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

Percentage Accurate: 75.0% → 86.0%

Time: 14.6s

Alternatives: 17

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 75.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 86.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(a + 1\right) + \frac{y \cdot b}{t}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t\_2}{t\_1}\\ \mathbf{if}\;t\_3 \leq 10^{+246}:\\ \;\;\;\;\frac{t\_2}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;t\_3 \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{t\_1} + \frac{\frac{y}{t}}{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ a 1.0) (/ (* y b) t)))
        (t_2 (+ x (/ (* y z) t)))
        (t_3 (/ t_2 t_1)))
   (if (<= t_3 1e+246)
     (/ t_2 (+ (+ a 1.0) (* y (/ b t))))
     (if (<= t_3 INFINITY)
       (* z (+ (/ (/ x z) t_1) (/ (/ y t) t_1)))
       (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= 1e+246) {
		tmp = t_2 / ((a + 1.0) + (y * (b / t)));
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = z * (((x / z) / t_1) + ((y / t) / t_1));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a + 1.0) + ((y * b) / t);
	double t_2 = x + ((y * z) / t);
	double t_3 = t_2 / t_1;
	double tmp;
	if (t_3 <= 1e+246) {
		tmp = t_2 / ((a + 1.0) + (y * (b / t)));
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = z * (((x / z) / t_1) + ((y / t) / t_1));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (a + 1.0) + ((y * b) / t)
	t_2 = x + ((y * z) / t)
	t_3 = t_2 / t_1
	tmp = 0
	if t_3 <= 1e+246:
		tmp = t_2 / ((a + 1.0) + (y * (b / t)))
	elif t_3 <= math.inf:
		tmp = z * (((x / z) / t_1) + ((y / t) / t_1))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))
	t_2 = Float64(x + Float64(Float64(y * z) / t))
	t_3 = Float64(t_2 / t_1)
	tmp = 0.0
	if (t_3 <= 1e+246)
		tmp = Float64(t_2 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	elseif (t_3 <= Inf)
		tmp = Float64(z * Float64(Float64(Float64(x / z) / t_1) + Float64(Float64(y / t) / t_1)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a + 1.0) + ((y * b) / t);
	t_2 = x + ((y * z) / t);
	t_3 = t_2 / t_1;
	tmp = 0.0;
	if (t_3 <= 1e+246)
		tmp = t_2 / ((a + 1.0) + (y * (b / t)));
	elseif (t_3 <= Inf)
		tmp = z * (((x / z) / t_1) + ((y / t) / 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[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $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+246], N[(t$95$2 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, Infinity], N[(z * N[(N[(N[(x / z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 1.00000000000000007e246

   1. Initial program 90.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 91.1%

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

   4. Applied egg-rr 91.1%

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

   if 1.00000000000000007e246 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < +inf.0

   1. Initial program 33.1%

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

   3. Taylor expanded in z around inf

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

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

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

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

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

      3. associate-/r* N/A

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

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

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

      5. /-lowering-/.f64 N/A

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

      6. associate-+r+ N/A

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

      7. +-commutative N/A

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

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

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

      9. /-lowering-/.f64 N/A

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

      10. *-commutative N/A

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

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

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

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

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

      13. associate-/r* N/A

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

      14. /-lowering-/.f64 N/A

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

      15. /-lowering-/.f64 N/A

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

      16. associate-+r+ N/A

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

      17. +-commutative N/A

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

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

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

   5. Simplified 90.2%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 10^{+246}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq \infty:\\ \;\;\;\;z \cdot \left(\frac{\frac{x}{z}}{\left(a + 1\right) + \frac{y \cdot b}{t}} + \frac{\frac{y}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;\frac{t\_1}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 4 \cdot 10^{+287}:\\ \;\;\;\;\frac{t\_1}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y z) t))))
   (if (<= (/ t_1 (+ (+ a 1.0) (/ (* y b) t))) 4e+287)
     (/ t_1 (+ (+ a 1.0) (* y (/ b t))))
     (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((y * z) / t);
	double tmp;
	if ((t_1 / ((a + 1.0) + ((y * b) / t))) <= 4e+287) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} 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)
    if ((t_1 / ((a + 1.0d0) + ((y * b) / t))) <= 4d+287) then
        tmp = t_1 / ((a + 1.0d0) + (y * (b / t)))
    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);
	double tmp;
	if ((t_1 / ((a + 1.0) + ((y * b) / t))) <= 4e+287) {
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((y * z) / t)
	tmp = 0
	if (t_1 / ((a + 1.0) + ((y * b) / t))) <= 4e+287:
		tmp = t_1 / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(y * z) / t))
	tmp = 0.0
	if (Float64(t_1 / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))) <= 4e+287)
		tmp = Float64(t_1 / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	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);
	tmp = 0.0;
	if ((t_1 / ((a + 1.0) + ((y * b) / t))) <= 4e+287)
		tmp = t_1 / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e+287], N[(t$95$1 / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t))) < 4.0000000000000003e287

