Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Percentage Accurate: 74.4% → 88.3%

Time: 18.7s

Alternatives: 17

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    code = (x + ((y * z) / t)) / ((a + 1.0d0) + ((y * b) / t))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 88.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_3 := 1 + \left(a + t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+297}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1)))
        (t_3 (+ 1.0 (+ a t_1))))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))
     (if (<= t_2 2e+297) t_2 (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_3 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	double t_3 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	} else if (t_2 <= 2e+297) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	t_3 = 1.0 + (a + t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)))
	elif t_2 <= 2e+297:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1))
	t_3 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))));
	elseif (t_2 <= 2e+297)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	t_3 = 1.0 + (a + t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * ((x / (z * t_3)) + (y / (t * t_3)));
	elseif (t_2 <= 2e+297)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z * N[(N[(x / N[(z * t$95$3), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+297], t$95$2, N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 36.1%

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

      1. associate-/l* 52.0%

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

      2. associate-/l* 51.6%

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

   3. Simplified 51.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 99.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e297

   1. Initial program 92.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing

   if 2e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 9.3%

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

      1. associate-/l* 21.5%

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

      2. associate-/l* 21.4%

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

   3. Simplified 21.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 90.0%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+297}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 2 \cdot 10^{+297}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+297))) (/ z b) t_1)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+297)) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+297)) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+297):
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+297))
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+297)))
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+297]], $MachinePrecision]], N[(z / b), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 2e297 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 15.6%

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

      1. associate-/l* 28.7%

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

      2. associate-/l* 28.5%

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

   3. Simplified 28.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 88.5%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e297

   1. Initial program 92.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty \lor \neg \left(\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 2 \cdot 10^{+297}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-84}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-196}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-218}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ (* t (/ x b)) (* y (/ z b))) y))
        (t_2 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))))
   (if (<= t -2.9e-18)
     t_2
     (if (<= t -1.2e-52)
       (* z (+ (/ (/ x z) (+ 1.0 (* b (/ y t)))) (/ 1.0 b)))
       (if (<= t -1.45e-84)
         t_2
         (if (<= t -3.5e-196)
           t_1
           (if (<= t -3e-218)
             (/ (+ x (* z (/ y t))) (+ a 1.0))
             (if (<= t 7e-212) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((t * (x / b)) + (y * (z / b))) / y;
	double t_2 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -2.9e-18) {
		tmp = t_2;
	} else if (t <= -1.2e-52) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -1.45e-84) {
		tmp = t_2;
	} else if (t <= -3.5e-196) {
		tmp = t_1;
	} else if (t <= -3e-218) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 7e-212) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((t * (x / b)) + (y * (z / b))) / y
    t_2 = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    if (t <= (-2.9d-18)) then
        tmp = t_2
    else if (t <= (-1.2d-52)) then
        tmp = z * (((x / z) / (1.0d0 + (b * (y / t)))) + (1.0d0 / b))
    else if (t <= (-1.45d-84)) then
        tmp = t_2
    else if (t <= (-3.5d-196)) then
        tmp = t_1
    else if (t <= (-3d-218)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (t <= 7d-212) 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 b) {
	double t_1 = ((t * (x / b)) + (y * (z / b))) / y;
	double t_2 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	double tmp;
	if (t <= -2.9e-18) {
		tmp = t_2;
	} else if (t <= -1.2e-52) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -1.45e-84) {
		tmp = t_2;
	} else if (t <= -3.5e-196) {
		tmp = t_1;
	} else if (t <= -3e-218) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 7e-212) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((t * (x / b)) + (y * (z / b))) / y
	t_2 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	tmp = 0
	if t <= -2.9e-18:
		tmp = t_2
	elif t <= -1.2e-52:
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b))
	elif t <= -1.45e-84:
		tmp = t_2
	elif t <= -3.5e-196:
		tmp = t_1
	elif t <= -3e-218:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif t <= 7e-212:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y)
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	tmp = 0.0
	if (t <= -2.9e-18)
		tmp = t_2;
	elseif (t <= -1.2e-52)
		tmp = Float64(z * Float64(Float64(Float64(x / z) / Float64(1.0 + Float64(b * Float64(y / t)))) + Float64(1.0 / b)));
	elseif (t <= -1.45e-84)
		tmp = t_2;
	elseif (t <= -3.5e-196)
		tmp = t_1;
	elseif (t <= -3e-218)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (t <= 7e-212)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((t * (x / b)) + (y * (z / b))) / y;
	t_2 = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	tmp = 0.0;
	if (t <= -2.9e-18)
		tmp = t_2;
	elseif (t <= -1.2e-52)
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	elseif (t <= -1.45e-84)
		tmp = t_2;
	elseif (t <= -3.5e-196)
		tmp = t_1;
	elseif (t <= -3e-218)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (t <= 7e-212)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-18], t$95$2, If[LessEqual[t, -1.2e-52], N[(z * N[(N[(N[(x / z), $MachinePrecision] / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.45e-84], t$95$2, If[LessEqual[t, -3.5e-196], t$95$1, If[LessEqual[t, -3e-218], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7e-212], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9e-18 or -1.2000000000000001e-52 < t < -1.4500000000000001e-84 or 6.9999999999999995e-212 < t

   1. Initial program 88.1%

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

      1. associate-/l* 91.2%

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

      2. associate-/l* 92.8%

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

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -2.9e-18 < t < -1.2000000000000001e-52

   1. Initial program 45.1%

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

      1. associate-/l* 45.0%

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

      2. associate-/l* 37.4%

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

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 69.3%

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

   6. Taylor expanded in y around inf 93.5%

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

   7. Taylor expanded in a around 0 93.5%

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

      1. associate-/r* 91.0%

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

      2. associate-/l* 91.0%

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

   9. Simplified 91.0%

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

   if -1.4500000000000001e-84 < t < -3.50000000000000004e-196 or -2.9999999999999998e-218 < t < 6.9999999999999995e-212

