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

Percentage Accurate: 75.3% → 87.9%

Time: 12.2s

Alternatives: 15

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: 87.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{t_1}\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 -5e-314)
     (/ (+ x (/ y (/ t z))) t_1)
     (if (<= t_2 0.0)
       (/ (+ z (* x (/ t y))) b)
       (if (<= t_2 5e+301) t_2 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -5e-314) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z + (x * (t / y))) / b;
	} else if (t_2 <= 5e+301) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = ((y * b) / t) + (a + 1.0d0)
    t_2 = (x + ((y * z) / t)) / t_1
    if (t_2 <= (-5d-314)) then
        tmp = (x + (y / (t / z))) / t_1
    else if (t_2 <= 0.0d0) then
        tmp = (z + (x * (t / y))) / b
    else if (t_2 <= 5d+301) then
        tmp = t_2
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -5e-314) {
		tmp = (x + (y / (t / z))) / t_1;
	} else if (t_2 <= 0.0) {
		tmp = (z + (x * (t / y))) / b;
	} else if (t_2 <= 5e+301) {
		tmp = t_2;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -5e-314:
		tmp = (x + (y / (t / z))) / t_1
	elif t_2 <= 0.0:
		tmp = (z + (x * (t / y))) / b
	elif t_2 <= 5e+301:
		tmp = t_2
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= -5e-314)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / t_1);
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	elseif (t_2 <= 5e+301)
		tmp = t_2;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -5e-314)
		tmp = (x + (y / (t / z))) / t_1;
	elseif (t_2 <= 0.0)
		tmp = (z + (x * (t / y))) / b;
	elseif (t_2 <= 5e+301)
		tmp = t_2;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -5e-314], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$2, 0.0], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[t$95$2, 5e+301], t$95$2, 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))) < -4.99999999982e-314

   1. Initial program 90.3%

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

      1. *-un-lft-identity 90.3%

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

      2. associate-/l* 92.7%

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

   3. Applied egg-rr 92.7%

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

   if -4.99999999982e-314 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 59.4%

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

      1. *-commutative 59.4%

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

      2. associate-/l* 53.7%

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

      3. associate-*l/ 63.6%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in y around inf 62.9%

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

      1. associate--l+ 62.9%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 65.0%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 65.0%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 65.0%

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

   6. Simplified 65.0%

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

   7. Taylor expanded in b around inf 73.7%

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

      1. +-commutative 73.7%

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

      2. associate-*l/ 73.7%

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

      3. *-commutative 73.7%

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

   9. Simplified 73.7%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 99.7%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 12.3%

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

      1. *-commutative 12.3%

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

      2. associate-/l* 25.4%

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

      3. associate-*l/ 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in t around 0 84.8%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -5 \cdot 10^{-314}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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 5e+301) 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 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0d0))
    if (t_1 <= 5d+301) then
        tmp = t_1
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= 5e+301) {
		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 <= 5e+301:
		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 <= 5e+301)
		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 <= 5e+301)
		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, 5e+301], 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 1) (/.f64 (*.f64 y b) t))) < 5.0000000000000004e301

   1. Initial program 88.6%

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

   if 5.0000000000000004e301 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 12.3%

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

      1. *-commutative 12.3%

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

      2. associate-/l* 25.4%

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

      3. associate-*l/ 29.1%

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

   3. Simplified 29.1%

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

   4. Taylor expanded in t around 0 84.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+301}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3: 53.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-162}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.58 \cdot 10^{+159} \lor \neg \left(t \leq 1.65 \cdot 10^{+196}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t + t \cdot a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -2.4e-40)
     t_1
     (if (<= t 2.9e-162)
       (/ z b)
       (if (<= t 6.2e-113)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= t 1.2e-48)
           (/ z b)
           (if (or (<= t 1.58e+159) (not (<= t 1.65e+196)))
             t_1
             (/ y (/ (+ t (* t a)) z)))))))))