   1. Initial program 90.3%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 91.1%

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

   4. Applied egg-rr 91.1%

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

   if 4.0000000000000003e287 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a #s(literal 1 binary64)) (/.f64 (*.f64 y b) t)))

   1. Initial program 3.5%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 84.3%

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

   5. Simplified 84.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \leq 4 \cdot 10^{+287}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 64.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 165:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.78 \cdot 10^{+106}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.4e+86)
   (/ z b)
   (if (<= y 165.0)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 1.78e+106)
       (/ (* y z) (* t (+ (+ a 1.0) (/ (* y b) t))))
       (if (<= y 9e+179) (/ x (+ (+ a 1.0) (* y (/ b t)))) (/ z b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.4e+86) {
		tmp = z / b;
	} else if (y <= 165.0) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.78e+106) {
		tmp = (y * z) / (t * ((a + 1.0) + ((y * b) / t)));
	} else if (y <= 9e+179) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} 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 (y <= (-2.4d+86)) then
        tmp = z / b
    else if (y <= 165.0d0) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 1.78d+106) then
        tmp = (y * z) / (t * ((a + 1.0d0) + ((y * b) / t)))
    else if (y <= 9d+179) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    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 (y <= -2.4e+86) {
		tmp = z / b;
	} else if (y <= 165.0) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.78e+106) {
		tmp = (y * z) / (t * ((a + 1.0) + ((y * b) / t)));
	} else if (y <= 9e+179) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.4e+86:
		tmp = z / b
	elif y <= 165.0:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 1.78e+106:
		tmp = (y * z) / (t * ((a + 1.0) + ((y * b) / t)))
	elif y <= 9e+179:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.4e+86)
		tmp = Float64(z / b);
	elseif (y <= 165.0)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 1.78e+106)
		tmp = Float64(Float64(y * z) / Float64(t * Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t))));
	elseif (y <= 9e+179)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.4e+86)
		tmp = z / b;
	elseif (y <= 165.0)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 1.78e+106)
		tmp = (y * z) / (t * ((a + 1.0) + ((y * b) / t)));
	elseif (y <= 9e+179)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.4e+86], N[(z / b), $MachinePrecision], If[LessEqual[y, 165.0], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.78e+106], N[(N[(y * z), $MachinePrecision] / N[(t * N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+179], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4e86 or 9.0000000000000005e179 < y

   1. Initial program 47.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 66.4%

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

   5. Simplified 66.4%

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

   if -2.4e86 < y < 165

   1. Initial program 92.1%

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

   3. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. +-lowering-+.f64 79.4%

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

   5. Simplified 79.4%

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

   if 165 < y < 1.77999999999999995e106

   1. Initial program 86.2%

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

   3. Taylor expanded in x around 0

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

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

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

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

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

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

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

      4. associate-+r+ N/A

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

      5. +-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

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

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

      10. +-lowering-+.f64 60.4%

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

   5. Simplified 60.4%

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

   if 1.77999999999999995e106 < y < 9.0000000000000005e179

   1. Initial program 88.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 93.9%

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

   4. Applied egg-rr 93.9%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 76.1%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 165:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.78 \cdot 10^{+106}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(\left(a + 1\right) + \frac{y \cdot b}{t}\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 64.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-97}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+179}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.8e+86)
   (/ z b)
   (if (<= y 9e-97)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 1.75e+179)
       (/ (+ x (* y (/ z t))) (+ 1.0 (* y (/ b t))))
       (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.8e+86) {
		tmp = z / b;
	} else if (y <= 9e-97) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.75e+179) {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	} 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 (y <= (-5.8d+86)) then
        tmp = z / b
    else if (y <= 9d-97) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 1.75d+179) then
        tmp = (x + (y * (z / t))) / (1.0d0 + (y * (b / t)))
    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 (y <= -5.8e+86) {
		tmp = z / b;
	} else if (y <= 9e-97) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 1.75e+179) {
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.8e+86:
		tmp = z / b
	elif y <= 9e-97:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 1.75e+179:
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.8e+86)
		tmp = Float64(z / b);
	elseif (y <= 9e-97)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 1.75e+179)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.8e+86)
		tmp = z / b;
	elseif (y <= 9e-97)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 1.75e+179)
		tmp = (x + (y * (z / t))) / (1.0 + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.8e+86], N[(z / b), $MachinePrecision], If[LessEqual[y, 9e-97], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e+179], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999981e86 or 1.75000000000000007e179 < y

