a), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 5.3e+42], N[(x / t), $MachinePrecision], If[LessEqual[z, 6.2e+92], N[(y / a), $MachinePrecision], If[LessEqual[z, 1.75e+124], N[((-x) / N[(z * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+222], (-N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), N[(y / a), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.0999999999999999e152 or -4.8e6 < z < -2.8999999999999998e-69 or 5.30000000000000028e42 < z < 6.2000000000000004e92 or 3.6000000000000002e222 < z

   1. Initial program 58.6%

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

      1. *-commutative 58.6%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in z around inf 69.9%

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

   if -1.0999999999999999e152 < z < -4.8e6

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in x around inf 63.8%

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

      1. *-commutative 63.8%

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

   6. Simplified 63.8%

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

   7. Taylor expanded in t around 0 48.8%

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

      1. associate-*r/ 48.8%

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

      2. neg-mul-1 48.8%

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

      3. *-commutative 48.8%

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

   9. Simplified 48.8%

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

   10. Taylor expanded in x around 0 48.8%

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

       1. mul-1-neg 48.8%

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

       2. associate-/l/ 54.2%

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

       3. distribute-neg-frac 54.2%

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

   12. Simplified 54.2%

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

   if -2.8999999999999998e-69 < z < 5.2e-84 or 1.0499999999999999e35 < z < 5.30000000000000028e42

   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 z around 0 66.2%

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

   if 5.2e-84 < z < 1.0499999999999999e35

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in x around inf 65.3%

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

      1. *-commutative 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in t around 0 43.4%

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

      1. mul-1-neg 43.4%

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

      2. associate-/r* 51.4%

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

   9. Simplified 51.4%

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

   if 6.2000000000000004e92 < z < 1.7500000000000001e124

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 74.1%

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

      1. *-commutative 74.1%

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

   6. Simplified 74.1%

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

   7. Taylor expanded in t around 0 47.8%

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

      1. associate-*r/ 47.8%

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

      2. neg-mul-1 47.8%

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

      3. *-commutative 47.8%

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

   9. Simplified 47.8%

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

   if 1.7500000000000001e124 < z < 3.6000000000000002e222

   1. Initial program 66.3%

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

      1. *-commutative 66.3%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in x around 0 33.7%

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

      1. mul-1-neg 33.7%

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

      2. associate-/l* 54.4%

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

      3. *-commutative 54.4%

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

   6. Simplified 54.4%

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

   7. Taylor expanded in t around inf 49.9%

      \[\leadsto -\frac{y}{\color{blue}{\frac{t}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+152}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4800000:\\ \;\;\;\;\frac{\frac{-x}{z}}{a}\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-84}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+35}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+124}:\\ \;\;\;\;\frac{-x}{z \cdot a}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+222}:\\ \;\;\;\;-\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 5: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{t}{z} - a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ t_3 := \frac{x - z \cdot y}{t}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 38000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (- (/ t z) a)))
        (t_2 (/ (- y (/ x z)) a))
        (t_3 (/ (- x (* z y)) t)))
   (if (<= z -3.2e+81)
     t_2
     (if (<= z -4e+52)
       t_1
       (if (<= z -1.1e-10)
         t_2
         (if (<= z 2.85e-74)
           t_3
           (if (<= z 1.15e-34)
             (/ x (- t (* z a)))
             (if (<= z 38000000.0) t_3 (if (<= z 3.5e+62) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double t_2 = (y - (x / z)) / a;
	double t_3 = (x - (z * y)) / t;
	double tmp;
	if (z <= -3.2e+81) {
		tmp = t_2;
	} else if (z <= -4e+52) {
		tmp = t_1;
	} else if (z <= -1.1e-10) {
		tmp = t_2;
	} else if (z <= 2.85e-74) {
		tmp = t_3;
	} else if (z <= 1.15e-34) {
		tmp = x / (t - (z * a));
	} else if (z <= 38000000.0) {
		tmp = t_3;
	} else if (z <= 3.5e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = -y / ((t / z) - a)
    t_2 = (y - (x / z)) / a
    t_3 = (x - (z * y)) / t
    if (z <= (-3.2d+81)) then
        tmp = t_2
    else if (z <= (-4d+52)) then
        tmp = t_1
    else if (z <= (-1.1d-10)) then
        tmp = t_2
    else if (z <= 2.85d-74) then
        tmp = t_3
    else if (z <= 1.15d-34) then
        tmp = x / (t - (z * a))
    else if (z <= 38000000.0d0) then
        tmp = t_3
    else if (z <= 3.5d+62) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double t_2 = (y - (x / z)) / a;
	double t_3 = (x - (z * y)) / t;
	double tmp;
	if (z <= -3.2e+81) {
		tmp = t_2;
	} else if (z <= -4e+52) {
		tmp = t_1;
	} else if (z <= -1.1e-10) {
		tmp = t_2;
	} else if (z <= 2.85e-74) {
		tmp = t_3;
	} else if (z <= 1.15e-34) {
		tmp = x / (t - (z * a));
	} else if (z <= 38000000.0) {
		tmp = t_3;
	} else if (z <= 3.5e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((t / z) - a)
	t_2 = (y - (x / z)) / a
	t_3 = (x - (z * y)) / t
	tmp = 0
	if z <= -3.2e+81:
		tmp = t_2
	elif z <= -4e+52:
		tmp = t_1
	elif z <= -1.1e-10:
		tmp = t_2
	elif z <= 2.85e-74:
		tmp = t_3
	elif z <= 1.15e-34:
		tmp = x / (t - (z * a))
	elif z <= 38000000.0:
		tmp = t_3
	elif z <= 3.5e+62:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(t / z) - a))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	t_3 = Float64(Float64(x - Float64(z * y)) / t)
	tmp = 0.0
	if (z <= -3.2e+81)
		tmp = t_2;
	elseif (z <= -4e+52)
		tmp = t_1;
	elseif (z <= -1.1e-10)
		tmp = t_2;
	elseif (z <= 2.85e-74)
		tmp = t_3;
	elseif (z <= 1.15e-34)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 38000000.0)
		tmp = t_3;
	elseif (z <= 3.5e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((t / z) - a);
	t_2 = (y - (x / z)) / a;
	t_3 = (x - (z * y)) / t;
	tmp = 0.0;
	if (z <= -3.2e+81)
		tmp = t_2;
	elseif (z <= -4e+52)
		tmp = t_1;
	elseif (z <= -1.1e-10)
		tmp = t_2;
	elseif (z <= 2.85e-74)
		tmp = t_3;
	elseif (z <= 1.15e-34)
		tmp = x / (t - (z * a));
	elseif (z <= 38000000.0)
		tmp = t_3;
	elseif (z <= 3.5e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[z, -3.2e+81], t$95$2, If[LessEqual[z, -4e+52], t$95$1, If[LessEqual[z, -1.1e-10], t$95$2, If[LessEqual[z, 2.85e-74], t$95$3, If[LessEqual[z, 1.15e-34], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 38000000.0], t$95$3, If[LessEqual[z, 3.5e+62], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2e81 or -4e52 < z < -1.09999999999999995e-10 or 3.8e7 < z < 3.49999999999999984e62

