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

Percentage Accurate: 94.2% → 96.7%

Time: 25.4s

Alternatives: 20

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.2% 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: 96.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{a + t}\\ \mathbf{if}\;\frac{z \cdot t_1}{t} + \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right) \cdot \left(c - b\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{t_1}} + \left(b - c\right) \cdot \left(\left(\frac{\frac{2}{t}}{3} - 0.8333333333333334\right) - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (sqrt (+ a t))))
   (if (<=
        (+
         (/ (* z t_1) t)
         (* (- (+ a 0.8333333333333334) (/ 2.0 (* t 3.0))) (- c b)))
        INFINITY)
     (/
      x
      (+
       x
       (*
        y
        (pow
         (exp 2.0)
         (+
          (/ z (/ t t_1))
          (* (- b c) (- (- (/ (/ 2.0 t) 3.0) 0.8333333333333334) a)))))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = sqrt((a + t));
	double tmp;
	if ((((z * t_1) / t) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b))) <= ((double) INFINITY)) {
		tmp = x / (x + (y * pow(exp(2.0), ((z / (t / t_1)) + ((b - c) * ((((2.0 / t) / 3.0) - 0.8333333333333334) - a))))));
	} else {
		tmp = 1.0;
	}
	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));
	double tmp;
	if ((((z * t_1) / t) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b))) <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.pow(Math.exp(2.0), ((z / (t / t_1)) + ((b - c) * ((((2.0 / t) / 3.0) - 0.8333333333333334) - a))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = math.sqrt((a + t))
	tmp = 0
	if (((z * t_1) / t) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b))) <= math.inf:
		tmp = x / (x + (y * math.pow(math.exp(2.0), ((z / (t / t_1)) + ((b - c) * ((((2.0 / t) / 3.0) - 0.8333333333333334) - a))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = sqrt(Float64(a + t))
	tmp = 0.0
	if (Float64(Float64(Float64(z * t_1) / t) + Float64(Float64(Float64(a + 0.8333333333333334) - Float64(2.0 / Float64(t * 3.0))) * Float64(c - b))) <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * (exp(2.0) ^ Float64(Float64(z / Float64(t / t_1)) + Float64(Float64(b - c) * Float64(Float64(Float64(Float64(2.0 / t) / 3.0) - 0.8333333333333334) - a)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = sqrt((a + t));
	tmp = 0.0;
	if ((((z * t_1) / t) + (((a + 0.8333333333333334) - (2.0 / (t * 3.0))) * (c - b))) <= Inf)
		tmp = x / (x + (y * (exp(2.0) ^ ((z / (t / t_1)) + ((b - c) * ((((2.0 / t) / 3.0) - 0.8333333333333334) - a))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(N[(z * t$95$1), $MachinePrecision] / t), $MachinePrecision] + N[(N[(N[(a + 0.8333333333333334), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x / N[(x + N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(z / N[(t / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(N[(N[(2.0 / t), $MachinePrecision] / 3.0), $MachinePrecision] - 0.8333333333333334), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

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. associate--l+ 99.2%

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

      4. metadata-eval 99.2%

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

      5. associate-/r* 99.2%

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

   3. Simplified 99.2%

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

   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 38.2%

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

   3. Taylor expanded in a around 0 55.9%

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

      1. +-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in x around inf 82.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{a + t}}{t} + \left(\left(a + 0.8333333333333334\right) - \frac{2}{t \cdot 3}\right) \cdot \left(c - b\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{\sqrt{a + t}}} + \left(b - c\right) \cdot \left(\left(\frac{\frac{2}{t}}{3} - 0.8333333333333334\right) - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2: 97.3% accurate, 0.4× speedup

Math

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

FPCore

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

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / fma(y, (exp(2.0) ^ fma(Float64(Float64(a + 0.8333333333333334) + Float64(-0.6666666666666666 / t)), Float64(c - b), Float64(Float64(z / t) * sqrt(Float64(a + 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[(N[(a + 0.8333333333333334), $MachinePrecision] + N[(-0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision] * N[(c - b), $MachinePrecision] + N[(N[(z / t), $MachinePrecision] * N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.2%

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

3. Simplified 98.1%

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

4. Final simplification 98.1%

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

Alternative 3: 96.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{a + t}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ a t))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a 0.8333333333333334))))))
   (if (<= t_1 INFINITY) (/ x (+ x (* y (exp (* 2.0 t_1))))) 1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((a + t))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * t_1))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