   1. Initial program 48.1%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 65.7%

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

   5. Simplified 65.7%

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

   if -5.79999999999999981e86 < y < 9.0000000000000002e-97

   1. Initial program 92.9%

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

   3. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. +-lowering-+.f64 82.8%

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

   5. Simplified 82.8%

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

   if 9.0000000000000002e-97 < y < 1.75000000000000007e179

   1. Initial program 86.2%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 86.3%

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

   4. Applied egg-rr 86.3%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 88.2%

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

   6. Applied egg-rr 88.2%

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

   7. Taylor expanded in a around 0

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

   9. Simplified 71.6%

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

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

       3. clear-num N/A

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

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

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

       5. /-lowering-/.f64 71.7%

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

   11. Applied egg-rr 71.7%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-97}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+179}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + \frac{y}{\frac{t}{b}}}\\ \mathbf{if}\;a + 1 \leq -50:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a + 1 \leq 2:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ a (/ y (/ t b))))))
   (if (<= (+ a 1.0) -50.0)
     t_1
     (if (<= (+ a 1.0) 2.0)
       (/ (+ x (/ (* y z) t)) (+ 1.0 (/ (* y b) t)))
       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 + (y / (t / b)));
	double tmp;
	if ((a + 1.0) <= -50.0) {
		tmp = t_1;
	} else if ((a + 1.0) <= 2.0) {
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t));
	} 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 + (y / (t / b)))
    if ((a + 1.0d0) <= (-50.0d0)) then
        tmp = t_1
    else if ((a + 1.0d0) <= 2.0d0) then
        tmp = (x + ((y * z) / t)) / (1.0d0 + ((y * b) / t))
    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 + (y / (t / b)));
	double tmp;
	if ((a + 1.0) <= -50.0) {
		tmp = t_1;
	} else if ((a + 1.0) <= 2.0) {
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (y * (z / t))) / (a + (y / (t / b)))
	tmp = 0
	if (a + 1.0) <= -50.0:
		tmp = t_1
	elif (a + 1.0) <= 2.0:
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t))
	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(y / Float64(t / b))))
	tmp = 0.0
	if (Float64(a + 1.0) <= -50.0)
		tmp = t_1;
	elseif (Float64(a + 1.0) <= 2.0)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(1.0 + Float64(Float64(y * b) / t)));
	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 + (y / (t / b)));
	tmp = 0.0;
	if ((a + 1.0) <= -50.0)
		tmp = t_1;
	elseif ((a + 1.0) <= 2.0)
		tmp = (x + ((y * z) / t)) / (1.0 + ((y * b) / t));
	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[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(a + 1.0), $MachinePrecision], -50.0], t$95$1, If[LessEqual[N[(a + 1.0), $MachinePrecision], 2.0], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 a #s(literal 1 binary64)) < -50 or 2 < (+.f64 a #s(literal 1 binary64))

