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

Percentage Accurate: 74.9% → 86.1%

Time: 14.8s

Alternatives: 11

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: 74.9% 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: 86.1% accurate, 0.3× speedup

Math

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

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 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 / 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 / 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 / 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(z / 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 / 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[(z / b), $MachinePrecision], If[LessEqual[t$95$1, 5e+280], t$95$1, N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -inf.0 or 5.0000000000000002e280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 11.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 79.2%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 79.2%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 5.0000000000000002e280

   1. Initial program 90.9%

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

Alternative 2: 65.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-178}:\\ \;\;\;\;\frac{t\_1}{a + 1}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-132}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{t\_1}{a + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= t -5.5e-178)
     (/ t_1 (+ a 1.0))
     (if (<= t 2.65e-132)
       (/ z b)
       (if (<= t 1.4e+58)
         (/ t_1 (+ a (/ (* y b) t)))
         (/ x (+ (+ a 1.0) (* b (/ y t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (t <= -5.5e-178) {
		tmp = t_1 / (a + 1.0);
	} else if (t <= 2.65e-132) {
		tmp = z / b;
	} else if (t <= 1.4e+58) {
		tmp = t_1 / (a + ((y * b) / t));
	} else {
		tmp = x / ((a + 1.0) + (b * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    if (t <= (-5.5d-178)) then
        tmp = t_1 / (a + 1.0d0)
    else if (t <= 2.65d-132) then
        tmp = z / b
    else if (t <= 1.4d+58) then
        tmp = t_1 / (a + ((y * b) / t))
    else
        tmp = x / ((a + 1.0d0) + (b * (y / 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 t_1 = x + (z * (y / t));
	double tmp;
	if (t <= -5.5e-178) {
		tmp = t_1 / (a + 1.0);
	} else if (t <= 2.65e-132) {
		tmp = z / b;
	} else if (t <= 1.4e+58) {
		tmp = t_1 / (a + ((y * b) / t));
	} else {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y / t))
	tmp = 0
	if t <= -5.5e-178:
		tmp = t_1 / (a + 1.0)
	elif t <= 2.65e-132:
		tmp = z / b
	elif t <= 1.4e+58:
		tmp = t_1 / (a + ((y * b) / t))
	else:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -5.5e-178)
		tmp = Float64(t_1 / Float64(a + 1.0));
	elseif (t <= 2.65e-132)
		tmp = Float64(z / b);
	elseif (t <= 1.4e+58)
		tmp = Float64(t_1 / Float64(a + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y / t));
	tmp = 0.0;
	if (t <= -5.5e-178)
		tmp = t_1 / (a + 1.0);
	elseif (t <= 2.65e-132)
		tmp = z / b;
	elseif (t <= 1.4e+58)
		tmp = t_1 / (a + ((y * b) / t));
	else
		tmp = x / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-178], N[(t$95$1 / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.65e-132], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.4e+58], N[(t$95$1 / N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.50000000000000028e-178

   1. Initial program 78.4%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 80.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 80.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \color{blue}{\left(1 + a\right)}\right) \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 66.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   7. Simplified 66.6%

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

   if -5.50000000000000028e-178 < t < 2.65000000000000015e-132

   1. Initial program 44.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 78.4%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 78.4%

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

   if 2.65000000000000015e-132 < t < 1.3999999999999999e58

   1. Initial program 89.2%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 84.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 84.7%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 71.4%

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

   if 1.3999999999999999e58 < t

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 79.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(\frac{b \cdot y}{t}\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(b \cdot \color{blue}{\frac{y}{t}}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(\frac{y}{t} \cdot \color{blue}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{b}\right)\right)\right) \]

      5. /-lowering-/.f64 79.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), b\right)\right)\right) \]