   1. Initial program 56.6%

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

      1. associate-/l* 43.2%

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

      2. associate-/l* 40.3%

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

   3. Simplified 40.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.6%

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

   6. Taylor expanded in y around 0 70.2%

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

      1. associate-/l* 67.4%

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

      2. associate-/l* 73.0%

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

   8. Simplified 73.0%

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

   if -3.50000000000000004e-196 < t < -2.9999999999999998e-218

   1. Initial program 100.0%

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

      1. associate-/l* 83.8%

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

      2. associate-/l* 67.1%

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

   3. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   7. Applied egg-rr 100.0%

      \[\leadsto \frac{x + \color{blue}{z \cdot \frac{y}{t}}}{1 + a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-52}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-84}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-218}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-212}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := \frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ t_3 := \frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-193}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-219}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-211}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t))))
        (t_2 (/ t_1 (+ (+ a 1.0) (* y (/ b t)))))
        (t_3 (/ (+ (* t (/ x b)) (* y (/ z b))) y)))
   (if (<= t -2.75e-18)
     t_2
     (if (<= t -3e-50)
       (* z (+ (/ (/ x z) (+ 1.0 (* b (/ y t)))) (/ 1.0 b)))
       (if (<= t -1.9e-77)
         (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))
         (if (<= t -4.4e-193)
           t_3
           (if (<= t -5.8e-219)
             (/ (+ x (* z (/ y t))) (+ a 1.0))
             (if (<= t 7.4e-211) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / ((a + 1.0) + (y * (b / t)));
	double t_3 = ((t * (x / b)) + (y * (z / b))) / y;
	double tmp;
	if (t <= -2.75e-18) {
		tmp = t_2;
	} else if (t <= -3e-50) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -1.9e-77) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= -4.4e-193) {
		tmp = t_3;
	} else if (t <= -5.8e-219) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 7.4e-211) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = t_1 / ((a + 1.0d0) + (y * (b / t)))
    t_3 = ((t * (x / b)) + (y * (z / b))) / y
    if (t <= (-2.75d-18)) then
        tmp = t_2
    else if (t <= (-3d-50)) then
        tmp = z * (((x / z) / (1.0d0 + (b * (y / t)))) + (1.0d0 / b))
    else if (t <= (-1.9d-77)) then
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= (-4.4d-193)) then
        tmp = t_3
    else if (t <= (-5.8d-219)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (t <= 7.4d-211) then
        tmp = t_3
    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 b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / ((a + 1.0) + (y * (b / t)));
	double t_3 = ((t * (x / b)) + (y * (z / b))) / y;
	double tmp;
	if (t <= -2.75e-18) {
		tmp = t_2;
	} else if (t <= -3e-50) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -1.9e-77) {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= -4.4e-193) {
		tmp = t_3;
	} else if (t <= -5.8e-219) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 7.4e-211) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	t_2 = t_1 / ((a + 1.0) + (y * (b / t)))
	t_3 = ((t * (x / b)) + (y * (z / b))) / y
	tmp = 0
	if t <= -2.75e-18:
		tmp = t_2
	elif t <= -3e-50:
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b))
	elif t <= -1.9e-77:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	elif t <= -4.4e-193:
		tmp = t_3
	elif t <= -5.8e-219:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif t <= 7.4e-211:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))))
	t_3 = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y)
	tmp = 0.0
	if (t <= -2.75e-18)
		tmp = t_2;
	elseif (t <= -3e-50)
		tmp = Float64(z * Float64(Float64(Float64(x / z) / Float64(1.0 + Float64(b * Float64(y / t)))) + Float64(1.0 / b)));
	elseif (t <= -1.9e-77)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= -4.4e-193)
		tmp = t_3;
	elseif (t <= -5.8e-219)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (t <= 7.4e-211)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	t_2 = t_1 / ((a + 1.0) + (y * (b / t)));
	t_3 = ((t * (x / b)) + (y * (z / b))) / y;
	tmp = 0.0;
	if (t <= -2.75e-18)
		tmp = t_2;
	elseif (t <= -3e-50)
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	elseif (t <= -1.9e-77)
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	elseif (t <= -4.4e-193)
		tmp = t_3;
	elseif (t <= -5.8e-219)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (t <= 7.4e-211)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.75e-18], t$95$2, If[LessEqual[t, -3e-50], N[(z * N[(N[(N[(x / z), $MachinePrecision] / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.9e-77], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.4e-193], t$95$3, If[LessEqual[t, -5.8e-219], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e-211], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.75e-18 or 7.3999999999999996e-211 < t

   1. Initial program 87.9%

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

      1. associate-/l* 91.2%

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

      2. associate-/l* 93.0%

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

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -2.75e-18 < t < -2.9999999999999999e-50

   1. Initial program 45.1%

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

      1. associate-/l* 45.0%

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

      2. associate-/l* 37.4%

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

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 69.3%

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

   6. Taylor expanded in y around inf 93.5%

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

   7. Taylor expanded in a around 0 93.5%

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

      1. associate-/r* 91.0%

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

      2. associate-/l* 91.0%

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

   9. Simplified 91.0%

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

   if -2.9999999999999999e-50 < t < -1.8999999999999999e-77

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 62.9%

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

      2. un-div-inv 63.1%

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

   6. Applied egg-rr 99.8%

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

   if -1.8999999999999999e-77 < t < -4.39999999999999953e-193 or -5.79999999999999968e-219 < t < 7.3999999999999996e-211