   1. Initial program 75.4%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 77.1%

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

   4. Applied egg-rr 77.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 78.8%

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

   6. Applied egg-rr 78.8%

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

   7. Taylor expanded in a around inf

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

   9. Simplified 77.4%

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

   if -50 < (+.f64 a #s(literal 1 binary64)) < 2

   1. Initial program 79.1%

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

   3. Taylor expanded in a around 0

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

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

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

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

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

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

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

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

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

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

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

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

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

      7. *-commutative N/A

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

      8. *-lowering-*.f64 78.6%

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

   5. Simplified 78.6%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a + 1 \leq -50:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;a + 1 \leq 2:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-173}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (* y (/ z t))) (+ (+ a 1.0) (/ y (/ t b))))))
   (if (<= t -8.5e-206) t_1 (if (<= t 5.8e-173) (/ z 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) + (y / (t / b)));
	double tmp;
	if (t <= -8.5e-206) {
		tmp = t_1;
	} else if (t <= 5.8e-173) {
		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 + (y * (z / t))) / ((a + 1.0d0) + (y / (t / b)))
    if (t <= (-8.5d-206)) then
        tmp = t_1
    else if (t <= 5.8d-173) 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 + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	double tmp;
	if (t <= -8.5e-206) {
		tmp = t_1;
	} else if (t <= 5.8e-173) {
		tmp = z / 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) + (y / (t / b)))
	tmp = 0
	if t <= -8.5e-206:
		tmp = t_1
	elif t <= 5.8e-173:
		tmp = z / 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(Float64(a + 1.0) + Float64(y / Float64(t / b))))
	tmp = 0.0
	if (t <= -8.5e-206)
		tmp = t_1;
	elseif (t <= 5.8e-173)
		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 + (y * (z / t))) / ((a + 1.0) + (y / (t / b)));
	tmp = 0.0;
	if (t <= -8.5e-206)
		tmp = t_1;
	elseif (t <= 5.8e-173)
		tmp = z / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.5e-206], t$95$1, If[LessEqual[t, 5.8e-173], N[(z / b), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.5000000000000005e-206 or 5.7999999999999997e-173 < t

   1. Initial program 85.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 84.6%

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

   4. Applied egg-rr 84.6%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 87.9%

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

   6. Applied egg-rr 87.9%

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

   if -8.5000000000000005e-206 < t < 5.7999999999999997e-173

   1. Initial program 34.3%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 70.2%

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

   5. Simplified 70.2%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-173}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+76}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y \cdot z}}}{a + 1}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.7e+86)
   (/ z b)
   (if (<= y 1.35e+76)
     (/ (+ x (/ 1.0 (/ t (* y z)))) (+ a 1.0))
     (if (<= y 1.25e+180) (/ x (+ (+ a 1.0) (* y (/ b t)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.7e+86) {
		tmp = z / b;
	} else if (y <= 1.35e+76) {
		tmp = (x + (1.0 / (t / (y * z)))) / (a + 1.0);
	} else if (y <= 1.25e+180) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} 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 (y <= (-4.7d+86)) then
        tmp = z / b
    else if (y <= 1.35d+76) then
        tmp = (x + (1.0d0 / (t / (y * z)))) / (a + 1.0d0)
    else if (y <= 1.25d+180) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    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 (y <= -4.7e+86) {
		tmp = z / b;
	} else if (y <= 1.35e+76) {
		tmp = (x + (1.0 / (t / (y * z)))) / (a + 1.0);
	} else if (y <= 1.25e+180) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.7e+86:
		tmp = z / b
	elif y <= 1.35e+76:
		tmp = (x + (1.0 / (t / (y * z)))) / (a + 1.0)
	elif y <= 1.25e+180:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.7e+86)
		tmp = Float64(z / b);
	elseif (y <= 1.35e+76)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(t / Float64(y * z)))) / Float64(a + 1.0));
	elseif (y <= 1.25e+180)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.7e+86)
		tmp = z / b;
	elseif (y <= 1.35e+76)
		tmp = (x + (1.0 / (t / (y * z)))) / (a + 1.0);
	elseif (y <= 1.25e+180)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.7e+86], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.35e+76], N[(N[(x + N[(1.0 / N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e+180], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7000000000000002e86 or 1.2499999999999999e180 < y

   1. Initial program 47.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 66.4%

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

   5. Simplified 66.4%

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

   if -4.7000000000000002e86 < y < 1.34999999999999995e76

   1. Initial program 91.2%

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

   3. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. +-lowering-+.f64 75.0%

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

   5. Simplified 75.0%

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

      1. clear-num N/A

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

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

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

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

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

      4. *-lowering-*.f64 75.0%

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

   7. Applied egg-rr 75.0%

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

   if 1.34999999999999995e76 < y < 1.2499999999999999e180

   1. Initial program 89.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 94.7%

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

   4. Applied egg-rr 94.7%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 69.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+76}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t}{y \cdot z}}}{a + 1}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.1e+85)
   (/ z b)
   (if (<= y 1.5e+74)
     (/ (+ x (/ (* y z) t)) (+ a 1.0))
     (if (<= y 8e+179) (/ x (+ (+ a 1.0) (* y (/ b t)))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.1e+85) {
		tmp = z / b;
	} else if (y <= 1.5e+74) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 8e+179) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} 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 (y <= (-5.1d+85)) then
        tmp = z / b
    else if (y <= 1.5d+74) then
        tmp = (x + ((y * z) / t)) / (a + 1.0d0)
    else if (y <= 8d+179) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    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 (y <= -5.1e+85) {
		tmp = z / b;
	} else if (y <= 1.5e+74) {
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	} else if (y <= 8e+179) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.1e+85:
		tmp = z / b
	elif y <= 1.5e+74:
		tmp = (x + ((y * z) / t)) / (a + 1.0)
	elif y <= 8e+179:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.1e+85)
		tmp = Float64(z / b);
	elseif (y <= 1.5e+74)
		tmp = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(a + 1.0));
	elseif (y <= 8e+179)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.1e+85)
		tmp = z / b;
	elseif (y <= 1.5e+74)
		tmp = (x + ((y * z) / t)) / (a + 1.0);
	elseif (y <= 8e+179)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.1e+85], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.5e+74], N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+179], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0999999999999998e85 or 7.99999999999999984e179 < y

