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

Percentage Accurate: 74.7% → 83.4%

Time: 16.0s

Alternatives: 14

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 74.7% 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: 83.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \left(a + \frac{y \cdot b}{t}\right)\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-214}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot t\_1} + \frac{y}{t \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ 1.0 (+ a (/ (* y b) t))))
        (t_2 (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))))
   (if (<= t -1.5e-180)
     t_2
     (if (<= t 1.6e-214)
       (+ (/ z b) (/ (* t x) (* y b)))
       (if (<= t 1.85e-38) (* z (+ (/ x (* z t_1)) (/ y (* t t_1)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + ((y * b) / t));
	double t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	double tmp;
	if (t <= -1.5e-180) {
		tmp = t_2;
	} else if (t <= 1.6e-214) {
		tmp = (z / b) + ((t * x) / (y * b));
	} else if (t <= 1.85e-38) {
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 1.0d0 + (a + ((y * b) / t))
    t_2 = (x + (y * (z / t))) / (a + (1.0d0 + (y * (b / t))))
    if (t <= (-1.5d-180)) then
        tmp = t_2
    else if (t <= 1.6d-214) then
        tmp = (z / b) + ((t * x) / (y * b))
    else if (t <= 1.85d-38) then
        tmp = z * ((x / (z * t_1)) + (y / (t * t_1)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 1.0 + (a + ((y * b) / t));
	double t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	double tmp;
	if (t <= -1.5e-180) {
		tmp = t_2;
	} else if (t <= 1.6e-214) {
		tmp = (z / b) + ((t * x) / (y * b));
	} else if (t <= 1.85e-38) {
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 1.0 + (a + ((y * b) / t))
	t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))))
	tmp = 0
	if t <= -1.5e-180:
		tmp = t_2
	elif t <= 1.6e-214:
		tmp = (z / b) + ((t * x) / (y * b))
	elif t <= 1.85e-38:
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -1.5e-180)
		tmp = t_2;
	elseif (t <= 1.6e-214)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)));
	elseif (t <= 1.85e-38)
		tmp = Float64(z * Float64(Float64(x / Float64(z * t_1)) + Float64(y / Float64(t * t_1))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 1.0 + (a + ((y * b) / t));
	t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	tmp = 0.0;
	if (t <= -1.5e-180)
		tmp = t_2;
	elseif (t <= 1.6e-214)
		tmp = (z / b) + ((t * x) / (y * b));
	elseif (t <= 1.85e-38)
		tmp = z * ((x / (z * t_1)) + (y / (t * t_1)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e-180], t$95$2, If[LessEqual[t, 1.6e-214], N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.85e-38], N[(z * N[(N[(x / N[(z * t$95$1), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.5e-180 or 1.85e-38 < t

   1. Initial program 80.7%

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

      1. *-un-lft-identity 80.7%

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

      2. *-un-lft-identity 80.7%

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

      3. associate-/l* 84.8%

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

      4. associate-+l+ 84.8%

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

      5. associate-/l* 91.2%

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

   4. Applied egg-rr 91.2%

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

   if -1.5e-180 < t < 1.60000000000000007e-214

   1. Initial program 43.7%

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

   3. Taylor expanded in b around inf 50.4%

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

   4. Taylor expanded in t around 0 87.0%

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

   if 1.60000000000000007e-214 < t < 1.85e-38

   1. Initial program 76.2%

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

   3. Taylor expanded in z around inf 86.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-180}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-214}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(\frac{x}{z \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)} + \frac{y}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 87.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq -1 \cdot 10^{-81}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1}\\ \mathbf{elif}\;t\_3 \leq 0:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+295}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

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_3 (/ t_2 t_1)))
   (if (<= t_3 -1e-81)
     (/ (+ x (* z (/ y t))) t_1)
     (if (<= t_3 0.0)
       (/ t_2 (+ (+ a 1.0) (/ y (/ t b))))
       (if (<= t_3 2e+295) t_3 (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y * b) / t) + (a + 1.0);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -1e-81) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	} else if (t_3 <= 2e+295) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = ((y * b) / t) + (a + 1.0d0)
    t_2 = x + ((y * z) / t)
    t_3 = t_2 / t_1
    if (t_3 <= (-1d-81)) then
        tmp = (x + (z * (y / t))) / t_1
    else if (t_3 <= 0.0d0) then
        tmp = t_2 / ((a + 1.0d0) + (y / (t / b)))
    else if (t_3 <= 2d+295) then
        tmp = t_3
    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);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= -1e-81) {
		tmp = (x + (z * (y / t))) / t_1;
	} else if (t_3 <= 0.0) {
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	} else if (t_3 <= 2e+295) {
		tmp = t_3;
	} 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_3 = t_2 / t_1
	tmp = 0
	if t_3 <= -1e-81:
		tmp = (x + (z * (y / t))) / t_1
	elif t_3 <= 0.0:
		tmp = t_2 / ((a + 1.0) + (y / (t / b)))
	elif t_3 <= 2e+295:
		tmp = t_3
	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(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / t_1)
	tmp = 0.0
	if (t_3 <= -1e-81)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / t_1);
	elseif (t_3 <= 0.0)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	elseif (t_3 <= 2e+295)
		tmp = t_3;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y * b) / t) + (a + 1.0);
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / t_1;
	tmp = 0.0;
	if (t_3 <= -1e-81)
		tmp = (x + (z * (y / t))) / t_1;
	elseif (t_3 <= 0.0)
		tmp = t_2 / ((a + 1.0) + (y / (t / b)));
	elseif (t_3 <= 2e+295)
		tmp = t_3;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$3, -1e-81], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$3, 0.0], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+295], t$95$3, N[(z / b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -9.9999999999999996e-82