   1. Initial program 56.5%

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

      1. associate-/l* 43.4%

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

      2. associate-/l* 40.6%

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

   3. Simplified 40.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.8%

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

   6. Taylor expanded in y around 0 69.8%

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

      1. associate-/l* 67.1%

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

      2. associate-/l* 72.4%

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

   8. Simplified 72.4%

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

   if -4.39999999999999953e-193 < t < -5.79999999999999968e-219

   1. Initial program 100.0%

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

      1. associate-/l* 83.8%

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

      2. associate-/l* 67.1%

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

   3. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   7. Applied egg-rr 100.0%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-18}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-50}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-219}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-211}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ t_2 := x + y \cdot \frac{z}{t}\\ t_3 := \frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{if}\;t \leq -2.75 \cdot 10^{-18}:\\ \;\;\;\;\frac{t\_2}{t\_1}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-196}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-217}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-220}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (* y (/ b t))))
        (t_2 (+ x (* y (/ z t))))
        (t_3 (/ (+ (* t (/ x b)) (* y (/ z b))) y)))
   (if (<= t -2.75e-18)
     (/ t_2 t_1)
     (if (<= t -8e-51)
       (* z (+ (/ (/ x z) (+ 1.0 (* b (/ y t)))) (/ 1.0 b)))
       (if (<= t -1.7e-77)
         (/ t_2 (+ (+ a 1.0) (/ y (/ t b))))
         (if (<= t -3.5e-196)
           t_3
           (if (<= t -3.35e-217)
             (/ (+ x (* z (/ y t))) (+ a 1.0))
             (if (<= t 2.5e-220) t_3 (/ (+ x (/ y (/ t z))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double t_2 = x + (y * (z / t));
	double t_3 = ((t * (x / b)) + (y * (z / b))) / y;
	double tmp;
	if (t <= -2.75e-18) {
		tmp = t_2 / t_1;
	} else if (t <= -8e-51) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -1.7e-77) {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= -3.5e-196) {
		tmp = t_3;
	} else if (t <= -3.35e-217) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 2.5e-220) {
		tmp = t_3;
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (a + 1.0d0) + (y * (b / t))
    t_2 = x + (y * (z / t))
    t_3 = ((t * (x / b)) + (y * (z / b))) / y
    if (t <= (-2.75d-18)) then
        tmp = t_2 / t_1
    else if (t <= (-8d-51)) then
        tmp = z * (((x / z) / (1.0d0 + (b * (y / t)))) + (1.0d0 / b))
    else if (t <= (-1.7d-77)) then
        tmp = t_2 / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= (-3.5d-196)) then
        tmp = t_3
    else if (t <= (-3.35d-217)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (t <= 2.5d-220) then
        tmp = t_3
    else
        tmp = (x + (y / (t / z))) / t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + (y * (b / t));
	double t_2 = x + (y * (z / t));
	double t_3 = ((t * (x / b)) + (y * (z / b))) / y;
	double tmp;
	if (t <= -2.75e-18) {
		tmp = t_2 / t_1;
	} else if (t <= -8e-51) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -1.7e-77) {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	} else if (t <= -3.5e-196) {
		tmp = t_3;
	} else if (t <= -3.35e-217) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 2.5e-220) {
		tmp = t_3;
	} else {
		tmp = (x + (y / (t / z))) / t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + (y * (b / t))
	t_2 = x + (y * (z / t))
	t_3 = ((t * (x / b)) + (y * (z / b))) / y
	tmp = 0
	if t <= -2.75e-18:
		tmp = t_2 / t_1
	elif t <= -8e-51:
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b))
	elif t <= -1.7e-77:
		tmp = t_2 / ((a + 1.0) + (y / (t / b)))
	elif t <= -3.5e-196:
		tmp = t_3
	elif t <= -3.35e-217:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif t <= 2.5e-220:
		tmp = t_3
	else:
		tmp = (x + (y / (t / z))) / t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	t_2 = Float64(x + Float64(y * Float64(z / t)))
	t_3 = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y)
	tmp = 0.0
	if (t <= -2.75e-18)
		tmp = Float64(t_2 / t_1);
	elseif (t <= -8e-51)
		tmp = Float64(z * Float64(Float64(Float64(x / z) / Float64(1.0 + Float64(b * Float64(y / t)))) + Float64(1.0 / b)));
	elseif (t <= -1.7e-77)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= -3.5e-196)
		tmp = t_3;
	elseif (t <= -3.35e-217)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (t <= 2.5e-220)
		tmp = t_3;
	else
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + (y * (b / t));
	t_2 = x + (y * (z / t));
	t_3 = ((t * (x / b)) + (y * (z / b))) / y;
	tmp = 0.0;
	if (t <= -2.75e-18)
		tmp = t_2 / t_1;
	elseif (t <= -8e-51)
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	elseif (t <= -1.7e-77)
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	elseif (t <= -3.5e-196)
		tmp = t_3;
	elseif (t <= -3.35e-217)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (t <= 2.5e-220)
		tmp = t_3;
	else
		tmp = (x + (y / (t / z))) / t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -2.75e-18], N[(t$95$2 / t$95$1), $MachinePrecision], If[LessEqual[t, -8e-51], N[(z * N[(N[(N[(x / z), $MachinePrecision] / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.7e-77], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-196], t$95$3, If[LessEqual[t, -3.35e-217], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-220], t$95$3, N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.75e-18

   1. Initial program 90.3%

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

      1. associate-/l* 97.1%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   if -2.75e-18 < t < -8.0000000000000001e-51

   1. Initial program 45.1%

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

      1. associate-/l* 45.0%

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

      2. associate-/l* 37.4%

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

   3. Simplified 37.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 69.3%

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

   6. Taylor expanded in y around inf 93.5%

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

   7. Taylor expanded in a around 0 93.5%

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

      1. associate-/r* 91.0%

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

      2. associate-/l* 91.0%

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

   9. Simplified 91.0%

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

   if -8.0000000000000001e-51 < t < -1.69999999999999991e-77

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

      1. clear-num 62.9%

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

      2. un-div-inv 63.1%

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

   6. Applied egg-rr 99.8%

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

   if -1.69999999999999991e-77 < t < -3.50000000000000004e-196 or -3.35e-217 < t < 2.5000000000000001e-220

