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

Percentage Accurate: 94.0% → 96.6%

Time: 24.9s

Alternatives: 22

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: 94.0% 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: 96.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(c - b\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right)\\ t_2 := \sqrt{a + t}\\ \mathbf{if}\;\frac{t_2 \cdot z}{t} + t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{t_2}} + t_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (- c b) (- (+ a 0.8333333333333334) (/ 2.0 (* t 3.0)))))
        (t_2 (sqrt (+ a t))))
   (if (<= (+ (/ (* t_2 z) t) t_1) INFINITY)
     (/ x (+ x (* y (pow (exp 2.0) (+ (/ z (/ t t_2)) t_1)))))
     (/ x (+ x (* y (exp (* -2.0 (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (c - b) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0)));
	double t_2 = sqrt((a + t));
	double tmp;
	if ((((t_2 * z) / t) + t_1) <= ((double) INFINITY)) {
		tmp = x / (x + (y * pow(exp(2.0), ((z / (t / t_2)) + t_1))));
	} else {
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (c - b) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0)));
	double t_2 = Math.sqrt((a + t));
	double tmp;
	if ((((t_2 * z) / t) + t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.pow(Math.exp(2.0), ((z / (t / t_2)) + t_1))));
	} else {
		tmp = x / (x + (y * Math.exp((-2.0 * (a * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (c - b) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0)))
	t_2 = math.sqrt((a + t))
	tmp = 0
	if (((t_2 * z) / t) + t_1) <= math.inf:
		tmp = x / (x + (y * math.pow(math.exp(2.0), ((z / (t / t_2)) + t_1))))
	else:
		tmp = x / (x + (y * math.exp((-2.0 * (a * b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(c - b) * Float64(Float64(a + 0.8333333333333334) - Float64(2.0 / Float64(t * 3.0))))
	t_2 = sqrt(Float64(a + t))
	tmp = 0.0
	if (Float64(Float64(Float64(t_2 * z) / t) + t_1) <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * (exp(2.0) ^ Float64(Float64(z / Float64(t / t_2)) + t_1)))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(a * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (c - b) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0)));
	t_2 = sqrt((a + t));
	tmp = 0.0;
	if ((((t_2 * z) / t) + t_1) <= Inf)
		tmp = x / (x + (y * (exp(2.0) ^ ((z / (t / t_2)) + t_1))));
	else
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(c - b), $MachinePrecision] * N[(N[(a + 0.8333333333333334), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(N[(t$95$2 * z), $MachinePrecision] / t), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(x / N[(x + N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(z / N[(t / t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(a * b), $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 98.4%

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

      1. exp-prod 98.4%

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

      2. associate-/l* 99.2%

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

      3. metadata-eval 99.2%

         \[\leadsto \frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \color{blue}{0.8333333333333334}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right)\right)}}} \]

   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 a around inf 70.8%

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

   3. Taylor expanded in c around 0 80.5%

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

4. Final simplification 98.5%

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

Alternative 2: 97.4% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (fma
   y
   (pow
    (exp 2.0)
    (fma
     (+ a (+ (/ -0.6666666666666666 t) 0.8333333333333334))
     (- 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((a + ((-0.6666666666666666 / t) + 0.8333333333333334)), (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(a + Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334)), 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[(a + N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $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 94.6%

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

3. Simplified 97.4%

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

4. Final simplification 97.4%

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

Alternative 3: 96.5% accurate, 0.7× speedup

Math

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

FPCore

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

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

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((math.sqrt((a + t)) * z) / t) + ((c - b) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0))))
	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 * (a * b)))))
	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(c - b) * Float64(Float64(a + 0.8333333333333334) - Float64(2.0 / Float64(t * 3.0)))))
	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(a * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((sqrt((a + t)) * z) / t) + ((c - b) * ((a + 0.8333333333333334) - (2.0 / (t * 3.0))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = x / (x + (y * exp((-2.0 * (a * b)))));
	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[(c - b), $MachinePrecision] * N[(N[(a + 0.8333333333333334), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $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[(a * b), $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 98.4%

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

   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 a around inf 70.8%

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

   3. Taylor expanded in c around 0 80.5%

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

4. Final simplification 97.7%

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

Alternative 4: 89.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-0.6666666666666666}{t} + 0.8333333333333334\\ \mathbf{if}\;t \leq 4.7 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + t_1 \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + t_1\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (/ -0.6666666666666666 t) 0.8333333333333334)))
   (if (<= t 4.7e-177)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (- (* z (sqrt a)) (* -0.6666666666666666 (- b c))) t))))))
     (if (<= t 4e+77)
       (/
        x
        (+ x (* y (exp (* 2.0 (+ (* z (sqrt (/ 1.0 t))) (* t_1 (- c b))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (+ a t_1) (- c b)))))))))))

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 (t <= 4.7e-177) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 4e+77) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + (t_1 * (c - b)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + t_1) * (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) :: t_1
    real(8) :: tmp
    t_1 = ((-0.6666666666666666d0) / t) + 0.8333333333333334d0
    if (t <= 4.7d-177) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) - ((-0.6666666666666666d0) * (b - c))) / t)))))
    else if (t <= 4d+77) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) + (t_1 * (c - b)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + t_1) * (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 t_1 = (-0.6666666666666666 / t) + 0.8333333333333334;
	double tmp;
	if (t <= 4.7e-177) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 4e+77) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) + (t_1 * (c - b)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + t_1) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (-0.6666666666666666 / t) + 0.8333333333333334
	tmp = 0
	if t <= 4.7e-177:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))))
	elif t <= 4e+77:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) + (t_1 * (c - b)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + t_1) * (c - b))))))
	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 (t <= 4.7e-177)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) - Float64(-0.6666666666666666 * Float64(b - c))) / t))))));
	elseif (t <= 4e+77)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) + Float64(t_1 * Float64(c - b))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + t_1) * Float64(c - b)))))));
	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 (t <= 4.7e-177)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	elseif (t <= 4e+77)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + (t_1 * (c - b)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((a + t_1) * (c - b))))));
	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[t, 4.7e-177], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] - N[(-0.6666666666666666 * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+77], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(t$95$1 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + t$95$1), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < 4.69999999999999967e-177

   1. Initial program 90.9%

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

   2. Taylor expanded in t around 0 91.1%

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

   if 4.69999999999999967e-177 < t < 3.99999999999999993e77

   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 90.9%

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

      1. *-commutative 90.9%

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

      2. *-commutative 90.9%

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

      3. cancel-sign-sub-inv 90.9%

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

      4. metadata-eval 90.9%

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

      5. associate-*r/ 90.9%

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

      6. metadata-eval 90.9%

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

   4. Simplified 90.9%

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

   if 3.99999999999999993e77 < t

   1. Initial program 93.2%

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

   2. Taylor expanded in z around 0 97.3%

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

      1. mul-1-neg 97.3%

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

      2. *-commutative 97.3%

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

      3. distribute-rgt-neg-in 97.3%

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

      4. cancel-sign-sub-inv 97.3%

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

      5. +-commutative 97.3%

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

      6. metadata-eval 97.3%

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

      7. associate-*r/ 97.3%

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

      8. metadata-eval 97.3%

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

      9. associate-+r+ 97.3%

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

      10. neg-sub0 97.3%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(0 - \left(b - c\right)\right)}\right)}} \]