   1. Initial program 83.6%

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

      1. *-commutative 83.6%

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

      2. associate-/l* 86.9%

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

   4. Applied egg-rr 86.9%

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

   if -9.9999999999999996e-82 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < -0.0

   1. Initial program 76.6%

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

      1. associate-/l* 80.8%

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

      2. clear-num 80.8%

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

      3. un-div-inv 80.8%

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

   4. Applied egg-rr 80.8%

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

   if -0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 2e295

   1. Initial program 99.8%

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

   if 2e295 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 5.9%

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

   3. Taylor expanded in y around inf 77.7%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-81}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+295}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ t_2 := \frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-86}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0)))
        (t_2 (+ (/ z b) (/ (* t x) (* y b)))))
   (if (<= t -1.6e+91)
     t_1
     (if (<= t -1.55e+73)
       (/ z b)
       (if (<= t -8.2e-103)
         t_1
         (if (<= t 1.6e-193)
           t_2
           (if (<= t 7.8e-159)
             (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
             (if (<= t 1.52e-86) t_2 (/ (+ 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 = (x + (y / (t / z))) / (a + 1.0);
	double t_2 = (z / b) + ((t * x) / (y * b));
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if (t <= -8.2e-103) {
		tmp = t_1;
	} else if (t <= 1.6e-193) {
		tmp = t_2;
	} else if (t <= 7.8e-159) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 1.52e-86) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / (a + 1.0d0)
    t_2 = (z / b) + ((t * x) / (y * b))
    if (t <= (-1.6d+91)) then
        tmp = t_1
    else if (t <= (-1.55d+73)) then
        tmp = z / b
    else if (t <= (-8.2d-103)) then
        tmp = t_1
    else if (t <= 1.6d-193) then
        tmp = t_2
    else if (t <= 7.8d-159) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (t <= 1.52d-86) then
        tmp = t_2
    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 = (x + (y / (t / z))) / (a + 1.0);
	double t_2 = (z / b) + ((t * x) / (y * b));
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if (t <= -8.2e-103) {
		tmp = t_1;
	} else if (t <= 1.6e-193) {
		tmp = t_2;
	} else if (t <= 7.8e-159) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 1.52e-86) {
		tmp = t_2;
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + 1.0)
	t_2 = (z / b) + ((t * x) / (y * b))
	tmp = 0
	if t <= -1.6e+91:
		tmp = t_1
	elif t <= -1.55e+73:
		tmp = z / b
	elif t <= -8.2e-103:
		tmp = t_1
	elif t <= 1.6e-193:
		tmp = t_2
	elif t <= 7.8e-159:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif t <= 1.52e-86:
		tmp = t_2
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0))
	t_2 = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)))
	tmp = 0.0
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = Float64(z / b);
	elseif (t <= -8.2e-103)
		tmp = t_1;
	elseif (t <= 1.6e-193)
		tmp = t_2;
	elseif (t <= 7.8e-159)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (t <= 1.52e-86)
		tmp = t_2;
	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 = (x + (y / (t / z))) / (a + 1.0);
	t_2 = (z / b) + ((t * x) / (y * b));
	tmp = 0.0;
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = z / b;
	elseif (t <= -8.2e-103)
		tmp = t_1;
	elseif (t <= 1.6e-193)
		tmp = t_2;
	elseif (t <= 7.8e-159)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (t <= 1.52e-86)
		tmp = t_2;
	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[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+91], t$95$1, If[LessEqual[t, -1.55e+73], N[(z / b), $MachinePrecision], If[LessEqual[t, -8.2e-103], t$95$1, If[LessEqual[t, 1.6e-193], t$95$2, If[LessEqual[t, 7.8e-159], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.52e-86], t$95$2, N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.59999999999999995e91 or -1.55e73 < t < -8.19999999999999992e-103

   1. Initial program 82.7%

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

      1. associate-/l* 87.5%

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

      2. clear-num 87.5%

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

      3. un-div-inv 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in y around 0 82.0%

