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

Percentage Accurate: 75.3% → 89.9%

Time: 18.1s

Alternatives: 16

Speedup: 0.6×

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: 75.3% 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: 89.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_3 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ t_4 := 1 + \left(a + t\_1\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_4} + \frac{y}{t \cdot t\_4}\right)\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{t\_3} + \frac{\frac{y}{t}}{t\_3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 (+ (+ a 1.0) (* y (/ b t))))
        (t_4 (+ 1.0 (+ a t_1))))
   (if (<= t_2 (- INFINITY))
     (* z (+ (/ x (* z t_4)) (/ y (* t t_4))))
     (if (<= t_2 5e+280)
       t_2
       (if (<= t_2 INFINITY)
         (* z (+ (/ (/ x z) t_3) (/ (/ y t) t_3)))
         (/ 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 = (a + 1.0) + (y * (b / t));
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	} else if (t_2 <= 5e+280) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3));
	} 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 = (a + 1.0) + (y * (b / t));
	double t_4 = 1.0 + (a + t_1);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	} else if (t_2 <= 5e+280) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3));
	} 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 = (a + 1.0) + (y * (b / t))
	t_4 = 1.0 + (a + t_1)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)))
	elif t_2 <= 5e+280:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3))
	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(Float64(a + 1.0) + Float64(y * Float64(b / t)))
	t_4 = Float64(1.0 + Float64(a + t_1))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_4)) + Float64(y / Float64(t * t_4))));
	elseif (t_2 <= 5e+280)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = Float64(z * Float64(Float64(Float64(x / z) / t_3) + Float64(Float64(y / t) / t_3)));
	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 = (a + 1.0) + (y * (b / t));
	t_4 = 1.0 + (a + t_1);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * ((x / (z * t_4)) + (y / (t * t_4)));
	elseif (t_2 <= 5e+280)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = z * (((x / z) / t_3) + ((y / t) / t_3));
	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[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = 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$4), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+280], t$95$2, If[LessEqual[t$95$2, Infinity], N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$3), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 26.8%

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

      1. associate-/l* 48.8%

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

      2. associate-/l* 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 92.4%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e280

   1. Initial program 92.3%

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

   if 5.0000000000000002e280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 38.4%

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

      1. associate-/l* 60.9%

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

      2. associate-/l* 60.9%

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

   3. Simplified 60.9%

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

   5. Taylor expanded in z around inf 88.3%

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

      1. associate-/r* 88.6%

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

      2. associate-+r+ 88.6%

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

      3. associate-*l/ 88.6%

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

      4. *-commutative 88.6%

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

      5. associate-/r* 88.5%

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

      6. associate-+r+ 88.5%

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

      7. associate-*l/ 88.5%

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

      8. *-commutative 88.5%

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

   7. Simplified 88.5%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.7%

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

      2. associate-/l* 10.8%

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

   3. Simplified 10.8%

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

   5. Taylor expanded in y around inf 94.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{\left(a + 1\right) + y \cdot \frac{b}{t}} + \frac{\frac{y}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + t\_1}\\ t_3 := 1 + \left(a + t\_1\right)\\ t_4 := z \cdot \left(\frac{x}{z \cdot t\_3} + \frac{y}{t \cdot t\_3}\right)\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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)))
        (t_4 (* z (+ (/ x (* z t_3)) (/ y (* t t_3))))))
   (if (<= t_2 (- INFINITY))
     t_4
     (if (<= t_2 5e+280) t_2 (if (<= t_2 INFINITY) t_4 (/ 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 t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_4;
	} else if (t_2 <= 5e+280) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_4;
	} 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 t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} else if (t_2 <= 5e+280) {
		tmp = t_2;
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_4;
	} 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)
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_4
	elif t_2 <= 5e+280:
		tmp = t_2
	elif t_2 <= math.inf:
		tmp = t_4
	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))
	t_4 = Float64(z * Float64(Float64(x / Float64(z * t_3)) + Float64(y / Float64(t * t_3))))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_4;
	elseif (t_2 <= 5e+280)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	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);
	t_4 = z * ((x / (z * t_3)) + (y / (t * t_3)));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_4;
	elseif (t_2 <= 5e+280)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_4;
	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]}, Block[{t$95$4 = 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, (-Infinity)], t$95$4, If[LessEqual[t$95$2, 5e+280], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$4, N[(z / b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0 or 5.0000000000000002e280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 33.3%