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 <= -2.4e-40) {
		tmp = t_1;
	} else if (t <= 2.9e-162) {
		tmp = z / b;
	} else if (t <= 6.2e-113) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.2e-48) {
		tmp = z / b;
	} else if ((t <= 1.58e+159) || !(t <= 1.65e+196)) {
		tmp = t_1;
	} else {
		tmp = y / ((t + (t * a)) / z);
	}
	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 <= (-2.4d-40)) then
        tmp = t_1
    else if (t <= 2.9d-162) then
        tmp = z / b
    else if (t <= 6.2d-113) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= 1.2d-48) then
        tmp = z / b
    else if ((t <= 1.58d+159) .or. (.not. (t <= 1.65d+196))) then
        tmp = t_1
    else
        tmp = y / ((t + (t * a)) / z)
    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 <= -2.4e-40) {
		tmp = t_1;
	} else if (t <= 2.9e-162) {
		tmp = z / b;
	} else if (t <= 6.2e-113) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.2e-48) {
		tmp = z / b;
	} else if ((t <= 1.58e+159) || !(t <= 1.65e+196)) {
		tmp = t_1;
	} else {
		tmp = y / ((t + (t * a)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -2.4e-40:
		tmp = t_1
	elif t <= 2.9e-162:
		tmp = z / b
	elif t <= 6.2e-113:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= 1.2e-48:
		tmp = z / b
	elif (t <= 1.58e+159) or not (t <= 1.65e+196):
		tmp = t_1
	else:
		tmp = y / ((t + (t * a)) / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -2.4e-40)
		tmp = t_1;
	elseif (t <= 2.9e-162)
		tmp = Float64(z / b);
	elseif (t <= 6.2e-113)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= 1.2e-48)
		tmp = Float64(z / b);
	elseif ((t <= 1.58e+159) || !(t <= 1.65e+196))
		tmp = t_1;
	else
		tmp = Float64(y / Float64(Float64(t + Float64(t * a)) / z));
	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 <= -2.4e-40)
		tmp = t_1;
	elseif (t <= 2.9e-162)
		tmp = z / b;
	elseif (t <= 6.2e-113)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= 1.2e-48)
		tmp = z / b;
	elseif ((t <= 1.58e+159) || ~((t <= 1.65e+196)))
		tmp = t_1;
	else
		tmp = y / ((t + (t * a)) / z);
	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, -2.4e-40], t$95$1, If[LessEqual[t, 2.9e-162], N[(z / b), $MachinePrecision], If[LessEqual[t, 6.2e-113], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-48], N[(z / b), $MachinePrecision], If[Or[LessEqual[t, 1.58e+159], N[Not[LessEqual[t, 1.65e+196]], $MachinePrecision]], t$95$1, N[(y / N[(N[(t + N[(t * a), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.39999999999999991e-40 or 1.2e-48 < t < 1.58000000000000007e159 or 1.6500000000000001e196 < t

   1. Initial program 84.2%

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

      1. *-commutative 84.2%

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

      2. associate-/l* 88.5%

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

      3. associate-*l/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in t around inf 60.2%

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

   if -2.39999999999999991e-40 < t < 2.9000000000000001e-162 or 6.20000000000000024e-113 < t < 1.2e-48

   1. Initial program 61.8%

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

      1. *-commutative 61.8%

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

      2. associate-/l* 57.8%

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

      3. associate-*l/ 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around 0 64.1%

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

   if 2.9000000000000001e-162 < t < 6.20000000000000024e-113

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.4%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 75.5%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. times-frac 69.9%

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

   7. Simplified 69.9%

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

   if 1.58000000000000007e159 < t < 1.6500000000000001e196

   1. Initial program 59.7%

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

      1. *-commutative 59.7%

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

      2. associate-/l* 79.2%

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

      3. associate-*l/ 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in y around 0 53.7%

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

   5. Taylor expanded in x around 0 26.9%

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

      1. associate-/l* 67.6%

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

      2. distribute-rgt-in 67.6%

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

      3. *-lft-identity 67.6%

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

      4. *-commutative 67.6%

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

   7. Simplified 67.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-162}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.58 \cdot 10^{+159} \lor \neg \left(t \leq 1.65 \cdot 10^{+196}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{t + t \cdot a}{z}}\\ \end{array} \]

Alternative 4: 79.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+72} \lor \neg \left(y \leq 3.7 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.52e+72) (not (<= y 3.7e+147)))
   (/ (+ z (* x (/ t y))) b)
   (/ (+ x (* y (/ z t))) (+ (* b (/ y t)) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.52e+72) || !(y <= 3.7e+147)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = (x + (y * (z / t))) / ((b * (y / 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 <= (-1.52d+72)) .or. (.not. (y <= 3.7d+147))) then
        tmp = (z + (x * (t / y))) / b
    else
        tmp = (x + (y * (z / t))) / ((b * (y / 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 <= -1.52e+72) || !(y <= 3.7e+147)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.52e+72) or not (y <= 3.7e+147):
		tmp = (z + (x * (t / y))) / b
	else:
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.52e+72) || !(y <= 3.7e+147))
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(Float64(b * Float64(y / 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 <= -1.52e+72) || ~((y <= 3.7e+147)))
		tmp = (z + (x * (t / y))) / b;
	else
		tmp = (x + (y * (z / t))) / ((b * (y / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.52e+72], N[Not[LessEqual[y, 3.7e+147]], $MachinePrecision]], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.52e72 or 3.7e147 < y