   1. Initial program 76.1%

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

      1. *-commutative 76.1%

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

   3. Simplified 76.1%

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

      1. clear-num 76.0%

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

      2. associate-/r/ 76.1%

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

      3. sub-neg 76.1%

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

      4. +-commutative 76.1%

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

      5. *-commutative 76.1%

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

      6. distribute-rgt-neg-in 76.1%

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

      7. fma-def 76.1%

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

   5. Applied egg-rr 76.1%

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

   6. Taylor expanded in x around 0 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. mul-1-neg 76.1%

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

      5. sub-neg 76.1%

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

      6. *-commutative 76.1%

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

      7. associate-/l* 80.9%

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

      8. mul-1-neg 80.9%

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

      9. sub-neg 80.9%

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

      10. *-commutative 80.9%

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

      11. div-sub 80.9%

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

      12. *-commutative 80.9%

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

      13. associate-*l/ 81.4%

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

      14. associate-/r/ 92.2%

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

      15. *-inverses 92.2%

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

      16. /-rgt-identity 92.2%

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

   8. Simplified 92.2%

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

   9. Taylor expanded in t around 0 79.6%

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

       1. sub-neg 79.6%

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

       2. mul-1-neg 79.6%

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

       3. remove-double-neg 79.6%

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

       4. +-commutative 79.6%

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

       5. mul-1-neg 79.6%

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

       6. associate-/l/ 87.1%

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

       7. sub-neg 87.1%

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

       8. div-sub 87.1%

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

   11. Simplified 87.1%

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

   if -3.2e81 < z < -4e52 or 3.49999999999999984e62 < z

   1. Initial program 61.2%

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

      1. *-commutative 61.2%

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

   3. Simplified 61.2%

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

      1. clear-num 60.2%

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

      2. associate-/r/ 61.1%

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

      3. sub-neg 61.1%

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

      4. +-commutative 61.1%

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

      5. *-commutative 61.1%

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

      6. distribute-rgt-neg-in 61.1%

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

      7. fma-def 61.1%

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

   5. Applied egg-rr 61.1%

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

   6. Taylor expanded in x around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-/l* 56.4%

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

      3. distribute-neg-frac 56.4%

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

      4. mul-1-neg 56.4%

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

      5. sub-neg 56.4%

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

      6. *-commutative 56.4%

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

      7. div-sub 56.4%

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

      8. *-commutative 56.4%

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

      9. associate-*l/ 69.7%

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

      10. associate-/r/ 73.7%

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

      11. *-inverses 73.7%

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

      12. /-rgt-identity 73.7%

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

   8. Simplified 73.7%

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

   if -1.09999999999999995e-10 < z < 2.85000000000000012e-74 or 1.15000000000000006e-34 < z < 3.8e7

   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 t around inf 83.1%

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

   if 2.85000000000000012e-74 < z < 1.15000000000000006e-34

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.6%

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

      1. *-commutative 88.6%

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

   6. Simplified 88.6%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+81}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+52}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{-74}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-34}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 38000000:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \]

