Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I

Percentage Accurate: 93.8% → 96.8%

Time: 25.1s

Alternatives: 20

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 93.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (exp
     (*
      2.0
      (-
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    code = x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\sqrt{a + t} \cdot z}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(0.8333333333333334 + a\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* (sqrt (+ a t)) z) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ 0.8333333333333334 a))))))
   (if (<= t_1 INFINITY)
     (/ x (+ x (* y (exp (* 2.0 t_1)))))
     (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((sqrt((a + t)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (0.8333333333333334 + a)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((Math.sqrt((a + t)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (0.8333333333333334 + a)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((math.sqrt((a + t)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (0.8333333333333334 + a)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * t_1))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(sqrt(Float64(a + t)) * z) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(0.8333333333333334 + a))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * t_1)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((sqrt((a + t)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (0.8333333333333334 + a)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3))))) < +inf.0

   1. Initial program 98.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   if +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 5 6)) (/.f64 2 (*.f64 t 3)))))

   1. Initial program 0.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 82.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 82.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 82.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sqrt{a + t} \cdot z}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(0.8333333333333334 + a\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\sqrt{a + t} \cdot z}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(0.8333333333333334 + a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(0.8333333333333334 - \left(\frac{0.6666666666666666}{t} - a\right), c - b, \sqrt{a + t} \cdot \frac{z}{t}\right)\right)}, x\right)} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (fma
   y
   (pow
    (exp 2.0)
    (fma
     (- 0.8333333333333334 (- (/ 0.6666666666666666 t) a))
     (- c b)
     (* (sqrt (+ a t)) (/ z t))))
   x)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / fma(y, pow(exp(2.0), fma((0.8333333333333334 - ((0.6666666666666666 / t) - a)), (c - b), (sqrt((a + t)) * (z / t)))), x);
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / fma(y, (exp(2.0) ^ fma(Float64(0.8333333333333334 - Float64(Float64(0.6666666666666666 / t) - a)), Float64(c - b), Float64(sqrt(Float64(a + t)) * Float64(z / t)))), x))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(0.8333333333333334 - N[(N[(0.6666666666666666 / t), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision] + N[(N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.2%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
2. Step-by-step derivation

   1. +-commutative 92.2%

      \[\leadsto \frac{x}{\color{blue}{y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)} + x}} \]

   2. fma-def 92.2%

      \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}, x\right)}} \]

3. Simplified 97.0%

   \[\leadsto \color{blue}{\frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right), c - b, \sqrt{t + a} \cdot \frac{z}{t}\right)\right)}, x\right)}} \]

4. Final simplification 97.0%

   \[\leadsto \frac{x}{\mathsf{fma}\left(y, {\left(e^{2}\right)}^{\left(\mathsf{fma}\left(0.8333333333333334 - \left(\frac{0.6666666666666666}{t} - a\right), c - b, \sqrt{a + t} \cdot \frac{z}{t}\right)\right)}, x\right)} \]

Alternative 3: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 10^{+76}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -8.2e-22)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 1.1e-186)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* (- c b) -0.6666666666666666)) t))))))
     (if (<= t 1e+76)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (+
             (* z (sqrt (/ 1.0 t)))
             (*
              (- c b)
              (+ 0.8333333333333334 (* 0.6666666666666666 (/ -1.0 t))))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -8.2e-22) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.1e-186) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 1e+76) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= (-8.2d-22)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1.1d-186) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((c - b) * (-0.6666666666666666d0))) / t)))))
    else if (t <= 1d+76) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) + ((c - b) * (0.8333333333333334d0 + (0.6666666666666666d0 * ((-1.0d0) / t)))))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + 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 c) {
	double tmp;
	if (t <= -8.2e-22) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.1e-186) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 1e+76) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -8.2e-22:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1.1e-186:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))))
	elif t <= 1e+76:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -8.2e-22)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1.1e-186)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(Float64(c - b) * -0.6666666666666666)) / t))))));
	elseif (t <= 1e+76)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) + Float64(Float64(c - b) * Float64(0.8333333333333334 + Float64(0.6666666666666666 * Float64(-1.0 / t))))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -8.2e-22)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1.1e-186)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	elseif (t <= 1e+76)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((c - b) * (0.8333333333333334 + (0.6666666666666666 * (-1.0 / t)))))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -8.2e-22], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-186], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e+76], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + N[(0.6666666666666666 * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -8.1999999999999999e-22

   1. Initial program 83.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 100.0%

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

   if -8.1999999999999999e-22 < t < 1.10000000000000007e-186

   1. Initial program 87.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 94.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   if 1.10000000000000007e-186 < t < 1e76

   1. Initial program 97.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around 0 90.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\sqrt{\frac{1}{t}} \cdot z - \left(0.8333333333333334 - 0.6666666666666666 \cdot \frac{1}{t}\right) \cdot \left(b - c\right)\right)}}} \]

   if 1e76 < t

   1. Initial program 93.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 96.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 96.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 96.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 10^{+76}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(c - b\right) \cdot \left(0.8333333333333334 + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 4: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 1950000000000:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{0.8333333333333334 + a}\right)}^{\left(b \cdot -2\right)}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.5e-16)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 1.52e-117)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* (- c b) -0.6666666666666666)) t))))))
     (if (<= t 2.4e-43)
       (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
       (if (<= t 1950000000000.0)
         (/ x (+ x (* y (pow (exp (+ 0.8333333333333334 a)) (* b -2.0)))))
         (if (<= t 1.7e+29)
           (/ x (+ x (* y (exp (* 2.0 (* z (sqrt (/ 1.0 t))))))))
           (/
            x
            (+
             x
             (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.5e-16) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.52e-117) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 2.4e-43) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 1950000000000.0) {
		tmp = x / (x + (y * pow(exp((0.8333333333333334 + a)), (b * -2.0))));
	} else if (t <= 1.7e+29) {
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.5d-16)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1.52d-117) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((c - b) * (-0.6666666666666666d0))) / t)))))
    else if (t <= 2.4d-43) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else if (t <= 1950000000000.0d0) then
        tmp = x / (x + (y * (exp((0.8333333333333334d0 + a)) ** (b * (-2.0d0)))))
    else if (t <= 1.7d+29) then
        tmp = x / (x + (y * exp((2.0d0 * (z * sqrt((1.0d0 / t)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + 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 c) {
	double tmp;
	if (t <= -1.5e-16) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.52e-117) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	} else if (t <= 2.4e-43) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 1950000000000.0) {
		tmp = x / (x + (y * Math.pow(Math.exp((0.8333333333333334 + a)), (b * -2.0))));
	} else if (t <= 1.7e+29) {
		tmp = x / (x + (y * Math.exp((2.0 * (z * Math.sqrt((1.0 / t)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.5e-16:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1.52e-117:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))))
	elif t <= 2.4e-43:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	elif t <= 1950000000000.0:
		tmp = x / (x + (y * math.pow(math.exp((0.8333333333333334 + a)), (b * -2.0))))
	elif t <= 1.7e+29:
		tmp = x / (x + (y * math.exp((2.0 * (z * math.sqrt((1.0 / t)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.5e-16)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1.52e-117)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(Float64(c - b) * -0.6666666666666666)) / t))))));
	elseif (t <= 2.4e-43)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	elseif (t <= 1950000000000.0)
		tmp = Float64(x / Float64(x + Float64(y * (exp(Float64(0.8333333333333334 + a)) ^ Float64(b * -2.0)))));
	elseif (t <= 1.7e+29)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(z * sqrt(Float64(1.0 / t))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.5e-16)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1.52e-117)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + ((c - b) * -0.6666666666666666)) / t)))));
	elseif (t <= 2.4e-43)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	elseif (t <= 1950000000000.0)
		tmp = x / (x + (y * (exp((0.8333333333333334 + a)) ^ (b * -2.0))));
	elseif (t <= 1.7e+29)
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.5e-16], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.52e-117], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(N[(c - b), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e-43], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1950000000000.0], N[(x / N[(x + N[(y * N[Power[N[Exp[N[(0.8333333333333334 + a), $MachinePrecision]], $MachinePrecision], N[(b * -2.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+29], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.49999999999999997e-16