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

   if -1.59999999999999995e91 < t < -1.55e73

   1. Initial program 21.2%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -8.19999999999999992e-103 < t < 1.60000000000000003e-193 or 7.79999999999999953e-159 < t < 1.52e-86

   1. Initial program 56.5%

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

   3. Taylor expanded in b around inf 49.2%

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

   4. Taylor expanded in t around 0 78.3%

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

   if 1.60000000000000003e-193 < t < 7.79999999999999953e-159

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 99.5%

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

   if 1.52e-86 < t

   1. Initial program 81.2%

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

      1. *-un-lft-identity 81.2%

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

      2. *-un-lft-identity 81.2%

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

      3. associate-/l* 84.7%

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

      4. associate-+l+ 84.7%

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

      5. associate-/l* 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around 0 75.5%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-193}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-86}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-180}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-152}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{t\_1 + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-125}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + t\_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* y b) t))
        (t_2 (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t)))))))
   (if (<= t -2e-180)
     t_2
     (if (<= t 1.1e-203)
       (+ (/ z b) (/ (* t x) (* y b)))
       (if (<= t 2e-152)
         (/ (+ x (* z (/ y t))) (+ t_1 (+ a 1.0)))
         (if (<= t 7.2e-125) (/ (* y z) (* t (+ 1.0 (+ a t_1)))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	double tmp;
	if (t <= -2e-180) {
		tmp = t_2;
	} else if (t <= 1.1e-203) {
		tmp = (z / b) + ((t * x) / (y * b));
	} else if (t <= 2e-152) {
		tmp = (x + (z * (y / t))) / (t_1 + (a + 1.0));
	} else if (t <= 7.2e-125) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * b) / t
    t_2 = (x + (y * (z / t))) / (a + (1.0d0 + (y * (b / t))))
    if (t <= (-2d-180)) then
        tmp = t_2
    else if (t <= 1.1d-203) then
        tmp = (z / b) + ((t * x) / (y * b))
    else if (t <= 2d-152) then
        tmp = (x + (z * (y / t))) / (t_1 + (a + 1.0d0))
    else if (t <= 7.2d-125) then
        tmp = (y * z) / (t * (1.0d0 + (a + t_1)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (y * b) / t;
	double t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	double tmp;
	if (t <= -2e-180) {
		tmp = t_2;
	} else if (t <= 1.1e-203) {
		tmp = (z / b) + ((t * x) / (y * b));
	} else if (t <= 2e-152) {
		tmp = (x + (z * (y / t))) / (t_1 + (a + 1.0));
	} else if (t <= 7.2e-125) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (y * b) / t
	t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))))
	tmp = 0
	if t <= -2e-180:
		tmp = t_2
	elif t <= 1.1e-203:
		tmp = (z / b) + ((t * x) / (y * b))
	elif t <= 2e-152:
		tmp = (x + (z * (y / t))) / (t_1 + (a + 1.0))
	elif t <= 7.2e-125:
		tmp = (y * z) / (t * (1.0 + (a + t_1)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(y * b) / t)
	t_2 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))))
	tmp = 0.0
	if (t <= -2e-180)
		tmp = t_2;
	elseif (t <= 1.1e-203)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)));
	elseif (t <= 2e-152)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(t_1 + Float64(a + 1.0)));
	elseif (t <= 7.2e-125)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + t_1))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (y * b) / t;
	t_2 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	tmp = 0.0;
	if (t <= -2e-180)
		tmp = t_2;
	elseif (t <= 1.1e-203)
		tmp = (z / b) + ((t * x) / (y * b));
	elseif (t <= 2e-152)
		tmp = (x + (z * (y / t))) / (t_1 + (a + 1.0));
	elseif (t <= 7.2e-125)
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-180], t$95$2, If[LessEqual[t, 1.1e-203], N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-152], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-125], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2e-180 or 7.2000000000000004e-125 < t