   7. Applied egg-rr 79.7%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-178}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{-132}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ \mathbf{if}\;t \leq -2.55 \cdot 10^{-211}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))))
   (if (<= t -2.55e-211)
     (/ t_1 (+ (+ a 1.0) (/ (* y b) t)))
     (if (<= t 6.8e-106) (/ z b) (/ t_1 (+ (+ a 1.0) (/ y (/ t b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (t <= -2.55e-211) {
		tmp = t_1 / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 6.8e-106) {
		tmp = z / b;
	} else {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    if (t <= (-2.55d-211)) then
        tmp = t_1 / ((a + 1.0d0) + ((y * b) / t))
    else if (t <= 6.8d-106) then
        tmp = z / b
    else
        tmp = t_1 / ((a + 1.0d0) + (y / (t / b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double tmp;
	if (t <= -2.55e-211) {
		tmp = t_1 / ((a + 1.0) + ((y * b) / t));
	} else if (t <= 6.8e-106) {
		tmp = z / b;
	} else {
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y / t))
	tmp = 0
	if t <= -2.55e-211:
		tmp = t_1 / ((a + 1.0) + ((y * b) / t))
	elif t <= 6.8e-106:
		tmp = z / b
	else:
		tmp = t_1 / ((a + 1.0) + (y / (t / b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	tmp = 0.0
	if (t <= -2.55e-211)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	elseif (t <= 6.8e-106)
		tmp = Float64(z / b);
	else
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y / t));
	tmp = 0.0;
	if (t <= -2.55e-211)
		tmp = t_1 / ((a + 1.0) + ((y * b) / t));
	elseif (t <= 6.8e-106)
		tmp = z / b;
	else
		tmp = t_1 / ((a + 1.0) + (y / (t / b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.55e-211], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-106], N[(z / b), $MachinePrecision], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.55000000000000006e-211

   1. Initial program 78.2%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 80.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 80.5%

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

   if -2.55000000000000006e-211 < t < 6.79999999999999965e-106

   1. Initial program 47.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 78.8%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 78.8%

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

   if 6.79999999999999965e-106 < t

   1. Initial program 87.0%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 87.9%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \left(\frac{y \cdot b}{t} + \color{blue}{\left(a + 1\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(\frac{y \cdot b}{t}\right), \color{blue}{\left(a + 1\right)}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{b}{t}\right), \left(\color{blue}{a} + 1\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{b}}\right), \left(a + 1\right)\right)\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{b}}\right), \left(\color{blue}{a} + 1\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{b}\right)\right), \left(\color{blue}{a} + 1\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, b\right)\right), \left(a + 1\right)\right)\right) \]

      8. +-lowering-+.f64 91.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, b\right)\right), \mathsf{+.f64}\left(a, \color{blue}{1}\right)\right)\right) \]

   6. Applied egg-rr 91.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{-211}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-129}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* z (/ y t))) (+ (+ a 1.0) (/ (* y b) t)))))
   (if (<= t -3.4e-212) t_1 (if (<= t 4.7e-129) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t <= -3.4e-212) {
		tmp = t_1;
	} else if (t <= 4.7e-129) {
		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 = (x + (z * (y / t))) / ((a + 1.0d0) + ((y * b) / t))
    if (t <= (-3.4d-212)) then
        tmp = t_1
    else if (t <= 4.7d-129) 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 = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	double tmp;
	if (t <= -3.4e-212) {
		tmp = t_1;
	} else if (t <= 4.7e-129) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t))
	tmp = 0
	if t <= -3.4e-212:
		tmp = t_1
	elif t <= 4.7e-129:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (t <= -3.4e-212)
		tmp = t_1;
	elseif (t <= 4.7e-129)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (y / t))) / ((a + 1.0) + ((y * b) / t));
	tmp = 0.0;
	if (t <= -3.4e-212)
		tmp = t_1;
	elseif (t <= 4.7e-129)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.4e-212], t$95$1, If[LessEqual[t, 4.7e-129], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.39999999999999998e-212 or 4.7000000000000002e-129 < t

   1. Initial program 82.9%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 84.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 84.0%