   1. Initial program 56.5%

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

      1. associate-/l* 43.4%

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

      2. associate-/l* 40.6%

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

   3. Simplified 40.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 44.8%

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

   6. Taylor expanded in y around 0 69.8%

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

      1. associate-/l* 67.1%

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

      2. associate-/l* 72.4%

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

   8. Simplified 72.4%

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

   if -3.50000000000000004e-196 < t < -3.35e-217

   1. Initial program 100.0%

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

      1. associate-/l* 83.8%

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

      2. associate-/l* 67.1%

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

   3. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   7. Applied egg-rr 100.0%

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

   if 2.5000000000000001e-220 < t

   1. Initial program 86.0%

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

      1. associate-/l* 86.4%

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

      2. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

      1. clear-num 89.6%

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

      2. un-div-inv 90.8%

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

   6. Applied egg-rr 90.8%

      \[\leadsto \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + y \cdot \frac{b}{t}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.75 \cdot 10^{-18}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-51}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-77}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-217}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-220}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-218}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-224}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-37}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.95e-16)
   (/ (+ x (* y (/ z t))) (+ a 1.0))
   (if (<= t -3.6e-195)
     (* z (+ (/ (/ x z) (+ 1.0 (* b (/ y t)))) (/ 1.0 b)))
     (if (<= t -2.1e-218)
       (/ (+ x (* z (/ y t))) (+ a 1.0))
       (if (<= t 3.8e-224)
         (/ (+ (* t (/ x b)) (* y (/ z b))) y)
         (if (<= t 4.7e-37)
           (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
           (/ x (+ 1.0 (+ a (* y (/ b t)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.95e-16) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= -3.6e-195) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -2.1e-218) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 3.8e-224) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (t <= 4.7e-37) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.95d-16)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (t <= (-3.6d-195)) then
        tmp = z * (((x / z) / (1.0d0 + (b * (y / t)))) + (1.0d0 / b))
    else if (t <= (-2.1d-218)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (t <= 3.8d-224) then
        tmp = ((t * (x / b)) + (y * (z / b))) / y
    else if (t <= 4.7d-37) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.95e-16) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (t <= -3.6e-195) {
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	} else if (t <= -2.1e-218) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 3.8e-224) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (t <= 4.7e-37) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.95e-16:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif t <= -3.6e-195:
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b))
	elif t <= -2.1e-218:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif t <= 3.8e-224:
		tmp = ((t * (x / b)) + (y * (z / b))) / y
	elif t <= 4.7e-37:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	else:
		tmp = x / (1.0 + (a + (y * (b / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.95e-16)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (t <= -3.6e-195)
		tmp = Float64(z * Float64(Float64(Float64(x / z) / Float64(1.0 + Float64(b * Float64(y / t)))) + Float64(1.0 / b)));
	elseif (t <= -2.1e-218)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (t <= 3.8e-224)
		tmp = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y);
	elseif (t <= 4.7e-37)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.95e-16)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (t <= -3.6e-195)
		tmp = z * (((x / z) / (1.0 + (b * (y / t)))) + (1.0 / b));
	elseif (t <= -2.1e-218)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (t <= 3.8e-224)
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	elseif (t <= 4.7e-37)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	else
		tmp = x / (1.0 + (a + (y * (b / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.95e-16], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.6e-195], N[(z * N[(N[(N[(x / z), $MachinePrecision] / N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.1e-218], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.8e-224], N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 4.7e-37], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.95000000000000011e-16

   1. Initial program 90.3%

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

      1. associate-/l* 97.1%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 80.8%