   1. Initial program 47.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 66.4%

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

   5. Simplified 66.4%

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

   if -5.0999999999999998e85 < y < 1.5e74

   1. Initial program 91.2%

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

   3. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. +-lowering-+.f64 75.0%

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

   5. Simplified 75.0%

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

   if 1.5e74 < y < 7.99999999999999984e179

   1. Initial program 89.7%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 94.7%

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

   4. Applied egg-rr 94.7%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 69.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+74}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-262}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.1e+85)
   (/ z b)
   (if (<= y -1.22e-262)
     (/ (+ x (* y (/ z t))) (+ a 1.0))
     (if (<= y 8.5e+179) (/ x (+ (+ a 1.0) (/ (* y b) t))) (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.1e+85) {
		tmp = z / b;
	} else if (y <= -1.22e-262) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (y <= 8.5e+179) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} 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 (y <= (-4.1d+85)) then
        tmp = z / b
    else if (y <= (-1.22d-262)) then
        tmp = (x + (y * (z / t))) / (a + 1.0d0)
    else if (y <= 8.5d+179) then
        tmp = x / ((a + 1.0d0) + ((y * b) / t))
    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 (y <= -4.1e+85) {
		tmp = z / b;
	} else if (y <= -1.22e-262) {
		tmp = (x + (y * (z / t))) / (a + 1.0);
	} else if (y <= 8.5e+179) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.1e+85:
		tmp = z / b
	elif y <= -1.22e-262:
		tmp = (x + (y * (z / t))) / (a + 1.0)
	elif y <= 8.5e+179:
		tmp = x / ((a + 1.0) + ((y * b) / t))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.1e+85)
		tmp = Float64(z / b);
	elseif (y <= -1.22e-262)
		tmp = Float64(Float64(x + Float64(y * Float64(z / t))) / Float64(a + 1.0));
	elseif (y <= 8.5e+179)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.1e+85)
		tmp = z / b;
	elseif (y <= -1.22e-262)
		tmp = (x + (y * (z / t))) / (a + 1.0);
	elseif (y <= 8.5e+179)
		tmp = x / ((a + 1.0) + ((y * b) / t));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.1e+85], N[(z / b), $MachinePrecision], If[LessEqual[y, -1.22e-262], N[(N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+179], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999978e85 or 8.49999999999999962e179 < y