   1. Initial program 43.2%

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

      1. *-commutative 43.2%

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

      2. associate-/l* 39.1%

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

      3. associate-*l/ 44.9%

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

   3. Simplified 44.9%

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

   4. Taylor expanded in y around inf 59.2%

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

      1. associate--l+ 59.2%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 56.0%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 55.9%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in b around inf 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-*l/ 78.3%

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

      3. *-commutative 78.3%

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

   9. Simplified 78.3%

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

   if -1.52e72 < y < 3.7e147

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-/l* 91.1%

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

      3. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

      1. associate-/r/ 33.7%

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

   5. Applied egg-rr 88.7%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+72} \lor \neg \left(y \leq 3.7 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 5: 82.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+72} \lor \neg \left(y \leq 3.7 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.4e+72) (not (<= y 3.7e+147)))
   (/ (+ z (* x (/ t y))) b)
   (/ (+ x (/ z (/ t y))) (+ (* b (/ y t)) (+ a 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.4e+72) || !(y <= 3.7e+147)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = (x + (z / (t / y))) / ((b * (y / 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 <= (-5.4d+72)) .or. (.not. (y <= 3.7d+147))) then
        tmp = (z + (x * (t / y))) / b
    else
        tmp = (x + (z / (t / y))) / ((b * (y / 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 <= -5.4e+72) || !(y <= 3.7e+147)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = (x + (z / (t / y))) / ((b * (y / t)) + (a + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.4e+72) or not (y <= 3.7e+147):
		tmp = (z + (x * (t / y))) / b
	else:
		tmp = (x + (z / (t / y))) / ((b * (y / t)) + (a + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.4e+72) || !(y <= 3.7e+147))
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	else
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(Float64(b * Float64(y / 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 <= -5.4e+72) || ~((y <= 3.7e+147)))
		tmp = (z + (x * (t / y))) / b;
	else
		tmp = (x + (z / (t / y))) / ((b * (y / t)) + (a + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.4e+72], N[Not[LessEqual[y, 3.7e+147]], $MachinePrecision]], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4000000000000001e72 or 3.7e147 < y

   1. Initial program 43.2%

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

      1. *-commutative 43.2%

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

      2. associate-/l* 39.1%

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

      3. associate-*l/ 44.9%

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

   3. Simplified 44.9%

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

   4. Taylor expanded in y around inf 59.2%

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

      1. associate--l+ 59.2%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 56.0%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 55.9%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 55.9%

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

   6. Simplified 55.9%

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

   7. Taylor expanded in b around inf 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-*l/ 78.3%

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

      3. *-commutative 78.3%

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

   9. Simplified 78.3%

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

   if -5.4000000000000001e72 < y < 3.7e147

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. associate-/l* 91.1%

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

      3. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+72} \lor \neg \left(y \leq 3.7 \cdot 10^{+147}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 6: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-53} \lor \neg \left(t \leq 9 \cdot 10^{-49}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -8.8e+212)
     t_1
     (if (<= t -2.6e-18)
       (/ x (+ 1.0 (+ a (/ (* y b) t))))
       (if (or (<= t -6.5e-53) (not (<= t 9e-49)))
         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 + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -8.8e+212) {
		tmp = t_1;
	} else if (t <= -2.6e-18) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((t <= -6.5e-53) || !(t <= 9e-49)) {
		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 + (y * (z / t))) / (a + 1.0d0)
    if (t <= (-8.8d+212)) then
        tmp = t_1
    else if (t <= (-2.6d-18)) then
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    else if ((t <= (-6.5d-53)) .or. (.not. (t <= 9d-49))) 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 + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -8.8e+212) {
		tmp = t_1;
	} else if (t <= -2.6e-18) {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	} else if ((t <= -6.5e-53) || !(t <= 9e-49)) {
		tmp = t_1;
	} else {
		tmp = (z + (x * (t / y))) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if t <= -8.8e+212:
		tmp = t_1
	elif t <= -2.6e-18:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	elif (t <= -6.5e-53) or not (t <= 9e-49):
		tmp = t_1
	else:
		tmp = (z + (x * (t / y))) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -8.8e+212)
		tmp = t_1;
	elseif (t <= -2.6e-18)
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	elseif ((t <= -6.5e-53) || !(t <= 9e-49))
		tmp = t_1;
	else
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / 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);
	tmp = 0.0;
	if (t <= -8.8e+212)
		tmp = t_1;
	elseif (t <= -2.6e-18)
		tmp = x / (1.0 + (a + ((y * b) / t)));
	elseif ((t <= -6.5e-53) || ~((t <= 9e-49)))
		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[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+212], t$95$1, If[LessEqual[t, -2.6e-18], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -6.5e-53], N[Not[LessEqual[t, 9e-49]], $MachinePrecision]], t$95$1, N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.7999999999999998e212 or -2.6e-18 < t < -6.4999999999999997e-53 or 9.0000000000000004e-49 < t