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

      1. associate-/l* 55.6%

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

      2. associate-/l* 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in z around inf 90.1%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e280

   1. Initial program 92.3%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 0.0%

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

      1. associate-/l* 0.7%

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

      2. associate-/l* 10.8%

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

   3. Simplified 10.8%

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

   5. Taylor expanded in y around inf 94.8%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\frac{z \cdot \left(1 + \frac{x}{z} \cdot \frac{t}{y}\right)}{b}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+280}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t_1 (- INFINITY))
     (/ (* z (+ 1.0 (* (/ x z) (/ t y)))) b)
     (if (<= t_1 5e+280) t_1 (/ z b)))))

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)) {
		tmp = (z * (1.0 + ((x / z) * (t / y)))) / b;
	} else if (t_1 <= 5e+280) {
		tmp = t_1;
	} 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 = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (z * (1.0 + ((x / z) * (t / y)))) / b;
	} else if (t_1 <= 5e+280) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	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:
		tmp = (z * (1.0 + ((x / z) * (t / y)))) / b
	elif t_1 <= 5e+280:
		tmp = t_1
	else:
		tmp = z / b
	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))
		tmp = Float64(Float64(z * Float64(1.0 + Float64(Float64(x / z) * Float64(t / y)))) / b);
	elseif (t_1 <= 5e+280)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	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)
		tmp = (z * (1.0 + ((x / z) * (t / y)))) / b;
	elseif (t_1 <= 5e+280)
		tmp = t_1;
	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[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(z * N[(1.0 + N[(N[(x / z), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+280], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 26.8%

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

      1. associate-/l* 48.8%

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

      2. associate-/l* 48.8%

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

   3. Simplified 48.8%

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

   5. Taylor expanded in z around inf 92.4%

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

   6. Taylor expanded in b around inf 69.3%

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

      1. times-frac 77.5%

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

   8. Simplified 77.5%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e280

   1. Initial program 92.3%

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

   if 5.0000000000000002e280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 18.1%

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

      1. associate-/l* 29.1%

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

      2. associate-/l* 34.4%

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

   3. Simplified 34.4%

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

   5. Taylor expanded in y around inf 78.5%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq -\infty:\\ \;\;\;\;\frac{z \cdot \left(1 + \frac{x}{z} \cdot \frac{t}{y}\right)}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 5 \cdot 10^{+280}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-161} \lor \neg \left(t \leq 2.22 \cdot 10^{-191} \lor \neg \left(t \leq 2.3 \cdot 10^{-131}\right) \land t \leq 7.6 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2e-161)
         (not
          (or (<= t 2.22e-191) (and (not (<= t 2.3e-131)) (<= t 7.6e-85)))))
   (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e-161) || !((t <= 2.22e-191) || (!(t <= 2.3e-131) && (t <= 7.6e-85)))) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / 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 <= (-2d-161)) .or. (.not. (t <= 2.22d-191) .or. (.not. (t <= 2.3d-131)) .and. (t <= 7.6d-85))) then
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z + ((x * t) / y)) / 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 <= -2e-161) || !((t <= 2.22e-191) || (!(t <= 2.3e-131) && (t <= 7.6e-85)))) {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2e-161) or not ((t <= 2.22e-191) or (not (t <= 2.3e-131) and (t <= 7.6e-85))):
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2e-161) || !((t <= 2.22e-191) || (!(t <= 2.3e-131) && (t <= 7.6e-85))))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2e-161) || ~(((t <= 2.22e-191) || (~((t <= 2.3e-131)) && (t <= 7.6e-85)))))
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2e-161], N[Not[Or[LessEqual[t, 2.22e-191], And[N[Not[LessEqual[t, 2.3e-131]], $MachinePrecision], LessEqual[t, 7.6e-85]]]], $MachinePrecision]], 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], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000006e-161 or 2.22e-191 < t < 2.30000000000000022e-131 or 7.5999999999999997e-85 < t