Alternative 6: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{t}{z} - a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{t} - \frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 320000000:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (- (/ t z) a))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.15e+82)
     t_2
     (if (<= z -2.3e+52)
       t_1
       (if (<= z -4.4e-12)
         t_2
         (if (<= z 1.2e-73)
           (- (/ x t) (/ (* z y) t))
           (if (<= z 1.7e-33)
             (/ x (- t (* z a)))
             (if (<= z 320000000.0)
               (/ (- x (* z y)) t)
               (if (<= z 2.9e+62) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.15e+82) {
		tmp = t_2;
	} else if (z <= -2.3e+52) {
		tmp = t_1;
	} else if (z <= -4.4e-12) {
		tmp = t_2;
	} else if (z <= 1.2e-73) {
		tmp = (x / t) - ((z * y) / t);
	} else if (z <= 1.7e-33) {
		tmp = x / (t - (z * a));
	} else if (z <= 320000000.0) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 2.9e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -y / ((t / z) - a)
    t_2 = (y - (x / z)) / a
    if (z <= (-1.15d+82)) then
        tmp = t_2
    else if (z <= (-2.3d+52)) then
        tmp = t_1
    else if (z <= (-4.4d-12)) then
        tmp = t_2
    else if (z <= 1.2d-73) then
        tmp = (x / t) - ((z * y) / t)
    else if (z <= 1.7d-33) then
        tmp = x / (t - (z * a))
    else if (z <= 320000000.0d0) then
        tmp = (x - (z * y)) / t
    else if (z <= 2.9d+62) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.15e+82) {
		tmp = t_2;
	} else if (z <= -2.3e+52) {
		tmp = t_1;
	} else if (z <= -4.4e-12) {
		tmp = t_2;
	} else if (z <= 1.2e-73) {
		tmp = (x / t) - ((z * y) / t);
	} else if (z <= 1.7e-33) {
		tmp = x / (t - (z * a));
	} else if (z <= 320000000.0) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 2.9e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((t / z) - a)
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.15e+82:
		tmp = t_2
	elif z <= -2.3e+52:
		tmp = t_1
	elif z <= -4.4e-12:
		tmp = t_2
	elif z <= 1.2e-73:
		tmp = (x / t) - ((z * y) / t)
	elif z <= 1.7e-33:
		tmp = x / (t - (z * a))
	elif z <= 320000000.0:
		tmp = (x - (z * y)) / t
	elif z <= 2.9e+62:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(t / z) - a))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.15e+82)
		tmp = t_2;
	elseif (z <= -2.3e+52)
		tmp = t_1;
	elseif (z <= -4.4e-12)
		tmp = t_2;
	elseif (z <= 1.2e-73)
		tmp = Float64(Float64(x / t) - Float64(Float64(z * y) / t));
	elseif (z <= 1.7e-33)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 320000000.0)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 2.9e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((t / z) - a);
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.15e+82)
		tmp = t_2;
	elseif (z <= -2.3e+52)
		tmp = t_1;
	elseif (z <= -4.4e-12)
		tmp = t_2;
	elseif (z <= 1.2e-73)
		tmp = (x / t) - ((z * y) / t);
	elseif (z <= 1.7e-33)
		tmp = x / (t - (z * a));
	elseif (z <= 320000000.0)
		tmp = (x - (z * y)) / t;
	elseif (z <= 2.9e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.15e+82], t$95$2, If[LessEqual[z, -2.3e+52], t$95$1, If[LessEqual[z, -4.4e-12], t$95$2, If[LessEqual[z, 1.2e-73], N[(N[(x / t), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e-33], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 320000000.0], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.9e+62], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.14999999999999994e82 or -2.3e52 < z < -4.39999999999999983e-12 or 3.2e8 < z < 2.89999999999999984e62

   1. Initial program 76.1%

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

      1. *-commutative 76.1%

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

   3. Simplified 76.1%

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

      1. clear-num 76.0%

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

      2. associate-/r/ 76.1%

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

      3. sub-neg 76.1%

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

      4. +-commutative 76.1%

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

      5. *-commutative 76.1%

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

      6. distribute-rgt-neg-in 76.1%

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

      7. fma-def 76.1%

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

   5. Applied egg-rr 76.1%

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

   6. Taylor expanded in x around 0 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. mul-1-neg 76.1%

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

      5. sub-neg 76.1%

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

      6. *-commutative 76.1%

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

      7. associate-/l* 80.9%

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

      8. mul-1-neg 80.9%

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

      9. sub-neg 80.9%

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

      10. *-commutative 80.9%

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

      11. div-sub 80.9%

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

      12. *-commutative 80.9%

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

      13. associate-*l/ 81.4%

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

      14. associate-/r/ 92.2%

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

      15. *-inverses 92.2%

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

      16. /-rgt-identity 92.2%

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

   8. Simplified 92.2%

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

   9. Taylor expanded in t around 0 79.6%

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

       1. sub-neg 79.6%

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

       2. mul-1-neg 79.6%

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

       3. remove-double-neg 79.6%

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

       4. +-commutative 79.6%

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

       5. mul-1-neg 79.6%

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

       6. associate-/l/ 87.1%

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

       7. sub-neg 87.1%

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

       8. div-sub 87.1%

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

   11. Simplified 87.1%

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

   if -1.14999999999999994e82 < z < -2.3e52 or 2.89999999999999984e62 < z

   1. Initial program 61.2%

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

      1. *-commutative 61.2%

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

   3. Simplified 61.2%

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

      1. clear-num 60.2%

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

      2. associate-/r/ 61.1%

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

      3. sub-neg 61.1%

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

      4. +-commutative 61.1%

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

      5. *-commutative 61.1%

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

      6. distribute-rgt-neg-in 61.1%

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

      7. fma-def 61.1%

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

   5. Applied egg-rr 61.1%

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

   6. Taylor expanded in x around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-/l* 56.4%

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

      3. distribute-neg-frac 56.4%

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

      4. mul-1-neg 56.4%

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

      5. sub-neg 56.4%

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

      6. *-commutative 56.4%

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

      7. div-sub 56.4%

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

      8. *-commutative 56.4%

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

      9. associate-*l/ 69.7%

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

      10. associate-/r/ 73.7%

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

      11. *-inverses 73.7%

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

      12. /-rgt-identity 73.7%

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

   8. Simplified 73.7%

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

   if -4.39999999999999983e-12 < z < 1.20000000000000003e-73

   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. Step-by-step derivation

      1. clear-num 98.9%

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

      2. associate-/r/ 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. mul-1-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 92.7%