   1. Initial program 83.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 100.0%

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

   if -1.49999999999999997e-16 < t < 1.52e-117

   1. Initial program 89.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 89.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   if 1.52e-117 < t < 2.4000000000000002e-43

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 42.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 89.9%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 2.4000000000000002e-43 < t < 1.95e12

   1. Initial program 86.7%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 67.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 67.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      2. metadata-eval 67.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      3. +-commutative 67.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   4. Simplified 67.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   5. Taylor expanded in t around inf 61.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{-2 \cdot \left(b \cdot \left(0.8333333333333334 + a\right)\right)}}} \]
   6. Step-by-step derivation

      1. associate-*r* 61.2%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(-2 \cdot b\right) \cdot \left(0.8333333333333334 + a\right)}}} \]

      2. +-commutative 61.2%

         \[\leadsto \frac{x}{x + y \cdot e^{\left(-2 \cdot b\right) \cdot \color{blue}{\left(a + 0.8333333333333334\right)}}} \]

      3. *-commutative 61.2%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(a + 0.8333333333333334\right) \cdot \left(-2 \cdot b\right)}}} \]

      4. exp-prod 80.6%

         \[\leadsto \frac{x}{x + y \cdot \color{blue}{{\left(e^{a + 0.8333333333333334}\right)}^{\left(-2 \cdot b\right)}}} \]

      5. +-commutative 80.6%

         \[\leadsto \frac{x}{x + y \cdot {\left(e^{\color{blue}{0.8333333333333334 + a}}\right)}^{\left(-2 \cdot b\right)}} \]

      6. *-commutative 80.6%

         \[\leadsto \frac{x}{x + y \cdot {\left(e^{0.8333333333333334 + a}\right)}^{\color{blue}{\left(b \cdot -2\right)}}} \]

   7. Simplified 80.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{{\left(e^{0.8333333333333334 + a}\right)}^{\left(b \cdot -2\right)}}} \]

   if 1.95e12 < t < 1.69999999999999991e29

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around 0 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\sqrt{\frac{1}{t}} \cdot z - \left(0.8333333333333334 - 0.6666666666666666 \cdot \frac{1}{t}\right) \cdot \left(b - c\right)\right)}}} \]

   3. Taylor expanded in z around inf 100.0%

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

   if 1.69999999999999991e29 < t

   1. Initial program 94.7%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 95.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 95.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 95.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + \left(c - b\right) \cdot -0.6666666666666666}{t}}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-43}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 1950000000000:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{0.8333333333333334 + a}\right)}^{\left(b \cdot -2\right)}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 5: 81.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a}\right)}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -2.95e-64)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t -3.8e-127)
     (/ x (+ x (* y (exp (* 2.0 (* (/ z t) (sqrt a)))))))
     (if (<= t 8.5e-242)
       (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
       (if (<= t 2e-192)
         (/ x (+ x (* y (exp (* 2.0 (* z (sqrt (/ 1.0 t))))))))
         (if (<= t 5.4e-10)
           (/
            x
            (+
             x
             (*
              y
              (exp
               (*
                2.0
                (*
                 b
                 (- (/ 0.6666666666666666 t) (+ 0.8333333333333334 a))))))))
           (/
            x
            (+
             x
             (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2.95e-64) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= -3.8e-127) {
		tmp = x / (x + (y * exp((2.0 * ((z / t) * sqrt(a))))));
	} else if (t <= 8.5e-242) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 2e-192) {
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	} else if (t <= 5.4e-10) {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (0.8333333333333334 + a)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= (-2.95d-64)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= (-3.8d-127)) then
        tmp = x / (x + (y * exp((2.0d0 * ((z / t) * sqrt(a))))))
    else if (t <= 8.5d-242) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else if (t <= 2d-192) then
        tmp = x / (x + (y * exp((2.0d0 * (z * sqrt((1.0d0 / t)))))))
    else if (t <= 5.4d-10) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (0.8333333333333334d0 + a)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + 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 c) {
	double tmp;
	if (t <= -2.95e-64) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= -3.8e-127) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z / t) * Math.sqrt(a))))));
	} else if (t <= 8.5e-242) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else if (t <= 2e-192) {
		tmp = x / (x + (y * Math.exp((2.0 * (z * Math.sqrt((1.0 / t)))))));
	} else if (t <= 5.4e-10) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (0.8333333333333334 + a)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -2.95e-64:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= -3.8e-127:
		tmp = x / (x + (y * math.exp((2.0 * ((z / t) * math.sqrt(a))))))
	elif t <= 8.5e-242:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	elif t <= 2e-192:
		tmp = x / (x + (y * math.exp((2.0 * (z * math.sqrt((1.0 / t)))))))
	elif t <= 5.4e-10:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (0.8333333333333334 + a)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -2.95e-64)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= -3.8e-127)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z / t) * sqrt(a)))))));
	elseif (t <= 8.5e-242)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	elseif (t <= 2e-192)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(z * sqrt(Float64(1.0 / t))))))));
	elseif (t <= 5.4e-10)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(0.8333333333333334 + a))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -2.95e-64)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= -3.8e-127)
		tmp = x / (x + (y * exp((2.0 * ((z / t) * sqrt(a))))));
	elseif (t <= 8.5e-242)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	elseif (t <= 2e-192)
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	elseif (t <= 5.4e-10)
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (0.8333333333333334 + a)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -2.95e-64], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.8e-127], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z / t), $MachinePrecision] * N[Sqrt[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.5e-242], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2e-192], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-10], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.94999999999999997e-64

   1. Initial program 86.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 95.6%

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

   if -2.94999999999999997e-64 < t < -3.80000000000000003e-127

   1. Initial program 83.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in z around inf 100.0%

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

   if -3.80000000000000003e-127 < t < 8.4999999999999997e-242

   1. Initial program 94.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 97.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 86.9%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 8.4999999999999997e-242 < t < 2.0000000000000002e-192

   1. Initial program 69.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around 0 62.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\sqrt{\frac{1}{t}} \cdot z - \left(0.8333333333333334 - 0.6666666666666666 \cdot \frac{1}{t}\right) \cdot \left(b - c\right)\right)}}} \]

