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

Percentage Accurate: 75.3% → 89.7%

Time: 13.4s

Alternatives: 12

Speedup: 0.8×

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: 89.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-320}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (* (/ y t) (/ z (+ 1.0 (+ a (* b (/ y t))))))
     (if (<= t_1 -1e-320)
       t_1
       (if (<= t_1 0.0)
         (/ (+ z (/ (* x t) y)) b)
         (if (<= t_1 5e+279) 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)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / (1.0 + (a + (b * (y / t)))));
	} else if (t_1 <= -1e-320) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t_1 <= 5e+279) {
		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)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / (1.0 + (a + (b * (y / t)))));
	} else if (t_1 <= -1e-320) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = (z + ((x * t) / y)) / b;
	} else if (t_1 <= 5e+279) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (y / t) * (z / (1.0 + (a + (b * (y / t)))))
	elif t_1 <= -1e-320:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = (z + ((x * t) / y)) / b
	elif t_1 <= 5e+279:
		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(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / Float64(1.0 + Float64(a + Float64(b * Float64(y / t))))));
	elseif (t_1 <= -1e-320)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	elseif (t_1 <= 5e+279)
		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)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (y / t) * (z / (1.0 + (a + (b * (y / t)))));
	elseif (t_1 <= -1e-320)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = (z + ((x * t) / y)) / b;
	elseif (t_1 <= 5e+279)
		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[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-320], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+279], t$95$1, 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 15.9%

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

      1. *-commutative 15.9%

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

      2. associate-*l/ 56.2%

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

      3. associate-+l+ 56.2%

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

      4. associate-*r/ 56.2%

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

      5. *-commutative 56.2%

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

   3. Simplified 56.2%

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

   4. Taylor expanded in x around 0 44.8%

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

      1. times-frac 74.7%

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

      2. associate-*r/ 68.3%

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

   6. Simplified 68.3%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -9.99989e-321 or -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e279

   1. Initial program 99.1%

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

   if -9.99989e-321 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 46.8%

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

      1. *-commutative 46.8%

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

      2. associate-*l/ 46.8%

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

      3. associate-+l+ 46.8%

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

      4. associate-*r/ 65.1%

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

      5. *-commutative 65.1%

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

   3. Simplified 65.1%

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

   4. Taylor expanded in b around inf 46.8%

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

   5. Taylor expanded in t around 0 61.0%

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

   6. Taylor expanded in b around 0 70.5%

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

   if 5.0000000000000002e279 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 8.1%

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

      1. *-commutative 8.1%

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

      2. associate-*l/ 16.1%

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

      3. associate-+l+ 16.1%

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

      4. associate-*r/ 23.4%

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

      5. *-commutative 23.4%

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

   3. Simplified 23.4%

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

   4. Taylor expanded in t around 0 85.2%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-320}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+279}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-274} \lor \neg \left(t \leq 2.1 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.15e-274) (not (<= t 2.1e-103)))
   (/ (+ 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 <= -3.15e-274) || !(t <= 2.1e-103)) {
		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 <= (-3.15d-274)) .or. (.not. (t <= 2.1d-103))) 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 <= -3.15e-274) || !(t <= 2.1e-103)) {
		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 <= -3.15e-274) or not (t <= 2.1e-103):
		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 <= -3.15e-274) || !(t <= 2.1e-103))
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(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 <= -3.15e-274) || ~((t <= 2.1e-103)))
		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, -3.15e-274], N[Not[LessEqual[t, 2.1e-103]], $MachinePrecision]], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $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 < -3.14999999999999978e-274 or 2.10000000000000005e-103 < t

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. associate-*l/ 81.6%

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

      3. associate-+l+ 81.6%

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

      4. associate-*r/ 85.3%

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

      5. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   if -3.14999999999999978e-274 < t < 2.10000000000000005e-103