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

      8. mul-1-neg 92.7%

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

      9. sub-neg 92.7%

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

      10. *-commutative 92.7%

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

      11. div-sub 92.7%

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

      12. *-commutative 92.7%

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

      13. associate-*l/ 87.8%

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

      14. associate-/r/ 92.8%

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

      15. *-inverses 92.8%

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

      16. /-rgt-identity 92.8%

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

   8. Simplified 92.8%

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

   9. Taylor expanded in a around 0 81.9%

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

   if 1.20000000000000003e-73 < z < 1.7e-33

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.6%

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

      1. *-commutative 88.6%

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

   6. Simplified 88.6%

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

   if 1.7e-33 < z < 3.2e8

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 100.0%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+82}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+52}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-73}:\\ \;\;\;\;\frac{x}{t} - \frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 320000000:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+62}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \]

Alternative 7: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{t}{z} - a}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{t} - \frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 245000000:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (- (/ t z) a))) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.85e+83)
     t_2
     (if (<= z -4.5e+53)
       t_1
       (if (<= z -6.5e-11)
         (- (/ y a) (/ x (* z a)))
         (if (<= z 1.5e-74)
           (- (/ x t) (/ (* z y) t))
           (if (<= z 1.8e-33)
             (/ x (- t (* z a)))
             (if (<= z 245000000.0)
               (/ (- x (* z y)) t)
               (if (<= z 3.95e+62) t_2 t_1)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.85e+83) {
		tmp = t_2;
	} else if (z <= -4.5e+53) {
		tmp = t_1;
	} else if (z <= -6.5e-11) {
		tmp = (y / a) - (x / (z * a));
	} else if (z <= 1.5e-74) {
		tmp = (x / t) - ((z * y) / t);
	} else if (z <= 1.8e-33) {
		tmp = x / (t - (z * a));
	} else if (z <= 245000000.0) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.95e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -y / ((t / z) - a)
    t_2 = (y - (x / z)) / a
    if (z <= (-1.85d+83)) then
        tmp = t_2
    else if (z <= (-4.5d+53)) then
        tmp = t_1
    else if (z <= (-6.5d-11)) then
        tmp = (y / a) - (x / (z * a))
    else if (z <= 1.5d-74) then
        tmp = (x / t) - ((z * y) / t)
    else if (z <= 1.8d-33) then
        tmp = x / (t - (z * a))
    else if (z <= 245000000.0d0) then
        tmp = (x - (z * y)) / t
    else if (z <= 3.95d+62) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / ((t / z) - a);
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.85e+83) {
		tmp = t_2;
	} else if (z <= -4.5e+53) {
		tmp = t_1;
	} else if (z <= -6.5e-11) {
		tmp = (y / a) - (x / (z * a));
	} else if (z <= 1.5e-74) {
		tmp = (x / t) - ((z * y) / t);
	} else if (z <= 1.8e-33) {
		tmp = x / (t - (z * a));
	} else if (z <= 245000000.0) {
		tmp = (x - (z * y)) / t;
	} else if (z <= 3.95e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / ((t / z) - a)
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.85e+83:
		tmp = t_2
	elif z <= -4.5e+53:
		tmp = t_1
	elif z <= -6.5e-11:
		tmp = (y / a) - (x / (z * a))
	elif z <= 1.5e-74:
		tmp = (x / t) - ((z * y) / t)
	elif z <= 1.8e-33:
		tmp = x / (t - (z * a))
	elif z <= 245000000.0:
		tmp = (x - (z * y)) / t
	elif z <= 3.95e+62:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(Float64(t / z) - a))
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.85e+83)
		tmp = t_2;
	elseif (z <= -4.5e+53)
		tmp = t_1;
	elseif (z <= -6.5e-11)
		tmp = Float64(Float64(y / a) - Float64(x / Float64(z * a)));
	elseif (z <= 1.5e-74)
		tmp = Float64(Float64(x / t) - Float64(Float64(z * y) / t));
	elseif (z <= 1.8e-33)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 245000000.0)
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	elseif (z <= 3.95e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / ((t / z) - a);
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.85e+83)
		tmp = t_2;
	elseif (z <= -4.5e+53)
		tmp = t_1;
	elseif (z <= -6.5e-11)
		tmp = (y / a) - (x / (z * a));
	elseif (z <= 1.5e-74)
		tmp = (x / t) - ((z * y) / t);
	elseif (z <= 1.8e-33)
		tmp = x / (t - (z * a));
	elseif (z <= 245000000.0)
		tmp = (x - (z * y)) / t;
	elseif (z <= 3.95e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(N[(t / z), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.85e+83], t$95$2, If[LessEqual[z, -4.5e+53], t$95$1, If[LessEqual[z, -6.5e-11], N[(N[(y / a), $MachinePrecision] - N[(x / N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-74], N[(N[(x / t), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e-33], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 245000000.0], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 3.95e+62], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.8500000000000001e83 or 2.45e8 < z < 3.9499999999999998e62