   3. Taylor expanded in z around inf 92.5%

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

   if 2.0000000000000002e-192 < t < 5.4e-10

   1. Initial program 96.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in b around inf 72.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 72.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\color{blue}{\frac{0.6666666666666666 \cdot 1}{t}} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      2. metadata-eval 72.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{\color{blue}{0.6666666666666666}}{t} - \left(0.8333333333333334 + a\right)\right)\right)}} \]

      3. +-commutative 72.9%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \color{blue}{\left(a + 0.8333333333333334\right)}\right)\right)}} \]

   4. Simplified 72.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}} \]

   if 5.4e-10 < t

   1. Initial program 94.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 93.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 93.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 93.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.95 \cdot 10^{-64}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-127}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a}\right)}}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(0.8333333333333334 + a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 6: 81.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a}\right)}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -2e-63)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t -7e-129)
     (/ x (+ x (* y (exp (* 2.0 (* (/ z t) (sqrt a)))))))
     (if (<= t 1.1e-45)
       (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
       (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2e-63) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= -7e-129) {
		tmp = x / (x + (y * exp((2.0 * ((z / t) * sqrt(a))))));
	} else if (t <= 1.1e-45) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= (-2d-63)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= (-7d-129)) then
        tmp = x / (x + (y * exp((2.0d0 * ((z / t) * sqrt(a))))))
    else if (t <= 1.1d-45) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + 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 c) {
	double tmp;
	if (t <= -2e-63) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= -7e-129) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z / t) * Math.sqrt(a))))));
	} else if (t <= 1.1e-45) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -2e-63:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= -7e-129:
		tmp = x / (x + (y * math.exp((2.0 * ((z / t) * math.sqrt(a))))))
	elif t <= 1.1e-45:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -2e-63)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= -7e-129)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z / t) * sqrt(a)))))));
	elseif (t <= 1.1e-45)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -2e-63)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= -7e-129)
		tmp = x / (x + (y * exp((2.0 * ((z / t) * sqrt(a))))));
	elseif (t <= 1.1e-45)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -2e-63], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7e-129], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z / t), $MachinePrecision] * N[Sqrt[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-45], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.00000000000000013e-63

   1. Initial program 86.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 95.6%

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

   if -2.00000000000000013e-63 < t < -6.9999999999999995e-129

   1. Initial program 83.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in z around inf 100.0%

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

   if -6.9999999999999995e-129 < t < 1.09999999999999997e-45

   1. Initial program 92.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 77.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 76.9%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 1.09999999999999997e-45 < t

   1. Initial program 94.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 89.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 89.6%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 89.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-63}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-129}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{t} \cdot \sqrt{a}\right)}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 7: 74.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+207} \lor \neg \left(t \leq 1.2 \cdot 10^{+275}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.8333333333333334 \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 5.6e-40)
   (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
   (if (or (<= t 1.2e+207) (not (<= t 1.2e+275)))
     (/ x (+ x (* y (exp (* 2.0 (* 0.8333333333333334 (- c b)))))))
     (/ x (+ x (* y (exp (* 2.0 (* a (- c b))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 5.6e-40) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else if ((t <= 1.2e+207) || !(t <= 1.2e+275)) {
		tmp = x / (x + (y * exp((2.0 * (0.8333333333333334 * (c - b))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= 5.6d-40) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else if ((t <= 1.2d+207) .or. (.not. (t <= 1.2d+275))) then
        tmp = x / (x + (y * exp((2.0d0 * (0.8333333333333334d0 * (c - b))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - 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 c) {
	double tmp;
	if (t <= 5.6e-40) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else if ((t <= 1.2e+207) || !(t <= 1.2e+275)) {
		tmp = x / (x + (y * Math.exp((2.0 * (0.8333333333333334 * (c - b))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 5.6e-40:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	elif (t <= 1.2e+207) or not (t <= 1.2e+275):
		tmp = x / (x + (y * math.exp((2.0 * (0.8333333333333334 * (c - b))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 5.6e-40)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	elseif ((t <= 1.2e+207) || !(t <= 1.2e+275))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(0.8333333333333334 * Float64(c - b)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 5.6e-40)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	elseif ((t <= 1.2e+207) || ~((t <= 1.2e+275)))
		tmp = x / (x + (y * exp((2.0 * (0.8333333333333334 * (c - b))))));
	else
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 5.6e-40], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.2e+207], N[Not[LessEqual[t, 1.2e+275]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(0.8333333333333334 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 5.5999999999999999e-40

   1. Initial program 90.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 79.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 73.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 5.5999999999999999e-40 < t < 1.2e207 or 1.19999999999999998e275 < t

   1. Initial program 95.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 87.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 87.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 87.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 78.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   if 1.2e207 < t < 1.19999999999999998e275

   1. Initial program 90.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 96.0%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 5.6 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+207} \lor \neg \left(t \leq 1.2 \cdot 10^{+275}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.8333333333333334 \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 8: 67.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+244} \lor \neg \left(t \leq 1.25 \cdot 10^{+276}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(2 \cdot c\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 6.5e-45)
   (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
   (if (or (<= t 3.6e+244) (not (<= t 1.25e+276)))
     (/ x (+ x (* y (exp (* c 1.6666666666666667)))))
     (/ x (+ x (* y (exp (* a (* 2.0 c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 6.5e-45) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else if ((t <= 3.6e+244) || !(t <= 1.25e+276)) {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * exp((a * (2.0 * c)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= 6.5d-45) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else if ((t <= 3.6d+244) .or. (.not. (t <= 1.25d+276))) then
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    else
        tmp = x / (x + (y * exp((a * (2.0d0 * c)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 6.5e-45) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else if ((t <= 3.6e+244) || !(t <= 1.25e+276)) {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * Math.exp((a * (2.0 * c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 6.5e-45:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	elif (t <= 3.6e+244) or not (t <= 1.25e+276):
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	else:
		tmp = x / (x + (y * math.exp((a * (2.0 * c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 6.5e-45)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	elseif ((t <= 3.6e+244) || !(t <= 1.25e+276))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(a * Float64(2.0 * c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 6.5e-45)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	elseif ((t <= 3.6e+244) || ~((t <= 1.25e+276)))
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	else
		tmp = x / (x + (y * exp((a * (2.0 * c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 6.5e-45], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 3.6e+244], N[Not[LessEqual[t, 1.25e+276]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(a * N[(2.0 * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < 6.4999999999999995e-45

   1. Initial program 90.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 79.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 73.8%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 6.4999999999999995e-45 < t < 3.6e244 or 1.25e276 < t

   1. Initial program 94.9%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 88.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 88.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 88.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 78.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in b around 0 67.0%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot c}}} \]

   if 3.6e244 < t < 1.25e276

   1. Initial program 89.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 98.2%

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

   3. Taylor expanded in c around inf 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{2 \cdot \left(a \cdot c\right)}}} \]
   4. Step-by-step derivation

      1. *-commutative 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\left(a \cdot c\right) \cdot 2}}} \]

      2. associate-*l* 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{a \cdot \left(c \cdot 2\right)}}} \]

   5. Simplified 82.0%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+244} \lor \neg \left(t \leq 1.25 \cdot 10^{+276}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{a \cdot \left(2 \cdot c\right)}}\\ \end{array} \]