   1. Initial program 40.9%

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

      1. *-commutative 40.9%

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

      2. associate-*l/ 32.9%

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

      3. associate-+l+ 32.9%

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

      4. associate-*r/ 28.0%

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

      5. *-commutative 28.0%

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

   3. Simplified 28.0%

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

   4. Taylor expanded in b around inf 38.7%

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

   5. Taylor expanded in t around 0 79.0%

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

   6. Taylor expanded in b around 0 80.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.15 \cdot 10^{-274} \lor \neg \left(t \leq 2.1 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 3: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-171} \lor \neg \left(t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3.6e-171) (not (<= t 1.05e-103)))
   (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ b (/ t y)))))
   (/ (+ z (/ (* x t) y)) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3.6e-171) || !(t <= 1.05e-103)) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} 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 <= (-3.6d-171)) .or. (.not. (t <= 1.05d-103))) then
        tmp = (x + (y / (t / z))) / (a + (1.0d0 + (b / (t / y))))
    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 <= -3.6e-171) || !(t <= 1.05e-103)) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3.6e-171) or not (t <= 1.05e-103):
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))))
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3.6e-171) || !(t <= 1.05e-103))
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	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 <= -3.6e-171) || ~((t <= 1.05e-103)))
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3.6e-171], N[Not[LessEqual[t, 1.05e-103]], $MachinePrecision]], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $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 < -3.60000000000000003e-171 or 1.05000000000000002e-103 < t

   1. Initial program 79.2%

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

      1. associate-/l* 82.0%

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

      2. associate-*l/ 88.1%

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

      3. *-commutative 88.1%

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

      4. cancel-sign-sub 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-*l/ 82.0%

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

      7. associate-+r- 82.0%

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

      8. associate-*l/ 88.1%

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

      9. *-commutative 88.1%

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

      10. cancel-sign-sub 88.1%

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

      11. *-commutative 88.1%

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

      12. associate-*l/ 82.0%

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

      13. *-commutative 82.0%

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

      14. associate-/l* 88.2%

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

   3. Simplified 88.2%

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

   if -3.60000000000000003e-171 < t < 1.05000000000000002e-103

   1. Initial program 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l/ 40.0%

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

      3. associate-+l+ 40.0%

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

      4. associate-*r/ 35.9%

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

      5. *-commutative 35.9%

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

   3. Simplified 35.9%

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

   4. Taylor expanded in b around inf 42.2%

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

   5. Taylor expanded in t around 0 77.2%

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

   6. Taylor expanded in b around 0 78.7%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-171} \lor \neg \left(t \leq 1.05 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 4: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-169} \lor \neg \left(t \leq 1.5 \cdot 10^{-103}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* b (/ y t)))))))
   (if (<= t -1e-35)
     t_1
     (if (<= t -7e-80)
       (* (/ y t) (/ z (+ a 1.0)))
       (if (or (<= t -1e-169) (not (<= t 1.5e-103)))
         t_1
         (/ (+ z (/ (* x t) y)) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (b * (y / t))));
	double tmp;
	if (t <= -1e-35) {
		tmp = t_1;
	} else if (t <= -7e-80) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((t <= -1e-169) || !(t <= 1.5e-103)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + (b * (y / t))))
    if (t <= (-1d-35)) then
        tmp = t_1
    else if (t <= (-7d-80)) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if ((t <= (-1d-169)) .or. (.not. (t <= 1.5d-103))) then
        tmp = t_1
    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 t_1 = x / (1.0 + (a + (b * (y / t))));
	double tmp;
	if (t <= -1e-35) {
		tmp = t_1;
	} else if (t <= -7e-80) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if ((t <= -1e-169) || !(t <= 1.5e-103)) {
		tmp = t_1;
	} else {
		tmp = (z + ((x * t) / y)) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (b * (y / t))))
	tmp = 0
	if t <= -1e-35:
		tmp = t_1
	elif t <= -7e-80:
		tmp = (y / t) * (z / (a + 1.0))
	elif (t <= -1e-169) or not (t <= 1.5e-103):
		tmp = t_1
	else:
		tmp = (z + ((x * t) / y)) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(b * Float64(y / t)))))
	tmp = 0.0
	if (t <= -1e-35)
		tmp = t_1;
	elseif (t <= -7e-80)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif ((t <= -1e-169) || !(t <= 1.5e-103))
		tmp = t_1;
	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)
	t_1 = x / (1.0 + (a + (b * (y / t))));
	tmp = 0.0;
	if (t <= -1e-35)
		tmp = t_1;
	elseif (t <= -7e-80)
		tmp = (y / t) * (z / (a + 1.0));
	elseif ((t <= -1e-169) || ~((t <= 1.5e-103)))
		tmp = t_1;
	else
		tmp = (z + ((x * t) / y)) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e-35], t$95$1, If[LessEqual[t, -7e-80], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -1e-169], N[Not[LessEqual[t, 1.5e-103]], $MachinePrecision]], t$95$1, N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.00000000000000001e-35 or -7.00000000000000029e-80 < t < -1.00000000000000002e-169 or 1.5e-103 < t