   1. Initial program 80.3%

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

      1. *-un-lft-identity 80.3%

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

      2. *-un-lft-identity 80.3%

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

      3. associate-/l* 84.0%

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

      4. associate-+l+ 84.0%

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

      5. associate-/l* 89.4%

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

   4. Applied egg-rr 89.4%

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

   if -2e-180 < t < 1.1e-203

   1. Initial program 44.1%

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

   3. Taylor expanded in b around inf 48.3%

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

   4. Taylor expanded in t around 0 85.4%

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

   if 1.1e-203 < t < 2.00000000000000013e-152

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 99.7%

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

   4. Applied egg-rr 99.7%

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

   if 2.00000000000000013e-152 < t < 7.2000000000000004e-125

   1. Initial program 56.3%

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

   3. Taylor expanded in x around 0 77.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-180}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-203}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-152}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-125}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ t_2 := \frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a (+ 1.0 (* y (/ b t))))))
        (t_2 (+ (/ z b) (/ (* t x) (* y b)))))
   (if (<= t -9.2e-179)
     t_1
     (if (<= t 2.15e-193)
       t_2
       (if (<= t 1.95e-159)
         (/ (* y z) (* t (+ 1.0 (+ a (/ (* y b) t)))))
         (if (<= t 1.9e-127) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	double t_2 = (z / b) + ((t * x) / (y * b));
	double tmp;
	if (t <= -9.2e-179) {
		tmp = t_1;
	} else if (t <= 2.15e-193) {
		tmp = t_2;
	} else if (t <= 1.95e-159) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 1.9e-127) {
		tmp = t_2;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = (x + (y * (z / t))) / (a + (1.0d0 + (y * (b / t))))
    t_2 = (z / b) + ((t * x) / (y * b))
    if (t <= (-9.2d-179)) then
        tmp = t_1
    else if (t <= 2.15d-193) then
        tmp = t_2
    else if (t <= 1.95d-159) then
        tmp = (y * z) / (t * (1.0d0 + (a + ((y * b) / t))))
    else if (t <= 1.9d-127) then
        tmp = t_2
    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 + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	double t_2 = (z / b) + ((t * x) / (y * b));
	double tmp;
	if (t <= -9.2e-179) {
		tmp = t_1;
	} else if (t <= 2.15e-193) {
		tmp = t_2;
	} else if (t <= 1.95e-159) {
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	} else if (t <= 1.9e-127) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))))
	t_2 = (z / b) + ((t * x) / (y * b))
	tmp = 0
	if t <= -9.2e-179:
		tmp = t_1
	elif t <= 2.15e-193:
		tmp = t_2
	elif t <= 1.95e-159:
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))))
	elif t <= 1.9e-127:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + Float64(1.0 + Float64(y * Float64(b / t)))))
	t_2 = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)))
	tmp = 0.0
	if (t <= -9.2e-179)
		tmp = t_1;
	elseif (t <= 2.15e-193)
		tmp = t_2;
	elseif (t <= 1.95e-159)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + Float64(Float64(y * b) / t)))));
	elseif (t <= 1.9e-127)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / (a + (1.0 + (y * (b / t))));
	t_2 = (z / b) + ((t * x) / (y * b));
	tmp = 0.0;
	if (t <= -9.2e-179)
		tmp = t_1;
	elseif (t <= 2.15e-193)
		tmp = t_2;
	elseif (t <= 1.95e-159)
		tmp = (y * z) / (t * (1.0 + (a + ((y * b) / t))));
	elseif (t <= 1.9e-127)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e-179], t$95$1, If[LessEqual[t, 2.15e-193], t$95$2, If[LessEqual[t, 1.95e-159], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.9e-127], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.1999999999999995e-179 or 1.90000000000000001e-127 < t

   1. Initial program 80.1%

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

      1. *-un-lft-identity 80.1%

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

      2. *-un-lft-identity 80.1%

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

      3. associate-/l* 83.3%

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

      4. associate-+l+ 83.3%

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

      5. associate-/l* 88.6%

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

   4. Applied egg-rr 88.6%

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

   if -9.1999999999999995e-179 < t < 2.1500000000000001e-193 or 1.94999999999999988e-159 < t < 1.90000000000000001e-127

   1. Initial program 49.1%

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

   3. Taylor expanded in b around inf 52.1%

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

   4. Taylor expanded in t around 0 87.6%

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

   if 2.1500000000000001e-193 < t < 1.94999999999999988e-159

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 99.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{-179}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-193}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-159}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \left(1 + y \cdot \frac{b}{t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-101} \lor \neg \left(t \leq 5 \cdot 10^{-86}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -1.6e+91)
     t_1
     (if (<= t -1.55e+73)
       (/ z b)
       (if (or (<= t -2.4e-101) (not (<= t 5e-86)))
         t_1
         (+ (/ z b) (/ (* t x) (* 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 <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if ((t <= -2.4e-101) || !(t <= 5e-86)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (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 <= (-1.6d+91)) then
        tmp = t_1
    else if (t <= (-1.55d+73)) then
        tmp = z / b
    else if ((t <= (-2.4d-101)) .or. (.not. (t <= 5d-86))) then
        tmp = t_1
    else
        tmp = (z / b) + ((t * x) / (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 <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if ((t <= -2.4e-101) || !(t <= 5e-86)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (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 <= -1.6e+91:
		tmp = t_1
	elif t <= -1.55e+73:
		tmp = z / b
	elif (t <= -2.4e-101) or not (t <= 5e-86):
		tmp = t_1
	else:
		tmp = (z / b) + ((t * x) / (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 <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = Float64(z / b);
	elseif ((t <= -2.4e-101) || !(t <= 5e-86))
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(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 <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = z / b;
	elseif ((t <= -2.4e-101) || ~((t <= 5e-86)))
		tmp = t_1;
	else
		tmp = (z / b) + ((t * x) / (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, -1.6e+91], t$95$1, If[LessEqual[t, -1.55e+73], N[(z / b), $MachinePrecision], If[Or[LessEqual[t, -2.4e-101], N[Not[LessEqual[t, 5e-86]], $MachinePrecision]], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999995e91 or -1.55e73 < t < -2.4e-101 or 4.9999999999999999e-86 < t