Alternative 9: 81.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-39}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 1e-39)
   (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
   (/ x (+ x (* y (exp (* 2.0 (* (- c b) (+ 0.8333333333333334 a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 1e-39) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= 1d-39) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (0.8333333333333334d0 + 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 c) {
	double tmp;
	if (t <= 1e-39) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 1e-39:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (0.8333333333333334 + a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 1e-39)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(0.8333333333333334 + a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 1e-39)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (0.8333333333333334 + a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 1e-39], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.99999999999999929e-40

   1. Initial program 90.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 79.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 73.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 9.99999999999999929e-40 < t

   1. Initial program 94.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 90.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 90.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 90.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-39}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(0.8333333333333334 + a\right)\right)}}\\ \end{array} \]

Alternative 10: 58.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot \left(a \cdot -2\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5e+83)
   (/ x (* y (exp (* (- c b) 1.6666666666666667))))
   (if (<= b 9e-149)
     (/ x (+ x (* y (exp (* c 1.6666666666666667)))))
     (/ x (+ x (* y (exp (* b (* a -2.0)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5e+83) {
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	} else if (b <= 9e-149) {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * exp((b * (a * -2.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5d+83)) then
        tmp = x / (y * exp(((c - b) * 1.6666666666666667d0)))
    else if (b <= 9d-149) then
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    else
        tmp = x / (x + (y * exp((b * (a * (-2.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5e+83) {
		tmp = x / (y * Math.exp(((c - b) * 1.6666666666666667)));
	} else if (b <= 9e-149) {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	} else {
		tmp = x / (x + (y * Math.exp((b * (a * -2.0)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5e+83:
		tmp = x / (y * math.exp(((c - b) * 1.6666666666666667)))
	elif b <= 9e-149:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	else:
		tmp = x / (x + (y * math.exp((b * (a * -2.0)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5e+83)
		tmp = Float64(x / Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667))));
	elseif (b <= 9e-149)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(b * Float64(a * -2.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -5e+83)
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	elseif (b <= 9e-149)
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	else
		tmp = x / (x + (y * exp((b * (a * -2.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5e+83], N[(x / N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-149], N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(b * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.00000000000000029e83

   1. Initial program 87.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 72.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 72.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 70.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around 0 65.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -5.00000000000000029e83 < b < 8.9999999999999996e-149

   1. Initial program 93.5%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 72.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 72.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 72.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 66.6%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in b around 0 65.2%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot c}}} \]

   if 8.9999999999999996e-149 < b

   1. Initial program 92.6%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 72.0%

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

   3. Taylor expanded in c around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. *-commutative 68.9%

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

      3. associate-*l* 68.9%

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

   5. Simplified 68.9%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-149}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot \left(a \cdot -2\right)}}\\ \end{array} \]

Alternative 11: 71.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 6.8e-40)
   (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 6.8e-40) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (t <= 6.8d-40) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - 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 c) {
	double tmp;
	if (t <= 6.8e-40) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 6.8e-40:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 6.8e-40)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 6.8e-40)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 6.8e-40], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.79999999999999968e-40

   1. Initial program 90.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around 0 79.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\sqrt{a} \cdot z - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}} \]

   3. Taylor expanded in a around 0 73.2%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{e^{1.3333333333333333 \cdot \frac{b - c}{t}}}} \]

   if 6.79999999999999968e-40 < t

   1. Initial program 94.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 71.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.8 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 12: 59.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.75e+84)
   (/ x (* y (exp (* (- c b) 1.6666666666666667))))
   (if (<= b 4.5e+88) (/ x (+ x (* y (exp (* c 1.6666666666666667))))) 1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.75e+84) {
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	} else if (b <= 4.5e+88) {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (b <= (-1.75d+84)) then
        tmp = x / (y * exp(((c - b) * 1.6666666666666667d0)))
    else if (b <= 4.5d+88) then
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.75e+84) {
		tmp = x / (y * Math.exp(((c - b) * 1.6666666666666667)));
	} else if (b <= 4.5e+88) {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.75e+84:
		tmp = x / (y * math.exp(((c - b) * 1.6666666666666667)))
	elif b <= 4.5e+88:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.75e+84)
		tmp = Float64(x / Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667))));
	elseif (b <= 4.5e+88)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -1.75e+84)
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	elseif (b <= 4.5e+88)
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.75e+84], N[(x / N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+88], N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if b < -1.7499999999999999e84

   1. Initial program 87.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 72.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 72.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 70.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around 0 65.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -1.7499999999999999e84 < b < 4.5e88

   1. Initial program 95.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 70.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 70.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 70.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 64.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in b around 0 63.6%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{1.6666666666666667 \cdot c}}} \]

   if 4.5e88 < b

   1. Initial program 86.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 79.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 79.1%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 79.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 69.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.75 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 56.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.6666666666666666}{t} - 0.8333333333333334\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-209}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(y \cdot c\right) \cdot \frac{t_1 \cdot t_1 - a \cdot a}{a + t_1}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (/ 0.6666666666666666 t) 0.8333333333333334)))
   (if (<= b -4.5e+83)
     (/ x (* y (exp (* (- c b) 1.6666666666666667))))
     (if (<= b -2.8e-209)
       1.0
       (if (<= b -5.8e-290)
         (/
          x
          (+
           x
           (- y (* 2.0 (* (* y c) (/ (- (* t_1 t_1) (* a a)) (+ a t_1)))))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.6666666666666666 / t) - 0.8333333333333334;
	double tmp;
	if (b <= -4.5e+83) {
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	} else if (b <= -2.8e-209) {
		tmp = 1.0;
	} else if (b <= -5.8e-290) {
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (0.6666666666666666d0 / t) - 0.8333333333333334d0
    if (b <= (-4.5d+83)) then
        tmp = x / (y * exp(((c - b) * 1.6666666666666667d0)))
    else if (b <= (-2.8d-209)) then
        tmp = 1.0d0
    else if (b <= (-5.8d-290)) then
        tmp = x / (x + (y - (2.0d0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.6666666666666666 / t) - 0.8333333333333334;
	double tmp;
	if (b <= -4.5e+83) {
		tmp = x / (y * Math.exp(((c - b) * 1.6666666666666667)));
	} else if (b <= -2.8e-209) {
		tmp = 1.0;
	} else if (b <= -5.8e-290) {
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (0.6666666666666666 / t) - 0.8333333333333334
	tmp = 0
	if b <= -4.5e+83:
		tmp = x / (y * math.exp(((c - b) * 1.6666666666666667)))
	elif b <= -2.8e-209:
		tmp = 1.0
	elif b <= -5.8e-290:
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(0.6666666666666666 / t) - 0.8333333333333334)
	tmp = 0.0
	if (b <= -4.5e+83)
		tmp = Float64(x / Float64(y * exp(Float64(Float64(c - b) * 1.6666666666666667))));
	elseif (b <= -2.8e-209)
		tmp = 1.0;
	elseif (b <= -5.8e-290)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(Float64(y * c) * Float64(Float64(Float64(t_1 * t_1) - Float64(a * a)) / Float64(a + t_1)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (0.6666666666666666 / t) - 0.8333333333333334;
	tmp = 0.0;
	if (b <= -4.5e+83)
		tmp = x / (y * exp(((c - b) * 1.6666666666666667)));
	elseif (b <= -2.8e-209)
		tmp = 1.0;
	elseif (b <= -5.8e-290)
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(0.6666666666666666 / t), $MachinePrecision] - 0.8333333333333334), $MachinePrecision]}, If[LessEqual[b, -4.5e+83], N[(x / N[(y * N[Exp[N[(N[(c - b), $MachinePrecision] * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.8e-209], 1.0, If[LessEqual[b, -5.8e-290], N[(x / N[(x + N[(y - N[(2.0 * N[(N[(y * c), $MachinePrecision] * N[(N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.4999999999999999e83