      11. associate--r- 97.3%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(\left(0 - b\right) + c\right)}\right)}} \]

      12. neg-sub0 97.3%

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

   4. Simplified 97.3%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.7 \cdot 10^{-177}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 5: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 2e-165)
   (/
    x
    (+
     x
     (*
      y
      (exp (* 2.0 (/ (- (* z (sqrt a)) (* -0.6666666666666666 (- b c))) t))))))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (*
        2.0
        (*
         (+ a (+ (/ -0.6666666666666666 t) 0.8333333333333334))
         (- c b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 2e-165) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + ((-0.6666666666666666 / t) + 0.8333333333333334)) * (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 <= 2d-165) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) - ((-0.6666666666666666d0) * (b - c))) / t)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + (((-0.6666666666666666d0) / t) + 0.8333333333333334d0)) * (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 <= 2e-165) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + ((-0.6666666666666666 / t) + 0.8333333333333334)) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 2e-165:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + ((-0.6666666666666666 / t) + 0.8333333333333334)) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 2e-165)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) - Float64(-0.6666666666666666 * Float64(b - c))) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334)) * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 2e-165)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	else
		tmp = x / (x + (y * exp((2.0 * ((a + ((-0.6666666666666666 / t) + 0.8333333333333334)) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 2e-165], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] - N[(-0.6666666666666666 * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2e-165

   1. Initial program 91.3%

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

   2. Taylor expanded in t around 0 90.5%

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

   if 2e-165 < t

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 90.5%

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

      1. mul-1-neg 90.5%

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

      2. *-commutative 90.5%

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

      3. distribute-rgt-neg-in 90.5%

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

      4. cancel-sign-sub-inv 90.5%

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

      5. +-commutative 90.5%

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

      6. metadata-eval 90.5%

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

      7. associate-*r/ 90.5%

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

      8. metadata-eval 90.5%

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

      9. associate-+r+ 90.5%

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

      10. neg-sub0 90.5%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(0 - \left(b - c\right)\right)}\right)}} \]

      11. associate--r- 90.5%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(\left(0 - b\right) + c\right)}\right)}} \]

      12. neg-sub0 90.5%

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

   4. Simplified 90.5%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{-165}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 6: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c - b}{t}\right)}}\\ \mathbf{if}\;t \leq 2 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* -0.6666666666666666 (/ (- c b) t)))))))))
   (if (<= t 2e-82)
     t_1
     (if (<= t 1.45e-28)
       1.0
       (if (<= t 3.25e-12)
         t_1
         (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))));
	double tmp;
	if (t <= 2e-82) {
		tmp = t_1;
	} else if (t <= 1.45e-28) {
		tmp = 1.0;
	} else if (t <= 3.25e-12) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	}
	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 = x / (x + (y * exp((2.0d0 * ((-0.6666666666666666d0) * ((c - b) / t))))))
    if (t <= 2d-82) then
        tmp = t_1
    else if (t <= 1.45d-28) then
        tmp = 1.0d0
    else if (t <= 3.25d-12) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    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 = x / (x + (y * Math.exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))));
	double tmp;
	if (t <= 2e-82) {
		tmp = t_1;
	} else if (t <= 1.45e-28) {
		tmp = 1.0;
	} else if (t <= 3.25e-12) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))))
	tmp = 0
	if t <= 2e-82:
		tmp = t_1
	elif t <= 1.45e-28:
		tmp = 1.0
	elif t <= 3.25e-12:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(-0.6666666666666666 * Float64(Float64(c - b) / t)))))))
	tmp = 0.0
	if (t <= 2e-82)
		tmp = t_1;
	elseif (t <= 1.45e-28)
		tmp = 1.0;
	elseif (t <= 3.25e-12)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))));
	tmp = 0.0;
	if (t <= 2e-82)
		tmp = t_1;
	elseif (t <= 1.45e-28)
		tmp = 1.0;
	elseif (t <= 3.25e-12)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(-0.6666666666666666 * N[(N[(c - b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2e-82], t$95$1, If[LessEqual[t, 1.45e-28], 1.0, If[LessEqual[t, 3.25e-12], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 2e-82 or 1.45000000000000006e-28 < t < 3.2500000000000001e-12

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. *-commutative 84.4%

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

      3. distribute-rgt-neg-in 84.4%

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

      4. cancel-sign-sub-inv 84.4%

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

      5. +-commutative 84.4%

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

      6. metadata-eval 84.4%

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

      7. associate-*r/ 84.4%

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

      8. metadata-eval 84.4%

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

      9. associate-+r+ 84.4%

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

      10. neg-sub0 84.4%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(0 - \left(b - c\right)\right)}\right)}} \]

      11. associate--r- 84.4%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(\left(0 - b\right) + c\right)}\right)}} \]

      12. neg-sub0 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in t around 0 79.9%