   1. Initial program 82.0%

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

      1. *-un-lft-identity 82.0%

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

      2. *-un-lft-identity 82.0%

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

      3. associate-/l* 86.2%

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

      4. associate-+l+ 86.2%

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

      5. associate-/l* 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in y around 0 79.0%

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

   if -1.59999999999999995e91 < t < -1.55e73

   1. Initial program 21.2%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -2.4e-101 < t < 4.9999999999999999e-86

   1. Initial program 59.9%

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

   3. Taylor expanded in b around inf 47.0%

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

   4. Taylor expanded in t around 0 73.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-101} \lor \neg \left(t \leq 5 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-34} \lor \neg \left(t \leq 6.2 \cdot 10^{-117}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ 1.0 (+ a (/ (* y b) t))))))
   (if (<= t -1.6e+91)
     t_1
     (if (<= t -1.8e+68)
       (/ z b)
       (if (or (<= t -7.2e-34) (not (<= t 6.2e-117)))
         t_1
         (+ (/ z b) (/ (* t x) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.8e+68) {
		tmp = z / b;
	} else if ((t <= -7.2e-34) || !(t <= 6.2e-117)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 + (a + ((y * b) / t)))
    if (t <= (-1.6d+91)) then
        tmp = t_1
    else if (t <= (-1.8d+68)) then
        tmp = z / b
    else if ((t <= (-7.2d-34)) .or. (.not. (t <= 6.2d-117))) then
        tmp = t_1
    else
        tmp = (z / b) + ((t * x) / (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 + (a + ((y * b) / t)));
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.8e+68) {
		tmp = z / b;
	} else if ((t <= -7.2e-34) || !(t <= 6.2e-117)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 + (a + ((y * b) / t)))
	tmp = 0
	if t <= -1.6e+91:
		tmp = t_1
	elif t <= -1.8e+68:
		tmp = z / b
	elif (t <= -7.2e-34) or not (t <= 6.2e-117):
		tmp = t_1
	else:
		tmp = (z / b) + ((t * x) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 + Float64(a + Float64(Float64(y * b) / t))))
	tmp = 0.0
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.8e+68)
		tmp = Float64(z / b);
	elseif ((t <= -7.2e-34) || !(t <= 6.2e-117))
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 + (a + ((y * b) / t)));
	tmp = 0.0;
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.8e+68)
		tmp = z / b;
	elseif ((t <= -7.2e-34) || ~((t <= 6.2e-117)))
		tmp = t_1;
	else
		tmp = (z / b) + ((t * x) / (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 + N[(a + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+91], t$95$1, If[LessEqual[t, -1.8e+68], N[(z / b), $MachinePrecision], If[Or[LessEqual[t, -7.2e-34], N[Not[LessEqual[t, 6.2e-117]], $MachinePrecision]], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999995e91 or -1.7999999999999999e68 < t < -7.20000000000000016e-34 or 6.20000000000000022e-117 < t

   1. Initial program 81.4%

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

   3. Taylor expanded in x around inf 70.7%

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

   if -1.59999999999999995e91 < t < -1.7999999999999999e68

   1. Initial program 34.1%

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

   3. Taylor expanded in y around inf 84.2%

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

   if -7.20000000000000016e-34 < t < 6.20000000000000022e-117

   1. Initial program 63.4%

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

   3. Taylor expanded in b around inf 47.5%

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

   4. Taylor expanded in t around 0 72.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-34} \lor \neg \left(t \leq 6.2 \cdot 10^{-117}\right):\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{y \cdot b}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-34} \lor \neg \left(t \leq 5.3 \cdot 10^{-86}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (+ a 1.0))))
   (if (<= t -1.6e+91)
     t_1
     (if (<= t -9.5e+67)
       (/ z b)
       (if (or (<= t -4.4e-34) (not (<= t 5.3e-86)))
         t_1
         (+ (/ z b) (/ (* t x) (* y b))))))))