   1. Initial program 82.7%

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

      1. *-commutative 82.7%

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

      2. associate-/l* 88.3%

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

      3. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

      1. associate-/r/ 39.3%

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

   5. Applied egg-rr 94.6%

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

   6. Taylor expanded in y around 0 77.0%

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

   if -8.7999999999999998e212 < t < -2.6e-18

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 87.9%

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

      3. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in x around inf 80.1%

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

   if -6.4999999999999997e-53 < t < 9.0000000000000004e-49

   1. Initial program 64.0%

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

      1. *-commutative 64.0%

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

      2. associate-/l* 60.2%

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

      3. associate-*l/ 57.0%

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

   3. Simplified 57.0%

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

   4. Taylor expanded in y around inf 63.1%

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

      1. associate--l+ 63.1%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 60.3%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 64.0%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 64.0%

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

   6. Simplified 64.0%

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

   7. Taylor expanded in b around inf 71.9%

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

      1. +-commutative 71.9%

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

      2. associate-*l/ 71.1%

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

      3. *-commutative 71.1%

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

   9. Simplified 71.1%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.8 \cdot 10^{+212}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-53} \lor \neg \left(t \leq 9 \cdot 10^{-49}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \end{array} \]

Alternative 7: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-52}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;y \leq 21000000 \lor \neg \left(y \leq 1.9 \cdot 10^{+56}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* x (/ t y))) b)))
   (if (<= y -2.5e+63)
     t_1
     (if (<= y 1.22e-52)
       (/ (+ x (/ z (/ t y))) (+ a 1.0))
       (if (or (<= y 21000000.0) (not (<= y 1.9e+56)))
         t_1
         (/ (+ x (* y (/ z t))) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (x * (t / y))) / b;
	double tmp;
	if (y <= -2.5e+63) {
		tmp = t_1;
	} else if (y <= 1.22e-52) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else if ((y <= 21000000.0) || !(y <= 1.9e+56)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z + (x * (t / y))) / b
    if (y <= (-2.5d+63)) then
        tmp = t_1
    else if (y <= 1.22d-52) then
        tmp = (x + (z / (t / y))) / (a + 1.0d0)
    else if ((y <= 21000000.0d0) .or. (.not. (y <= 1.9d+56))) then
        tmp = t_1
    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 t_1 = (z + (x * (t / y))) / b;
	double tmp;
	if (y <= -2.5e+63) {
		tmp = t_1;
	} else if (y <= 1.22e-52) {
		tmp = (x + (z / (t / y))) / (a + 1.0);
	} else if ((y <= 21000000.0) || !(y <= 1.9e+56)) {
		tmp = t_1;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (x * (t / y))) / b
	tmp = 0
	if y <= -2.5e+63:
		tmp = t_1
	elif y <= 1.22e-52:
		tmp = (x + (z / (t / y))) / (a + 1.0)
	elif (y <= 21000000.0) or not (y <= 1.9e+56):
		tmp = t_1
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(x * Float64(t / y))) / b)
	tmp = 0.0
	if (y <= -2.5e+63)
		tmp = t_1;
	elseif (y <= 1.22e-52)
		tmp = Float64(Float64(x + Float64(z / Float64(t / y))) / Float64(a + 1.0));
	elseif ((y <= 21000000.0) || !(y <= 1.9e+56))
		tmp = t_1;
	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)
	t_1 = (z + (x * (t / y))) / b;
	tmp = 0.0;
	if (y <= -2.5e+63)
		tmp = t_1;
	elseif (y <= 1.22e-52)
		tmp = (x + (z / (t / y))) / (a + 1.0);
	elseif ((y <= 21000000.0) || ~((y <= 1.9e+56)))
		tmp = t_1;
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -2.5e+63], t$95$1, If[LessEqual[y, 1.22e-52], N[(N[(x + N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 21000000.0], N[Not[LessEqual[y, 1.9e+56]], $MachinePrecision]], t$95$1, N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000005e63 or 1.22e-52 < y < 2.1e7 or 1.89999999999999998e56 < y

   1. Initial program 48.5%

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

      1. *-commutative 48.5%

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

      2. associate-/l* 51.3%

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

      3. associate-*l/ 55.3%

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

   3. Simplified 55.3%

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

   4. Taylor expanded in y around inf 54.6%

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

      1. associate--l+ 54.6%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 52.3%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 54.2%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in b around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*l/ 73.3%