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

   if -2.95000000000000011e-16 < t < -3.6e-195

   1. Initial program 60.4%

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

      1. associate-/l* 53.2%

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

      2. associate-/l* 49.5%

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

   3. Simplified 49.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 65.8%

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

   6. Taylor expanded in y around inf 71.6%

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

   7. Taylor expanded in a around 0 69.8%

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

      1. associate-/r* 70.7%

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

      2. associate-/l* 70.6%

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

   9. Simplified 70.6%

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

   if -3.6e-195 < t < -2.09999999999999994e-218

   1. Initial program 100.0%

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

      1. associate-/l* 83.8%

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

      2. associate-/l* 67.1%

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

   3. Simplified 67.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

   7. Applied egg-rr 100.0%

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

   if -2.09999999999999994e-218 < t < 3.80000000000000002e-224

   1. Initial program 56.4%

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

      1. associate-/l* 42.0%

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

      2. associate-/l* 39.3%

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

   3. Simplified 39.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 48.9%

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

   6. Taylor expanded in y around 0 78.0%

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

      1. associate-/l* 73.0%

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

      2. associate-/l* 75.5%

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

   8. Simplified 75.5%

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

   if 3.80000000000000002e-224 < t < 4.7000000000000003e-37

   1. Initial program 85.7%

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

      1. associate-/l* 83.4%

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

      2. associate-/l* 79.4%

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

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.4%

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

   if 4.7000000000000003e-37 < t

   1. Initial program 86.1%

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

      1. associate-/l* 87.6%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.3%

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

      1. associate-*l/ 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-16}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-218}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-224}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-37}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{if}\;y \leq -4.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ a 1.0))))
   (if (<= y -4.3e+81)
     (/ (+ (* t (/ x b)) (* y (/ z b))) y)
     (if (<= y -2.8e-71)
       t_1
       (if (<= y -8.8e-92)
         (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
         (if (<= y 2.4e-137)
           t_1
           (if (<= y 5.8e+92) (/ x (+ 1.0 (+ a (/ y (/ t b))))) (/ z b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (y <= -4.3e+81) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (y <= -2.8e-71) {
		tmp = t_1;
	} else if (y <= -8.8e-92) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (y <= 2.4e-137) {
		tmp = t_1;
	} else if (y <= 5.8e+92) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (z * (y / t))) / (a + 1.0d0)
    if (y <= (-4.3d+81)) then
        tmp = ((t * (x / b)) + (y * (z / b))) / y
    else if (y <= (-2.8d-71)) then
        tmp = t_1
    else if (y <= (-8.8d-92)) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (y <= 2.4d-137) then
        tmp = t_1
    else if (y <= 5.8d+92) then
        tmp = x / (1.0d0 + (a + (y / (t / b))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / (a + 1.0);
	double tmp;
	if (y <= -4.3e+81) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (y <= -2.8e-71) {
		tmp = t_1;
	} else if (y <= -8.8e-92) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (y <= 2.4e-137) {
		tmp = t_1;
	} else if (y <= 5.8e+92) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / (a + 1.0)
	tmp = 0
	if y <= -4.3e+81:
		tmp = ((t * (x / b)) + (y * (z / b))) / y
	elif y <= -2.8e-71:
		tmp = t_1
	elif y <= -8.8e-92:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif y <= 2.4e-137:
		tmp = t_1
	elif y <= 5.8e+92:
		tmp = x / (1.0 + (a + (y / (t / b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (y <= -4.3e+81)
		tmp = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y);
	elseif (y <= -2.8e-71)
		tmp = t_1;
	elseif (y <= -8.8e-92)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (y <= 2.4e-137)
		tmp = t_1;
	elseif (y <= 5.8e+92)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / (a + 1.0);
	tmp = 0.0;
	if (y <= -4.3e+81)
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	elseif (y <= -2.8e-71)
		tmp = t_1;
	elseif (y <= -8.8e-92)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (y <= 2.4e-137)
		tmp = t_1;
	elseif (y <= 5.8e+92)
		tmp = x / (1.0 + (a + (y / (t / b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.3e+81], N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, -2.8e-71], t$95$1, If[LessEqual[y, -8.8e-92], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-137], t$95$1, If[LessEqual[y, 5.8e+92], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.3000000000000001e81

   1. Initial program 55.6%

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

      1. associate-/l* 60.7%

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

      2. associate-/l* 65.9%

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

   3. Simplified 65.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.7%

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

   6. Taylor expanded in y around 0 58.3%

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

      1. associate-/l* 58.3%

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

      2. associate-/l* 70.9%

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

   8. Simplified 70.9%

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

   if -4.3000000000000001e81 < y < -2.8e-71 or -8.79999999999999949e-92 < y < 2.4e-137

   1. Initial program 95.0%

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

      1. associate-/l* 85.7%

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

      2. associate-/l* 82.1%

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

   3. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 79.3%

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

      1. *-commutative 79.3%

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

      2. associate-/l* 80.4%

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

   7. Applied egg-rr 80.4%

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

   if -2.8e-71 < y < -8.79999999999999949e-92

   1. Initial program 56.6%

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

      1. associate-/l* 56.6%

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

      2. associate-/l* 55.8%

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

   3. Simplified 55.8%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 73.7%

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

   if 2.4e-137 < y < 5.8000000000000001e92

   1. Initial program 85.8%

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

      1. associate-/l* 87.8%

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

      2. associate-/l* 85.7%

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

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.8%

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

      1. associate-*l/ 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

   9. Applied egg-rr 79.9%

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

   if 5.8000000000000001e92 < y

   1. Initial program 51.1%

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

      1. associate-/l* 53.8%

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

      2. associate-/l* 56.6%

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

   3. Simplified 56.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.1%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+81}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-71}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-137}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+92}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \frac{y}{t}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+243}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+84} \lor \neg \left(y \leq 8.6 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + t\_1} + \frac{1}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (/ y t))))
   (if (<= y -5.5e+243)
     (/ (+ (* t (/ x b)) (* y (/ z b))) y)
     (if (or (<= y -3.7e+84) (not (<= y 8.6e+101)))
       (* z (+ (/ (/ x z) (+ 1.0 t_1)) (/ 1.0 b)))
       (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y / t);
	double tmp;
	if (y <= -5.5e+243) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if ((y <= -3.7e+84) || !(y <= 8.6e+101)) {
		tmp = z * (((x / z) / (1.0 + t_1)) + (1.0 / b));
	} else {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (y / t)
    if (y <= (-5.5d+243)) then
        tmp = ((t * (x / b)) + (y * (z / b))) / y
    else if ((y <= (-3.7d+84)) .or. (.not. (y <= 8.6d+101))) then
        tmp = z * (((x / z) / (1.0d0 + t_1)) + (1.0d0 / b))
    else
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (y / t);
	double tmp;
	if (y <= -5.5e+243) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if ((y <= -3.7e+84) || !(y <= 8.6e+101)) {
		tmp = z * (((x / z) / (1.0 + t_1)) + (1.0 / b));
	} else {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (y / t)
	tmp = 0
	if y <= -5.5e+243:
		tmp = ((t * (x / b)) + (y * (z / b))) / y
	elif (y <= -3.7e+84) or not (y <= 8.6e+101):
		tmp = z * (((x / z) / (1.0 + t_1)) + (1.0 / b))
	else:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(y / t))
	tmp = 0.0
	if (y <= -5.5e+243)
		tmp = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y);
	elseif ((y <= -3.7e+84) || !(y <= 8.6e+101))
		tmp = Float64(z * Float64(Float64(Float64(x / z) / Float64(1.0 + t_1)) + Float64(1.0 / b)));
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (y / t);
	tmp = 0.0;
	if (y <= -5.5e+243)
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	elseif ((y <= -3.7e+84) || ~((y <= 8.6e+101)))
		tmp = z * (((x / z) / (1.0 + t_1)) + (1.0 / b));
	else
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.5e+243], N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[y, -3.7e+84], N[Not[LessEqual[y, 8.6e+101]], $MachinePrecision]], N[(z * N[(N[(N[(x / z), $MachinePrecision] / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.50000000000000003e243