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

   if -3.39999999999999998e-212 < t < 4.7000000000000002e-129

   1. Initial program 42.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 80.4%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 80.4%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-212}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-129}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{t}\\ t_2 := \frac{t\_1}{a + \frac{y \cdot b}{t}}\\ \mathbf{if}\;a \leq -28000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 0.6:\\ \;\;\;\;\frac{t\_1}{1 + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y t)))) (t_2 (/ t_1 (+ a (/ (* y b) t)))))
   (if (<= a -28000.0) t_2 (if (<= a 0.6) (/ t_1 (+ 1.0 (/ y (/ t b)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double t_2 = t_1 / (a + ((y * b) / t));
	double tmp;
	if (a <= -28000.0) {
		tmp = t_2;
	} else if (a <= 0.6) {
		tmp = t_1 / (1.0 + (y / (t / b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / t))
    t_2 = t_1 / (a + ((y * b) / t))
    if (a <= (-28000.0d0)) then
        tmp = t_2
    else if (a <= 0.6d0) then
        tmp = t_1 / (1.0d0 + (y / (t / b)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (y / t));
	double t_2 = t_1 / (a + ((y * b) / t));
	double tmp;
	if (a <= -28000.0) {
		tmp = t_2;
	} else if (a <= 0.6) {
		tmp = t_1 / (1.0 + (y / (t / b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (y / t))
	t_2 = t_1 / (a + ((y * b) / t))
	tmp = 0
	if a <= -28000.0:
		tmp = t_2
	elif a <= 0.6:
		tmp = t_1 / (1.0 + (y / (t / b)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(y / t)))
	t_2 = Float64(t_1 / Float64(a + Float64(Float64(y * b) / t)))
	tmp = 0.0
	if (a <= -28000.0)
		tmp = t_2;
	elseif (a <= 0.6)
		tmp = Float64(t_1 / Float64(1.0 + Float64(y / Float64(t / b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (y / t));
	t_2 = t_1 / (a + ((y * b) / t));
	tmp = 0.0;
	if (a <= -28000.0)
		tmp = t_2;
	elseif (a <= 0.6)
		tmp = t_1 / (1.0 + (y / (t / b)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -28000.0], t$95$2, If[LessEqual[a, 0.6], N[(t$95$1 / N[(1.0 + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if a < -28000 or 0.599999999999999978 < a

   1. Initial program 77.7%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 78.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 78.3%

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

   5. Taylor expanded in a around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\color{blue}{a}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 77.2%

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

   if -28000 < a < 0.599999999999999978

   1. Initial program 71.5%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 69.8%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 69.8%

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

      1. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \left(\frac{y \cdot b}{t} + \color{blue}{\left(a + 1\right)}\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(\frac{y \cdot b}{t}\right), \color{blue}{\left(a + 1\right)}\right)\right) \]

      3. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{b}{t}\right), \left(\color{blue}{a} + 1\right)\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(y \cdot \frac{1}{\frac{t}{b}}\right), \left(a + 1\right)\right)\right) \]

      5. un-div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\left(\frac{y}{\frac{t}{b}}\right), \left(\color{blue}{a} + 1\right)\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \left(\frac{t}{b}\right)\right), \left(\color{blue}{a} + 1\right)\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, b\right)\right), \left(a + 1\right)\right)\right) \]

      8. +-lowering-+.f64 67.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, b\right)\right), \mathsf{+.f64}\left(a, \color{blue}{1}\right)\right)\right) \]

   6. Applied egg-rr 67.6%

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

   7. Taylor expanded in a around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(y, \mathsf{/.f64}\left(t, b\right)\right), \color{blue}{1}\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 66.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -28000:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 0.6:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{1 + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + \frac{y \cdot b}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-178}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.5e-178)
   (/ (+ x (* z (/ y t))) (+ a 1.0))
   (if (<= t 1.2e+22) (/ z b) (/ x (+ (+ a 1.0) (* b (/ y t)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -5.5e-178) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 1.2e+22) {
		tmp = z / b;
	} else {
		tmp = x / ((a + 1.0) + (b * (y / 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 <= (-5.5d-178)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (t <= 1.2d+22) then
        tmp = z / b
    else
        tmp = x / ((a + 1.0d0) + (b * (y / 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 <= -5.5e-178) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 1.2e+22) {
		tmp = z / b;
	} else {
		tmp = x / ((a + 1.0) + (b * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -5.5e-178:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif t <= 1.2e+22:
		tmp = z / b
	else:
		tmp = x / ((a + 1.0) + (b * (y / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -5.5e-178)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (t <= 1.2e+22)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -5.5e-178)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (t <= 1.2e+22)
		tmp = z / b;
	else
		tmp = x / ((a + 1.0) + (b * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -5.5e-178], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e+22], N[(z / b), $MachinePrecision], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.50000000000000028e-178