   1. Initial program 79.9%

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

      1. *-commutative 79.9%

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

      2. associate-*l/ 82.9%

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

      3. associate-+l+ 82.9%

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

      4. associate-*r/ 87.0%

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

      5. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in x around inf 63.0%

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

      1. associate-*r/ 65.6%

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

   6. Simplified 65.6%

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

   if -1.00000000000000001e-35 < t < -7.00000000000000029e-80

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

      2. associate-*l/ 63.3%

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

      3. associate-+l+ 63.3%

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

      4. associate-*r/ 63.3%

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

      5. *-commutative 63.3%

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

   3. Simplified 63.3%

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

   4. Taylor expanded in b around 0 58.8%

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

   5. Taylor expanded in x around 0 71.3%

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

      1. times-frac 71.1%

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

   7. Simplified 71.1%

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

   if -1.00000000000000002e-169 < t < 1.5e-103

   1. Initial program 45.3%

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

      1. *-commutative 45.3%

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

      2. associate-*l/ 40.0%

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

      3. associate-+l+ 40.0%

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

      4. associate-*r/ 35.9%

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

      5. *-commutative 35.9%

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

   3. Simplified 35.9%

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

   4. Taylor expanded in b around inf 42.2%

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

   5. Taylor expanded in t around 0 77.2%

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

   6. Taylor expanded in b around 0 78.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-169} \lor \neg \left(t \leq 1.5 \cdot 10^{-103}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 5: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+61} \lor \neg \left(y \leq 1.42 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.1e+61) (not (<= y 1.42e+38)))
   (/ (+ z (/ (* x t) y)) b)
   (/ (+ x (* (* y z) (/ 1.0 t))) (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.1e+61) || !(y <= 1.42e+38)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) * (1.0 / 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 ((y <= (-1.1d+61)) .or. (.not. (y <= 1.42d+38))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = (x + ((y * z) * (1.0d0 / 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 ((y <= -1.1e+61) || !(y <= 1.42e+38)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = (x + ((y * z) * (1.0 / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.1e+61) or not (y <= 1.42e+38):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = (x + ((y * z) * (1.0 / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.1e+61) || !(y <= 1.42e+38))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.1e+61) || ~((y <= 1.42e+38)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = (x + ((y * z) * (1.0 / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.1e+61], N[Not[LessEqual[y, 1.42e+38]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1e61 or 1.4200000000000001e38 < y

   1. Initial program 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-*l/ 50.5%

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

      3. associate-+l+ 50.5%

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

      4. associate-*r/ 59.5%

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

      5. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in b around inf 26.3%

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

   5. Taylor expanded in t around 0 57.9%

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

   6. Taylor expanded in b around 0 61.7%

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

   if -1.1e61 < y < 1.4200000000000001e38

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 86.5%

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

      3. associate-+l+ 86.5%

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

      4. associate-*r/ 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in b around 0 78.8%

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

      1. div-inv 78.9%

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

   6. Applied egg-rr 78.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+61} \lor \neg \left(y \leq 1.42 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{a + 1}\\ \end{array} \]

Alternative 6: 67.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+61} \lor \neg \left(y \leq 2.3 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+61) (not (<= y 2.3e+38)))
   (/ (+ 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 ((y <= -1.3e+61) || !(y <= 2.3e+38)) {
		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 ((y <= (-1.3d+61)) .or. (.not. (y <= 2.3d+38))) 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 ((y <= -1.3e+61) || !(y <= 2.3e+38)) {
		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 (y <= -1.3e+61) or not (y <= 2.3e+38):
		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 ((y <= -1.3e+61) || !(y <= 2.3e+38))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(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 ((y <= -1.3e+61) || ~((y <= 2.3e+38)))
		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[Or[LessEqual[y, -1.3e+61], N[Not[LessEqual[y, 2.3e+38]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999986e61 or 2.3000000000000001e38 < y