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

   if 2e-82 < t < 1.45000000000000006e-28

   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 inf 45.8%

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

   3. Taylor expanded in a around 0 45.7%

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

   4. Taylor expanded in x around inf 81.8%

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

   if 3.2500000000000001e-12 < t

   1. Initial program 95.6%

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

   2. Taylor expanded in t around inf 94.7%

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

      1. mul-1-neg 94.7%

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

      2. *-commutative 94.7%

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

      3. distribute-rgt-neg-in 94.7%

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

      4. distribute-neg-in 94.7%

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

      5. metadata-eval 94.7%

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

   4. Simplified 94.7%

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

   5. Taylor expanded in a around 0 84.4%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c - b}{t}\right)}}\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c - b}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 7: 81.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c - b}{t}\right)}}\\ \mathbf{if}\;t \leq 7.8 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* -0.6666666666666666 (/ (- c b) t)))))))))
   (if (<= t 7.8e-82)
     t_1
     (if (<= t 1.4e-28)
       1.0
       (if (<= t 3e-12)
         t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* (- c b) (- a -0.8333333333333334))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))));
	double tmp;
	if (t <= 7.8e-82) {
		tmp = t_1;
	} else if (t <= 1.4e-28) {
		tmp = 1.0;
	} else if (t <= 3e-12) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (a - -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) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * ((-0.6666666666666666d0) * ((c - b) / t))))))
    if (t <= 7.8d-82) then
        tmp = t_1
    else if (t <= 1.4d-28) then
        tmp = 1.0d0
    else if (t <= 3d-12) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((c - b) * (a - (-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 t_1 = x / (x + (y * Math.exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))));
	double tmp;
	if (t <= 7.8e-82) {
		tmp = t_1;
	} else if (t <= 1.4e-28) {
		tmp = 1.0;
	} else if (t <= 3e-12) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((c - b) * (a - -0.8333333333333334))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))))
	tmp = 0
	if t <= 7.8e-82:
		tmp = t_1
	elif t <= 1.4e-28:
		tmp = 1.0
	elif t <= 3e-12:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((c - b) * (a - -0.8333333333333334))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(-0.6666666666666666 * Float64(Float64(c - b) / t)))))))
	tmp = 0.0
	if (t <= 7.8e-82)
		tmp = t_1;
	elseif (t <= 1.4e-28)
		tmp = 1.0;
	elseif (t <= 3e-12)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(c - b) * Float64(a - -0.8333333333333334)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (-0.6666666666666666 * ((c - b) / t))))));
	tmp = 0.0;
	if (t <= 7.8e-82)
		tmp = t_1;
	elseif (t <= 1.4e-28)
		tmp = 1.0;
	elseif (t <= 3e-12)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((c - b) * (a - -0.8333333333333334))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(-0.6666666666666666 * N[(N[(c - b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 7.8e-82], t$95$1, If[LessEqual[t, 1.4e-28], 1.0, If[LessEqual[t, 3e-12], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(c - b), $MachinePrecision] * N[(a - -0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < 7.79999999999999947e-82 or 1.3999999999999999e-28 < t < 3.0000000000000001e-12

   1. Initial program 93.1%

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

   2. Taylor expanded in z around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. *-commutative 84.4%

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

      3. distribute-rgt-neg-in 84.4%

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

      4. cancel-sign-sub-inv 84.4%

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

      5. +-commutative 84.4%

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

      6. metadata-eval 84.4%

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

      7. associate-*r/ 84.4%

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

      8. metadata-eval 84.4%

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

      9. associate-+r+ 84.4%

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

      10. neg-sub0 84.4%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(0 - \left(b - c\right)\right)}\right)}} \]

      11. associate--r- 84.4%

          \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(\left(0 - b\right) + c\right)}\right)}} \]

      12. neg-sub0 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in t around 0 79.9%

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

   if 7.79999999999999947e-82 < t < 1.3999999999999999e-28

   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 inf 45.8%

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

   3. Taylor expanded in a around 0 45.7%

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

   4. Taylor expanded in x around inf 81.8%

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

   if 3.0000000000000001e-12 < t

   1. Initial program 95.6%

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

   2. Taylor expanded in t around inf 94.7%

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

      1. mul-1-neg 94.7%

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

      2. *-commutative 94.7%

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

      3. distribute-rgt-neg-in 94.7%

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

      4. distribute-neg-in 94.7%

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

      5. metadata-eval 94.7%

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

   4. Simplified 94.7%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c - b}{t}\right)}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(-0.6666666666666666 \cdot \frac{c - b}{t}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(c - b\right) \cdot \left(a - -0.8333333333333334\right)\right)}}\\ \end{array} \]

Alternative 8: 87.9% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

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 * ((a + (((-0.6666666666666666d0) / t) + 0.8333333333333334d0)) * (c - b))))))
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 * ((a + ((-0.6666666666666666 / t) + 0.8333333333333334)) * (c - b))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.exp((2.0 * ((a + ((-0.6666666666666666 / t) + 0.8333333333333334)) * (c - b))))))

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * exp((2.0 * ((a + ((-0.6666666666666666 / t) + 0.8333333333333334)) * (c - b))))));
end

Wolfram

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

Derivation

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 z around 0 87.9%

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

   1. mul-1-neg 87.9%

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

   2. *-commutative 87.9%

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

   3. distribute-rgt-neg-in 87.9%

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

   4. cancel-sign-sub-inv 87.9%

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

   5. +-commutative 87.9%

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

   6. metadata-eval 87.9%

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

   7. associate-*r/ 87.9%

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

   8. metadata-eval 87.9%

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

   9. associate-+r+ 87.9%

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

   10. neg-sub0 87.9%

       \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(0 - \left(b - c\right)\right)}\right)}} \]

   11. associate--r- 87.9%

       \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + \left(0.8333333333333334 + \frac{-0.6666666666666666}{t}\right)\right) \cdot \color{blue}{\left(\left(0 - b\right) + c\right)}\right)}} \]

   12. neg-sub0 87.9%

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

4. Simplified 87.9%

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

5. Final simplification 87.9%

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

Alternative 9: 56.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(b - c\right) \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* -2.0 (* a b))))))))
   (if (<= b -1.4e+55)
     t_1
     (if (<= b -2.5e+19)
       1.0
       (if (<= b -3.6e-65)
         t_1
         (if (<= b 7.2e-195)
           1.0
           (if (<= b 3.1e-162)
             (/ x (+ x (- y (* 2.0 (* (- b c) (* y a))))))
             1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((-2.0 * (a * b)))));
	double tmp;
	if (b <= -1.4e+55) {
		tmp = t_1;
	} else if (b <= -2.5e+19) {
		tmp = 1.0;
	} else if (b <= -3.6e-65) {
		tmp = t_1;
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 3.1e-162) {
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * 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) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((-2.0d0) * (a * b)))))
    if (b <= (-1.4d+55)) then
        tmp = t_1
    else if (b <= (-2.5d+19)) then
        tmp = 1.0d0
    else if (b <= (-3.6d-65)) then
        tmp = t_1
    else if (b <= 7.2d-195) then
        tmp = 1.0d0
    else if (b <= 3.1d-162) then
        tmp = x / (x + (y - (2.0d0 * ((b - c) * (y * 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 t_1 = x / (x + (y * Math.exp((-2.0 * (a * b)))));
	double tmp;
	if (b <= -1.4e+55) {
		tmp = t_1;
	} else if (b <= -2.5e+19) {
		tmp = 1.0;
	} else if (b <= -3.6e-65) {
		tmp = t_1;
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 3.1e-162) {
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((-2.0 * (a * b)))))
	tmp = 0
	if b <= -1.4e+55:
		tmp = t_1
	elif b <= -2.5e+19:
		tmp = 1.0
	elif b <= -3.6e-65:
		tmp = t_1
	elif b <= 7.2e-195:
		tmp = 1.0
	elif b <= 3.1e-162:
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(a * b))))))
	tmp = 0.0
	if (b <= -1.4e+55)
		tmp = t_1;
	elseif (b <= -2.5e+19)
		tmp = 1.0;
	elseif (b <= -3.6e-65)
		tmp = t_1;
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 3.1e-162)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(Float64(b - c) * Float64(y * a))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((-2.0 * (a * b)))));
	tmp = 0.0;
	if (b <= -1.4e+55)
		tmp = t_1;
	elseif (b <= -2.5e+19)
		tmp = 1.0;
	elseif (b <= -3.6e-65)
		tmp = t_1;
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 3.1e-162)
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+55], t$95$1, If[LessEqual[b, -2.5e+19], 1.0, If[LessEqual[b, -3.6e-65], t$95$1, If[LessEqual[b, 7.2e-195], 1.0, If[LessEqual[b, 3.1e-162], N[(x / N[(x + N[(y - N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.4e55 or -2.5e19 < b < -3.5999999999999998e-65