   1. Initial program 47.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 66.4%

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

   5. Simplified 66.4%

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

   if -4.09999999999999978e85 < y < -1.2199999999999999e-262

   1. Initial program 87.3%

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

   3. Taylor expanded in b around 0

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

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

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

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

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

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

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

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

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

      5. +-lowering-+.f64 80.9%

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

   5. Simplified 80.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 79.5%

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

   7. Applied egg-rr 79.5%

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

   if -1.2199999999999999e-262 < y < 8.49999999999999962e179

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

      5. /-lowering-/.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. +-lowering-+.f64 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.22 \cdot 10^{-262}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{z}{t}\\ t_2 := \frac{t\_1}{a + \frac{y}{\frac{t}{b}}}\\ \mathbf{if}\;a \leq -1:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 0.43:\\ \;\;\;\;\frac{t\_1}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ z t)))) (t_2 (/ t_1 (+ a (/ y (/ t b))))))
   (if (<= a -1.0) t_2 (if (<= a 0.43) (/ t_1 (+ 1.0 (* y (/ b t)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / (a + (y / (t / b)));
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= 0.43) {
		tmp = t_1 / (1.0 + (y * (b / t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (y * (z / t))
    t_2 = t_1 / (a + (y / (t / b)))
    if (a <= (-1.0d0)) then
        tmp = t_2
    else if (a <= 0.43d0) then
        tmp = t_1 / (1.0d0 + (y * (b / t)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y * (z / t));
	double t_2 = t_1 / (a + (y / (t / b)));
	double tmp;
	if (a <= -1.0) {
		tmp = t_2;
	} else if (a <= 0.43) {
		tmp = t_1 / (1.0 + (y * (b / t)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (y * (z / t))
	t_2 = t_1 / (a + (y / (t / b)))
	tmp = 0
	if a <= -1.0:
		tmp = t_2
	elif a <= 0.43:
		tmp = t_1 / (1.0 + (y * (b / t)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y * Float64(z / t)))
	t_2 = Float64(t_1 / Float64(a + Float64(y / Float64(t / b))))
	tmp = 0.0
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= 0.43)
		tmp = Float64(t_1 / Float64(1.0 + Float64(y * Float64(b / t))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (y * (z / t));
	t_2 = t_1 / (a + (y / (t / b)));
	tmp = 0.0;
	if (a <= -1.0)
		tmp = t_2;
	elseif (a <= 0.43)
		tmp = t_1 / (1.0 + (y * (b / t)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.0], t$95$2, If[LessEqual[a, 0.43], N[(t$95$1 / N[(1.0 + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 0.429999999999999993 < a

   1. Initial program 75.6%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 77.3%

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

   4. Applied egg-rr 77.3%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 79.0%

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

   6. Applied egg-rr 79.0%

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

   7. Taylor expanded in a around inf

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

   9. Simplified 77.6%

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

   if -1 < a < 0.429999999999999993

   1. Initial program 79.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 74.1%

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

   4. Applied egg-rr 74.1%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 77.0%

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

   6. Applied egg-rr 77.0%

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

   7. Taylor expanded in a around 0

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

   9. Simplified 76.5%

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

       1. clear-num N/A

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

       2. associate-/r/ N/A

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

       3. clear-num N/A

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

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

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

       5. /-lowering-/.f64 76.6%

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

   11. Applied egg-rr 76.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \frac{y}{\frac{t}{b}}}\\ \mathbf{elif}\;a \leq 0.43:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{1 + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + \frac{y}{\frac{t}{b}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 42.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+54}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-198}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 450000000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -4e+54)
   (/ x a)
   (if (<= a -4.4e-198)
     (/ z b)
     (if (<= a 2.85e-108) x (if (<= a 450000000000.0) (/ z b) (/ x a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -4e+54) {
		tmp = x / a;
	} else if (a <= -4.4e-198) {
		tmp = z / b;
	} else if (a <= 2.85e-108) {
		tmp = x;
	} else if (a <= 450000000000.0) {
		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 <= (-4d+54)) then
        tmp = x / a
    else if (a <= (-4.4d-198)) then
        tmp = z / b
    else if (a <= 2.85d-108) then
        tmp = x
    else if (a <= 450000000000.0d0) 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 <= -4e+54) {
		tmp = x / a;
	} else if (a <= -4.4e-198) {
		tmp = z / b;
	} else if (a <= 2.85e-108) {
		tmp = x;
	} else if (a <= 450000000000.0) {
		tmp = z / b;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -4e+54:
		tmp = x / a
	elif a <= -4.4e-198:
		tmp = z / b
	elif a <= 2.85e-108:
		tmp = x
	elif a <= 450000000000.0:
		tmp = z / b
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -4e+54)
		tmp = Float64(x / a);
	elseif (a <= -4.4e-198)
		tmp = Float64(z / b);
	elseif (a <= 2.85e-108)
		tmp = x;
	elseif (a <= 450000000000.0)
		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 <= -4e+54)
		tmp = x / a;
	elseif (a <= -4.4e-198)
		tmp = z / b;
	elseif (a <= 2.85e-108)
		tmp = x;
	elseif (a <= 450000000000.0)
		tmp = z / b;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -4e+54], N[(x / a), $MachinePrecision], If[LessEqual[a, -4.4e-198], N[(z / b), $MachinePrecision], If[LessEqual[a, 2.85e-108], x, If[LessEqual[a, 450000000000.0], N[(z / b), $MachinePrecision], N[(x / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.0000000000000003e54 or 4.5e11 < a

   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* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 77.6%

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

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 63.4%

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

   8. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 57.2%

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

   10. Simplified 57.2%

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

   if -4.0000000000000003e54 < a < -4.4000000000000001e-198 or 2.85e-108 < a < 4.5e11