   1. Initial program 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-*l/ 50.5%

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

      3. associate-+l+ 50.5%

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

      4. associate-*r/ 59.5%

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

      5. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in b around inf 26.3%

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

   5. Taylor expanded in t around 0 57.9%

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

   6. Taylor expanded in b around 0 61.7%

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

   if -1.29999999999999986e61 < y < 2.3000000000000001e38

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 86.5%

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

      3. associate-+l+ 86.5%

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

      4. associate-*r/ 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in b around 0 76.1%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+61} \lor \neg \left(y \leq 2.3 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 7: 69.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+61} \lor \neg \left(y \leq 1.02 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5e+61) (not (<= y 1.02e+38)))
   (/ (+ 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 ((y <= -5e+61) || !(y <= 1.02e+38)) {
		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 ((y <= (-5d+61)) .or. (.not. (y <= 1.02d+38))) 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 ((y <= -5e+61) || !(y <= 1.02e+38)) {
		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 (y <= -5e+61) or not (y <= 1.02e+38):
		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 ((y <= -5e+61) || !(y <= 1.02e+38))
		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 ((y <= -5e+61) || ~((y <= 1.02e+38)))
		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[Or[LessEqual[y, -5e+61], N[Not[LessEqual[y, 1.02e+38]], $MachinePrecision]], 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 2 regimes

2. if y < -5.00000000000000018e61 or 1.02000000000000006e38 < y

   1. Initial program 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-*l/ 50.5%

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

      3. associate-+l+ 50.5%

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

      4. associate-*r/ 59.5%

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

      5. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in b around inf 26.3%

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

   5. Taylor expanded in t around 0 57.9%

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

   6. Taylor expanded in b around 0 61.7%

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

   if -5.00000000000000018e61 < y < 1.02000000000000006e38

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 86.5%

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

      3. associate-+l+ 86.5%

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

      4. associate-*r/ 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in b around 0 78.8%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+61} \lor \neg \left(y \leq 1.02 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \end{array} \]

Alternative 8: 59.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+60} \lor \neg \left(y \leq 3.7 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7.5e+60) (not (<= y 3.7e-25)))
   (/ (+ z (/ (* x t) y)) b)
   (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7.5e+60) || !(y <= 3.7e-25)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (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 ((y <= (-7.5d+60)) .or. (.not. (y <= 3.7d-25))) then
        tmp = (z + ((x * t) / y)) / b
    else
        tmp = x / (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 ((y <= -7.5e+60) || !(y <= 3.7e-25)) {
		tmp = (z + ((x * t) / y)) / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7.5e+60) or not (y <= 3.7e-25):
		tmp = (z + ((x * t) / y)) / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7.5e+60) || !(y <= 3.7e-25))
		tmp = Float64(Float64(z + Float64(Float64(x * t) / y)) / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7.5e+60) || ~((y <= 3.7e-25)))
		tmp = (z + ((x * t) / y)) / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7.5e+60], N[Not[LessEqual[y, 3.7e-25]], $MachinePrecision]], N[(N[(z + N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.5e60 or 3.70000000000000009e-25 < y

   1. Initial program 47.2%

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

      1. *-commutative 47.2%

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

      2. associate-*l/ 52.6%

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

      3. associate-+l+ 52.6%

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

      4. associate-*r/ 60.5%

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

      5. *-commutative 60.5%

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

   3. Simplified 60.5%

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

   4. Taylor expanded in b around inf 27.3%

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

   5. Taylor expanded in t around 0 56.1%

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

   6. Taylor expanded in b around 0 59.4%

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

   if -7.5e60 < y < 3.70000000000000009e-25

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*l/ 88.6%

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

      3. associate-+l+ 88.6%

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

      4. associate-*r/ 83.8%

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

      5. *-commutative 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in t around inf 61.9%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+60} \lor \neg \left(y \leq 3.7 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 9: 56.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+61} \lor \neg \left(y \leq 2.8 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.05e+61) (not (<= y 2.8e+36))) (/ z b) (/ x (+ a 1.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.05e+61) || !(y <= 2.8e+36)) {
		tmp = z / b;
	} else {
		tmp = x / (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 ((y <= (-1.05d+61)) .or. (.not. (y <= 2.8d+36))) then
        tmp = z / b
    else
        tmp = x / (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 ((y <= -1.05e+61) || !(y <= 2.8e+36)) {
		tmp = z / b;
	} else {
		tmp = x / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.05e+61) or not (y <= 2.8e+36):
		tmp = z / b
	else:
		tmp = x / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.05e+61) || !(y <= 2.8e+36))
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.05e+61) || ~((y <= 2.8e+36)))
		tmp = z / b;
	else
		tmp = x / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.05e+61], N[Not[LessEqual[y, 2.8e+36]], $MachinePrecision]], N[(z / b), $MachinePrecision], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0500000000000001e61 or 2.8000000000000001e36 < y