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((a + t))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.exp((2.0 * t_1))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((z * math.sqrt((a + t))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * t_1))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(a + t))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + 0.8333333333333334))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * t_1)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((z * sqrt((a + t))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + 0.8333333333333334), $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], 1.0]]

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 38.2%

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

   3. Taylor expanded in a around 0 55.9%

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

      1. +-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in x around inf 82.4%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{a + t}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{a + t}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 90.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -5e+39)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 4.2e-238)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (- (* z (sqrt a)) (* -0.6666666666666666 (- b c))) t))))))
     (if (<= t 1.1e+116)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (+
             (* z (sqrt (/ 1.0 t)))
             (* (+ (/ -0.6666666666666666 t) 0.8333333333333334) (- c b))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (+ a 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 <= -5e+39) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 4.2e-238) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 1.1e+116) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + 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 <= (-5d+39)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 4.2d-238) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) - ((-0.6666666666666666d0) * (b - c))) / t)))))
    else if (t <= 1.1d+116) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) + ((((-0.6666666666666666d0) / t) + 0.8333333333333334d0) * (c - b)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + 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 <= -5e+39) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 4.2e-238) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	} else if (t <= 1.1e+116) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -5e+39:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 4.2e-238:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))))
	elif t <= 1.1e+116:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -5e+39)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 4.2e-238)
		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 <= 1.1e+116)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) + Float64(Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334) * Float64(c - b))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 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 <= -5e+39)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 4.2e-238)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) - (-0.6666666666666666 * (b - c))) / t)))));
	elseif (t <= 1.1e+116)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -5e+39], 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, 4.2e-238], 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, 1.1e+116], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision] * 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 + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.00000000000000015e39

   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 100.0%

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

   if -5.00000000000000015e39 < t < 4.2000000000000002e-238

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0 96.9%

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

   if 4.2000000000000002e-238 < t < 1.1e116

   1. Initial program 98.1%

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

   2. Taylor expanded in a around 0 90.7%

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

      1. *-commutative 90.7%

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

      2. *-commutative 90.7%

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

      3. cancel-sign-sub-inv 90.7%

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

      4. metadata-eval 90.7%

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

      5. associate-*r/ 90.7%

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

      6. metadata-eval 90.7%

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

   4. Simplified 90.7%

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

   if 1.1e116 < 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 t around inf 93.5%

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

      1. +-commutative 93.5%

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

      2. *-commutative 93.5%

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

      3. associate-*r* 93.5%

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

      4. neg-mul-1 93.5%

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

      5. neg-sub0 93.5%

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

      6. associate--r- 93.5%

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

      7. neg-sub0 93.5%

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

      8. +-commutative 93.5%

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

      9. sub-neg 93.5%

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

   4. Simplified 93.5%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+39}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} - -0.6666666666666666 \cdot \left(b - c\right)}{t}}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+116}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 5: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.9e+31)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 4.4e-159)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
     (if (<= t 2.4e+58)
       (/ x (+ x (* y (exp (* 2.0 (* z (sqrt (/ 1.0 t))))))))
       (/ x (+ x (* y (exp (* 2.0 (* (+ a 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 <= -1.9e+31) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 4.4e-159) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 2.4e+58) {
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((a + 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 <= (-1.9d+31)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 4.4d-159) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 2.4d+58) then
        tmp = x / (x + (y * exp((2.0d0 * (z * sqrt((1.0d0 / t)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((a + 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 <= -1.9e+31) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 4.4e-159) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 2.4e+58) {
		tmp = x / (x + (y * Math.exp((2.0 * (z * Math.sqrt((1.0 / t)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.9e+31:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 4.4e-159:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 2.4e+58:
		tmp = x / (x + (y * math.exp((2.0 * (z * math.sqrt((1.0 / t)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.9e+31)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 4.4e-159)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	elseif (t <= 2.4e+58)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(z * sqrt(Float64(1.0 / t))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 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 <= -1.9e+31)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 4.4e-159)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 2.4e+58)
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.9e+31], 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, 4.4e-159], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+58], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9000000000000001e31