   1. Initial program 84.7%

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

      1. associate-/l* 86.7%

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

      2. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   if -2.00000000000000006e-161 < t < 2.22e-191 or 2.30000000000000022e-131 < t < 7.5999999999999997e-85

   1. Initial program 58.7%

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

      1. associate-/l* 52.5%

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

      2. associate-/l* 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in z around inf 70.2%

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

   6. Taylor expanded in b around inf 76.1%

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

      1. times-frac 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in z around 0 77.9%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-161} \lor \neg \left(t \leq 2.22 \cdot 10^{-191} \lor \neg \left(t \leq 2.3 \cdot 10^{-131}\right) \land t \leq 7.6 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + y \cdot \frac{b}{t}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{t\_1}\\ t_3 := \frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{if}\;t \leq -1.28 \cdot 10^{-163}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-191}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t\_1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-86}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

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_1))
        (t_3 (/ (+ z (/ (* x t) y)) b)))
   (if (<= t -1.28e-163)
     t_2
     (if (<= t 1.08e-191)
       t_3
       (if (<= t 3.7e-131)
         (/ (+ x (/ y (/ t z))) t_1)
         (if (<= t 1.25e-86) t_3 t_2))))))

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))) / t_1;
	double t_3 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -1.28e-163) {
		tmp = t_2;
	} else if (t <= 1.08e-191) {
		tmp = t_3;
	} else if (t <= 3.7e-131) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 1.25e-86) {
		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 = (a + 1.0d0) + (y * (b / t))
    t_2 = (x + (y * (z / t))) / t_1
    t_3 = (z + ((x * t) / y)) / b
    if (t <= (-1.28d-163)) then
        tmp = t_2
    else if (t <= 1.08d-191) then
        tmp = t_3
    else if (t <= 3.7d-131) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t <= 1.25d-86) 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 = (a + 1.0) + (y * (b / t));
	double t_2 = (x + (y * (z / t))) / t_1;
	double t_3 = (z + ((x * t) / y)) / b;
	double tmp;
	if (t <= -1.28e-163) {
		tmp = t_2;
	} else if (t <= 1.08e-191) {
		tmp = t_3;
	} else if (t <= 3.7e-131) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t <= 1.25e-86) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	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_1
	t_3 = (z + ((x * t) / y)) / b
	tmp = 0
	if t <= -1.28e-163:
		tmp = t_2
	elif t <= 1.08e-191:
		tmp = t_3
	elif t <= 3.7e-131:
		tmp = (x + (y / (t / z))) / t_1
	elif t <= 1.25e-86:
		tmp = t_3
	else:
		tmp = t_2
	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(Float64(x + Float64(y * Float64(z / t))) / t_1)
	t_3 = Float64(Float64(z + Float64(Float64(x * t) / y)) / b)
	tmp = 0.0
	if (t <= -1.28e-163)
		tmp = t_2;
	elseif (t <= 1.08e-191)
		tmp = t_3;
	elseif (t <= 3.7e-131)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t <= 1.25e-86)
		tmp = t_3;
	else
		tmp = t_2;
	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_1;
	t_3 = (z + ((x * t) / y)) / b;
	tmp = 0.0;
	if (t <= -1.28e-163)
		tmp = t_2;
	elseif (t <= 1.08e-191)
		tmp = t_3;
	elseif (t <= 3.7e-131)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t <= 1.25e-86)
		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[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[t, -1.28e-163], t$95$2, If[LessEqual[t, 1.08e-191], t$95$3, If[LessEqual[t, 3.7e-131], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t, 1.25e-86], t$95$3, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.28e-163 or 1.25e-86 < t

   1. Initial program 84.0%

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

      1. associate-/l* 86.8%

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

      2. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   if -1.28e-163 < t < 1.07999999999999996e-191 or 3.7000000000000002e-131 < t < 1.25e-86