   1. Initial program 92.5%

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

   2. Taylor expanded in a around inf 81.0%

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

   3. Taylor expanded in c around 0 82.5%

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

   if -1.4e55 < b < -2.5e19 or -3.5999999999999998e-65 < b < 7.2e-195 or 3.0999999999999999e-162 < b

   1. Initial program 95.0%

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

   2. Taylor expanded in a around inf 52.3%

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

   3. Taylor expanded in a around 0 35.4%

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

   4. Taylor expanded in x around inf 65.2%

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

   if 7.2e-195 < b < 3.0999999999999999e-162

   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 inf 51.6%

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

   3. Taylor expanded in a around 0 60.3%

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

      1. associate-*r* 68.4%

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

   5. Simplified 68.4%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -3.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(b - c\right) \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 67.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -5.6 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))))
   (if (<= t -5.6e-239)
     t_1
     (if (<= t 1.25e-242)
       (/ x (+ x (* y (- 1.0 (* 2.0 (* a (- b c)))))))
       (if (<= t 170.0) 1.0 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	double tmp;
	if (t <= -5.6e-239) {
		tmp = t_1;
	} else if (t <= 1.25e-242) {
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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 = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    if (t <= (-5.6d-239)) then
        tmp = t_1
    else if (t <= 1.25d-242) then
        tmp = x / (x + (y * (1.0d0 - (2.0d0 * (a * (b - c))))))
    else if (t <= 170.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	double tmp;
	if (t <= -5.6e-239) {
		tmp = t_1;
	} else if (t <= 1.25e-242) {
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	tmp = 0
	if t <= -5.6e-239:
		tmp = t_1
	elif t <= 1.25e-242:
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))))
	elif t <= 170.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))))
	tmp = 0.0
	if (t <= -5.6e-239)
		tmp = t_1;
	elseif (t <= 1.25e-242)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 - Float64(2.0 * Float64(a * Float64(b - c)))))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	tmp = 0.0;
	if (t <= -5.6e-239)
		tmp = t_1;
	elseif (t <= 1.25e-242)
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.6e-239], t$95$1, If[LessEqual[t, 1.25e-242], N[(x / N[(x + N[(y * N[(1.0 - N[(2.0 * N[(a * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 170.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.60000000000000025e-239 or 170 < 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 93.1%

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

      1. mul-1-neg 93.1%

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

      2. *-commutative 93.1%

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

      3. distribute-rgt-neg-in 93.1%

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

      4. distribute-neg-in 93.1%

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

      5. metadata-eval 93.1%

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

   4. Simplified 93.1%

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

   5. Taylor expanded in a around 0 85.3%

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

   if -5.60000000000000025e-239 < t < 1.25e-242

   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 42.7%

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

   3. Taylor expanded in a around 0 64.5%

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

      1. *-commutative 64.5%

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

      2. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   if 1.25e-242 < t < 170

   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 a around inf 29.6%

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

   3. Taylor expanded in a around 0 32.2%

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

   4. Taylor expanded in x around inf 62.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 11: 68.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -5.6e-239)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 2.8e-243)
     (/ x (+ x (* y (- 1.0 (* 2.0 (* a (- b c)))))))
     (if (<= t 170.0)
       1.0
       (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -5.6e-239) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 2.8e-243) {
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	}
	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-239)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 2.8d-243) then
        tmp = x / (x + (y * (1.0d0 - (2.0d0 * (a * (b - c))))))
    else if (t <= 170.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    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-239) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 2.8e-243) {
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -5.6e-239:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 2.8e-243:
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))))
	elif t <= 170.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -5.6e-239)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 2.8e-243)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 - Float64(2.0 * Float64(a * Float64(b - c)))))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -5.6e-239)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 2.8e-243)
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -5.6e-239], 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, 2.8e-243], N[(x / N[(x + N[(y * N[(1.0 - N[(2.0 * N[(a * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 170.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.60000000000000025e-239

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf 87.9%

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

   if -5.60000000000000025e-239 < t < 2.79999999999999994e-243

   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 42.7%

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

   3. Taylor expanded in a around 0 64.5%

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

      1. *-commutative 64.5%

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

      2. *-commutative 64.5%

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

   5. Simplified 64.5%

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

   if 2.79999999999999994e-243 < t < 170

   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 a around inf 29.6%

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

   3. Taylor expanded in a around 0 32.2%

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

   4. Taylor expanded in x around inf 62.0%

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

   if 170 < t

   1. Initial program 95.4%

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

   2. Taylor expanded in t around inf 95.5%

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

      1. mul-1-neg 95.5%

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

      2. *-commutative 95.5%

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

      3. distribute-rgt-neg-in 95.5%

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

      4. distribute-neg-in 95.5%

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

      5. metadata-eval 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in a around 0 85.8%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.6 \cdot 10^{-239}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 12: 71.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -4.3e-259)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 2e-169)
     (/ x (+ x (* y (exp (* 2.0 (* b (/ 0.6666666666666666 t)))))))
     (if (<= t 170.0)
       1.0
       (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.3e-259) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 2e-169) {
		tmp = x / (x + (y * exp((2.0 * (b * (0.6666666666666666 / t))))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	}
	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 <= (-4.3d-259)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 2d-169) then
        tmp = x / (x + (y * exp((2.0d0 * (b * (0.6666666666666666d0 / t))))))
    else if (t <= 170.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    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 <= -4.3e-259) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 2e-169) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * (0.6666666666666666 / t))))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -4.3e-259:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 2e-169:
		tmp = x / (x + (y * math.exp((2.0 * (b * (0.6666666666666666 / t))))))
	elif t <= 170.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -4.3e-259)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 2e-169)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(0.6666666666666666 / t)))))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -4.3e-259)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 2e-169)
		tmp = x / (x + (y * exp((2.0 * (b * (0.6666666666666666 / t))))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -4.3e-259], 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, 2e-169], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 170.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.3000000000000001e-259