   1. Initial program 69.0%

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

      1. *-commutative 69.0%

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

   3. Simplified 69.0%

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

      1. clear-num 68.9%

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

      2. associate-/r/ 69.0%

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

      3. sub-neg 69.0%

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

      4. +-commutative 69.0%

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

      5. *-commutative 69.0%

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

      6. distribute-rgt-neg-in 69.0%

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

      7. fma-def 69.0%

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

   5. Applied egg-rr 69.0%

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

   6. Taylor expanded in x around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. mul-1-neg 69.0%

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

      5. sub-neg 69.0%

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

      6. *-commutative 69.0%

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

      7. associate-/l* 75.2%

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

      8. mul-1-neg 75.2%

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

      9. sub-neg 75.2%

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

      10. *-commutative 75.2%

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

      11. div-sub 75.2%

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

      12. *-commutative 75.2%

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

      13. associate-*l/ 75.9%

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

      14. associate-/r/ 89.9%

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

      15. *-inverses 89.9%

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

      16. /-rgt-identity 89.9%

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

   8. Simplified 89.9%

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

   9. Taylor expanded in t around 0 75.5%

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

       1. sub-neg 75.5%

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

       2. mul-1-neg 75.5%

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

       3. remove-double-neg 75.5%

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

       4. +-commutative 75.5%

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

       5. mul-1-neg 75.5%

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

       6. associate-/l/ 85.3%

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

       7. sub-neg 85.3%

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

       8. div-sub 85.3%

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

   11. Simplified 85.3%

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

   if -1.8500000000000001e83 < z < -4.5000000000000002e53 or 3.9499999999999998e62 < z

   1. Initial program 61.2%

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

      1. *-commutative 61.2%

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

   3. Simplified 61.2%

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

      1. clear-num 60.2%

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

      2. associate-/r/ 61.1%

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

      3. sub-neg 61.1%

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

      4. +-commutative 61.1%

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

      5. *-commutative 61.1%

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

      6. distribute-rgt-neg-in 61.1%

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

      7. fma-def 61.1%

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

   5. Applied egg-rr 61.1%

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

   6. Taylor expanded in x around 0 36.3%

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

      1. mul-1-neg 36.3%

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

      2. associate-/l* 56.4%

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

      3. distribute-neg-frac 56.4%

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

      4. mul-1-neg 56.4%

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

      5. sub-neg 56.4%

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

      6. *-commutative 56.4%

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

      7. div-sub 56.4%

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

      8. *-commutative 56.4%

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

      9. associate-*l/ 69.7%

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

      10. associate-/r/ 73.7%

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

      11. *-inverses 73.7%

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

      12. /-rgt-identity 73.7%

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

   8. Simplified 73.7%

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

   if -4.5000000000000002e53 < z < -6.49999999999999953e-11

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 93.0%

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

      1. associate-*r* 93.0%

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

      2. neg-mul-1 93.0%

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

      3. *-commutative 93.0%

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

   6. Simplified 93.0%

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

   7. Taylor expanded in x around 0 93.3%

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

      1. +-commutative 93.3%

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

      2. mul-1-neg 93.3%

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

      3. unsub-neg 93.3%

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

      4. *-commutative 93.3%

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

   9. Simplified 93.3%

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

   if -6.49999999999999953e-11 < z < 1.50000000000000003e-74

   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. Step-by-step derivation

      1. clear-num 98.9%

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

      2. associate-/r/ 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. *-commutative 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. mul-1-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-/l* 92.7%

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

      8. mul-1-neg 92.7%

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

      9. sub-neg 92.7%

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

      10. *-commutative 92.7%

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

      11. div-sub 92.7%

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

      12. *-commutative 92.7%

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

      13. associate-*l/ 87.8%

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

      14. associate-/r/ 92.8%

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

      15. *-inverses 92.8%

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

      16. /-rgt-identity 92.8%

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

   8. Simplified 92.8%

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

   9. Taylor expanded in a around 0 81.9%

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

   if 1.50000000000000003e-74 < z < 1.80000000000000017e-33

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.6%

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

      1. *-commutative 88.6%

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

   6. Simplified 88.6%

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

   if 1.80000000000000017e-33 < z < 2.45e8

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{\frac{x - y \cdot z}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+83}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{y}{a} - \frac{x}{z \cdot a}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{t} - \frac{z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 245000000:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 3.95 \cdot 10^{+62}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{t}{z} - a}\\ \end{array} \]