   1. Initial program 58.7%

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

      1. associate-/l* 52.5%

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

      2. associate-/l* 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in z around inf 70.2%

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

   6. Taylor expanded in b around inf 76.1%

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

      1. times-frac 68.2%

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

   8. Simplified 68.2%

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

   9. Taylor expanded in z around 0 77.9%

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

   if 1.07999999999999996e-191 < t < 3.7000000000000002e-131

   1. Initial program 92.9%

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

      1. associate-/l* 86.4%

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

      2. associate-/l* 73.5%

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

   3. Simplified 73.5%

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

      1. clear-num 73.6%

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

      2. un-div-inv 73.7%

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

   6. Applied egg-rr 73.7%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.28 \cdot 10^{-163}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-191}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-131}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-86}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-143}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-161} \lor \neg \left(t \leq 9.6 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.9e-85)
   (/ x (+ (+ a 1.0) (/ y (/ t b))))
   (if (<= t -1.75e-143)
     (/ z b)
     (if (or (<= t -3.1e-161) (not (<= t 9.6e-60)))
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (/ (+ z (/ (* x t) y)) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.9e-85) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} else if (t <= -1.75e-143) {
		tmp = z / b;
	} else if ((t <= -3.1e-161) || !(t <= 9.6e-60)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / 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 <= (-2.9d-85)) then
        tmp = x / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= (-1.75d-143)) then
        tmp = z / b
    else if ((t <= (-3.1d-161)) .or. (.not. (t <= 9.6d-60))) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / 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 <= -2.9e-85) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} else if (t <= -1.75e-143) {
		tmp = z / b;
	} else if ((t <= -3.1e-161) || !(t <= 9.6e-60)) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.9e-85:
		tmp = x / ((a + 1.0) + (y / (t / b)))
	elif t <= -1.75e-143:
		tmp = z / b
	elif (t <= -3.1e-161) or not (t <= 9.6e-60):
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.9e-85)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= -1.75e-143)
		tmp = Float64(z / b);
	elseif ((t <= -3.1e-161) || !(t <= 9.6e-60))
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.9e-85)
		tmp = x / ((a + 1.0) + (y / (t / b)));
	elseif (t <= -1.75e-143)
		tmp = z / b;
	elseif ((t <= -3.1e-161) || ~((t <= 9.6e-60)))
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.9e-85], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e-143], N[(z / b), $MachinePrecision], If[Or[LessEqual[t, -3.1e-161], N[Not[LessEqual[t, 9.6e-60]], $MachinePrecision]], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.9000000000000002e-85

   1. Initial program 84.8%

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

      1. associate-/l* 88.0%

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

      2. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf 83.2%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.2%

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

   7. Applied egg-rr 83.2%

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

   if -2.9000000000000002e-85 < t < -1.75000000000000003e-143

   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* 56.7%

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

      2. associate-/l* 44.8%

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

   3. Simplified 44.8%

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

   5. Taylor expanded in y around inf 75.8%

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

   if -1.75000000000000003e-143 < t < -3.0999999999999999e-161 or 9.60000000000000038e-60 < t

   1. Initial program 85.3%

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

      1. associate-/l* 87.9%

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

      2. associate-/l* 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in b around 0 78.5%