   1. Initial program 92.9%

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

   2. Taylor expanded in a around inf 84.4%

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

   if -4.3000000000000001e-259 < t < 2.00000000000000004e-169

   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 b around inf 69.1%

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

      1. associate-*r/ 69.1%

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

      2. metadata-eval 69.1%

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

      3. +-commutative 69.1%

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

   4. Simplified 69.1%

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

   5. Taylor expanded in t around 0 69.2%

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

   if 2.00000000000000004e-169 < t < 170

   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 inf 33.1%

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

   3. Taylor expanded in a around 0 39.4%

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

   4. Taylor expanded in x around inf 66.3%

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

   if 170 < t

   1. Initial program 95.4%

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

   2. Taylor expanded in t around inf 95.5%

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

      1. mul-1-neg 95.5%

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

      2. *-commutative 95.5%

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

      3. distribute-rgt-neg-in 95.5%

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

      4. distribute-neg-in 95.5%

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

      5. metadata-eval 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in a around 0 85.8%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-169}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \frac{0.6666666666666666}{t}\right)}}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 13: 72.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-234}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{-0.6666666666666666 \cdot c}{t}}}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.7e-234)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 6.2e-96)
     (/ x (+ x (* y (exp (* 2.0 (/ (* -0.6666666666666666 c) t))))))
     (if (<= t 170.0)
       1.0
       (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.7e-234) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 6.2e-96) {
		tmp = x / (x + (y * exp((2.0 * ((-0.6666666666666666 * c) / t)))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	}
	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 <= (-1.7d-234)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 6.2d-96) then
        tmp = x / (x + (y * exp((2.0d0 * (((-0.6666666666666666d0) * c) / t)))))
    else if (t <= 170.0d0) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    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 <= -1.7e-234) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 6.2e-96) {
		tmp = x / (x + (y * Math.exp((2.0 * ((-0.6666666666666666 * c) / t)))));
	} else if (t <= 170.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.7e-234:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 6.2e-96:
		tmp = x / (x + (y * math.exp((2.0 * ((-0.6666666666666666 * c) / t)))))
	elif t <= 170.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.7e-234)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 6.2e-96)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(-0.6666666666666666 * c) / t))))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.7e-234)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 6.2e-96)
		tmp = x / (x + (y * exp((2.0 * ((-0.6666666666666666 * c) / t)))));
	elseif (t <= 170.0)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.7e-234], 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, 6.2e-96], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(-0.6666666666666666 * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 170.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.69999999999999993e-234

   1. Initial program 93.6%

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

   2. Taylor expanded in a around inf 87.6%

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

   if -1.69999999999999993e-234 < t < 6.1999999999999998e-96

   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 c around inf 69.7%

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

      1. cancel-sign-sub-inv 69.7%

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

      2. +-commutative 69.7%

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

      3. metadata-eval 69.7%

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

      4. associate-*r/ 69.7%

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

      5. metadata-eval 69.7%

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

      6. associate-+r+ 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in t around 0 71.0%

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

      1. associate-*r/ 71.0%

         \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{-0.6666666666666666 \cdot c}{t}}}} \]

   7. Simplified 71.0%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{-0.6666666666666666 \cdot c}{t}}}} \]

   if 6.1999999999999998e-96 < t < 170

   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 inf 39.2%

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

   3. Taylor expanded in a around 0 31.9%

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

   4. Taylor expanded in x around inf 67.7%

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

   if 170 < t

   1. Initial program 95.4%

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

   2. Taylor expanded in t around inf 95.5%

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

      1. mul-1-neg 95.5%

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

      2. *-commutative 95.5%

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

      3. distribute-rgt-neg-in 95.5%

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

      4. distribute-neg-in 95.5%

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

      5. metadata-eval 95.5%

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

   4. Simplified 95.5%

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

   5. Taylor expanded in a around 0 85.8%

      \[\leadsto \frac{x}{x + \color{blue}{y \cdot e^{-1.6666666666666667 \cdot \left(b - c\right)}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-234}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{-0.6666666666666666 \cdot c}{t}}}\\ \mathbf{elif}\;t \leq 170:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 14: 57.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(b - c\right) \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.8e+33)
   (/ x (+ x (* y (exp (* b -1.6666666666666667)))))
   (if (<= b 7.2e-195)
     1.0
     (if (<= b 4.5e-163) (/ x (+ x (- y (* 2.0 (* (- b c) (* y a)))))) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.8e+33) {
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 4.5e-163) {
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * 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 (b <= (-2.8d+33)) then
        tmp = x / (x + (y * exp((b * (-1.6666666666666667d0)))))
    else if (b <= 7.2d-195) then
        tmp = 1.0d0
    else if (b <= 4.5d-163) then
        tmp = x / (x + (y - (2.0d0 * ((b - c) * (y * 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 (b <= -2.8e+33) {
		tmp = x / (x + (y * Math.exp((b * -1.6666666666666667))));
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 4.5e-163) {
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.8e+33:
		tmp = x / (x + (y * math.exp((b * -1.6666666666666667))))
	elif b <= 7.2e-195:
		tmp = 1.0
	elif b <= 4.5e-163:
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.8e+33)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(b * -1.6666666666666667)))));
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 4.5e-163)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(Float64(b - c) * Float64(y * 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 (b <= -2.8e+33)
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 4.5e-163)
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.8e+33], N[(x / N[(x + N[(y * N[Exp[N[(b * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-195], 1.0, If[LessEqual[b, 4.5e-163], N[(x / N[(x + N[(y - N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.8000000000000001e33

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. *-commutative 70.3%

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

      3. distribute-rgt-neg-in 70.3%

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

      4. distribute-neg-in 70.3%

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

      5. metadata-eval 70.3%

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

   4. Simplified 70.3%

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

   5. Taylor expanded in a around 0 65.6%

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

   6. Taylor expanded in b around inf 70.3%

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

   if -2.8000000000000001e33 < b < 7.2e-195 or 4.4999999999999997e-163 < b

   1. Initial program 95.7%

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

   2. Taylor expanded in a around inf 56.0%

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

   3. Taylor expanded in a around 0 36.9%

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

   4. Taylor expanded in x around inf 64.7%

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

   if 7.2e-195 < b < 4.4999999999999997e-163

   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 inf 51.6%

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

   3. Taylor expanded in a around 0 60.3%

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

      1. associate-*r* 68.4%

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

   5. Simplified 68.4%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-163}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(b - c\right) \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15: 50.7% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot c\right)\right)}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4.8e-35)
   (/ x (+ x (* y (* 2.0 (* a c)))))
   (if (<= b 7.2e-195)
     1.0
     (if (<= b 1.5e-158)
       (/ x (+ x (* y (+ (* 2.0 (* c (+ a 0.8333333333333334))) 1.0))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.8e-35) {
		tmp = x / (x + (y * (2.0 * (a * c))));
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 1.5e-158) {
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	} 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 <= (-4.8d-35)) then
        tmp = x / (x + (y * (2.0d0 * (a * c))))
    else if (b <= 7.2d-195) then
        tmp = 1.0d0
    else if (b <= 1.5d-158) then
        tmp = x / (x + (y * ((2.0d0 * (c * (a + 0.8333333333333334d0))) + 1.0d0)))
    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 <= -4.8e-35) {
		tmp = x / (x + (y * (2.0 * (a * c))));
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 1.5e-158) {
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4.8e-35:
		tmp = x / (x + (y * (2.0 * (a * c))))
	elif b <= 7.2e-195:
		tmp = 1.0
	elif b <= 1.5e-158:
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4.8e-35)
		tmp = Float64(x / Float64(x + Float64(y * Float64(2.0 * Float64(a * c)))));
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 1.5e-158)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334))) + 1.0))));
	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 <= -4.8e-35)
		tmp = x / (x + (y * (2.0 * (a * c))));
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 1.5e-158)
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4.8e-35], N[(x / N[(x + N[(y * N[(2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-195], 1.0, If[LessEqual[b, 1.5e-158], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.8000000000000003e-35