   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 100.0%

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

   if -1.9000000000000001e31 < t < 4.4e-159

   1. Initial program 88.8%

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

   2. Taylor expanded in t around 0 93.4%

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

   if 4.4e-159 < t < 2.4e58

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 88.3%

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

      1. *-commutative 88.3%

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

      2. *-commutative 88.3%

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

      3. cancel-sign-sub-inv 88.3%

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

      4. metadata-eval 88.3%

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

      5. associate-*r/ 88.3%

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

      6. metadata-eval 88.3%

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

   4. Simplified 88.3%

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

   5. Taylor expanded in z around inf 75.3%

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

   if 2.4e58 < t

   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 t around inf 92.4%

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

      1. +-commutative 92.4%

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

      2. *-commutative 92.4%

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

      3. associate-*r* 92.4%

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

      4. neg-mul-1 92.4%

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

      5. neg-sub0 92.4%

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

      6. associate--r- 92.4%

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

      7. neg-sub0 92.4%

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

      8. +-commutative 92.4%

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

      9. sub-neg 92.4%

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

   4. Simplified 92.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 6: 77.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))))
   (if (<= t -3.6e-234)
     t_1
     (if (<= t 4.2e-159)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))
       (if (<= t 4.8e+58)
         (/ x (+ x (* y (exp (* 2.0 (* z (sqrt (/ 1.0 t))))))))
         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((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	double tmp;
	if (t <= -3.6e-234) {
		tmp = t_1;
	} else if (t <= 4.2e-159) {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else if (t <= 4.8e+58) {
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	} 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((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    if (t <= (-3.6d-234)) then
        tmp = t_1
    else if (t <= 4.2d-159) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    else if (t <= 4.8d+58) then
        tmp = x / (x + (y * exp((2.0d0 * (z * sqrt((1.0d0 / t)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	double tmp;
	if (t <= -3.6e-234) {
		tmp = t_1;
	} else if (t <= 4.2e-159) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	} else if (t <= 4.8e+58) {
		tmp = x / (x + (y * Math.exp((2.0 * (z * Math.sqrt((1.0 / t)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	tmp = 0
	if t <= -3.6e-234:
		tmp = t_1
	elif t <= 4.2e-159:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	elif t <= 4.8e+58:
		tmp = x / (x + (y * math.exp((2.0 * (z * math.sqrt((1.0 / t)))))))
	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(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))))
	tmp = 0.0
	if (t <= -3.6e-234)
		tmp = t_1;
	elseif (t <= 4.2e-159)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))));
	elseif (t <= 4.8e+58)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(z * sqrt(Float64(1.0 / t))))))));
	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((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	tmp = 0.0;
	if (t <= -3.6e-234)
		tmp = t_1;
	elseif (t <= 4.2e-159)
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	elseif (t <= 4.8e+58)
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	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[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.6e-234], t$95$1, If[LessEqual[t, 4.2e-159], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e+58], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999998e-234 or 4.8e58 < 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 t around inf 89.4%