Alternative 8: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{-x}{a}}{z}\\ \mathbf{if}\;z \leq -1.05 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+117} \lor \neg \left(z \leq 3.6 \cdot 10^{+222}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{y}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (/ (- x) a) z)))
   (if (<= z -1.05e+120)
     (/ y a)
     (if (<= z -4500000.0)
       t_1
       (if (<= z -4e-69)
         (/ y a)
         (if (<= z 5.2e-82)
           (/ x t)
           (if (<= z 3.5e+29)
             t_1
             (if (or (<= z 2.2e+117) (not (<= z 3.6e+222)))
               (/ y a)
               (- (/ y (/ t z)))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-x / a) / z;
	double tmp;
	if (z <= -1.05e+120) {
		tmp = y / a;
	} else if (z <= -4500000.0) {
		tmp = t_1;
	} else if (z <= -4e-69) {
		tmp = y / a;
	} else if (z <= 5.2e-82) {
		tmp = x / t;
	} else if (z <= 3.5e+29) {
		tmp = t_1;
	} else if ((z <= 2.2e+117) || !(z <= 3.6e+222)) {
		tmp = y / a;
	} else {
		tmp = -(y / (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-x / a) / z
    if (z <= (-1.05d+120)) then
        tmp = y / a
    else if (z <= (-4500000.0d0)) then
        tmp = t_1
    else if (z <= (-4d-69)) then
        tmp = y / a
    else if (z <= 5.2d-82) then
        tmp = x / t
    else if (z <= 3.5d+29) then
        tmp = t_1
    else if ((z <= 2.2d+117) .or. (.not. (z <= 3.6d+222))) then
        tmp = y / a
    else
        tmp = -(y / (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (-x / a) / z;
	double tmp;
	if (z <= -1.05e+120) {
		tmp = y / a;
	} else if (z <= -4500000.0) {
		tmp = t_1;
	} else if (z <= -4e-69) {
		tmp = y / a;
	} else if (z <= 5.2e-82) {
		tmp = x / t;
	} else if (z <= 3.5e+29) {
		tmp = t_1;
	} else if ((z <= 2.2e+117) || !(z <= 3.6e+222)) {
		tmp = y / a;
	} else {
		tmp = -(y / (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-x / a) / z
	tmp = 0
	if z <= -1.05e+120:
		tmp = y / a
	elif z <= -4500000.0:
		tmp = t_1
	elif z <= -4e-69:
		tmp = y / a
	elif z <= 5.2e-82:
		tmp = x / t
	elif z <= 3.5e+29:
		tmp = t_1
	elif (z <= 2.2e+117) or not (z <= 3.6e+222):
		tmp = y / a
	else:
		tmp = -(y / (t / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-x) / a) / z)
	tmp = 0.0
	if (z <= -1.05e+120)
		tmp = Float64(y / a);
	elseif (z <= -4500000.0)
		tmp = t_1;
	elseif (z <= -4e-69)
		tmp = Float64(y / a);
	elseif (z <= 5.2e-82)
		tmp = Float64(x / t);
	elseif (z <= 3.5e+29)
		tmp = t_1;
	elseif ((z <= 2.2e+117) || !(z <= 3.6e+222))
		tmp = Float64(y / a);
	else
		tmp = Float64(-Float64(y / Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-x / a) / z;
	tmp = 0.0;
	if (z <= -1.05e+120)
		tmp = y / a;
	elseif (z <= -4500000.0)
		tmp = t_1;
	elseif (z <= -4e-69)
		tmp = y / a;
	elseif (z <= 5.2e-82)
		tmp = x / t;
	elseif (z <= 3.5e+29)
		tmp = t_1;
	elseif ((z <= 2.2e+117) || ~((z <= 3.6e+222)))
		tmp = y / a;
	else
		tmp = -(y / (t / z));
	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, -1.05e+120], N[(y / a), $MachinePrecision], If[LessEqual[z, -4500000.0], t$95$1, If[LessEqual[z, -4e-69], N[(y / a), $MachinePrecision], If[LessEqual[z, 5.2e-82], N[(x / t), $MachinePrecision], If[LessEqual[z, 3.5e+29], t$95$1, If[Or[LessEqual[z, 2.2e+117], N[Not[LessEqual[z, 3.6e+222]], $MachinePrecision]], N[(y / a), $MachinePrecision], (-N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision])]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.05e120 or -4.5e6 < z < -3.9999999999999999e-69 or 3.49999999999999979e29 < z < 2.20000000000000014e117 or 3.6000000000000002e222 < 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 64.4%

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

   if -1.05e120 < z < -4.5e6 or 5.2e-82 < z < 3.49999999999999979e29

   1. Initial program 89.1%

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

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in x around inf 63.6%

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

      1. *-commutative 63.6%

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

   6. Simplified 63.6%

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

   7. Taylor expanded in t around 0 46.2%

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

      1. mul-1-neg 46.2%

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

      2. associate-/r* 53.2%

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

   9. Simplified 53.2%

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

   if -3.9999999999999999e-69 < z < 5.2e-82

   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 z around 0 66.5%

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

   if 2.20000000000000014e117 < z < 3.6000000000000002e222

   1. Initial program 71.2%

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

      1. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in x around 0 36.7%

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

      1. mul-1-neg 36.7%

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

      2. associate-/l* 54.3%

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

      3. *-commutative 54.3%

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

   6. Simplified 54.3%

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

   7. Taylor expanded in t around inf 46.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+120}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq -4500000:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{\frac{-x}{a}}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+117} \lor \neg \left(z \leq 3.6 \cdot 10^{+222}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;-\frac{y}{\frac{t}{z}}\\ \end{array} \]

Alternative 9: 72.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - z \cdot y}{t}\\ t_2 := \frac{y - \frac{x}{z}}{a}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 26000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- x (* z y)) t)) (t_2 (/ (- y (/ x z)) a)))
   (if (<= z -1.55e-9)
     t_2
     (if (<= z 3.5e-73)
       t_1
       (if (<= z 1.25e-33)
         (/ x (- t (* z a)))
         (if (<= z 26000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.55e-9) {
		tmp = t_2;
	} else if (z <= 3.5e-73) {
		tmp = t_1;
	} else if (z <= 1.25e-33) {
		tmp = x / (t - (z * a));
	} else if (z <= 26000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (z * y)) / t
    t_2 = (y - (x / z)) / a
    if (z <= (-1.55d-9)) then
        tmp = t_2
    else if (z <= 3.5d-73) then
        tmp = t_1
    else if (z <= 1.25d-33) then
        tmp = x / (t - (z * a))
    else if (z <= 26000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x - (z * y)) / t;
	double t_2 = (y - (x / z)) / a;
	double tmp;
	if (z <= -1.55e-9) {
		tmp = t_2;
	} else if (z <= 3.5e-73) {
		tmp = t_1;
	} else if (z <= 1.25e-33) {
		tmp = x / (t - (z * a));
	} else if (z <= 26000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x - (z * y)) / t
	t_2 = (y - (x / z)) / a
	tmp = 0
	if z <= -1.55e-9:
		tmp = t_2
	elif z <= 3.5e-73:
		tmp = t_1
	elif z <= 1.25e-33:
		tmp = x / (t - (z * a))
	elif z <= 26000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x - Float64(z * y)) / t)
	t_2 = Float64(Float64(y - Float64(x / z)) / a)
	tmp = 0.0
	if (z <= -1.55e-9)
		tmp = t_2;
	elseif (z <= 3.5e-73)
		tmp = t_1;
	elseif (z <= 1.25e-33)
		tmp = Float64(x / Float64(t - Float64(z * a)));
	elseif (z <= 26000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x - (z * y)) / t;
	t_2 = (y - (x / z)) / a;
	tmp = 0.0;
	if (z <= -1.55e-9)
		tmp = t_2;
	elseif (z <= 3.5e-73)
		tmp = t_1;
	elseif (z <= 1.25e-33)
		tmp = x / (t - (z * a));
	elseif (z <= 26000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y - N[(x / z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[z, -1.55e-9], t$95$2, If[LessEqual[z, 3.5e-73], t$95$1, If[LessEqual[z, 1.25e-33], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 26000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000002e-9 or 2.6e7 < z