   1. Initial program 91.9%

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

   2. Taylor expanded in c around inf 54.4%

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

      1. cancel-sign-sub-inv 54.4%

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

      2. +-commutative 54.4%

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

      3. metadata-eval 54.4%

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

      4. associate-*r/ 54.4%

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

      5. metadata-eval 54.4%

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

      6. associate-+r+ 54.4%

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

   4. Simplified 54.4%

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

   5. Taylor expanded in c around 0 41.7%

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

   6. Taylor expanded in t around inf 45.8%

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

   7. Taylor expanded in a around inf 48.0%

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

      1. *-commutative 48.0%

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

   9. Simplified 48.0%

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

   if -4.8000000000000003e-35 < b < 7.2e-195 or 1.5e-158 < b

   1. Initial program 95.3%

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

   2. Taylor expanded in a around inf 55.1%

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

   3. Taylor expanded in a around 0 36.9%

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

   4. Taylor expanded in x around inf 65.1%

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

   if 7.2e-195 < b < 1.5e-158

   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 75.8%

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

      1. cancel-sign-sub-inv 75.8%

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

      2. +-commutative 75.8%

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

      3. metadata-eval 75.8%

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

      4. associate-*r/ 75.8%

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

      5. metadata-eval 75.8%

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

      6. associate-+r+ 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in c around 0 67.8%

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

   6. Taylor expanded in t around inf 67.8%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot c\right)\right)}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16: 52.7% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -7.8e-65)
   (/ x (+ x (* y (- 1.0 (* 2.0 (* a (- b c)))))))
   (if (<= b 7e-195)
     1.0
     (if (<= b 1.3e-148)
       (/ x (+ x (* y (+ (* 2.0 (* c (+ a 0.8333333333333334))) 1.0))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -7.8e-65) {
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	} else if (b <= 7e-195) {
		tmp = 1.0;
	} else if (b <= 1.3e-148) {
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	} 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 <= (-7.8d-65)) then
        tmp = x / (x + (y * (1.0d0 - (2.0d0 * (a * (b - c))))))
    else if (b <= 7d-195) then
        tmp = 1.0d0
    else if (b <= 1.3d-148) then
        tmp = x / (x + (y * ((2.0d0 * (c * (a + 0.8333333333333334d0))) + 1.0d0)))
    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 <= -7.8e-65) {
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	} else if (b <= 7e-195) {
		tmp = 1.0;
	} else if (b <= 1.3e-148) {
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -7.8e-65:
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))))
	elif b <= 7e-195:
		tmp = 1.0
	elif b <= 1.3e-148:
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -7.8e-65)
		tmp = Float64(x / Float64(x + Float64(y * Float64(1.0 - Float64(2.0 * Float64(a * Float64(b - c)))))));
	elseif (b <= 7e-195)
		tmp = 1.0;
	elseif (b <= 1.3e-148)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334))) + 1.0))));
	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 <= -7.8e-65)
		tmp = x / (x + (y * (1.0 - (2.0 * (a * (b - c))))));
	elseif (b <= 7e-195)
		tmp = 1.0;
	elseif (b <= 1.3e-148)
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -7.8e-65], N[(x / N[(x + N[(y * N[(1.0 - N[(2.0 * N[(a * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-195], 1.0, If[LessEqual[b, 1.3e-148], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.8000000000000007e-65

   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 a around inf 73.1%

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

   3. Taylor expanded in a around 0 54.1%

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

      1. *-commutative 54.1%

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

      2. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   if -7.8000000000000007e-65 < b < 7.00000000000000028e-195 or 1.30000000000000004e-148 < b

   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 a around inf 53.5%

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

   3. Taylor expanded in a around 0 35.8%

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

   4. Taylor expanded in x around inf 65.7%

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

   if 7.00000000000000028e-195 < b < 1.30000000000000004e-148

   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 77.7%

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

      1. cancel-sign-sub-inv 77.7%

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

      2. +-commutative 77.7%

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

      3. metadata-eval 77.7%

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

      4. associate-*r/ 77.7%

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

      5. metadata-eval 77.7%

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

      6. associate-+r+ 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in c around 0 62.8%

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

   6. Taylor expanded in t around inf 62.8%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.8 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(1 - 2 \cdot \left(a \cdot \left(b - c\right)\right)\right)}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-148}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17: 52.3% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4.6e-65)
   (/ x (+ x (- y (* 2.0 (* a (* y (- b c)))))))
   (if (<= b 7e-195)
     1.0
     (if (<= b 2.2e-158)
       (/ x (+ x (* y (+ (* 2.0 (* c (+ a 0.8333333333333334))) 1.0))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.6e-65) {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	} else if (b <= 7e-195) {
		tmp = 1.0;
	} else if (b <= 2.2e-158) {
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	} 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 <= (-4.6d-65)) then
        tmp = x / (x + (y - (2.0d0 * (a * (y * (b - c))))))
    else if (b <= 7d-195) then
        tmp = 1.0d0
    else if (b <= 2.2d-158) then
        tmp = x / (x + (y * ((2.0d0 * (c * (a + 0.8333333333333334d0))) + 1.0d0)))
    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 <= -4.6e-65) {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	} else if (b <= 7e-195) {
		tmp = 1.0;
	} else if (b <= 2.2e-158) {
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4.6e-65:
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))))
	elif b <= 7e-195:
		tmp = 1.0
	elif b <= 2.2e-158:
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4.6e-65)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(a * Float64(y * Float64(b - c)))))));
	elseif (b <= 7e-195)
		tmp = 1.0;
	elseif (b <= 2.2e-158)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334))) + 1.0))));
	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 <= -4.6e-65)
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	elseif (b <= 7e-195)
		tmp = 1.0;
	elseif (b <= 2.2e-158)
		tmp = x / (x + (y * ((2.0 * (c * (a + 0.8333333333333334))) + 1.0)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4.6e-65], N[(x / N[(x + N[(y - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e-195], 1.0, If[LessEqual[b, 2.2e-158], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.5999999999999999e-65

   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 a around inf 73.1%

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

   3. Taylor expanded in a around 0 56.3%

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

   if -4.5999999999999999e-65 < b < 7.00000000000000028e-195 or 2.2000000000000001e-158 < b

   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 a around inf 53.8%

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

   3. Taylor expanded in a around 0 35.6%

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

   4. Taylor expanded in x around inf 65.4%

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

   if 7.00000000000000028e-195 < b < 2.2000000000000001e-158

   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 75.8%

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

      1. cancel-sign-sub-inv 75.8%

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

      2. +-commutative 75.8%

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

      3. metadata-eval 75.8%

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

      4. associate-*r/ 75.8%

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

      5. metadata-eval 75.8%

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

      6. associate-+r+ 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in c around 0 67.8%