   1. Initial program 74.0%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 49.8%

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

   5. Simplified 49.8%

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

   if -4.4000000000000001e-198 < a < 2.85e-108

   1. Initial program 83.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 77.5%

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

   4. Applied egg-rr 77.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 79.2%

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

   6. Applied egg-rr 79.2%

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

   7. Taylor expanded in a around 0

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

   9. Simplified 79.2%

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

   10. Taylor expanded in t around inf

       \[\leadsto \color{blue}{x} \]
   11. Step-by-step derivation

   12. Simplified 49.1%

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

Alternative 12: 60.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -5.7e+20)
   (/ z b)
   (if (<= y 8.2e+179) (/ x (+ (+ a 1.0) (/ (* y b) t))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -5.7e+20) {
		tmp = z / b;
	} else if (y <= 8.2e+179) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} 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 (y <= (-5.7d+20)) then
        tmp = z / b
    else if (y <= 8.2d+179) then
        tmp = x / ((a + 1.0d0) + ((y * b) / t))
    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 (y <= -5.7e+20) {
		tmp = z / b;
	} else if (y <= 8.2e+179) {
		tmp = x / ((a + 1.0) + ((y * b) / t));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -5.7e+20:
		tmp = z / b
	elif y <= 8.2e+179:
		tmp = x / ((a + 1.0) + ((y * b) / t))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -5.7e+20)
		tmp = Float64(z / b);
	elseif (y <= 8.2e+179)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -5.7e+20)
		tmp = z / b;
	elseif (y <= 8.2e+179)
		tmp = x / ((a + 1.0) + ((y * b) / t));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -5.7e+20], N[(z / b), $MachinePrecision], If[LessEqual[y, 8.2e+179], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.7e20 or 8.20000000000000021e179 < y

   1. Initial program 47.1%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 64.7%

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

   5. Simplified 64.7%

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

   if -5.7e20 < y < 8.20000000000000021e179

   1. Initial program 93.0%

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

   3. Taylor expanded in x around inf

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

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

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

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

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

      5. /-lowering-/.f64 N/A

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

      6. *-commutative N/A

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

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

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

      8. +-lowering-+.f64 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+20}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.5e+86)
   (/ z b)
   (if (<= y 8e+179) (/ x (+ (+ a 1.0) (/ y (/ t b)))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.5e+86) {
		tmp = z / b;
	} else if (y <= 8e+179) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} 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 (y <= (-6.5d+86)) then
        tmp = z / b
    else if (y <= 8d+179) then
        tmp = x / ((a + 1.0d0) + (y / (t / b)))
    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 (y <= -6.5e+86) {
		tmp = z / b;
	} else if (y <= 8e+179) {
		tmp = x / ((a + 1.0) + (y / (t / b)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.5e+86:
		tmp = z / b
	elif y <= 8e+179:
		tmp = x / ((a + 1.0) + (y / (t / b)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.5e+86)
		tmp = Float64(z / b);
	elseif (y <= 8e+179)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y / Float64(t / b))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.5e+86)
		tmp = z / b;
	elseif (y <= 8e+179)
		tmp = x / ((a + 1.0) + (y / (t / b)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.5e+86], N[(z / b), $MachinePrecision], If[LessEqual[y, 8e+179], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999996e86 or 7.99999999999999984e179 < y

   1. Initial program 47.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 66.4%

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

   5. Simplified 66.4%

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

   if -6.49999999999999996e86 < y < 7.99999999999999984e179

   1. Initial program 91.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 65.8%

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

      1. +-commutative N/A

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

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

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

      3. *-commutative N/A

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

      4. clear-num N/A

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

      5. div-inv N/A

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

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

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

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

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

      8. +-lowering-+.f64 65.8%

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

   9. Applied egg-rr 65.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+179}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + \frac{y}{\frac{t}{b}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.45e+86)
   (/ z b)
   (if (<= y 1.95e+180) (/ x (+ (+ a 1.0) (* y (/ b t)))) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.45e+86) {
		tmp = z / b;
	} else if (y <= 1.95e+180) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} 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 (y <= (-2.45d+86)) then
        tmp = z / b
    else if (y <= 1.95d+180) then
        tmp = x / ((a + 1.0d0) + (y * (b / t)))
    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 (y <= -2.45e+86) {
		tmp = z / b;
	} else if (y <= 1.95e+180) {
		tmp = x / ((a + 1.0) + (y * (b / t)));
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.45e+86:
		tmp = z / b
	elif y <= 1.95e+180:
		tmp = x / ((a + 1.0) + (y * (b / t)))
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.45e+86)
		tmp = Float64(z / b);
	elseif (y <= 1.95e+180)
		tmp = Float64(x / Float64(Float64(a + 1.0) + Float64(y * Float64(b / t))));
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.45e+86)
		tmp = z / b;
	elseif (y <= 1.95e+180)
		tmp = x / ((a + 1.0) + (y * (b / t)));
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.45e+86], N[(z / b), $MachinePrecision], If[LessEqual[y, 1.95e+180], N[(x / N[(N[(a + 1.0), $MachinePrecision] + N[(y * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.45e86 or 1.95e180 < y