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

   if -3.0999999999999999e-161 < t < 9.60000000000000038e-60

   1. Initial program 66.8%

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

      1. associate-/l* 60.7%

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

      2. associate-/l* 53.5%

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

   3. Simplified 53.5%

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

   5. Taylor expanded in z around inf 74.5%

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

   6. Taylor expanded in b around inf 68.1%

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

      1. times-frac 62.0%

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

   8. Simplified 62.0%

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

   9. Taylor expanded in z around 0 71.3%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-143}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-161} \lor \neg \left(t \leq 9.6 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+125}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-165}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -3.1e+125)
   (/ (+ z (/ (* x t) y)) b)
   (if (<= y 4e-165)
     (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (* b (/ y t))))
     (/ (+ 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) {
	double tmp;
	if (y <= -3.1e+125) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 4e-165) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (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 <= (-3.1d+125)) then
        tmp = (z + ((x * t) / y)) / b
    else if (y <= 4d-165) then
        tmp = (x + ((y * z) / t)) / ((a + 1.0d0) + (b * (y / t)))
    else
        tmp = (x + (y * (z / t))) / ((a + 1.0d0) + (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 <= -3.1e+125) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (y <= 4e-165) {
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	} else {
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -3.1e+125:
		tmp = (z + ((x * t) / y)) / b
	elif y <= 4e-165:
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)))
	else:
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -3.1e+125)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (y <= 4e-165)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -3.1e+125)
		tmp = (z + ((x * t) / y)) / b;
	elseif (y <= 4e-165)
		tmp = (x + ((y * z) / t)) / ((a + 1.0) + (b * (y / t)));
	else
		tmp = (x + (y * (z / t))) / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -3.1e+125], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[y, 4e-165], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1e125

   1. Initial program 44.7%

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

      1. associate-/l* 47.3%

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

      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 z around inf 54.1%

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

   6. Taylor expanded in b around inf 72.9%

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

      1. times-frac 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in z around 0 72.9%

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

   if -3.1e125 < y < 4e-165

   1. Initial program 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-/l* 94.0%

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

   4. Applied egg-rr 94.0%

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

   if 4e-165 < y

   1. Initial program 71.8%

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

      1. associate-/l* 77.5%

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

      2. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+125}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-165}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \left(\left(1 + b \cdot \frac{y}{t}\right) + -1\right)}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-210}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -7.1e-149)
   (/ x (+ (+ a 1.0) (+ (+ 1.0 (* b (/ y t))) -1.0)))
   (if (<= t -7e-210)
     (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
     (if (<= t 2.1e-58)
       (/ (+ z (/ (* x t) y)) b)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -7.1e-149) {
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0));
	} else if (t <= -7e-210) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 2.1e-58) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	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 <= (-7.1d-149)) then
        tmp = x / ((a + 1.0d0) + ((1.0d0 + (b * (y / t))) + (-1.0d0)))
    else if (t <= (-7d-210)) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (t <= 2.1d-58) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    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 <= -7.1e-149) {
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0));
	} else if (t <= -7e-210) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 2.1e-58) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -7.1e-149:
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0))
	elif t <= -7e-210:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif t <= 2.1e-58:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -7.1e-149)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(1.0 + Float64(b * Float64(y / t))) + -1.0)));
	elseif (t <= -7e-210)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (t <= 2.1e-58)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -7.1e-149)
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0));
	elseif (t <= -7e-210)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (t <= 2.1e-58)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -7.1e-149], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e-210], 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[t, 2.1e-58], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.1000000000000002e-149

   1. Initial program 82.8%

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

      1. associate-/l* 85.7%

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

      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. Taylor expanded in x around inf 78.5%

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

      1. expm1-log1p-u 67.4%

         \[\leadsto \frac{x}{\left(a + 1\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \frac{b}{t}\right)\right)}} \]

      2. expm1-undefine 67.4%

         \[\leadsto \frac{x}{\left(a + 1\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \frac{b}{t}\right)} - 1\right)}} \]