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

   6. Taylor expanded in t around inf 67.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-158}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 18: 52.3% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(b - c\right) \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -1.6e-65)
   (/ x (+ x (- y (* 2.0 (* a (* y (- b c)))))))
   (if (<= b 7.2e-195)
     1.0
     (if (<= b 2.5e-151) (/ x (+ x (- y (* 2.0 (* (- b c) (* y a)))))) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -1.6e-65) {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 2.5e-151) {
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * 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 (b <= (-1.6d-65)) then
        tmp = x / (x + (y - (2.0d0 * (a * (y * (b - c))))))
    else if (b <= 7.2d-195) then
        tmp = 1.0d0
    else if (b <= 2.5d-151) then
        tmp = x / (x + (y - (2.0d0 * ((b - c) * (y * 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 (b <= -1.6e-65) {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	} else if (b <= 7.2e-195) {
		tmp = 1.0;
	} else if (b <= 2.5e-151) {
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -1.6e-65:
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))))
	elif b <= 7.2e-195:
		tmp = 1.0
	elif b <= 2.5e-151:
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -1.6e-65)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(a * Float64(y * Float64(b - c)))))));
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 2.5e-151)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(Float64(b - c) * Float64(y * 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 (b <= -1.6e-65)
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	elseif (b <= 7.2e-195)
		tmp = 1.0;
	elseif (b <= 2.5e-151)
		tmp = x / (x + (y - (2.0 * ((b - c) * (y * a)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -1.6e-65], N[(x / N[(x + N[(y - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-195], 1.0, If[LessEqual[b, 2.5e-151], N[(x / N[(x + N[(y - N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6e-65

   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 a around inf 73.1%

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

   3. Taylor expanded in a around 0 56.3%

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

   if -1.6e-65 < b < 7.2e-195 or 2.50000000000000002e-151 < b

   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 a around inf 53.5%

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

   3. Taylor expanded in a around 0 35.8%

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

   4. Taylor expanded in x around inf 65.7%

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

   if 7.2e-195 < b < 2.50000000000000002e-151

   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 inf 55.3%

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

   3. Taylor expanded in a around 0 55.9%

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

      1. associate-*r* 63.4%

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

   5. Simplified 63.4%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-151}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(\left(b - c\right) \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19: 51.0% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-222}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;\frac{-0.75}{c} \cdot \frac{x \cdot t}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-253}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -4.6e-222)
   1.0
   (if (<= t -8.5e-254)
     (* (/ -0.75 c) (/ (* x t) y))
     (if (<= t 1.2e-253)
       (/ x (+ x (* -1.3333333333333333 (/ c (/ t y)))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -4.6e-222) {
		tmp = 1.0;
	} else if (t <= -8.5e-254) {
		tmp = (-0.75 / c) * ((x * t) / y);
	} else if (t <= 1.2e-253) {
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))));
	} 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 (t <= (-4.6d-222)) then
        tmp = 1.0d0
    else if (t <= (-8.5d-254)) then
        tmp = ((-0.75d0) / c) * ((x * t) / y)
    else if (t <= 1.2d-253) then
        tmp = x / (x + ((-1.3333333333333333d0) * (c / (t / y))))
    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 (t <= -4.6e-222) {
		tmp = 1.0;
	} else if (t <= -8.5e-254) {
		tmp = (-0.75 / c) * ((x * t) / y);
	} else if (t <= 1.2e-253) {
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -4.6e-222:
		tmp = 1.0
	elif t <= -8.5e-254:
		tmp = (-0.75 / c) * ((x * t) / y)
	elif t <= 1.2e-253:
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -4.6e-222)
		tmp = 1.0;
	elseif (t <= -8.5e-254)
		tmp = Float64(Float64(-0.75 / c) * Float64(Float64(x * t) / y));
	elseif (t <= 1.2e-253)
		tmp = Float64(x / Float64(x + Float64(-1.3333333333333333 * Float64(c / Float64(t / y)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -4.6e-222)
		tmp = 1.0;
	elseif (t <= -8.5e-254)
		tmp = (-0.75 / c) * ((x * t) / y);
	elseif (t <= 1.2e-253)
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -4.6e-222], 1.0, If[LessEqual[t, -8.5e-254], N[(N[(-0.75 / c), $MachinePrecision] * N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-253], N[(x / N[(x + N[(-1.3333333333333333 * N[(c / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.6000000000000003e-222 or 1.20000000000000005e-253 < t

   1. Initial program 94.8%

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

   2. Taylor expanded in a around inf 61.0%

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

   3. Taylor expanded in a around 0 34.5%

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

   4. Taylor expanded in x around inf 58.1%

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

   if -4.6000000000000003e-222 < t < -8.49999999999999963e-254

   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 68.0%

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

      1. cancel-sign-sub-inv 68.0%

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

      2. +-commutative 68.0%

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

      3. metadata-eval 68.0%

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

      4. associate-*r/ 68.0%

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

      5. metadata-eval 68.0%

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

      6. associate-+r+ 68.0%

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

   4. Simplified 68.0%

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

   5. Taylor expanded in c around 0 56.9%

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

   6. Taylor expanded in t around 0 46.4%

      \[\leadsto \color{blue}{-0.75 \cdot \frac{t \cdot x}{c \cdot y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 46.4%

         \[\leadsto \color{blue}{\frac{-0.75 \cdot \left(t \cdot x\right)}{c \cdot y}} \]

      2. times-frac 79.1%

         \[\leadsto \color{blue}{\frac{-0.75}{c} \cdot \frac{t \cdot x}{y}} \]

   8. Simplified 79.1%

      \[\leadsto \color{blue}{\frac{-0.75}{c} \cdot \frac{t \cdot x}{y}} \]

   if -8.49999999999999963e-254 < t < 1.20000000000000005e-253

   1. Initial program 88.2%

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

   2. Taylor expanded in c around inf 77.2%

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

      1. cancel-sign-sub-inv 77.2%

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

      2. +-commutative 77.2%

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

      3. metadata-eval 77.2%

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

      4. associate-*r/ 77.2%

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

      5. metadata-eval 77.2%

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

      6. associate-+r+ 77.2%

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

   4. Simplified 77.2%

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

   5. Taylor expanded in c around 0 61.9%

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

   6. Taylor expanded in t around 0 62.0%

      \[\leadsto \frac{x}{x + \color{blue}{-1.3333333333333333 \cdot \frac{c \cdot y}{t}}} \]
   7. Step-by-step derivation