   1. Initial program 36.2%

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

      1. associate-/l* 36.2%

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

      2. associate-/l* 50.4%

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

   3. Simplified 50.4%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 49.6%

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

   6. Taylor expanded in y around 0 54.7%

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

      1. associate-/l* 62.2%

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

      2. associate-/l* 69.7%

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

   8. Simplified 69.7%

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

   if -5.50000000000000003e243 < y < -3.7e84 or 8.6000000000000002e101 < y

   1. Initial program 56.3%

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

      1. associate-/l* 61.3%

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

      2. associate-/l* 63.9%

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

   3. Simplified 63.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 68.4%

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

   6. Taylor expanded in y around inf 81.7%

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

   7. Taylor expanded in a around 0 80.4%

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

      1. associate-/r* 77.7%

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

      2. associate-/l* 80.2%

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

   9. Simplified 80.2%

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

   if -3.7e84 < y < 8.6000000000000002e101

   1. Initial program 89.9%

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. *-commutative 89.9%

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

      2. associate-/l* 89.3%

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

   4. Applied egg-rr 89.3%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+243}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{+84} \lor \neg \left(y \leq 8.6 \cdot 10^{+101}\right):\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{1 + b \cdot \frac{y}{t}} + \frac{1}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-142}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.5e+79)
   (/ z b)
   (if (<= y 4e-142)
     (/ (+ x (* z (/ y t))) (+ a 1.0))
     (if (<= y 3.8e+89) (/ x (+ 1.0 (+ a (/ y (/ t b))))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e+79) {
		tmp = z / b;
	} else if (y <= 4e-142) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (y <= 3.8e+89) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (y <= (-3.5d+79)) then
        tmp = z / b
    else if (y <= 4d-142) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (y <= 3.8d+89) then
        tmp = x / (1.0d0 + (a + (y / (t / b))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -3.5e+79) {
		tmp = z / b;
	} else if (y <= 4e-142) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (y <= 3.8e+89) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.5e+79:
		tmp = z / b
	elif y <= 4e-142:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif y <= 3.8e+89:
		tmp = x / (1.0 + (a + (y / (t / b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.5e+79)
		tmp = Float64(z / b);
	elseif (y <= 4e-142)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (y <= 3.8e+89)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.5e+79)
		tmp = z / b;
	elseif (y <= 4e-142)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (y <= 3.8e+89)
		tmp = x / (1.0 + (a + (y / (t / b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.5e+79], N[(z / b), $MachinePrecision], If[LessEqual[y, 4e-142], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+89], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.4999999999999998e79 or 3.80000000000000023e89 < y

   1. Initial program 53.9%

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

      1. associate-/l* 58.1%

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

      2. associate-/l* 62.3%

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

   3. Simplified 62.3%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.6%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -3.4999999999999998e79 < y < 4.0000000000000002e-142

   1. Initial program 91.5%

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

      1. associate-/l* 83.0%

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

      2. associate-/l* 79.7%

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

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-/l* 76.4%

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

   7. Applied egg-rr 76.4%

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

   if 4.0000000000000002e-142 < y < 3.80000000000000023e89

   1. Initial program 85.8%

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

      1. associate-/l* 87.8%

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

      2. associate-/l* 85.7%

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

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.8%

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

      1. associate-*l/ 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

   9. Applied egg-rr 79.9%

      \[\leadsto \frac{x}{1 + \left(a + \color{blue}{\frac{y}{\frac{t}{b}}}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-142}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+80}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-137}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.08e+80)
   (/ (+ (* t (/ x b)) (* y (/ z b))) y)
   (if (<= y 7.4e-137)
     (/ (+ x (* z (/ y t))) (+ a 1.0))
     (if (<= y 1.5e+94) (/ x (+ 1.0 (+ a (/ y (/ t b))))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.08e+80) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (y <= 7.4e-137) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (y <= 1.5e+94) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.08d+80)) then
        tmp = ((t * (x / b)) + (y * (z / b))) / y
    else if (y <= 7.4d-137) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (y <= 1.5d+94) then
        tmp = x / (1.0d0 + (a + (y / (t / b))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.08e+80) {
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	} else if (y <= 7.4e-137) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (y <= 1.5e+94) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.08e+80:
		tmp = ((t * (x / b)) + (y * (z / b))) / y
	elif y <= 7.4e-137:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif y <= 1.5e+94:
		tmp = x / (1.0 + (a + (y / (t / b))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.08e+80)
		tmp = Float64(Float64(Float64(t * Float64(x / b)) + Float64(y * Float64(z / b))) / y);
	elseif (y <= 7.4e-137)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (y <= 1.5e+94)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.08e+80)
		tmp = ((t * (x / b)) + (y * (z / b))) / y;
	elseif (y <= 7.4e-137)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (y <= 1.5e+94)
		tmp = x / (1.0 + (a + (y / (t / b))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.08e+80], N[(N[(N[(t * N[(x / b), $MachinePrecision]), $MachinePrecision] + N[(y * N[(z / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7.4e-137], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+94], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.08e80

   1. Initial program 55.6%

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

      1. associate-/l* 60.7%

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

      2. associate-/l* 65.9%

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

   3. Simplified 65.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around inf 51.7%

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

   6. Taylor expanded in y around 0 58.3%

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

      1. associate-/l* 58.3%

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

      2. associate-/l* 70.9%

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

   8. Simplified 70.9%

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

   if -1.08e80 < y < 7.4e-137

   1. Initial program 91.5%

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

      1. associate-/l* 83.0%

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

      2. associate-/l* 79.7%

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

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in b around 0 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-/l* 76.4%