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 <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -9.5e+67) {
		tmp = z / b;
	} else if ((t <= -4.4e-34) || !(t <= 5.3e-86)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (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 / (a + 1.0d0)
    if (t <= (-1.6d+91)) then
        tmp = t_1
    else if (t <= (-9.5d+67)) then
        tmp = z / b
    else if ((t <= (-4.4d-34)) .or. (.not. (t <= 5.3d-86))) then
        tmp = t_1
    else
        tmp = (z / b) + ((t * x) / (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 / (a + 1.0);
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -9.5e+67) {
		tmp = z / b;
	} else if ((t <= -4.4e-34) || !(t <= 5.3e-86)) {
		tmp = t_1;
	} else {
		tmp = (z / b) + ((t * x) / (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a + 1.0)
	tmp = 0
	if t <= -1.6e+91:
		tmp = t_1
	elif t <= -9.5e+67:
		tmp = z / b
	elif (t <= -4.4e-34) or not (t <= 5.3e-86):
		tmp = t_1
	else:
		tmp = (z / b) + ((t * x) / (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -9.5e+67)
		tmp = Float64(z / b);
	elseif ((t <= -4.4e-34) || !(t <= 5.3e-86))
		tmp = t_1;
	else
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)));
	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 <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -9.5e+67)
		tmp = z / b;
	elseif ((t <= -4.4e-34) || ~((t <= 5.3e-86)))
		tmp = t_1;
	else
		tmp = (z / b) + ((t * x) / (y * b));
	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, -1.6e+91], t$95$1, If[LessEqual[t, -9.5e+67], N[(z / b), $MachinePrecision], If[Or[LessEqual[t, -4.4e-34], N[Not[LessEqual[t, 5.3e-86]], $MachinePrecision]], t$95$1, N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59999999999999995e91 or -9.5000000000000002e67 < t < -4.3999999999999998e-34 or 5.2999999999999997e-86 < t

   1. Initial program 80.9%

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

   3. Taylor expanded in y around 0 68.4%

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

   if -1.59999999999999995e91 < t < -9.5000000000000002e67

   1. Initial program 34.1%

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

   3. Taylor expanded in y around inf 84.2%

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

   if -4.3999999999999998e-34 < t < 5.2999999999999997e-86

   1. Initial program 65.0%

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

   3. Taylor expanded in b around inf 47.6%

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

   4. Taylor expanded in t around 0 71.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{+67}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-34} \lor \neg \left(t \leq 5.3 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y (/ t z))) (+ a 1.0))))
   (if (<= t -1.6e+91)
     t_1
     (if (<= t -1.55e+73)
       (/ z b)
       (if (<= t -1.75e-102)
         t_1
         (if (<= t 4.8e-86)
           (+ (/ z b) (/ (* t x) (* y b)))
           (/ (+ x (* y (/ z t))) (+ a 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if (t <= -1.75e-102) {
		tmp = t_1;
	} else if (t <= 4.8e-86) {
		tmp = (z / b) + ((t * x) / (y * b));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / (t / z))) / (a + 1.0d0)
    if (t <= (-1.6d+91)) then
        tmp = t_1
    else if (t <= (-1.55d+73)) then
        tmp = z / b
    else if (t <= (-1.75d-102)) then
        tmp = t_1
    else if (t <= 4.8d-86) then
        tmp = (z / b) + ((t * x) / (y * b))
    else
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y / (t / z))) / (a + 1.0);
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if (t <= -1.75e-102) {
		tmp = t_1;
	} else if (t <= 4.8e-86) {
		tmp = (z / b) + ((t * x) / (y * b));
	} else {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y / (t / z))) / (a + 1.0)
	tmp = 0
	if t <= -1.6e+91:
		tmp = t_1
	elif t <= -1.55e+73:
		tmp = z / b
	elif t <= -1.75e-102:
		tmp = t_1
	elif t <= 4.8e-86:
		tmp = (z / b) + ((t * x) / (y * b))
	else:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + 1.0))
	tmp = 0.0
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = Float64(z / b);
	elseif (t <= -1.75e-102)
		tmp = t_1;
	elseif (t <= 4.8e-86)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)));
	else
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y / (t / z))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = z / b;
	elseif (t <= -1.75e-102)
		tmp = t_1;
	elseif (t <= 4.8e-86)
		tmp = (z / b) + ((t * x) / (y * b));
	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[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+91], t$95$1, If[LessEqual[t, -1.55e+73], N[(z / b), $MachinePrecision], If[LessEqual[t, -1.75e-102], t$95$1, If[LessEqual[t, 4.8e-86], N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.59999999999999995e91 or -1.55e73 < t < -1.74999999999999993e-102

   1. Initial program 82.7%

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

      1. associate-/l* 87.5%

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

      2. clear-num 87.5%

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

      3. un-div-inv 87.5%

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

   4. Applied egg-rr 87.5%

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

   5. Taylor expanded in y around 0 82.0%

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

   if -1.59999999999999995e91 < t < -1.55e73

   1. Initial program 21.2%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -1.74999999999999993e-102 < t < 4.80000000000000026e-86