      3. log1p-undefine 67.4%

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

      4. add-exp-log 78.5%

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

      5. associate-*r/ 74.6%

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

      6. *-commutative 74.6%

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

      7. associate-/l* 79.5%

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

   7. Applied egg-rr 79.5%

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

   if -7.1000000000000002e-149 < t < -7.00000000000000031e-210

   1. Initial program 80.5%

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

      1. associate-/l* 74.2%

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

      2. associate-/l* 61.7%

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

   3. Simplified 61.7%

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

   5. Taylor expanded in x around 0 86.7%

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

   if -7.00000000000000031e-210 < t < 2.09999999999999988e-58

   1. Initial program 66.6%

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

      1. associate-/l* 59.8%

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

      2. associate-/l* 54.3%

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

   3. Simplified 54.3%

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

   5. Taylor expanded in z around inf 71.2%

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

   6. Taylor expanded in b around inf 68.0%

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

      1. times-frac 61.1%

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

   8. Simplified 61.1%

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

   9. Taylor expanded in z around 0 71.6%

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

   if 2.09999999999999988e-58 < t

   1. Initial program 83.7%

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

      1. associate-/l* 87.9%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in b around 0 77.5%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.1 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \left(\left(1 + b \cdot \frac{y}{t}\right) + -1\right)}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-210}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-96} \lor \neg \left(t \leq 4.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -7.4e-96) (not (<= t 4.8e-63)))
   (/ x (+ 1.0 (+ a (/ (* y b) t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -7.4e-96) || !(t <= 4.8e-63)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z + ((x * t) / y)) / 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 <= (-7.4d-96)) .or. (.not. (t <= 4.8d-63))) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else
        tmp = (z + ((x * t) / y)) / 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 <= -7.4e-96) || !(t <= 4.8e-63)) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -7.4e-96) or not (t <= 4.8e-63):
		tmp = x / (1.0 + (a + ((y * b) / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -7.4e-96) || !(t <= 4.8e-63))
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -7.4e-96) || ~((t <= 4.8e-63)))
		tmp = x / (1.0 + (a + ((y * b) / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -7.4e-96], N[Not[LessEqual[t, 4.8e-63]], $MachinePrecision]], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.39999999999999972e-96 or 4.8000000000000001e-63 < t

   1. Initial program 84.6%

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

      1. associate-/l* 88.2%

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

      2. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

   5. Taylor expanded in x around inf 75.8%

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

   if -7.39999999999999972e-96 < t < 4.8000000000000001e-63

   1. Initial program 67.7%

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

      1. associate-/l* 61.4%

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

      2. associate-/l* 55.2%

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

   3. Simplified 55.2%

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

   5. Taylor expanded in z around inf 74.3%

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

   6. Taylor expanded in b around inf 64.2%

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

      1. times-frac 57.9%

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

   8. Simplified 57.9%

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

   9. Taylor expanded in z around 0 66.9%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.4 \cdot 10^{-96} \lor \neg \left(t \leq 4.8 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-88} \lor \neg \left(t \leq 7.3 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.4e-88) (not (<= t 7.3e-63)))
   (/ x (+ (+ a 1.0) (* y (/ b t))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.4e-88) || !(t <= 7.3e-63)) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / 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-88)) .or. (.not. (t <= 7.3d-63))) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    else
        tmp = (z + ((x * t) / y)) / 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-88) || !(t <= 7.3e-63)) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.4e-88) or not (t <= 7.3e-63):
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.4e-88) || !(t <= 7.3e-63))
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.4e-88) || ~((t <= 7.3e-63)))
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.4e-88], N[Not[LessEqual[t, 7.3e-63]], $MachinePrecision]], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4000000000000001e-88 or 7.3000000000000002e-63 < t

   1. Initial program 84.4%

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

      1. associate-/l* 88.0%

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

      2. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 79.0%

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

   if -4.4000000000000001e-88 < t < 7.3000000000000002e-63

   1. Initial program 68.3%

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

      1. associate-/l* 62.3%

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

      2. associate-/l* 55.1%

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

   3. Simplified 55.1%

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

   5. Taylor expanded in z around inf 74.8%

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

   6. Taylor expanded in b around inf 63.9%

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

      1. times-frac 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in z around 0 66.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{-88} \lor \neg \left(t \leq 7.3 \cdot 10^{-63}\right):\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.8e-93)
   (/ x (+ (+ a 1.0) (/ y (/ t b))))
   (if (<= t 4.8e-63)
     (/ (+ z (/ (* x t) y)) b)
     (/ x (+ (+ a 1.0) (* y (/ b t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.8e-93) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 4.8e-63) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / ((a + 1.0) + (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 <= (-6.8d-93)) then
        tmp = x / ((a + 1.0d0) + (y / (t / b)))
    else if (t <= 4.8d-63) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / ((a + 1.0d0) + (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 <= -6.8e-93) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} else if (t <= 4.8e-63) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.8e-93:
		tmp = x / ((a + 1.0) + (y / (t / b)))
	elif t <= 4.8e-63:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.8e-93)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t <= 4.8e-63)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + 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 <= -6.8e-93)
		tmp = x / ((a + 1.0) + (y / (t / b)));
	elseif (t <= 4.8e-63)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / ((a + 1.0) + (y * (b / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.8e-93], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-63], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.80000000000000002e-93