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

      3. *-commutative 73.3%

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

   9. Simplified 73.3%

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

   if -2.50000000000000005e63 < y < 1.22e-52

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-/l* 94.1%

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

      3. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around 0 74.2%

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

   if 2.1e7 < y < 1.89999999999999998e56

   1. Initial program 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 80.1%

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

      3. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

      1. associate-/r/ 61.2%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in y around 0 80.5%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-52}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;y \leq 21000000 \lor \neg \left(y \leq 1.9 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 8: 68.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 7200000 \lor \neg \left(y \leq 3 \cdot 10^{+57}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* x (/ t y))) b)))
   (if (<= y -1.32e+70)
     t_1
     (if (<= y 6.5e-53)
       (/ (+ x (/ (* y z) t)) (+ a 1.0))
       (if (or (<= y 7200000.0) (not (<= y 3e+57)))
         t_1
         (/ (+ x (* y (/ z t))) (+ a 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (x * (t / y))) / b;
	double tmp;
	if (y <= -1.32e+70) {
		tmp = t_1;
	} else if (y <= 6.5e-53) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 7200000.0) || !(y <= 3e+57)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z + (x * (t / y))) / b
    if (y <= (-1.32d+70)) then
        tmp = t_1
    else if (y <= 6.5d-53) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if ((y <= 7200000.0d0) .or. (.not. (y <= 3d+57))) then
        tmp = t_1
    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 t_1 = (z + (x * (t / y))) / b;
	double tmp;
	if (y <= -1.32e+70) {
		tmp = t_1;
	} else if (y <= 6.5e-53) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if ((y <= 7200000.0) || !(y <= 3e+57)) {
		tmp = t_1;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (x * (t / y))) / b
	tmp = 0
	if y <= -1.32e+70:
		tmp = t_1
	elif y <= 6.5e-53:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif (y <= 7200000.0) or not (y <= 3e+57):
		tmp = t_1
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(x * Float64(t / y))) / b)
	tmp = 0.0
	if (y <= -1.32e+70)
		tmp = t_1;
	elseif (y <= 6.5e-53)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif ((y <= 7200000.0) || !(y <= 3e+57))
		tmp = t_1;
	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)
	t_1 = (z + (x * (t / y))) / b;
	tmp = 0.0;
	if (y <= -1.32e+70)
		tmp = t_1;
	elseif (y <= 6.5e-53)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif ((y <= 7200000.0) || ~((y <= 3e+57)))
		tmp = t_1;
	else
		tmp = (x + (y * (z / t))) / (a + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -1.32e+70], t$95$1, If[LessEqual[y, 6.5e-53], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 7200000.0], N[Not[LessEqual[y, 3e+57]], $MachinePrecision]], t$95$1, N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3199999999999999e70 or 6.4999999999999997e-53 < y < 7.2e6 or 3e57 < y

   1. Initial program 48.5%

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

      1. *-commutative 48.5%

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

      2. associate-/l* 51.3%

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

      3. associate-*l/ 55.3%

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

   3. Simplified 55.3%

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

   4. Taylor expanded in y around inf 54.6%

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

      1. associate--l+ 54.6%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 52.3%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 54.2%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in b around inf 72.3%

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

      1. +-commutative 72.3%

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

      2. associate-*l/ 73.3%

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

      3. *-commutative 73.3%

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

   9. Simplified 73.3%

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

   if -1.3199999999999999e70 < y < 6.4999999999999997e-53

   1. Initial program 94.4%

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

      1. *-commutative 94.4%

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

      2. associate-/l* 94.1%

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

      3. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in b around 0 74.5%

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

   if 7.2e6 < y < 3e57

   1. Initial program 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 80.1%

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

      3. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

      1. associate-/r/ 61.2%

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

   5. Applied egg-rr 80.4%

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

   6. Taylor expanded in y around 0 80.5%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.32 \cdot 10^{+70}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-53}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 7200000 \lor \neg \left(y \leq 3 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]