   1. Initial program 44.4%

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

      1. *-commutative 44.4%

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

      2. associate-*l/ 50.5%

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

      3. associate-+l+ 50.5%

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

      4. associate-*r/ 59.5%

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

      5. *-commutative 59.5%

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

   3. Simplified 59.5%

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

   4. Taylor expanded in t around 0 53.0%

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

   if -1.0500000000000001e61 < y < 2.8000000000000001e36

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-*l/ 86.5%

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

      3. associate-+l+ 86.5%

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

      4. associate-*r/ 82.1%

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

      5. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in t around inf 59.1%

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+61} \lor \neg \left(y \leq 2.8 \cdot 10^{+36}\right):\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 10: 40.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -435000000 \lor \neg \left(a \leq 1.32 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -435000000.0) (not (<= a 1.32e+14))) (/ x a) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -435000000.0) || !(a <= 1.32e+14)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-435000000.0d0)) .or. (.not. (a <= 1.32d+14))) then
        tmp = x / a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -435000000.0) || !(a <= 1.32e+14)) {
		tmp = x / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -435000000.0) or not (a <= 1.32e+14):
		tmp = x / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -435000000.0) || !(a <= 1.32e+14))
		tmp = Float64(x / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -435000000.0) || ~((a <= 1.32e+14)))
		tmp = x / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -435000000.0], N[Not[LessEqual[a, 1.32e+14]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -4.35e8 or 1.32e14 < a

   1. Initial program 67.3%

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

      1. *-commutative 67.3%

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

      2. associate-*l/ 68.2%

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

      3. associate-+l+ 68.2%

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

      4. associate-*r/ 70.2%

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

      5. *-commutative 70.2%

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

   3. Simplified 70.2%

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

   4. Taylor expanded in x around inf 55.2%

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

      1. associate-*r/ 58.0%

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

   6. Simplified 58.0%

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

   7. Taylor expanded in a around inf 48.0%

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

   if -4.35e8 < a < 1.32e14

   1. Initial program 72.4%

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

      1. *-commutative 72.4%

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

      2. associate-*l/ 72.6%

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

      3. associate-+l+ 72.6%

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

      4. associate-*r/ 73.9%

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

      5. *-commutative 73.9%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in t around inf 29.6%

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

   5. Taylor expanded in a around 0 28.4%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -435000000 \lor \neg \left(a \leq 1.32 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 43.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+116} \lor \neg \left(a \leq 6.5 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7.2e+116) (not (<= a 6.5e+49))) (/ x a) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7.2e+116) || !(a <= 6.5e+49)) {
		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 ((a <= (-7.2d+116)) .or. (.not. (a <= 6.5d+49))) 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 ((a <= -7.2e+116) || !(a <= 6.5e+49)) {
		tmp = x / a;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7.2e+116) or not (a <= 6.5e+49):
		tmp = x / a
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7.2e+116) || !(a <= 6.5e+49))
		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 ((a <= -7.2e+116) || ~((a <= 6.5e+49)))
		tmp = x / a;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7.2e+116], N[Not[LessEqual[a, 6.5e+49]], $MachinePrecision]], N[(x / a), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.19999999999999941e116 or 6.5000000000000005e49 < a

   1. Initial program 72.4%

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

      1. *-commutative 72.4%

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

      2. associate-*l/ 73.6%

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

      3. associate-+l+ 73.6%

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

      4. associate-*r/ 76.4%

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

      5. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   4. Taylor expanded in x around inf 61.4%

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

      1. associate-*r/ 64.2%

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

   6. Simplified 64.2%

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

   7. Taylor expanded in a around inf 55.6%

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

   if -7.19999999999999941e116 < a < 6.5000000000000005e49

   1. Initial program 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-*l/ 68.0%

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

      3. associate-+l+ 68.0%

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

      4. associate-*r/ 69.0%

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

      5. *-commutative 69.0%

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

   3. Simplified 69.0%

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

   4. Taylor expanded in t around 0 41.7%

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

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.2 \cdot 10^{+116} \lor \neg \left(a \leq 6.5 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12: 19.1% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.6%

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

   1. *-commutative 69.6%

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

   2. associate-*l/ 70.2%

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

   3. associate-+l+ 70.2%

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

   4. associate-*r/ 71.9%

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

   5. *-commutative 71.9%

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

3. Simplified 71.9%

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

4. Taylor expanded in t around inf 39.5%

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

5. Taylor expanded in a around 0 15.1%

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

6. Final simplification 15.1%

   \[\leadsto x \]

Developer target: 79.6% accurate, 0.7× 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 2023309 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (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))))