   1. Initial program 78.4%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \left(\frac{y}{t} \cdot z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y}{t}\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

      3. /-lowering-/.f64 80.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]

   4. Applied egg-rr 80.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \color{blue}{\left(1 + a\right)}\right) \]
   6. Step-by-step derivation

      1. +-lowering-+.f64 66.6%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), z\right)\right), \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   7. Simplified 66.6%

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

   if -5.50000000000000028e-178 < t < 1.2e22

   1. Initial program 60.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 68.1%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 68.1%

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

   if 1.2e22 < t

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 76.8%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(\frac{b \cdot y}{t}\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(b \cdot \color{blue}{\frac{y}{t}}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(\frac{y}{t} \cdot \color{blue}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{b}\right)\right)\right) \]

      5. /-lowering-/.f64 76.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), b\right)\right)\right) \]

   7. Applied egg-rr 76.8%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-178}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{-115}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ (+ a 1.0) (* b (/ y t))))))
   (if (<= t -1.8e-115) t_1 (if (<= t 1.2e+22) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t <= -1.8e-115) {
		tmp = t_1;
	} else if (t <= 1.2e+22) {
		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 = x / ((a + 1.0d0) + (b * (y / t)))
    if (t <= (-1.8d-115)) then
        tmp = t_1
    else if (t <= 1.2d+22) 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 = x / ((a + 1.0) + (b * (y / t)));
	double tmp;
	if (t <= -1.8e-115) {
		tmp = t_1;
	} else if (t <= 1.2e+22) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / ((a + 1.0) + (b * (y / t)))
	tmp = 0
	if t <= -1.8e-115:
		tmp = t_1
	elif t <= 1.2e+22:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(Float64(a + 1.0) + Float64(b * Float64(y / t))))
	tmp = 0.0
	if (t <= -1.8e-115)
		tmp = t_1;
	elseif (t <= 1.2e+22)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / ((a + 1.0) + (b * (y / t)));
	tmp = 0.0;
	if (t <= -1.8e-115)
		tmp = t_1;
	elseif (t <= 1.2e+22)
		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[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e-115], t$95$1, If[LessEqual[t, 1.2e+22], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.80000000000000005e-115 or 1.2e22 < t

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 71.3%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(\frac{b \cdot y}{t}\right)\right)\right) \]

      2. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(b \cdot \color{blue}{\frac{y}{t}}\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \left(\frac{y}{t} \cdot \color{blue}{b}\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{*.f64}\left(\left(\frac{y}{t}\right), \color{blue}{b}\right)\right)\right) \]

      5. /-lowering-/.f64 71.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, t\right), b\right)\right)\right) \]

   7. Applied egg-rr 71.9%

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

   if -1.80000000000000005e-115 < t < 1.2e22

   1. Initial program 60.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 64.3%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 64.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + b \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+22}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (* y (/ b t)))))))
   (if (<= t -6.6e-113) t_1 (if (<= t 1.2e+22) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -6.6e-113) {
		tmp = t_1;
	} else if (t <= 1.2e+22) {
		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 = x / (1.0d0 + (a + (y * (b / t))))
    if (t <= (-6.6d-113)) then
        tmp = t_1
    else if (t <= 1.2d+22) 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 = x / (1.0 + (a + (y * (b / t))));
	double tmp;
	if (t <= -6.6e-113) {
		tmp = t_1;
	} else if (t <= 1.2e+22) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + (y * (b / t))))
	tmp = 0
	if t <= -6.6e-113:
		tmp = t_1
	elif t <= 1.2e+22:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -6.6e-113)
		tmp = t_1;
	elseif (t <= 1.2e+22)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + (y * (b / t))));
	tmp = 0.0;
	if (t <= -6.6e-113)
		tmp = t_1;
	elseif (t <= 1.2e+22)
		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[(x / N[(1.0 + N[(a + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.6e-113], t$95$1, If[LessEqual[t, 1.2e+22], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.60000000000000041e-113 or 1.2e22 < t