Alternative 9: 59.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 48000000 \lor \neg \left(y \leq 3.1 \cdot 10^{+55}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ z (* x (/ t y))) b)))
   (if (<= y -3e-28)
     t_1
     (if (<= y 5e-55)
       (/ x (+ a 1.0))
       (if (or (<= y 48000000.0) (not (<= y 3.1e+55)))
         t_1
         (+ x (* y (/ z t))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + (x * (t / y))) / b;
	double tmp;
	if (y <= -3e-28) {
		tmp = t_1;
	} else if (y <= 5e-55) {
		tmp = x / (a + 1.0);
	} else if ((y <= 48000000.0) || !(y <= 3.1e+55)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / 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 = (z + (x * (t / y))) / b
    if (y <= (-3d-28)) then
        tmp = t_1
    else if (y <= 5d-55) then
        tmp = x / (a + 1.0d0)
    else if ((y <= 48000000.0d0) .or. (.not. (y <= 3.1d+55))) then
        tmp = t_1
    else
        tmp = x + (y * (z / 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 = (z + (x * (t / y))) / b;
	double tmp;
	if (y <= -3e-28) {
		tmp = t_1;
	} else if (y <= 5e-55) {
		tmp = x / (a + 1.0);
	} else if ((y <= 48000000.0) || !(y <= 3.1e+55)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + (x * (t / y))) / b
	tmp = 0
	if y <= -3e-28:
		tmp = t_1
	elif y <= 5e-55:
		tmp = x / (a + 1.0)
	elif (y <= 48000000.0) or not (y <= 3.1e+55):
		tmp = t_1
	else:
		tmp = x + (y * (z / t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + Float64(x * Float64(t / y))) / b)
	tmp = 0.0
	if (y <= -3e-28)
		tmp = t_1;
	elseif (y <= 5e-55)
		tmp = Float64(x / Float64(a + 1.0));
	elseif ((y <= 48000000.0) || !(y <= 3.1e+55))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(z / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + (x * (t / y))) / b;
	tmp = 0.0;
	if (y <= -3e-28)
		tmp = t_1;
	elseif (y <= 5e-55)
		tmp = x / (a + 1.0);
	elseif ((y <= 48000000.0) || ~((y <= 3.1e+55)))
		tmp = t_1;
	else
		tmp = x + (y * (z / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]}, If[LessEqual[y, -3e-28], t$95$1, If[LessEqual[y, 5e-55], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 48000000.0], N[Not[LessEqual[y, 3.1e+55]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.00000000000000003e-28 or 5.0000000000000002e-55 < y < 4.8e7 or 3.09999999999999994e55 < y

   1. Initial program 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-/l* 56.2%

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

      3. associate-*l/ 59.6%

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

   3. Simplified 59.6%

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

   4. Taylor expanded in y around inf 51.4%

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

      1. associate--l+ 51.4%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 48.8%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 51.3%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 51.3%

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

   6. Simplified 51.3%

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

   7. Taylor expanded in b around inf 67.7%

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

      1. +-commutative 67.7%

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

      2. associate-*l/ 68.6%

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

      3. *-commutative 68.6%

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

   9. Simplified 68.6%

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

   if -3.00000000000000003e-28 < y < 5.0000000000000002e-55

   1. Initial program 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-/l* 95.0%

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

      3. associate-*l/ 95.0%

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

   3. Simplified 95.0%

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

   4. Taylor expanded in t around inf 62.6%

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

   if 4.8e7 < y < 3.09999999999999994e55

   1. Initial program 70.7%

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

      1. *-commutative 70.7%

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

      2. associate-/l* 80.1%

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

      3. associate-*l/ 80.1%

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

   3. Simplified 80.1%

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

   4. Taylor expanded in y around 0 80.2%

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

   5. Taylor expanded in a around 0 51.7%

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

      1. +-commutative 51.7%

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

      2. *-commutative 51.7%

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

      3. associate-/l* 61.0%

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

   7. Simplified 61.0%

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

      1. associate-/r/ 61.2%

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

   9. Applied egg-rr 61.2%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-28}:\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 48000000 \lor \neg \left(y \leq 3.1 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \end{array} \]

Alternative 10: 55.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-116}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.3e-39)
     t_1
     (if (<= t 5.7e-164)
       (/ z b)
       (if (<= t 1.05e-116)
         (* (/ y t) (/ z (+ a 1.0)))
         (if (<= t 1.25e-48) (/ 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 <= -1.3e-39) {
		tmp = t_1;
	} else if (t <= 5.7e-164) {
		tmp = z / b;
	} else if (t <= 1.05e-116) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.25e-48) {
		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 <= (-1.3d-39)) then
        tmp = t_1
    else if (t <= 5.7d-164) then
        tmp = z / b
    else if (t <= 1.05d-116) then
        tmp = (y / t) * (z / (a + 1.0d0))
    else if (t <= 1.25d-48) 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 <= -1.3e-39) {
		tmp = t_1;
	} else if (t <= 5.7e-164) {
		tmp = z / b;
	} else if (t <= 1.05e-116) {
		tmp = (y / t) * (z / (a + 1.0));
	} else if (t <= 1.25e-48) {
		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 <= -1.3e-39:
		tmp = t_1
	elif t <= 5.7e-164:
		tmp = z / b
	elif t <= 1.05e-116:
		tmp = (y / t) * (z / (a + 1.0))
	elif t <= 1.25e-48:
		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 <= -1.3e-39)
		tmp = t_1;
	elseif (t <= 5.7e-164)
		tmp = Float64(z / b);
	elseif (t <= 1.05e-116)
		tmp = Float64(Float64(y / t) * Float64(z / Float64(a + 1.0)));
	elseif (t <= 1.25e-48)
		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 <= -1.3e-39)
		tmp = t_1;
	elseif (t <= 5.7e-164)
		tmp = z / b;
	elseif (t <= 1.05e-116)
		tmp = (y / t) * (z / (a + 1.0));
	elseif (t <= 1.25e-48)
		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, -1.3e-39], t$95$1, If[LessEqual[t, 5.7e-164], N[(z / b), $MachinePrecision], If[LessEqual[t, 1.05e-116], N[(N[(y / t), $MachinePrecision] * N[(z / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.25e-48], N[(z / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e-39 or 1.25e-48 < t