   1. Initial program 68.1%

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

      1. *-commutative 68.1%

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

   3. Simplified 68.1%

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

      1. clear-num 67.5%

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

      2. associate-/r/ 68.0%

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

      3. sub-neg 68.0%

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

      4. +-commutative 68.0%

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

      5. *-commutative 68.0%

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

      6. distribute-rgt-neg-in 68.0%

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

      7. fma-def 68.0%

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

   5. Applied egg-rr 68.0%

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

   6. Taylor expanded in x around 0 68.1%

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

      1. +-commutative 68.1%

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

      2. mul-1-neg 68.1%

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

      3. unsub-neg 68.1%

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

      4. mul-1-neg 68.1%

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

      5. sub-neg 68.1%

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

      6. *-commutative 68.1%

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

      7. associate-/l* 81.1%

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

      8. mul-1-neg 81.1%

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

      9. sub-neg 81.1%

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

      10. *-commutative 81.1%

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

      11. div-sub 81.1%

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

      12. *-commutative 81.1%

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

      13. associate-*l/ 85.8%

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

      14. associate-/r/ 95.7%

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

      15. *-inverses 95.7%

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

      16. /-rgt-identity 95.7%

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

   8. Simplified 95.7%

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

   9. Taylor expanded in t around 0 67.9%

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

       1. sub-neg 67.9%

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

       2. mul-1-neg 67.9%

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

       3. remove-double-neg 67.9%

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

       4. +-commutative 67.9%

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

       5. mul-1-neg 67.9%

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

       6. associate-/l/ 72.0%

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

       7. sub-neg 72.0%

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

       8. div-sub 72.0%

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

   11. Simplified 72.0%

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

   if -1.55000000000000002e-9 < z < 3.4999999999999998e-73 or 1.25000000000000007e-33 < z < 2.6e7

   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 t around inf 83.1%

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

   if 3.4999999999999998e-73 < z < 1.25000000000000007e-33

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 88.6%

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

      1. *-commutative 88.6%

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

   6. Simplified 88.6%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{elif}\;z \leq 26000000:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{x}{z}}{a}\\ \end{array} \]

Alternative 10: 59.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-127} \lor \neg \left(a \leq 1.62 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.85e+36)
   (/ y a)
   (if (or (<= a -7.2e-127) (not (<= a 1.62e-102)))
     (/ x (- t (* z a)))
     (/ (- x (* z y)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.85e+36) {
		tmp = y / a;
	} else if ((a <= -7.2e-127) || !(a <= 1.62e-102)) {
		tmp = x / (t - (z * a));
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.85d+36)) then
        tmp = y / a
    else if ((a <= (-7.2d-127)) .or. (.not. (a <= 1.62d-102))) then
        tmp = x / (t - (z * a))
    else
        tmp = (x - (z * y)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.85e+36) {
		tmp = y / a;
	} else if ((a <= -7.2e-127) || !(a <= 1.62e-102)) {
		tmp = x / (t - (z * a));
	} else {
		tmp = (x - (z * y)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.85e+36:
		tmp = y / a
	elif (a <= -7.2e-127) or not (a <= 1.62e-102):
		tmp = x / (t - (z * a))
	else:
		tmp = (x - (z * y)) / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.85e+36)
		tmp = Float64(y / a);
	elseif ((a <= -7.2e-127) || !(a <= 1.62e-102))
		tmp = Float64(x / Float64(t - Float64(z * a)));
	else
		tmp = Float64(Float64(x - Float64(z * y)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.85e+36)
		tmp = y / a;
	elseif ((a <= -7.2e-127) || ~((a <= 1.62e-102)))
		tmp = x / (t - (z * a));
	else
		tmp = (x - (z * y)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.85e+36], N[(y / a), $MachinePrecision], If[Or[LessEqual[a, -7.2e-127], N[Not[LessEqual[a, 1.62e-102]], $MachinePrecision]], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(z * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.85000000000000014e36

   1. Initial program 67.4%

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

      1. *-commutative 67.4%

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

   3. Simplified 67.4%

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

   4. Taylor expanded in z around inf 63.9%

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

   if -1.85000000000000014e36 < a < -7.1999999999999999e-127 or 1.61999999999999996e-102 < a

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. *-commutative 65.0%

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

   6. Simplified 65.0%

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

   if -7.1999999999999999e-127 < a < 1.61999999999999996e-102

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

   3. Simplified 91.7%

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

   4. Taylor expanded in t around inf 74.9%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-127} \lor \neg \left(a \leq 1.62 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - z \cdot y}{t}\\ \end{array} \]