      1. associate-/l* 67.5%

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

   8. Simplified 67.5%

      \[\leadsto \frac{x}{x + \color{blue}{-1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-222}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-254}:\\ \;\;\;\;\frac{-0.75}{c} \cdot \frac{x \cdot t}{y}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-253}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 20: 49.6% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot c\right)\right)}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-292}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5e-35)
   (/ x (+ x (* y (* 2.0 (* a c)))))
   (if (<= b 3.7e-292)
     1.0
     (if (<= b 5e-126)
       (/ x (+ x (* -1.3333333333333333 (/ c (/ t y)))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5e-35) {
		tmp = x / (x + (y * (2.0 * (a * c))));
	} else if (b <= 3.7e-292) {
		tmp = 1.0;
	} else if (b <= 5e-126) {
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))));
	} 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 <= (-5d-35)) then
        tmp = x / (x + (y * (2.0d0 * (a * c))))
    else if (b <= 3.7d-292) then
        tmp = 1.0d0
    else if (b <= 5d-126) then
        tmp = x / (x + ((-1.3333333333333333d0) * (c / (t / y))))
    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 <= -5e-35) {
		tmp = x / (x + (y * (2.0 * (a * c))));
	} else if (b <= 3.7e-292) {
		tmp = 1.0;
	} else if (b <= 5e-126) {
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5e-35:
		tmp = x / (x + (y * (2.0 * (a * c))))
	elif b <= 3.7e-292:
		tmp = 1.0
	elif b <= 5e-126:
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5e-35)
		tmp = Float64(x / Float64(x + Float64(y * Float64(2.0 * Float64(a * c)))));
	elseif (b <= 3.7e-292)
		tmp = 1.0;
	elseif (b <= 5e-126)
		tmp = Float64(x / Float64(x + Float64(-1.3333333333333333 * Float64(c / Float64(t / y)))));
	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 <= -5e-35)
		tmp = x / (x + (y * (2.0 * (a * c))));
	elseif (b <= 3.7e-292)
		tmp = 1.0;
	elseif (b <= 5e-126)
		tmp = x / (x + (-1.3333333333333333 * (c / (t / y))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5e-35], N[(x / N[(x + N[(y * N[(2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-292], 1.0, If[LessEqual[b, 5e-126], N[(x / N[(x + N[(-1.3333333333333333 * N[(c / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.99999999999999964e-35

   1. Initial program 91.9%

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

   2. Taylor expanded in c around inf 54.4%

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

      1. cancel-sign-sub-inv 54.4%

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

      2. +-commutative 54.4%

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

      3. metadata-eval 54.4%

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

      4. associate-*r/ 54.4%

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

      5. metadata-eval 54.4%

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

      6. associate-+r+ 54.4%

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

   4. Simplified 54.4%

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

   5. Taylor expanded in c around 0 41.7%

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

   6. Taylor expanded in t around inf 45.8%

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

   7. Taylor expanded in a around inf 48.0%

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

      1. *-commutative 48.0%

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

   9. Simplified 48.0%

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

   if -4.99999999999999964e-35 < b < 3.69999999999999997e-292 or 5.00000000000000006e-126 < b

   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 a around inf 58.2%

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

   3. Taylor expanded in a around 0 38.8%

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

   4. Taylor expanded in x around inf 68.2%

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

   if 3.69999999999999997e-292 < b < 5.00000000000000006e-126

   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 66.7%

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

      1. cancel-sign-sub-inv 66.7%

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

      2. +-commutative 66.7%

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

      3. metadata-eval 66.7%

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

      4. associate-*r/ 66.7%

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

      5. metadata-eval 66.7%

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

      6. associate-+r+ 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in c around 0 46.8%

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

   6. Taylor expanded in t around 0 48.2%

      \[\leadsto \frac{x}{x + \color{blue}{-1.3333333333333333 \cdot \frac{c \cdot y}{t}}} \]
   7. Step-by-step derivation

      1. associate-/l* 51.1%

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

   8. Simplified 51.1%

      \[\leadsto \frac{x}{x + \color{blue}{-1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot c\right)\right)}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-292}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{x + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 21: 50.9% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.7 \cdot 10^{-233}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-300}:\\ \;\;\;\;\frac{-0.75}{c} \cdot \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -7.7e-233)
   1.0
   (if (<= t 2.3e-300) (* (/ -0.75 c) (/ (* x t) y)) 1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -7.7e-233) {
		tmp = 1.0;
	} else if (t <= 2.3e-300) {
		tmp = (-0.75 / c) * ((x * t) / y);
	} 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 (t <= (-7.7d-233)) then
        tmp = 1.0d0
    else if (t <= 2.3d-300) then
        tmp = ((-0.75d0) / c) * ((x * t) / y)
    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 (t <= -7.7e-233) {
		tmp = 1.0;
	} else if (t <= 2.3e-300) {
		tmp = (-0.75 / c) * ((x * t) / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -7.7e-233:
		tmp = 1.0
	elif t <= 2.3e-300:
		tmp = (-0.75 / c) * ((x * t) / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -7.7e-233)
		tmp = 1.0;
	elseif (t <= 2.3e-300)
		tmp = Float64(Float64(-0.75 / c) * Float64(Float64(x * t) / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -7.7e-233)
		tmp = 1.0;
	elseif (t <= 2.3e-300)
		tmp = (-0.75 / c) * ((x * t) / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -7.7e-233], 1.0, If[LessEqual[t, 2.3e-300], N[(N[(-0.75 / c), $MachinePrecision] * N[(N[(x * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -7.70000000000000007e-233 or 2.30000000000000001e-300 < t

   1. Initial program 95.0%

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

   2. Taylor expanded in a around inf 60.1%

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

   3. Taylor expanded in a around 0 34.8%

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

   4. Taylor expanded in x around inf 57.7%

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

   if -7.70000000000000007e-233 < t < 2.30000000000000001e-300

   1. Initial program 89.5%

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

   2. Taylor expanded in c around inf 64.4%

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

      1. cancel-sign-sub-inv 64.4%

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

      2. +-commutative 64.4%

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

      3. metadata-eval 64.4%

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

      4. associate-*r/ 64.4%

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

      5. metadata-eval 64.4%

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

      6. associate-+r+ 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in c around 0 59.3%

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

   6. Taylor expanded in t around 0 49.5%

      \[\leadsto \color{blue}{-0.75 \cdot \frac{t \cdot x}{c \cdot y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 49.5%

         \[\leadsto \color{blue}{\frac{-0.75 \cdot \left(t \cdot x\right)}{c \cdot y}} \]

      2. times-frac 70.0%

         \[\leadsto \color{blue}{\frac{-0.75}{c} \cdot \frac{t \cdot x}{y}} \]

   8. Simplified 70.0%

      \[\leadsto \color{blue}{\frac{-0.75}{c} \cdot \frac{t \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.7 \cdot 10^{-233}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-300}:\\ \;\;\;\;\frac{-0.75}{c} \cdot \frac{x \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 22: 51.9% 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 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 a around inf 59.6%

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

3. Taylor expanded in a around 0 34.9%

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

4. Taylor expanded in x around inf 55.2%

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

5. Final simplification 55.2%

   \[\leadsto 1 \]

Developer target: 95.9% 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 2023318 
(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)))))))))))