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 88.1%

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

      3. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 57.8%

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

   if -1.3e-39 < t < 5.70000000000000023e-164 or 1.05e-116 < t < 1.25e-48

   1. Initial program 61.8%

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

      1. *-commutative 61.8%

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

      2. associate-/l* 57.8%

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

      3. associate-*l/ 54.5%

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

   3. Simplified 54.5%

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

   4. Taylor expanded in t around 0 64.1%

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

   if 5.70000000000000023e-164 < t < 1.05e-116

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 99.4%

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

      3. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 75.5%

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

   5. Taylor expanded in y around 0 69.9%

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

      1. times-frac 69.9%

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

   7. Simplified 69.9%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-39}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq 5.7 \cdot 10^{-164}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-116}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a + 1}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-48}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a + 1}\\ \end{array} \]

Alternative 11: 66.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+68} \lor \neg \left(y \leq 4.9 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.15e+68) (not (<= y 4.9e+55)))
   (/ (+ z (* x (/ t y))) b)
   (/ x (+ 1.0 (+ a (/ (* y b) t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+68) || !(y <= 4.9e+55)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.15d+68)) .or. (.not. (y <= 4.9d+55))) then
        tmp = (z + (x * (t / y))) / b
    else
        tmp = x / (1.0d0 + (a + ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.15e+68) || !(y <= 4.9e+55)) {
		tmp = (z + (x * (t / y))) / b;
	} else {
		tmp = x / (1.0 + (a + ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.15e+68) or not (y <= 4.9e+55):
		tmp = (z + (x * (t / y))) / b
	else:
		tmp = x / (1.0 + (a + ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.15e+68) || !(y <= 4.9e+55))
		tmp = Float64(Float64(z + Float64(x * Float64(t / y))) / b);
	else
		tmp = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.15e+68) || ~((y <= 4.9e+55)))
		tmp = (z + (x * (t / y))) / b;
	else
		tmp = x / (1.0 + (a + ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.15e+68], N[Not[LessEqual[y, 4.9e+55]], $MachinePrecision]], N[(N[(z + N[(x * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e68 or 4.90000000000000015e55 < y

   1. Initial program 45.4%

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

      1. *-commutative 45.4%

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

      2. associate-/l* 47.4%

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

      3. associate-*l/ 52.0%

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

   3. Simplified 52.0%

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

   4. Taylor expanded in y around inf 54.5%

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

      1. associate--l+ 54.5%

         \[\leadsto \color{blue}{\frac{t \cdot x}{y \cdot b} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right)} \]

      2. times-frac 52.0%

         \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x}{b}} + \left(\frac{z}{b} - \frac{t \cdot \left(\left(1 + a\right) \cdot z\right)}{y \cdot {b}^{2}}\right) \]

      3. associate-*r* 54.2%

         \[\leadsto \frac{t}{y} \cdot \frac{x}{b} + \left(\frac{z}{b} - \frac{\color{blue}{\left(t \cdot \left(1 + a\right)\right) \cdot z}}{y \cdot {b}^{2}}\right) \]

      4. unpow2 54.2%

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

   6. Simplified 54.2%

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

   7. Taylor expanded in b around inf 73.2%

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

      1. +-commutative 73.2%

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

      2. associate-*l/ 74.4%

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

      3. *-commutative 74.4%

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

   9. Simplified 74.4%

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

   if -1.15e68 < y < 4.90000000000000015e55

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-/l* 92.5%

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

      3. associate-*l/ 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in x around inf 67.4%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+68} \lor \neg \left(y \leq 4.9 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{z + x \cdot \frac{t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \end{array} \]