Alternative 11: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+222}:\\ \;\;\;\;-\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e-69)
   (/ y a)
   (if (<= z 2.65e-31)
     (/ x t)
     (if (<= z 5.3e+222) (- (/ y (/ t z))) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e-69) {
		tmp = y / a;
	} else if (z <= 2.65e-31) {
		tmp = x / t;
	} else if (z <= 5.3e+222) {
		tmp = -(y / (t / z));
	} 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 <= (-4d-69)) then
        tmp = y / a
    else if (z <= 2.65d-31) then
        tmp = x / t
    else if (z <= 5.3d+222) then
        tmp = -(y / (t / z))
    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 <= -4e-69) {
		tmp = y / a;
	} else if (z <= 2.65e-31) {
		tmp = x / t;
	} else if (z <= 5.3e+222) {
		tmp = -(y / (t / z));
	} else {
		tmp = y / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e-69:
		tmp = y / a
	elif z <= 2.65e-31:
		tmp = x / t
	elif z <= 5.3e+222:
		tmp = -(y / (t / z))
	else:
		tmp = y / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e-69)
		tmp = Float64(y / a);
	elseif (z <= 2.65e-31)
		tmp = Float64(x / t);
	elseif (z <= 5.3e+222)
		tmp = Float64(-Float64(y / Float64(t / z)));
	else
		tmp = Float64(y / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e-69)
		tmp = y / a;
	elseif (z <= 2.65e-31)
		tmp = x / t;
	elseif (z <= 5.3e+222)
		tmp = -(y / (t / z));
	else
		tmp = y / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e-69], N[(y / a), $MachinePrecision], If[LessEqual[z, 2.65e-31], N[(x / t), $MachinePrecision], If[LessEqual[z, 5.3e+222], (-N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), N[(y / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.9999999999999999e-69 or 5.29999999999999993e222 < z

   1. Initial program 68.4%

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

      1. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   4. Taylor expanded in z around inf 59.2%

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

   if -3.9999999999999999e-69 < z < 2.65e-31

   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 z around 0 63.0%

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

   if 2.65e-31 < z < 5.29999999999999993e222

   1. Initial program 75.1%

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

      1. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in x around 0 40.0%

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

      1. mul-1-neg 40.0%

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

      2. associate-/l* 53.0%

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

      3. *-commutative 53.0%

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

   6. Simplified 53.0%

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

   7. Taylor expanded in t around inf 38.1%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{a}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{t}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+222}:\\ \;\;\;\;-\frac{y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a}\\ \end{array} \]

Alternative 12: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+150} \lor \neg \left(z \leq 5.1 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.2e+150) (not (<= z 5.1e+219))) (/ y a) (/ x (- t (* z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+150) || !(z <= 5.1e+219)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.2d+150)) .or. (.not. (z <= 5.1d+219))) then
        tmp = y / a
    else
        tmp = x / (t - (z * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.2e+150) || !(z <= 5.1e+219)) {
		tmp = y / a;
	} else {
		tmp = x / (t - (z * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.2e+150) or not (z <= 5.1e+219):
		tmp = y / a
	else:
		tmp = x / (t - (z * a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.2e+150) || !(z <= 5.1e+219))
		tmp = Float64(y / a);
	else
		tmp = Float64(x / Float64(t - Float64(z * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.2e+150) || ~((z <= 5.1e+219)))
		tmp = y / a;
	else
		tmp = x / (t - (z * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.2e+150], N[Not[LessEqual[z, 5.1e+219]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / N[(t - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.19999999999999996e150 or 5.09999999999999993e219 < z

   1. Initial program 47.8%

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

      1. *-commutative 47.8%

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

   3. Simplified 47.8%

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

   4. Taylor expanded in z around inf 75.1%

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

   if -4.19999999999999996e150 < z < 5.09999999999999993e219

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in x around inf 65.0%

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

      1. *-commutative 65.0%

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

   6. Simplified 65.0%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+150} \lor \neg \left(z \leq 5.1 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t - z \cdot a}\\ \end{array} \]

Alternative 13: 55.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-69} \lor \neg \left(z \leq 6.5 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.95e-69) (not (<= z 6.5e+45))) (/ y a) (/ x t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.95e-69) || !(z <= 6.5e+45)) {
		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 <= (-1.95d-69)) .or. (.not. (z <= 6.5d+45))) 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 <= -1.95e-69) || !(z <= 6.5e+45)) {
		tmp = y / a;
	} else {
		tmp = x / t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.95e-69) or not (z <= 6.5e+45):
		tmp = y / a
	else:
		tmp = x / t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.95e-69) || !(z <= 6.5e+45))
		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 <= -1.95e-69) || ~((z <= 6.5e+45)))
		tmp = y / a;
	else
		tmp = x / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.95e-69], N[Not[LessEqual[z, 6.5e+45]], $MachinePrecision]], N[(y / a), $MachinePrecision], N[(x / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9499999999999999e-69 or 6.50000000000000034e45 < z

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in z around inf 49.9%

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

   if -1.9499999999999999e-69 < z < 6.50000000000000034e45

   1. Initial program 98.2%

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

      1. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 59.3%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-69} \lor \neg \left(z \leq 6.5 \cdot 10^{+45}\right):\\ \;\;\;\;\frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{t}\\ \end{array} \]

Alternative 14: 35.9% 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 82.3%

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

   1. *-commutative 82.3%

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

3. Simplified 82.3%

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

4. Taylor expanded in z around 0 34.3%

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

5. Final simplification 34.3%

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

Developer target: 97.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023334 
(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))))