   1. Initial program 87.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 72.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 72.7%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 72.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 70.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around 0 65.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}} \]

   if -4.4999999999999999e83 < b < -2.80000000000000012e-209 or -5.79999999999999989e-290 < b

   1. Initial program 92.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 74.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 74.3%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 74.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 67.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 60.0%

      \[\leadsto \color{blue}{1} \]

   if -2.80000000000000012e-209 < b < -5.79999999999999989e-290

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in c around inf 74.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 74.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)}} \]

      2. metadata-eval 74.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)}} \]

      3. +-commutative 74.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - \frac{0.6666666666666666}{t}\right)\right)}} \]

   4. Simplified 74.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}} \]

   5. Taylor expanded in c around 0 41.6%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \color{blue}{\left(\left(c \cdot y\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}\right)} \]

      2. +-commutative 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)} \]

      3. associate-*r/ 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)\right)} \]

      4. metadata-eval 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)\right)} \]

      5. associate-+r- 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}\right)\right)} \]

   7. Simplified 41.7%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}} \]
   8. Step-by-step derivation

      1. flip-+ 58.2%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\frac{a \cdot a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right) \cdot \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}{a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}}\right)\right)} \]

   9. Applied egg-rr 58.2%

      \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\frac{a \cdot a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right) \cdot \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}{a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y \cdot e^{\left(c - b\right) \cdot 1.6666666666666667}}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-209}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(y \cdot c\right) \cdot \frac{\left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right) \cdot \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right) - a \cdot a}{a + \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14: 53.5% accurate, 5.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.6666666666666666}{t} - 0.8333333333333334\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-209}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(y \cdot c\right) \cdot \frac{t_1 \cdot t_1 - a \cdot a}{a + t_1}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (- (/ 0.6666666666666666 t) 0.8333333333333334)))
   (if (<= b -7.5e+88)
     (/ x (+ x (* y (+ 1.0 (* (- c b) (* 2.0 a))))))
     (if (<= b -2e-209)
       1.0
       (if (<= b -1.16e-289)
         (/
          x
          (+
           x
           (- y (* 2.0 (* (* y c) (/ (- (* t_1 t_1) (* a a)) (+ a t_1)))))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.6666666666666666 / t) - 0.8333333333333334;
	double tmp;
	if (b <= -7.5e+88) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if (b <= -2e-209) {
		tmp = 1.0;
	} else if (b <= -1.16e-289) {
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (0.6666666666666666d0 / t) - 0.8333333333333334d0
    if (b <= (-7.5d+88)) then
        tmp = x / (x + (y * (1.0d0 + ((c - b) * (2.0d0 * a)))))
    else if (b <= (-2d-209)) then
        tmp = 1.0d0
    else if (b <= (-1.16d-289)) then
        tmp = x / (x + (y - (2.0d0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.6666666666666666 / t) - 0.8333333333333334;
	double tmp;
	if (b <= -7.5e+88) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if (b <= -2e-209) {
		tmp = 1.0;
	} else if (b <= -1.16e-289) {
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (0.6666666666666666 / t) - 0.8333333333333334
	tmp = 0
	if b <= -7.5e+88:
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))))
	elif b <= -2e-209:
		tmp = 1.0
	elif b <= -1.16e-289:
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(0.6666666666666666 / t) - 0.8333333333333334)
	tmp = 0.0
	if (b <= -7.5e+88)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a))))));
	elseif (b <= -2e-209)
		tmp = 1.0;
	elseif (b <= -1.16e-289)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(Float64(y * c) * Float64(Float64(Float64(t_1 * t_1) - Float64(a * a)) / Float64(a + t_1)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (0.6666666666666666 / t) - 0.8333333333333334;
	tmp = 0.0;
	if (b <= -7.5e+88)
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	elseif (b <= -2e-209)
		tmp = 1.0;
	elseif (b <= -1.16e-289)
		tmp = x / (x + (y - (2.0 * ((y * c) * (((t_1 * t_1) - (a * a)) / (a + t_1))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(0.6666666666666666 / t), $MachinePrecision] - 0.8333333333333334), $MachinePrecision]}, If[LessEqual[b, -7.5e+88], N[(x / N[(x + N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-209], 1.0, If[LessEqual[b, -1.16e-289], N[(x / N[(x + N[(y - N[(2.0 * N[(N[(y * c), $MachinePrecision] * N[(N[(N[(t$95$1 * t$95$1), $MachinePrecision] - N[(a * a), $MachinePrecision]), $MachinePrecision] / N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.50000000000000031e88

   1. Initial program 86.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 58.4%

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

   3. Taylor expanded in a around 0 56.1%

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

      1. associate-*r* 56.1%

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

   5. Simplified 56.1%

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

   if -7.50000000000000031e88 < b < -2.0000000000000001e-209 or -1.15999999999999998e-289 < b

   1. Initial program 92.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 74.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 74.4%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 74.4%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 67.9%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 59.7%

      \[\leadsto \color{blue}{1} \]

   if -2.0000000000000001e-209 < b < -1.15999999999999998e-289

   1. Initial program 100.0%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in c around inf 74.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 74.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)}} \]

      2. metadata-eval 74.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)}} \]

      3. +-commutative 74.8%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - \frac{0.6666666666666666}{t}\right)\right)}} \]

   4. Simplified 74.8%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}} \]

   5. Taylor expanded in c around 0 41.6%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \color{blue}{\left(\left(c \cdot y\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}\right)} \]

      2. +-commutative 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)} \]

      3. associate-*r/ 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)\right)} \]

      4. metadata-eval 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)\right)} \]

      5. associate-+r- 41.7%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}\right)\right)} \]

   7. Simplified 41.7%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}} \]
   8. Step-by-step derivation

      1. flip-+ 58.2%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\frac{a \cdot a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right) \cdot \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}{a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}}\right)\right)} \]