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

      1. +-commutative 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-*r* 89.4%

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

      4. neg-mul-1 89.4%

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

      5. neg-sub0 89.4%

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

      6. associate--r- 89.4%

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

      7. neg-sub0 89.4%

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

      8. +-commutative 89.4%

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

      9. sub-neg 89.4%

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

   4. Simplified 89.4%

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

   if -3.5999999999999998e-234 < t < 4.1999999999999998e-159

   1. Initial program 87.7%

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

   2. Taylor expanded in b around inf 71.1%

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

      1. associate-*r/ 71.1%

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

      2. metadata-eval 71.1%

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

      3. +-commutative 71.1%

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

   4. Simplified 71.1%

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

   if 4.1999999999999998e-159 < t < 4.8e58

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 88.3%

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

      1. *-commutative 88.3%

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

      2. *-commutative 88.3%

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

      3. cancel-sign-sub-inv 88.3%

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

      4. metadata-eval 88.3%

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

      5. associate-*r/ 88.3%

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

      6. metadata-eval 88.3%

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

   4. Simplified 88.3%

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

   5. Taylor expanded in z around inf 75.3%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-234}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-159}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 7: 58.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ t_2 := \frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{if}\;c \leq -1.12 \cdot 10^{+256}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-136}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 115000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* -2.0 (* a b)))))))
        (t_2 (/ x (* y (exp (* -1.3333333333333333 (/ c t)))))))
   (if (<= c -1.12e+256)
     1.0
     (if (<= c -2.3e+234)
       t_2
       (if (<= c -5.5e+157)
         1.0
         (if (<= c -1.36e+119)
           t_2
           (if (<= c -5.5e-136)
             1.0
             (if (<= c 1.85e-120)
               t_1
               (if (<= c 1.1e-75)
                 1.0
                 (if (<= c 115000000.0)
                   t_1
                   (/ x (+ x (* y (exp (* 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 * (a * b)))));
	double t_2 = x / (y * exp((-1.3333333333333333 * (c / t))));
	double tmp;
	if (c <= -1.12e+256) {
		tmp = 1.0;
	} else if (c <= -2.3e+234) {
		tmp = t_2;
	} else if (c <= -5.5e+157) {
		tmp = 1.0;
	} else if (c <= -1.36e+119) {
		tmp = t_2;
	} else if (c <= -5.5e-136) {
		tmp = 1.0;
	} else if (c <= 1.85e-120) {
		tmp = t_1;
	} else if (c <= 1.1e-75) {
		tmp = 1.0;
	} else if (c <= 115000000.0) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((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) :: t_2
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((-2.0d0) * (a * b)))))
    t_2 = x / (y * exp(((-1.3333333333333333d0) * (c / t))))
    if (c <= (-1.12d+256)) then
        tmp = 1.0d0
    else if (c <= (-2.3d+234)) then
        tmp = t_2
    else if (c <= (-5.5d+157)) then
        tmp = 1.0d0
    else if (c <= (-1.36d+119)) then
        tmp = t_2
    else if (c <= (-5.5d-136)) then
        tmp = 1.0d0
    else if (c <= 1.85d-120) then
        tmp = t_1
    else if (c <= 1.1d-75) then
        tmp = 1.0d0
    else if (c <= 115000000.0d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((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 * (a * b)))));
	double t_2 = x / (y * Math.exp((-1.3333333333333333 * (c / t))));
	double tmp;
	if (c <= -1.12e+256) {
		tmp = 1.0;
	} else if (c <= -2.3e+234) {
		tmp = t_2;
	} else if (c <= -5.5e+157) {
		tmp = 1.0;
	} else if (c <= -1.36e+119) {
		tmp = t_2;
	} else if (c <= -5.5e-136) {
		tmp = 1.0;
	} else if (c <= 1.85e-120) {
		tmp = t_1;
	} else if (c <= 1.1e-75) {
		tmp = 1.0;
	} else if (c <= 115000000.0) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((-2.0 * (a * b)))))
	t_2 = x / (y * math.exp((-1.3333333333333333 * (c / t))))
	tmp = 0
	if c <= -1.12e+256:
		tmp = 1.0
	elif c <= -2.3e+234:
		tmp = t_2
	elif c <= -5.5e+157:
		tmp = 1.0
	elif c <= -1.36e+119:
		tmp = t_2
	elif c <= -5.5e-136:
		tmp = 1.0
	elif c <= 1.85e-120:
		tmp = t_1
	elif c <= 1.1e-75:
		tmp = 1.0
	elif c <= 115000000.0:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((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(a * b))))))
	t_2 = Float64(x / Float64(y * exp(Float64(-1.3333333333333333 * Float64(c / t)))))
	tmp = 0.0
	if (c <= -1.12e+256)
		tmp = 1.0;
	elseif (c <= -2.3e+234)
		tmp = t_2;
	elseif (c <= -5.5e+157)
		tmp = 1.0;
	elseif (c <= -1.36e+119)
		tmp = t_2;
	elseif (c <= -5.5e-136)
		tmp = 1.0;
	elseif (c <= 1.85e-120)
		tmp = t_1;
	elseif (c <= 1.1e-75)
		tmp = 1.0;
	elseif (c <= 115000000.0)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(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 * (a * b)))));
	t_2 = x / (y * exp((-1.3333333333333333 * (c / t))));
	tmp = 0.0;
	if (c <= -1.12e+256)
		tmp = 1.0;
	elseif (c <= -2.3e+234)
		tmp = t_2;
	elseif (c <= -5.5e+157)
		tmp = 1.0;
	elseif (c <= -1.36e+119)
		tmp = t_2;
	elseif (c <= -5.5e-136)
		tmp = 1.0;
	elseif (c <= 1.85e-120)
		tmp = t_1;
	elseif (c <= 1.1e-75)
		tmp = 1.0;
	elseif (c <= 115000000.0)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((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[(a * b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[Exp[N[(-1.3333333333333333 * N[(c / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.12e+256], 1.0, If[LessEqual[c, -2.3e+234], t$95$2, If[LessEqual[c, -5.5e+157], 1.0, If[LessEqual[c, -1.36e+119], t$95$2, If[LessEqual[c, -5.5e-136], 1.0, If[LessEqual[c, 1.85e-120], t$95$1, If[LessEqual[c, 1.1e-75], 1.0, If[LessEqual[c, 115000000.0], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.12000000000000005e256 or -2.3000000000000001e234 < c < -5.5000000000000003e157 or -1.35999999999999995e119 < c < -5.4999999999999999e-136 or 1.85e-120 < c < 1.10000000000000003e-75