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + \left(a + \frac{b \cdot y}{t}\right)\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{\left(a + \frac{b \cdot y}{t}\right)}\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \color{blue}{\left(\frac{b \cdot y}{t}\right)}\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(\frac{y \cdot b}{t}\right)\right)\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \left(y \cdot \color{blue}{\frac{b}{t}}\right)\right)\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{b}{t}\right)}\right)\right)\right)\right) \]

      7. /-lowering-/.f64 71.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \mathsf{+.f64}\left(a, \mathsf{*.f64}\left(y, \mathsf{/.f64}\left(b, \color{blue}{t}\right)\right)\right)\right)\right) \]

   5. Simplified 71.3%

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

   if -6.60000000000000041e-113 < t < 1.2e22

   1. Initial program 60.4%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 64.3%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 64.3%

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

Alternative 9: 55.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -3.3e-13) t_1 (if (<= t 4.5e+62) (/ z b) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a + 1.0);
	double tmp;
	if (t <= -3.3e-13) {
		tmp = t_1;
	} else if (t <= 4.5e+62) {
		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 = x / (a + 1.0d0)
    if (t <= (-3.3d-13)) then
        tmp = t_1
    else if (t <= 4.5d+62) 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 = x / (a + 1.0);
	double tmp;
	if (t <= -3.3e-13) {
		tmp = t_1;
	} else if (t <= 4.5e+62) {
		tmp = z / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -3.3e-13:
		tmp = t_1
	elif t <= 4.5e+62:
		tmp = z / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -3.3e-13)
		tmp = t_1;
	elseif (t <= 4.5e+62)
		tmp = Float64(z / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a + 1.0);
	tmp = 0.0;
	if (t <= -3.3e-13)
		tmp = t_1;
	elseif (t <= 4.5e+62)
		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[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.3e-13], t$95$1, If[LessEqual[t, 4.5e+62], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.3000000000000001e-13 or 4.49999999999999999e62 < t

   1. Initial program 85.7%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{x}{1 + a}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(1 + a\right)}\right) \]

      2. +-lowering-+.f64 67.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(1, \color{blue}{a}\right)\right) \]

   5. Simplified 67.9%

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

   if -3.3000000000000001e-13 < t < 4.49999999999999999e62

   1. Initial program 64.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 58.9%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 58.9%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+62}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -66:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+66}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -66.0) (/ x a) (if (<= t 7.5e+66) (/ z b) (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -66.0) {
		tmp = x / a;
	} else if (t <= 7.5e+66) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-66.0d0)) then
        tmp = x / a
    else if (t <= 7.5d+66) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -66.0) {
		tmp = x / a;
	} else if (t <= 7.5e+66) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -66.0:
		tmp = x / a
	elif t <= 7.5e+66:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -66.0)
		tmp = Float64(x / a);
	elseif (t <= 7.5e+66)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -66.0)
		tmp = x / a;
	elseif (t <= 7.5e+66)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -66.0], N[(x / a), $MachinePrecision], If[LessEqual[t, 7.5e+66], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -66 or 7.50000000000000024e66 < t

   1. Initial program 85.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 75.9%

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

   6. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{x}{a}} \]
   7. Step-by-step derivation

      1. /-lowering-/.f64 39.7%

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{a}\right) \]

   8. Simplified 39.7%

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

   if -66 < t < 7.50000000000000024e66

   1. Initial program 65.0%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{z}{b}} \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 58.4%

         \[\leadsto \mathsf{/.f64}\left(z, \color{blue}{b}\right) \]

   5. Simplified 58.4%

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

Alternative 11: 25.6% 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 74.4%

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

3. Taylor expanded in x around inf

   \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{+.f64}\left(\mathsf{+.f64}\left(a, 1\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, b\right), t\right)\right)\right) \]
4. Step-by-step derivation

5. Simplified 53.7%

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

6. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{x}{a}} \]
7. Step-by-step derivation

   1. /-lowering-/.f64 26.5%

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{a}\right) \]

8. Simplified 26.5%

   \[\leadsto \color{blue}{\frac{x}{a}} \]
9. Add Preprocessing

Developer Target 1: 78.9% 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 2024164 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1707385670788761/12500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))) (if (< t 1518483551868623/5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ z b) (* 1 (* (+ x (* (/ y t) z)) (/ 1 (+ (+ a 1) (* (/ y t) b))))))))

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