   9. Applied egg-rr 58.2%

      \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\frac{a \cdot a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right) \cdot \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}{a - \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)}}\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-209}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -1.16 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(y \cdot c\right) \cdot \frac{\left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right) \cdot \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right) - a \cdot a}{a + \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15: 52.6% accurate, 10.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(2 \cdot c\right) \cdot \left(a - \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -6.6e-16)
   1.0
   (if (<= c -5.5e-213)
     (/ x (+ x (* y (+ 1.0 (* (- c b) (* 2.0 a))))))
     (if (<= c 1.2e+79)
       1.0
       (/
        x
        (*
         y
         (+
          1.0
          (*
           (* 2.0 c)
           (- a (- (/ 0.6666666666666666 t) 0.8333333333333334))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -6.6e-16) {
		tmp = 1.0;
	} else if (c <= -5.5e-213) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if (c <= 1.2e+79) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 + ((2.0 * c) * (a - ((0.6666666666666666 / t) - 0.8333333333333334)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (c <= (-6.6d-16)) then
        tmp = 1.0d0
    else if (c <= (-5.5d-213)) then
        tmp = x / (x + (y * (1.0d0 + ((c - b) * (2.0d0 * a)))))
    else if (c <= 1.2d+79) then
        tmp = 1.0d0
    else
        tmp = x / (y * (1.0d0 + ((2.0d0 * c) * (a - ((0.6666666666666666d0 / t) - 0.8333333333333334d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -6.6e-16) {
		tmp = 1.0;
	} else if (c <= -5.5e-213) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if (c <= 1.2e+79) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 + ((2.0 * c) * (a - ((0.6666666666666666 / t) - 0.8333333333333334)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -6.6e-16:
		tmp = 1.0
	elif c <= -5.5e-213:
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))))
	elif c <= 1.2e+79:
		tmp = 1.0
	else:
		tmp = x / (y * (1.0 + ((2.0 * c) * (a - ((0.6666666666666666 / t) - 0.8333333333333334)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -6.6e-16)
		tmp = 1.0;
	elseif (c <= -5.5e-213)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a))))));
	elseif (c <= 1.2e+79)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * Float64(1.0 + Float64(Float64(2.0 * c) * Float64(a - Float64(Float64(0.6666666666666666 / t) - 0.8333333333333334))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -6.6e-16)
		tmp = 1.0;
	elseif (c <= -5.5e-213)
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	elseif (c <= 1.2e+79)
		tmp = 1.0;
	else
		tmp = x / (y * (1.0 + ((2.0 * c) * (a - ((0.6666666666666666 / t) - 0.8333333333333334)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -6.6e-16], 1.0, If[LessEqual[c, -5.5e-213], N[(x / N[(x + N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.2e+79], 1.0, N[(x / N[(y * N[(1.0 + N[(N[(2.0 * c), $MachinePrecision] * N[(a - N[(N[(0.6666666666666666 / t), $MachinePrecision] - 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -6.59999999999999976e-16 or -5.50000000000000008e-213 < c < 1.19999999999999993e79

   1. Initial program 92.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 66.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{1} \]

   if -6.59999999999999976e-16 < c < -5.50000000000000008e-213

   1. Initial program 97.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 65.2%

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

   3. Taylor expanded in a around 0 61.0%

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

      1. associate-*r* 61.0%

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

   5. Simplified 61.0%

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

   if 1.19999999999999993e79 < c

   1. Initial program 86.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in c around inf 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)}} \]

      2. metadata-eval 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)}} \]

      3. +-commutative 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - \frac{0.6666666666666666}{t}\right)\right)}} \]

   4. Simplified 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}} \]

   5. Taylor expanded in c around 0 47.4%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \color{blue}{\left(\left(c \cdot y\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}\right)} \]

      2. +-commutative 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)} \]

      3. associate-*r/ 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)\right)} \]

      4. metadata-eval 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)\right)} \]

      5. associate-+r- 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}\right)\right)} \]

   7. Simplified 47.4%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}} \]

   8. Taylor expanded in y around inf 51.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + 2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 51.0%

         \[\leadsto \frac{x}{y \cdot \left(1 + \color{blue}{\left(2 \cdot c\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)}\right)} \]

      2. associate-*r/ 51.0%

         \[\leadsto \frac{x}{y \cdot \left(1 + \left(2 \cdot c\right) \cdot \left(\left(0.8333333333333334 + a\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)} \]

      3. metadata-eval 51.0%

         \[\leadsto \frac{x}{y \cdot \left(1 + \left(2 \cdot c\right) \cdot \left(\left(0.8333333333333334 + a\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)} \]

      4. +-commutative 51.0%

         \[\leadsto \frac{x}{y \cdot \left(1 + \left(2 \cdot c\right) \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - \frac{0.6666666666666666}{t}\right)\right)} \]

      5. associate-+r- 51.0%

         \[\leadsto \frac{x}{y \cdot \left(1 + \left(2 \cdot c\right) \cdot \color{blue}{\left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}\right)} \]

   10. Simplified 51.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + \left(2 \cdot c\right) \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -6.6 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;c \leq 1.2 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \left(2 \cdot c\right) \cdot \left(a - \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)\right)\right)}\\ \end{array} \]

Alternative 16: 52.2% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-213} \lor \neg \left(c \leq 3.2 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.9e-17)
   1.0
   (if (or (<= c -1.25e-213) (not (<= c 3.2e+79)))
     (/ x (+ x (* y (+ 1.0 (* (- c b) (* 2.0 a))))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.9e-17) {
		tmp = 1.0;
	} else if ((c <= -1.25e-213) || !(c <= 3.2e+79)) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (c <= (-2.9d-17)) then
        tmp = 1.0d0
    else if ((c <= (-1.25d-213)) .or. (.not. (c <= 3.2d+79))) then
        tmp = x / (x + (y * (1.0d0 + ((c - b) * (2.0d0 * a)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.9e-17) {
		tmp = 1.0;
	} else if ((c <= -1.25e-213) || !(c <= 3.2e+79)) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.9e-17:
		tmp = 1.0
	elif (c <= -1.25e-213) or not (c <= 3.2e+79):
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.9e-17)
		tmp = 1.0;
	elseif ((c <= -1.25e-213) || !(c <= 3.2e+79))
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -2.9e-17)
		tmp = 1.0;
	elseif ((c <= -1.25e-213) || ~((c <= 3.2e+79)))
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.9e-17], 1.0, If[Or[LessEqual[c, -1.25e-213], N[Not[LessEqual[c, 3.2e+79]], $MachinePrecision]], N[(x / N[(x + N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if c < -2.9000000000000003e-17 or -1.24999999999999994e-213 < c < 3.20000000000000003e79

   1. Initial program 92.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 66.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{1} \]

   if -2.9000000000000003e-17 < c < -1.24999999999999994e-213 or 3.20000000000000003e79 < c

   1. Initial program 92.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 70.1%

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

   3. Taylor expanded in a around 0 56.1%

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

      1. associate-*r* 56.1%

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

   5. Simplified 56.1%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.9 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-213} \lor \neg \left(c \leq 3.2 \cdot 10^{+79}\right):\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17: 52.2% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-205}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1.2e-20)
   1.0
   (if (<= c -1.65e-205)
     (/ x (+ x (* y (+ 1.0 (* (- c b) (* 2.0 a))))))
     (if (<= c 1.42e+79) 1.0 (/ x (+ x (+ y (* 2.0 (* a (* y (- c b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.2e-20) {
		tmp = 1.0;
	} else if (c <= -1.65e-205) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if (c <= 1.42e+79) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (c <= (-1.2d-20)) then
        tmp = 1.0d0
    else if (c <= (-1.65d-205)) then
        tmp = x / (x + (y * (1.0d0 + ((c - b) * (2.0d0 * a)))))
    else if (c <= 1.42d+79) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + (2.0d0 * (a * (y * (c - 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 c) {
	double tmp;
	if (c <= -1.2e-20) {
		tmp = 1.0;
	} else if (c <= -1.65e-205) {
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	} else if (c <= 1.42e+79) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1.2e-20:
		tmp = 1.0
	elif c <= -1.65e-205:
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))))
	elif c <= 1.42e+79:
		tmp = 1.0
	else:
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1.2e-20)
		tmp = 1.0;
	elseif (c <= -1.65e-205)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(Float64(c - b) * Float64(2.0 * a))))));
	elseif (c <= 1.42e+79)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -1.2e-20)
		tmp = 1.0;
	elseif (c <= -1.65e-205)
		tmp = x / (x + (y * (1.0 + ((c - b) * (2.0 * a)))));
	elseif (c <= 1.42e+79)
		tmp = 1.0;
	else
		tmp = x / (x + (y + (2.0 * (a * (y * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1.2e-20], 1.0, If[LessEqual[c, -1.65e-205], N[(x / N[(x + N[(y * N[(1.0 + N[(N[(c - b), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.42e+79], 1.0, N[(x / N[(x + N[(y + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.19999999999999996e-20 or -1.65e-205 < c < 1.41999999999999998e79