   1. Initial program 84.8%

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

      1. associate-/l* 88.0%

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

      2. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in x around inf 83.2%

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

      1. clear-num 83.2%

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

      2. un-div-inv 83.2%

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

   7. Applied egg-rr 83.2%

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

   if -6.80000000000000002e-93 < t < 4.8000000000000001e-63

   1. Initial program 68.3%

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

      1. associate-/l* 62.3%

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

      2. associate-/l* 55.1%

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

   3. Simplified 55.1%

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

   5. Taylor expanded in z around inf 74.8%

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

   6. Taylor expanded in b around inf 63.9%

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

      1. times-frac 57.7%

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

   8. Simplified 57.7%

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

   9. Taylor expanded in z around 0 66.6%

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

   if 4.8000000000000001e-63 < t

   1. Initial program 83.9%

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

      1. associate-/l* 88.0%

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

      2. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x around inf 74.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \left(\left(1 + b \cdot \frac{y}{t}\right) + -1\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.35e-102)
   (/ x (+ (+ a 1.0) (+ (+ 1.0 (* b (/ y t))) -1.0)))
   (if (<= t 3.2e-61)
     (/ (+ z (/ (* x t) y)) b)
     (/ (+ x (/ (* y z) t)) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.35e-102) {
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0));
	} else if (t <= 3.2e-61) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	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 <= (-1.35d-102)) then
        tmp = x / ((a + 1.0d0) + ((1.0d0 + (b * (y / t))) + (-1.0d0)))
    else if (t <= 3.2d-61) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    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 <= -1.35e-102) {
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0));
	} else if (t <= 3.2e-61) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.35e-102:
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0))
	elif t <= 3.2e-61:
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.35e-102)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(1.0 + Float64(b * Float64(y / t))) + -1.0)));
	elseif (t <= 3.2e-61)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.35e-102)
		tmp = x / ((a + 1.0) + ((1.0 + (b * (y / t))) + -1.0));
	elseif (t <= 3.2e-61)
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.35e-102], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(1.0 + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-61], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.35e-102

   1. Initial program 85.1%

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

      1. associate-/l* 88.3%

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

      2. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 81.4%

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

      1. expm1-log1p-u 71.0%

         \[\leadsto \frac{x}{\left(a + 1\right) + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(y \cdot \frac{b}{t}\right)\right)}} \]

      2. expm1-undefine 71.0%

         \[\leadsto \frac{x}{\left(a + 1\right) + \color{blue}{\left(e^{\mathsf{log1p}\left(y \cdot \frac{b}{t}\right)} - 1\right)}} \]

      3. log1p-undefine 71.0%

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

      4. add-exp-log 81.4%

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

      5. associate-*r/ 77.2%

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

      6. *-commutative 77.2%

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

      7. associate-/l* 82.6%

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

   7. Applied egg-rr 82.6%

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

   if -1.35e-102 < t < 3.2000000000000001e-61

   1. Initial program 68.0%

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

      1. associate-/l* 61.9%

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

      2. associate-/l* 55.7%

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

   3. Simplified 55.7%

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

   5. Taylor expanded in z around inf 74.6%

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

   6. Taylor expanded in b around inf 64.6%

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

      1. times-frac 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around 0 67.3%

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

   if 3.2000000000000001e-61 < t

   1. Initial program 83.7%

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

      1. associate-/l* 87.9%

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

      2. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in b around 0 77.5%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \left(\left(1 + b \cdot \frac{y}{t}\right) + -1\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-61}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-97} \lor \neg \left(t \leq 8.8 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -4.5e-97) (not (<= t 8.8e-57)))
   (/ x (+ a 1.0))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -4.5e-97) || !(t <= 8.8e-57)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / 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 <= (-4.5d-97)) .or. (.not. (t <= 8.8d-57))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = (z + ((x * t) / y)) / 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 <= -4.5e-97) || !(t <= 8.8e-57)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -4.5e-97) or not (t <= 8.8e-57):
		tmp = x / (a + 1.0)
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -4.5e-97) || !(t <= 8.8e-57))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -4.5e-97) || ~((t <= 8.8e-57)))
		tmp = x / (a + 1.0);
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -4.5e-97], N[Not[LessEqual[t, 8.8e-57]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5000000000000001e-97 or 8.79999999999999994e-57 < t