   1. Initial program 59.9%

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

   3. Taylor expanded in b around inf 47.0%

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

   4. Taylor expanded in t around 0 73.8%

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

   if 4.80000000000000026e-86 < t

   1. Initial program 81.2%

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

      1. *-un-lft-identity 81.2%

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

      2. *-un-lft-identity 81.2%

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

      3. associate-/l* 84.7%

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

      4. associate-+l+ 84.7%

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

      5. associate-/l* 88.2%

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

   4. Applied egg-rr 88.2%

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

   5. Taylor expanded in y around 0 75.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-102}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-86}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-101}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a 1.0))))
   (if (<= t -1.6e+91)
     t_1
     (if (<= t -1.55e+73)
       (/ z b)
       (if (<= t -2.25e-101)
         (/ (+ x (* z (/ y t))) (+ a 1.0))
         (if (<= t 2.35e-85) (+ (/ z b) (/ (* t x) (* y b))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if (t <= -2.25e-101) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 2.35e-85) {
		tmp = (z / b) + ((t * x) / (y * 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 + (y * (z / t))) / (a + 1.0d0)
    if (t <= (-1.6d+91)) then
        tmp = t_1
    else if (t <= (-1.55d+73)) then
        tmp = z / b
    else if (t <= (-2.25d-101)) then
        tmp = (x + (z * (y / t))) / (a + 1.0d0)
    else if (t <= 2.35d-85) then
        tmp = (z / b) + ((t * x) / (y * 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 + (y * (z / t))) / (a + 1.0);
	double tmp;
	if (t <= -1.6e+91) {
		tmp = t_1;
	} else if (t <= -1.55e+73) {
		tmp = z / b;
	} else if (t <= -2.25e-101) {
		tmp = (x + (z * (y / t))) / (a + 1.0);
	} else if (t <= 2.35e-85) {
		tmp = (z / b) + ((t * x) / (y * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + 1.0)
	tmp = 0
	if t <= -1.6e+91:
		tmp = t_1
	elif t <= -1.55e+73:
		tmp = z / b
	elif t <= -2.25e-101:
		tmp = (x + (z * (y / t))) / (a + 1.0)
	elif t <= 2.35e-85:
		tmp = (z / b) + ((t * x) / (y * b))
	else:
		tmp = t_1
	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 <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = Float64(z / b);
	elseif (t <= -2.25e-101)
		tmp = Float64(Float64(x + Float64(z * Float64(y / t))) / Float64(a + 1.0));
	elseif (t <= 2.35e-85)
		tmp = Float64(Float64(z / b) + Float64(Float64(t * x) / Float64(y * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (y * (z / t))) / (a + 1.0);
	tmp = 0.0;
	if (t <= -1.6e+91)
		tmp = t_1;
	elseif (t <= -1.55e+73)
		tmp = z / b;
	elseif (t <= -2.25e-101)
		tmp = (x + (z * (y / t))) / (a + 1.0);
	elseif (t <= 2.35e-85)
		tmp = (z / b) + ((t * x) / (y * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.6e+91], t$95$1, If[LessEqual[t, -1.55e+73], N[(z / b), $MachinePrecision], If[LessEqual[t, -2.25e-101], N[(N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.35e-85], N[(N[(z / b), $MachinePrecision] + N[(N[(t * x), $MachinePrecision] / N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.59999999999999995e91 or 2.35000000000000005e-85 < t