   1. Initial program 92.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 66.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{1} \]

   if -1.19999999999999996e-20 < c < -1.65e-205

   1. Initial program 97.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 65.2%

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

   3. Taylor expanded in a around 0 61.0%

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

      1. associate-*r* 61.0%

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

   5. Simplified 61.0%

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

   if 1.41999999999999998e79 < c

   1. Initial program 86.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 75.2%

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

   3. Taylor expanded in a around 0 50.9%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 50.9%

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

   5. Simplified 50.9%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.2 \cdot 10^{-20}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-205}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + \left(c - b\right) \cdot \left(2 \cdot a\right)\right)}\\ \mathbf{elif}\;c \leq 1.42 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \end{array} \]

Alternative 18: 51.9% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + -2 \cdot \left(a \cdot b\right)\right)}\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -9.5e-24)
   1.0
   (if (<= c -6.8e-208)
     (/ x (+ x (* y (+ 1.0 (* -2.0 (* a b))))))
     (if (<= c 6.8e+78)
       1.0
       (* 0.5 (/ x (* y (* c (+ 0.8333333333333334 a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.5e-24) {
		tmp = 1.0;
	} else if (c <= -6.8e-208) {
		tmp = x / (x + (y * (1.0 + (-2.0 * (a * b)))));
	} else if (c <= 6.8e+78) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (c <= (-9.5d-24)) then
        tmp = 1.0d0
    else if (c <= (-6.8d-208)) then
        tmp = x / (x + (y * (1.0d0 + ((-2.0d0) * (a * b)))))
    else if (c <= 6.8d+78) then
        tmp = 1.0d0
    else
        tmp = 0.5d0 * (x / (y * (c * (0.8333333333333334d0 + 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 c) {
	double tmp;
	if (c <= -9.5e-24) {
		tmp = 1.0;
	} else if (c <= -6.8e-208) {
		tmp = x / (x + (y * (1.0 + (-2.0 * (a * b)))));
	} else if (c <= 6.8e+78) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -9.5e-24:
		tmp = 1.0
	elif c <= -6.8e-208:
		tmp = x / (x + (y * (1.0 + (-2.0 * (a * b)))))
	elif c <= 6.8e+78:
		tmp = 1.0
	else:
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -9.5e-24)
		tmp = 1.0;
	elseif (c <= -6.8e-208)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 + Float64(-2.0 * Float64(a * b))))));
	elseif (c <= 6.8e+78)
		tmp = 1.0;
	else
		tmp = Float64(0.5 * Float64(x / Float64(y * Float64(c * Float64(0.8333333333333334 + a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -9.5e-24)
		tmp = 1.0;
	elseif (c <= -6.8e-208)
		tmp = x / (x + (y * (1.0 + (-2.0 * (a * b)))));
	elseif (c <= 6.8e+78)
		tmp = 1.0;
	else
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -9.5e-24], 1.0, If[LessEqual[c, -6.8e-208], N[(x / N[(x + N[(y * N[(1.0 + N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e+78], 1.0, N[(0.5 * N[(x / N[(y * N[(c * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.50000000000000029e-24 or -6.8e-208 < c < 6.80000000000000014e78

   1. Initial program 92.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 71.5%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 71.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 66.3%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 59.0%

      \[\leadsto \color{blue}{1} \]

   if -9.50000000000000029e-24 < c < -6.8e-208

   1. Initial program 97.8%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in a around inf 65.2%

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

   3. Taylor expanded in c around 0 65.2%

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

      1. *-commutative 65.2%

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

      2. *-commutative 65.2%

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

      3. associate-*l* 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in b around 0 58.9%

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

      1. *-commutative 58.9%

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

   8. Simplified 58.9%

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

   if 6.80000000000000014e78 < c

   1. Initial program 86.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in c around inf 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)}} \]

      2. metadata-eval 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)}} \]

      3. +-commutative 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - \frac{0.6666666666666666}{t}\right)\right)}} \]

   4. Simplified 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}} \]

   5. Taylor expanded in c around 0 47.4%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \color{blue}{\left(\left(c \cdot y\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}\right)} \]

      2. +-commutative 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)} \]

      3. associate-*r/ 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)\right)} \]

      4. metadata-eval 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)\right)} \]

      5. associate-+r- 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}\right)\right)} \]

   7. Simplified 47.4%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}} \]

   8. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{\frac{x}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(0.8333333333333334 + a\right)\right)\right)\right)}} \]

   9. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{c \cdot \left(y \cdot \left(0.8333333333333334 + a\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 42.1%

          \[\leadsto 0.5 \cdot \frac{x}{\color{blue}{\left(c \cdot y\right) \cdot \left(0.8333333333333334 + a\right)}} \]

       2. *-commutative 42.1%

          \[\leadsto 0.5 \cdot \frac{x}{\color{blue}{\left(y \cdot c\right)} \cdot \left(0.8333333333333334 + a\right)} \]

       3. associate-*l* 46.5%

          \[\leadsto 0.5 \cdot \frac{x}{\color{blue}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}} \]

   11. Simplified 46.5%

       \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{-24}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 + -2 \cdot \left(a \cdot b\right)\right)}\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}\\ \end{array} \]

Alternative 19: 52.9% accurate, 17.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 7.2 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 7.2e+80) 1.0 (* 0.5 (/ x (* y (* c (+ 0.8333333333333334 a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 7.2e+80) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: tmp
    if (c <= 7.2d+80) then
        tmp = 1.0d0
    else
        tmp = 0.5d0 * (x / (y * (c * (0.8333333333333334d0 + 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 c) {
	double tmp;
	if (c <= 7.2e+80) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 7.2e+80:
		tmp = 1.0
	else:
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 7.2e+80)
		tmp = 1.0;
	else
		tmp = Float64(0.5 * Float64(x / Float64(y * Float64(c * Float64(0.8333333333333334 + a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 7.2e+80)
		tmp = 1.0;
	else
		tmp = 0.5 * (x / (y * (c * (0.8333333333333334 + a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 7.2e+80], 1.0, N[(0.5 * N[(x / N[(y * N[(c * N[(0.8333333333333334 + a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 7.1999999999999999e80

   1. Initial program 93.4%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in t around inf 70.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
   3. Step-by-step derivation

      1. +-commutative 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

      2. *-commutative 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

      3. associate-*r* 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

      4. neg-mul-1 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      5. neg-sub0 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      6. associate--r- 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      7. neg-sub0 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      8. +-commutative 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

      9. sub-neg 70.2%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   4. Simplified 70.2%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   5. Taylor expanded in a around 0 64.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