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

   7. Applied egg-rr 76.4%

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

   if 7.4e-137 < y < 1.5e94

   1. Initial program 85.8%

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

      1. associate-/l* 87.8%

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

      2. associate-/l* 85.7%

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

   3. Simplified 85.7%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 79.8%

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

      1. associate-*l/ 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

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

      1. clear-num 79.8%

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

      2. un-div-inv 79.9%

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

   9. Applied egg-rr 79.9%

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

   if 1.5e94 < y

   1. Initial program 51.1%

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

      1. associate-/l* 53.8%

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

      2. associate-/l* 56.6%

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

   3. Simplified 56.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 69.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+80}:\\ \;\;\;\;\frac{t \cdot \frac{x}{b} + y \cdot \frac{z}{b}}{y}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-137}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+94}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+212}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-8}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -3.8e+212)
   x
   (if (<= t -2.7e+144)
     (/ x a)
     (if (<= t -5.8e-16) x (if (<= t 8e-8) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+212) {
		tmp = x;
	} else if (t <= -2.7e+144) {
		tmp = x / a;
	} else if (t <= -5.8e-16) {
		tmp = x;
	} else if (t <= 8e-8) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (t <= (-3.8d+212)) then
        tmp = x
    else if (t <= (-2.7d+144)) then
        tmp = x / a
    else if (t <= (-5.8d-16)) then
        tmp = x
    else if (t <= 8d-8) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -3.8e+212) {
		tmp = x;
	} else if (t <= -2.7e+144) {
		tmp = x / a;
	} else if (t <= -5.8e-16) {
		tmp = x;
	} else if (t <= 8e-8) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -3.8e+212:
		tmp = x
	elif t <= -2.7e+144:
		tmp = x / a
	elif t <= -5.8e-16:
		tmp = x
	elif t <= 8e-8:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -3.8e+212)
		tmp = x;
	elseif (t <= -2.7e+144)
		tmp = Float64(x / a);
	elseif (t <= -5.8e-16)
		tmp = x;
	elseif (t <= 8e-8)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -3.8e+212)
		tmp = x;
	elseif (t <= -2.7e+144)
		tmp = x / a;
	elseif (t <= -5.8e-16)
		tmp = x;
	elseif (t <= 8e-8)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -3.8e+212], x, If[LessEqual[t, -2.7e+144], N[(x / a), $MachinePrecision], If[LessEqual[t, -5.8e-16], x, If[LessEqual[t, 8e-8], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.79999999999999988e212 or -2.70000000000000015e144 < t < -5.7999999999999996e-16

   1. Initial program 88.4%

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

      1. associate-/l* 97.9%

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

      2. associate-/l* 98.0%

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

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   6. Taylor expanded in a around 0 51.8%

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

   if -3.79999999999999988e212 < t < -2.70000000000000015e144 or 8.0000000000000002e-8 < t

   1. Initial program 88.5%

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

      1. associate-/l* 91.1%

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

      2. associate-/l* 96.0%

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

   3. Simplified 96.0%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 74.8%

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

      1. associate-*l/ 78.4%

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

      2. *-commutative 78.4%

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

   7. Simplified 78.4%

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

   8. Taylor expanded in a around inf 44.9%

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

   if -5.7999999999999996e-16 < t < 8.0000000000000002e-8

   1. Initial program 67.0%

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

      1. associate-/l* 57.7%

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

      2. associate-/l* 53.9%

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

   3. Simplified 53.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 56.9%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+212}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-8}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-18} \lor \neg \left(t \leq 4.5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.4e-18) (not (<= t 4.5e-37)))
   (/ x (+ 1.0 (+ a (* y (/ b t)))))
   (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.4e-18) || !(t <= 4.5e-37)) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-4.4d-18)) .or. (.not. (t <= 4.5d-37))) then
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.4e-18) || !(t <= 4.5e-37)) {
		tmp = x / (1.0 + (a + (y * (b / t))));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.4e-18) or not (t <= 4.5e-37):
		tmp = x / (1.0 + (a + (y * (b / t))))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.4e-18) || !(t <= 4.5e-37))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.4e-18) || ~((t <= 4.5e-37)))
		tmp = x / (1.0 + (a + (y * (b / t))));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.4e-18], N[Not[LessEqual[t, 4.5e-37]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3999999999999997e-18 or 4.5000000000000004e-37 < t

   1. Initial program 88.3%

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

      1. associate-/l* 92.7%

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

      2. associate-/l* 95.5%

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

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.9%

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

      1. associate-*l/ 79.0%

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

      2. *-commutative 79.0%

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

   7. Simplified 79.0%

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

   if -4.3999999999999997e-18 < t < 4.5000000000000004e-37

   1. Initial program 65.9%

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

      1. associate-/l* 56.9%

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

      2. associate-/l* 52.9%

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

   3. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 58.3%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-18} \lor \neg \left(t \leq 4.5 \cdot 10^{-37}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+83} \lor \neg \left(y \leq 9.5 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.05e+83) (not (<= y 9.5e+91)))
   (/ z b)
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e+83) || !(y <= 9.5e+91)) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.05d+83)) .or. (.not. (y <= 9.5d+91))) then
        tmp = z / b
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.05e+83) || !(y <= 9.5e+91)) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.05e+83) or not (y <= 9.5e+91):
		tmp = z / b
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.05e+83) || !(y <= 9.5e+91))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.05e+83) || ~((y <= 9.5e+91)))
		tmp = z / b;
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.05e+83], N[Not[LessEqual[y, 9.5e+91]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05e83 or 9.5000000000000001e91 < y

   1. Initial program 53.3%

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

      1. associate-/l* 57.6%

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

      2. associate-/l* 61.9%

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

   3. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 68.3%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if -2.05e83 < y < 9.5000000000000001e91