Alternative 12: 56.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-36} \lor \neg \left(t \leq 1.22 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2e-36) (not (<= t 1.22e-48))) (/ x (+ a 1.0)) (/ z b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e-36) || !(t <= 1.22e-48)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2d-36)) .or. (.not. (t <= 1.22d-48))) then
        tmp = x / (a + 1.0d0)
    else
        tmp = z / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2e-36) || !(t <= 1.22e-48)) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2e-36) or not (t <= 1.22e-48):
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2e-36) || !(t <= 1.22e-48))
		tmp = Float64(x / Float64(a + 1.0));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2e-36) || ~((t <= 1.22e-48)))
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2e-36], N[Not[LessEqual[t, 1.22e-48]], $MachinePrecision]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.9999999999999999e-36 or 1.21999999999999993e-48 < t

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 88.1%

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

      3. associate-*l/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 57.8%

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

   if -1.9999999999999999e-36 < t < 1.21999999999999993e-48

   1. Initial program 64.6%

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

      1. *-commutative 64.6%

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

      2. associate-/l* 60.9%

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

      3. associate-*l/ 57.8%

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

   3. Simplified 57.8%

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

   4. Taylor expanded in t around 0 60.6%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-36} \lor \neg \left(t \leq 1.22 \cdot 10^{-48}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13: 41.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 27000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4.2e-12) (/ x a) (if (<= a 27000000000000.0) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4.2e-12) {
		tmp = x / a;
	} else if (a <= 27000000000000.0) {
		tmp = x;
	} 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 (a <= (-4.2d-12)) then
        tmp = x / a
    else if (a <= 27000000000000.0d0) then
        tmp = x
    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 (a <= -4.2e-12) {
		tmp = x / a;
	} else if (a <= 27000000000000.0) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4.2e-12:
		tmp = x / a
	elif a <= 27000000000000.0:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4.2e-12)
		tmp = Float64(x / a);
	elseif (a <= 27000000000000.0)
		tmp = x;
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -4.2e-12)
		tmp = x / a;
	elseif (a <= 27000000000000.0)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4.2e-12], N[(x / a), $MachinePrecision], If[LessEqual[a, 27000000000000.0], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -4.19999999999999988e-12 or 2.7e13 < a

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. associate-/l* 75.2%

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

      3. associate-*l/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in x around inf 53.7%

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

   5. Taylor expanded in a around inf 46.4%

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

   if -4.19999999999999988e-12 < a < 2.7e13

   1. Initial program 74.7%

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

      1. *-commutative 74.7%

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

      2. associate-/l* 77.7%

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

      3. associate-*l/ 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in t around inf 34.6%

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

   5. Taylor expanded in a around 0 33.5%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 27000000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14: 41.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.5e+19) (/ x a) (if (<= t 2.3e+18) (/ z b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.5e+19) {
		tmp = x / a;
	} else if (t <= 2.3e+18) {
		tmp = z / b;
	} 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 (t <= (-2.5d+19)) then
        tmp = x / a
    else if (t <= 2.3d+18) then
        tmp = z / b
    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 (t <= -2.5e+19) {
		tmp = x / a;
	} else if (t <= 2.3e+18) {
		tmp = z / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.5e+19:
		tmp = x / a
	elif t <= 2.3e+18:
		tmp = z / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.5e+19)
		tmp = Float64(x / a);
	elseif (t <= 2.3e+18)
		tmp = Float64(z / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.5e+19)
		tmp = x / a;
	elseif (t <= 2.3e+18)
		tmp = z / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.5e+19], N[(x / a), $MachinePrecision], If[LessEqual[t, 2.3e+18], N[(z / b), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5e19

   1. Initial program 85.0%

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

      1. *-commutative 85.0%

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

      2. associate-/l* 89.8%

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

      3. associate-*l/ 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in x around inf 76.1%

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

   5. Taylor expanded in a around inf 43.4%

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

   if -2.5e19 < t < 2.3e18

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. associate-/l* 66.5%

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

      3. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in t around 0 52.8%

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

   if 2.3e18 < t

   1. Initial program 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-/l* 85.6%

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

      3. associate-*l/ 92.2%

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

   3. Simplified 92.2%

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

   4. Taylor expanded in t around inf 51.9%

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

   5. Taylor expanded in a around 0 34.2%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+18}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 19.4% 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 75.2%

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

   1. *-commutative 75.2%

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

   2. associate-/l* 76.5%

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

   3. associate-*l/ 78.1%

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

3. Simplified 78.1%

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

4. Taylor expanded in t around inf 40.3%

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

5. Taylor expanded in a around 0 19.2%

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

6. Final simplification 19.2%

   \[\leadsto x \]

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 2023199 
(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))))