   1. Initial program 84.5%

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

      1. associate-/l* 88.1%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in y around 0 67.5%

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

   if -4.5000000000000001e-97 < t < 8.79999999999999994e-57

   1. Initial program 68.0%

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

      1. associate-/l* 61.9%

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

      2. associate-/l* 55.7%

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

   3. Simplified 55.7%

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

   5. Taylor expanded in z around inf 74.6%

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

   6. Taylor expanded in b around inf 64.6%

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

      1. times-frac 58.4%

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

   8. Simplified 58.4%

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

   9. Taylor expanded in z around 0 67.3%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-97} \lor \neg \left(t \leq 8.8 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 55.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-103} \lor \neg \left(t \leq 1.05 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -6.6e-103) (not (<= t 1.05e-58))) (/ 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 <= -6.6e-103) || !(t <= 1.05e-58)) {
		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 <= (-6.6d-103)) .or. (.not. (t <= 1.05d-58))) 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 <= -6.6e-103) || !(t <= 1.05e-58)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -6.6e-103) or not (t <= 1.05e-58):
		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 <= -6.6e-103) || !(t <= 1.05e-58))
		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 <= -6.6e-103) || ~((t <= 1.05e-58)))
		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, -6.6e-103], N[Not[LessEqual[t, 1.05e-58]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.59999999999999979e-103 or 1.04999999999999994e-58 < t

   1. Initial program 84.5%

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

      1. associate-/l* 88.1%

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

      2. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

   5. Taylor expanded in y around 0 67.5%

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

   if -6.59999999999999979e-103 < t < 1.04999999999999994e-58

   1. Initial program 68.0%

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

      1. associate-/l* 61.9%

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

      2. associate-/l* 55.7%

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

   3. Simplified 55.7%

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

   5. Taylor expanded in y around inf 57.4%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-103} \lor \neg \left(t \leq 1.05 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 42.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-23} \lor \neg \left(t \leq 6.2 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.6e-23) (not (<= t 6.2e-43))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.6e-23) || !(t <= 6.2e-43)) {
		tmp = x / a;
	} 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 <= (-2.6d-23)) .or. (.not. (t <= 6.2d-43))) then
        tmp = x / a
    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 <= -2.6e-23) || !(t <= 6.2e-43)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.6e-23) or not (t <= 6.2e-43):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.6e-23) || !(t <= 6.2e-43))
		tmp = Float64(x / a);
	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 <= -2.6e-23) || ~((t <= 6.2e-43)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.6e-23], N[Not[LessEqual[t, 6.2e-43]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6e-23 or 6.1999999999999999e-43 < t

   1. Initial program 85.5%

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

      1. associate-/l* 89.6%

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

      2. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in x around inf 81.3%

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

   6. Taylor expanded in a around inf 36.2%

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

   if -2.6e-23 < t < 6.1999999999999999e-43

   1. Initial program 70.0%

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

      1. associate-/l* 65.0%

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

      2. associate-/l* 59.1%

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

   3. Simplified 59.1%

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

   5. Taylor expanded in y around inf 53.4%

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

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{-23} \lor \neg \left(t \leq 6.2 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 25.4% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

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 / a
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.5%

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

   1. associate-/l* 78.6%

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

   2. associate-/l* 78.6%

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

3. Simplified 78.6%

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

5. Taylor expanded in x around inf 59.8%

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

6. Taylor expanded in a around inf 25.2%

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

7. Final simplification 25.2%

   \[\leadsto \frac{x}{a} \]
8. Add Preprocessing

Developer target: 79.8% 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 2024055 
(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))))