   1. Initial program 79.6%

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

      1. *-un-lft-identity 79.6%

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

      2. *-un-lft-identity 79.6%

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

      3. associate-/l* 84.7%

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

      4. associate-+l+ 84.7%

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

      5. associate-/l* 91.3%

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

   4. Applied egg-rr 91.3%

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

   5. Taylor expanded in y around 0 78.6%

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

   if -1.59999999999999995e91 < t < -1.55e73

   1. Initial program 21.2%

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

   3. Taylor expanded in y around inf 100.0%

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

   if -1.55e73 < t < -2.2499999999999999e-101

   1. Initial program 93.2%

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

      1. associate-/l* 93.2%

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

      2. clear-num 93.2%

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

      3. un-div-inv 93.3%

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

   4. Applied egg-rr 93.3%

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

      1. associate-/r/ 90.2%

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

   6. Applied egg-rr 90.2%

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

   7. Taylor expanded in y around 0 80.5%

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

   if -2.2499999999999999e-101 < t < 2.35000000000000005e-85

   1. Initial program 59.9%

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

   3. Taylor expanded in b around inf 47.0%

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

   4. Taylor expanded in t around 0 73.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-101}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 2.35 \cdot 10^{-85}:\\ \;\;\;\;\frac{z}{b} + \frac{t \cdot x}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91} \lor \neg \left(t \leq -1.25 \cdot 10^{+68}\right) \land \left(t \leq -9 \cdot 10^{-35} \lor \neg \left(t \leq 9 \cdot 10^{-118}\right)\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.6e+91)
         (and (not (<= t -1.25e+68)) (or (<= t -9e-35) (not (<= t 9e-118)))))
   (/ 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 <= -1.6e+91) || (!(t <= -1.25e+68) && ((t <= -9e-35) || !(t <= 9e-118)))) {
		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 <= (-1.6d+91)) .or. (.not. (t <= (-1.25d+68))) .and. (t <= (-9d-35)) .or. (.not. (t <= 9d-118))) 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 <= -1.6e+91) || (!(t <= -1.25e+68) && ((t <= -9e-35) || !(t <= 9e-118)))) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.6e+91) or (not (t <= -1.25e+68) and ((t <= -9e-35) or not (t <= 9e-118))):
		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 <= -1.6e+91) || (!(t <= -1.25e+68) && ((t <= -9e-35) || !(t <= 9e-118))))
		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 <= -1.6e+91) || (~((t <= -1.25e+68)) && ((t <= -9e-35) || ~((t <= 9e-118)))))
		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, -1.6e+91], And[N[Not[LessEqual[t, -1.25e+68]], $MachinePrecision], Or[LessEqual[t, -9e-35], N[Not[LessEqual[t, 9e-118]], $MachinePrecision]]]], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.59999999999999995e91 or -1.2500000000000001e68 < t < -9.0000000000000002e-35 or 9.0000000000000001e-118 < t

   1. Initial program 81.4%

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

   3. Taylor expanded in y around 0 67.9%

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

   if -1.59999999999999995e91 < t < -1.2500000000000001e68 or -9.0000000000000002e-35 < t < 9.0000000000000001e-118

   1. Initial program 61.5%

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

   3. Taylor expanded in y around inf 65.4%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+91} \lor \neg \left(t \leq -1.25 \cdot 10^{+68}\right) \land \left(t \leq -9 \cdot 10^{-35} \lor \neg \left(t \leq 9 \cdot 10^{-118}\right)\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 41.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.35 \cdot 10^{+87}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-54}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-144}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.35e+87)
   (/ x a)
   (if (<= a -5.1e-54)
     (/ z b)
     (if (<= a 1.3e-144) x (if (<= a 3.4e-5) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.35e+87) {
		tmp = x / a;
	} else if (a <= -5.1e-54) {
		tmp = z / b;
	} else if (a <= 1.3e-144) {
		tmp = x;
	} else if (a <= 3.4e-5) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= (-3.35d+87)) then
        tmp = x / a
    else if (a <= (-5.1d-54)) then
        tmp = z / b
    else if (a <= 1.3d-144) then
        tmp = x
    else if (a <= 3.4d-5) then
        tmp = z / b
    else
        tmp = x / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.35e+87) {
		tmp = x / a;
	} else if (a <= -5.1e-54) {
		tmp = z / b;
	} else if (a <= 1.3e-144) {
		tmp = x;
	} else if (a <= 3.4e-5) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.35e+87:
		tmp = x / a
	elif a <= -5.1e-54:
		tmp = z / b
	elif a <= 1.3e-144:
		tmp = x
	elif a <= 3.4e-5:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.35e+87)
		tmp = Float64(x / a);
	elseif (a <= -5.1e-54)
		tmp = Float64(z / b);
	elseif (a <= 1.3e-144)
		tmp = x;
	elseif (a <= 3.4e-5)
		tmp = Float64(z / b);
	else
		tmp = Float64(x / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= -3.35e+87)
		tmp = x / a;
	elseif (a <= -5.1e-54)
		tmp = z / b;
	elseif (a <= 1.3e-144)
		tmp = x;
	elseif (a <= 3.4e-5)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.35e+87], N[(x / a), $MachinePrecision], If[LessEqual[a, -5.1e-54], N[(z / b), $MachinePrecision], If[LessEqual[a, 1.3e-144], x, If[LessEqual[a, 3.4e-5], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.3500000000000002e87 or 3.4e-5 < a

   1. Initial program 78.3%

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

   3. Taylor expanded in y around 0 63.0%

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

   4. Taylor expanded in a around inf 60.5%

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

   if -3.3500000000000002e87 < a < -5.1000000000000001e-54 or 1.3e-144 < a < 3.4e-5

   1. Initial program 71.4%

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

   3. Taylor expanded in y around inf 50.9%

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

   if -5.1000000000000001e-54 < a < 1.3e-144

   1. Initial program 72.2%

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

   3. Taylor expanded in y around 0 46.9%

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

   4. Taylor expanded in a around 0 46.9%

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

Alternative 13: 40.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -1.0) (not (<= a 1.0))) (/ x a) x))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -1.0], N[Not[LessEqual[a, 1.0]], $MachinePrecision]], N[(x / a), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 1 < a

   1. Initial program 77.3%

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

   3. Taylor expanded in y around 0 56.0%

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

   4. Taylor expanded in a around inf 54.6%

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

   if -1 < a < 1

   1. Initial program 71.6%

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

   3. Taylor expanded in y around 0 40.1%

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

   4. Taylor expanded in a around 0 39.0%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \lor \neg \left(a \leq 1\right):\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 19.7% 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 74.2%

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

3. Taylor expanded in y around 0 47.5%

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

4. Taylor expanded in a around 0 22.7%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Developer target: 78.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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