   1. Initial program 89.9%

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

      1. associate-/l* 84.5%

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

      2. associate-/l* 81.5%

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

   3. Simplified 81.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 73.1%

      \[\leadsto \color{blue}{\frac{x}{1 + \left(a + \frac{b \cdot y}{t}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+83} \lor \neg \left(y \leq 9.5 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.2e-16)
   (/ x (+ 1.0 (+ a (/ y (/ t b)))))
   (if (<= t 6.8e-36) (/ z b) (/ x (+ 1.0 (+ a (* y (/ b t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e-16) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else if (t <= 6.8e-36) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.2d-16)) then
        tmp = x / (1.0d0 + (a + (y / (t / b))))
    else if (t <= 6.8d-36) then
        tmp = z / b
    else
        tmp = x / (1.0d0 + (a + (y * (b / t))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.2e-16) {
		tmp = x / (1.0 + (a + (y / (t / b))));
	} else if (t <= 6.8e-36) {
		tmp = z / b;
	} else {
		tmp = x / (1.0 + (a + (y * (b / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.2e-16:
		tmp = x / (1.0 + (a + (y / (t / b))))
	elif t <= 6.8e-36:
		tmp = z / b
	else:
		tmp = x / (1.0 + (a + (y * (b / t))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.2e-16)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y / Float64(t / b)))));
	elseif (t <= 6.8e-36)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.2e-16)
		tmp = x / (1.0 + (a + (y / (t / b))));
	elseif (t <= 6.8e-36)
		tmp = z / b;
	else
		tmp = x / (1.0 + (a + (y * (b / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.2e-16], N[(x / N[(1.0 + N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-36], N[(z / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.20000000000000002e-16

   1. Initial program 90.3%

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

      1. associate-/l* 97.1%

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

      2. associate-/l* 97.1%

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

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 78.3%

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

      1. associate-*l/ 78.3%

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

      2. *-commutative 78.3%

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

   7. Simplified 78.3%

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

      1. clear-num 78.3%

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

      2. un-div-inv 78.4%

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

   9. Applied egg-rr 78.4%

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

   if -1.20000000000000002e-16 < t < 6.8000000000000005e-36

   1. Initial program 65.9%

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

      1. associate-/l* 56.9%

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

      2. associate-/l* 52.9%

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

   3. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 58.3%

      \[\leadsto \color{blue}{\frac{z}{b}} \]

   if 6.8000000000000005e-36 < t

   1. Initial program 86.1%

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

      1. associate-/l* 87.6%

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

      2. associate-/l* 93.6%

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

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 75.3%

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

      1. associate-*l/ 79.8%

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

      2. *-commutative 79.8%

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

   7. Simplified 79.8%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 56.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-18} \lor \neg \left(t \leq 1.35 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.5e-18) (not (<= t 1.35e-35))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.5e-18) || !(t <= 1.35e-35)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3.5d-18)) .or. (.not. (t <= 1.35d-35))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.5e-18) || !(t <= 1.35e-35)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.5e-18) or not (t <= 1.35e-35):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.5e-18) || !(t <= 1.35e-35))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3.5e-18) || ~((t <= 1.35e-35)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.5e-18], N[Not[LessEqual[t, 1.35e-35]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999999e-18 or 1.3499999999999999e-35 < t

   1. Initial program 88.3%

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

      1. associate-/l* 92.7%

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

      2. associate-/l* 95.5%

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

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.5%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   if -3.4999999999999999e-18 < t < 1.3499999999999999e-35

   1. Initial program 65.9%

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

      1. associate-/l* 56.9%

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

      2. associate-/l* 52.9%

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

   3. Simplified 52.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 58.3%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-18} \lor \neg \left(t \leq 1.35 \cdot 10^{-35}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-15} \lor \neg \left(a \leq 2.1 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -4e-15) (not (<= a 2.1e-9))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4e-15) || !(a <= 2.1e-9)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-4d-15)) .or. (.not. (a <= 2.1d-9))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -4e-15) || !(a <= 2.1e-9)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -4e-15) or not (a <= 2.1e-9):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -4e-15) || !(a <= 2.1e-9))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -4e-15) || ~((a <= 2.1e-9)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -4e-15], N[Not[LessEqual[a, 2.1e-9]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -4.0000000000000003e-15 or 2.10000000000000019e-9 < a

   1. Initial program 75.1%

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

      1. associate-/l* 72.2%

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

      2. associate-/l* 70.6%

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

   3. Simplified 70.6%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 54.9%

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

      1. associate-*l/ 53.3%

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

      2. *-commutative 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in a around inf 44.6%

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

   if -4.0000000000000003e-15 < a < 2.10000000000000019e-9

   1. Initial program 79.8%

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

      1. associate-/l* 78.3%

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

      2. associate-/l* 78.9%

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

   3. Simplified 78.9%

      \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 40.3%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

   6. Taylor expanded in a around 0 40.2%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-15} \lor \neg \left(a \leq 2.1 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 19.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 77.5%

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

   1. associate-/l* 75.3%

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

   2. associate-/l* 74.8%

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

3. Simplified 74.8%

   \[\leadsto \color{blue}{\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 43.0%

   \[\leadsto \color{blue}{\frac{x}{1 + a}} \]

6. Taylor expanded in a around 0 22.6%

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

7. Final simplification 22.6%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))
   (if (< t -1.3659085366310088e-271)
     t_1
     (if (< t 3.036967103737246e-130) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 * ((x + ((y / t) * z)) * (1.0d0 / ((a + 1.0d0) + ((y / t) * b))))
    if (t < (-1.3659085366310088d-271)) then
        tmp = t_1
    else if (t < 3.036967103737246d-130) then
        tmp = z / b
    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 b) {
	double t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	double tmp;
	if (t < -1.3659085366310088e-271) {
		tmp = t_1;
	} else if (t < 3.036967103737246e-130) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))))
	tmp = 0
	if t < -1.3659085366310088e-271:
		tmp = t_1
	elif t < 3.036967103737246e-130:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 * Float64(Float64(x + Float64(Float64(y / t) * z)) * Float64(1.0 / Float64(Float64(a + 1.0) + Float64(Float64(y / t) * b)))))
	tmp = 0.0
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 * ((x + ((y / t) * z)) * (1.0 / ((a + 1.0) + ((y / t) * b))));
	tmp = 0.0;
	if (t < -1.3659085366310088e-271)
		tmp = t_1;
	elseif (t < 3.036967103737246e-130)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 * N[(N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -1.3659085366310088e-271], t$95$1, If[Less[t, 3.036967103737246e-130], N[(z / b), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024060 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))