   1. Initial program 47.4%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 66.4%

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

   5. Simplified 66.4%

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

   if -2.45e86 < y < 1.95e180

   1. Initial program 91.0%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 89.4%

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

   4. Applied egg-rr 89.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 65.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+180}:\\ \;\;\;\;\frac{x}{\left(a + 1\right) + y \cdot \frac{b}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 54.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 47:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.25e+86) (/ z b) (if (<= y 47.0) (/ x (+ a 1.0)) (/ z b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.25e+86) {
		tmp = z / b;
	} else if (y <= 47.0) {
		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 (y <= (-1.25d+86)) then
        tmp = z / b
    else if (y <= 47.0d0) 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 (y <= -1.25e+86) {
		tmp = z / b;
	} else if (y <= 47.0) {
		tmp = x / (a + 1.0);
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.25e+86:
		tmp = z / b
	elif y <= 47.0:
		tmp = x / (a + 1.0)
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.25e+86)
		tmp = Float64(z / b);
	elseif (y <= 47.0)
		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 (y <= -1.25e+86)
		tmp = z / b;
	elseif (y <= 47.0)
		tmp = x / (a + 1.0);
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.25e+86], N[(z / b), $MachinePrecision], If[LessEqual[y, 47.0], N[(x / N[(a + 1.0), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2499999999999999e86 or 47 < y

   1. Initial program 60.1%

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

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 56.9%

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

   5. Simplified 56.9%

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

   if -1.2499999999999999e86 < y < 47

   1. Initial program 92.1%

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

   3. Taylor expanded in y around 0

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

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

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

      2. +-lowering-+.f64 64.7%

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

   5. Simplified 64.7%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+86}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 47:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 40.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -1.0) (/ x a) (if (<= a 4.8e-15) x (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -1.0) {
		tmp = x / a;
	} else if (a <= 4.8e-15) {
		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 <= (-1.0d0)) then
        tmp = x / a
    else if (a <= 4.8d-15) 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 <= -1.0) {
		tmp = x / a;
	} else if (a <= 4.8e-15) {
		tmp = x;
	} else {
		tmp = x / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -1.0:
		tmp = x / a
	elif a <= 4.8e-15:
		tmp = x
	else:
		tmp = x / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -1.0)
		tmp = Float64(x / a);
	elseif (a <= 4.8e-15)
		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 <= -1.0)
		tmp = x / a;
	elseif (a <= 4.8e-15)
		tmp = x;
	else
		tmp = x / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -1.0], N[(x / a), $MachinePrecision], If[LessEqual[a, 4.8e-15], x, N[(x / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1 or 4.7999999999999999e-15 < a

   1. Initial program 75.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 77.4%

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

   4. Applied egg-rr 77.4%

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

   5. Taylor expanded in x around inf

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

   7. Simplified 58.7%

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

   8. Taylor expanded in a around inf

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

      1. /-lowering-/.f64 51.2%

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

   10. Simplified 51.2%

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

   if -1 < a < 4.7999999999999999e-15

   1. Initial program 78.8%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

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

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

      4. /-lowering-/.f64 73.9%

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

   4. Applied egg-rr 73.9%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

      5. /-lowering-/.f64 76.8%

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

   6. Applied egg-rr 76.8%

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

   7. Taylor expanded in a around 0

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

   9. Simplified 76.3%

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

   10. Taylor expanded in t around inf

       \[\leadsto \color{blue}{x} \]
   11. Step-by-step derivation

   12. Simplified 35.4%

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

Alternative 17: 19.3% 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 77.4%

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

   1. associate-/l* N/A

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

   2. *-commutative N/A

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

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

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

   4. /-lowering-/.f64 75.6%

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

4. Applied egg-rr 75.6%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

   5. /-lowering-/.f64 77.9%

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

6. Applied egg-rr 77.9%

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

7. Taylor expanded in a around 0

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

9. Simplified 49.5%

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

10. Taylor expanded in t around inf

    \[\leadsto \color{blue}{x} \]
11. Step-by-step derivation

12. Simplified 20.3%

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

Developer Target 1: 79.2% 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 2024161 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

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

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