   6. Taylor expanded in x around inf 55.4%

      \[\leadsto \color{blue}{1} \]

   if 7.1999999999999999e80 < c

   1. Initial program 86.2%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   2. Taylor expanded in c around inf 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}}} \]
   3. Step-by-step derivation

      1. associate-*r/ 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)}} \]

      2. metadata-eval 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(0.8333333333333334 + a\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)}} \]

      3. +-commutative 82.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - \frac{0.6666666666666666}{t}\right)\right)}} \]

   4. Simplified 82.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}} \]

   5. Taylor expanded in c around 0 47.4%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)\right)}} \]
   6. Step-by-step derivation

      1. associate-*r* 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \color{blue}{\left(\left(c \cdot y\right) \cdot \left(\left(0.8333333333333334 + a\right) - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)}\right)} \]

      2. +-commutative 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} - 0.6666666666666666 \cdot \frac{1}{t}\right)\right)\right)} \]

      3. associate-*r/ 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \color{blue}{\frac{0.6666666666666666 \cdot 1}{t}}\right)\right)\right)} \]

      4. metadata-eval 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{\color{blue}{0.6666666666666666}}{t}\right)\right)\right)} \]

      5. associate-+r- 47.4%

         \[\leadsto \frac{x}{x + \left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \color{blue}{\left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)}\right)\right)} \]

   7. Simplified 47.4%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + 2 \cdot \left(\left(c \cdot y\right) \cdot \left(a + \left(0.8333333333333334 - \frac{0.6666666666666666}{t}\right)\right)\right)\right)}} \]

   8. Taylor expanded in t around inf 47.3%

      \[\leadsto \color{blue}{\frac{x}{x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(0.8333333333333334 + a\right)\right)\right)\right)}} \]

   9. Taylor expanded in c around inf 42.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{c \cdot \left(y \cdot \left(0.8333333333333334 + a\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 42.1%

          \[\leadsto 0.5 \cdot \frac{x}{\color{blue}{\left(c \cdot y\right) \cdot \left(0.8333333333333334 + a\right)}} \]

       2. *-commutative 42.1%

          \[\leadsto 0.5 \cdot \frac{x}{\color{blue}{\left(y \cdot c\right)} \cdot \left(0.8333333333333334 + a\right)} \]

       3. associate-*l* 46.5%

          \[\leadsto 0.5 \cdot \frac{x}{\color{blue}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}} \]

   11. Simplified 46.5%

       \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 7.2 \cdot 10^{+80}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{y \cdot \left(c \cdot \left(0.8333333333333334 + a\right)\right)}\\ \end{array} \]

Alternative 20: 52.0% accurate, 231.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b, c):
	return 1.0

Julia

function code(x, y, z, t, a, b, c)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := 1.0

Derivation

1. Initial program 92.2%

   \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

2. Taylor expanded in t around inf 72.5%

   \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(-1 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(b - c\right)\right)\right)}}} \]
3. Step-by-step derivation

   1. +-commutative 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \left(\color{blue}{\left(a + 0.8333333333333334\right)} \cdot \left(b - c\right)\right)\right)}} \]

   2. *-commutative 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(-1 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(a + 0.8333333333333334\right)\right)}\right)}} \]

   3. associate-*r* 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(-1 \cdot \left(b - c\right)\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

   4. neg-mul-1 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(-\left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   5. neg-sub0 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(0 - \left(b - c\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   6. associate--r- 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(\left(0 - b\right) + c\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   7. neg-sub0 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(\color{blue}{\left(-b\right)} + c\right) \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   8. +-commutative 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c + \left(-b\right)\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

   9. sub-neg 72.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\left(c - b\right)} \cdot \left(a + 0.8333333333333334\right)\right)}} \]

4. Simplified 72.5%

   \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(c - b\right) \cdot \left(a + 0.8333333333333334\right)\right)}}} \]

5. Taylor expanded in a around 0 66.5%

   \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \color{blue}{0.8333333333333334}\right)}} \]

6. Taylor expanded in x around inf 51.9%

   \[\leadsto \color{blue}{1} \]

7. Final simplification 51.9%

   \[\leadsto 1 \]

Developer target: 95.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ t_2 := a - \frac{5}{6}\\ \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{t_1 \cdot \left(\left(3 \cdot t\right) \cdot t_2\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(t_2 \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot t_2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{t_1}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (sqrt (+ t a)))) (t_2 (- a (/ 5.0 6.0))))
   (if (< t -2.118326644891581e-50)
     (/
      x
      (+
       x
       (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b)))))))
     (if (< t 5.196588770651547e-123)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (/
             (-
              (* t_1 (* (* 3.0 t) t_2))
              (*
               (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0)
               (* t_2 (* (- b c) t))))
             (* (* (* t t) 3.0) t_2)))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (/ t_1 t)
             (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    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), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * sqrt((t + a))
    t_2 = a - (5.0d0 / 6.0d0)
    if (t < (-2.118326644891581d-50)) then
        tmp = x / (x + (y * exp((2.0d0 * (((a * c) + (0.8333333333333334d0 * c)) - (a * b))))))
    else if (t < 5.196588770651547d-123) then
        tmp = x / (x + (y * exp((2.0d0 * (((t_1 * ((3.0d0 * t) * t_2)) - (((((5.0d0 / 6.0d0) + a) * (3.0d0 * t)) - 2.0d0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0d0) * t_2))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((t_1 / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * Math.sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * Math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * Math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * math.sqrt((t + a))
	t_2 = a - (5.0 / 6.0)
	tmp = 0
	if t < -2.118326644891581e-50:
		tmp = x / (x + (y * math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))))
	elif t < 5.196588770651547e-123:
		tmp = x / (x + (y * math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * sqrt(Float64(t + a)))
	t_2 = Float64(a - Float64(5.0 / 6.0))
	tmp = 0.0
	if (t < -2.118326644891581e-50)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(a * c) + Float64(0.8333333333333334 * c)) - Float64(a * b)))))));
	elseif (t < 5.196588770651547e-123)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(t_1 * Float64(Float64(3.0 * t) * t_2)) - Float64(Float64(Float64(Float64(Float64(5.0 / 6.0) + a) * Float64(3.0 * t)) - 2.0) * Float64(t_2 * Float64(Float64(b - c) * t)))) / Float64(Float64(Float64(t * t) * 3.0) * t_2)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(t_1 / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * sqrt((t + a));
	t_2 = a - (5.0 / 6.0);
	tmp = 0.0;
	if (t < -2.118326644891581e-50)
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	elseif (t < 5.196588770651547e-123)
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -2.118326644891581e-50], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(a * c), $MachinePrecision] + N[(0.8333333333333334 * c), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[t, 5.196588770651547e-123], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(t$95$1 * N[(N[(3.0 * t), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(5.0 / 6.0), $MachinePrecision] + a), $MachinePrecision] * N[(3.0 * t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision] * N[(t$95$2 * N[(N[(b - c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * t), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(t$95$1 / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (* 3.0 t) (- a (/ 5.0 6.0)))) (* (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0) (* (- a (/ 5.0 6.0)) (* (- b c) t)))) (* (* (* t t) 3.0) (- a (/ 5.0 6.0))))))))) (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))

  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))