   1. Initial program 97.6%

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

   2. Taylor expanded in a around inf 54.7%

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

   3. Taylor expanded in a around 0 44.3%

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

      1. +-commutative 44.3%

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

   5. Simplified 44.3%

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

   6. Taylor expanded in x around inf 70.9%

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

   if -1.12000000000000005e256 < c < -2.3000000000000001e234 or -5.5000000000000003e157 < c < -1.35999999999999995e119

   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 c around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 88.0%

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

   6. Taylor expanded in x around 0 81.9%

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

   if -5.4999999999999999e-136 < c < 1.85e-120 or 1.10000000000000003e-75 < c < 1.15e8

   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 66.1%

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

   3. Taylor expanded in c around 0 67.1%

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

   if 1.15e8 < c

   1. Initial program 88.8%

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

   2. Taylor expanded in t around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. *-commutative 73.4%

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

      3. associate-*r* 73.4%

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

      4. neg-mul-1 73.4%

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

      5. neg-sub0 73.4%

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

      6. associate--r- 73.4%

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

      7. neg-sub0 73.4%

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

      8. +-commutative 73.4%

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

      9. sub-neg 73.4%

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

   4. Simplified 73.4%

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

   5. Taylor expanded in a around 0 67.2%

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

   6. Taylor expanded in c around inf 67.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{+256}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-136}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.85 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 115000000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(a \cdot b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 8: 52.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b - c\right)\\ t_2 := \frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{if}\;c \leq -3.7 \cdot 10^{+253}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-308}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-175}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(t_1 \cdot t_1\right)\right)}\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (- b c)))
        (t_2 (/ x (* y (exp (* -1.3333333333333333 (/ c t)))))))
   (if (<= c -3.7e+253)
     1.0
     (if (<= c -2.3e+234)
       t_2
       (if (<= c -5.5e+157)
         1.0
         (if (<= c -1.36e+119)
           t_2
           (if (<= c 7.8e-308)
             1.0
             (if (<= c 1.15e-175)
               (/ x (- x (* y (- -1.0 (* 2.0 (* t_1 t_1))))))
               (if (<= c 1.1e-75)
                 1.0
                 (/ x (* y (exp (* 1.6666666666666667 (- c b))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b - c);
	double t_2 = x / (y * exp((-1.3333333333333333 * (c / t))));
	double tmp;
	if (c <= -3.7e+253) {
		tmp = 1.0;
	} else if (c <= -2.3e+234) {
		tmp = t_2;
	} else if (c <= -5.5e+157) {
		tmp = 1.0;
	} else if (c <= -1.36e+119) {
		tmp = t_2;
	} else if (c <= 7.8e-308) {
		tmp = 1.0;
	} else if (c <= 1.15e-175) {
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	} else if (c <= 1.1e-75) {
		tmp = 1.0;
	} else {
		tmp = x / (y * exp((1.6666666666666667 * (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) :: t_2
    real(8) :: tmp
    t_1 = a * (b - c)
    t_2 = x / (y * exp(((-1.3333333333333333d0) * (c / t))))
    if (c <= (-3.7d+253)) then
        tmp = 1.0d0
    else if (c <= (-2.3d+234)) then
        tmp = t_2
    else if (c <= (-5.5d+157)) then
        tmp = 1.0d0
    else if (c <= (-1.36d+119)) then
        tmp = t_2
    else if (c <= 7.8d-308) then
        tmp = 1.0d0
    else if (c <= 1.15d-175) then
        tmp = x / (x - (y * ((-1.0d0) - (2.0d0 * (t_1 * t_1)))))
    else if (c <= 1.1d-75) then
        tmp = 1.0d0
    else
        tmp = x / (y * exp((1.6666666666666667d0 * (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 = a * (b - c);
	double t_2 = x / (y * Math.exp((-1.3333333333333333 * (c / t))));
	double tmp;
	if (c <= -3.7e+253) {
		tmp = 1.0;
	} else if (c <= -2.3e+234) {
		tmp = t_2;
	} else if (c <= -5.5e+157) {
		tmp = 1.0;
	} else if (c <= -1.36e+119) {
		tmp = t_2;
	} else if (c <= 7.8e-308) {
		tmp = 1.0;
	} else if (c <= 1.15e-175) {
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	} else if (c <= 1.1e-75) {
		tmp = 1.0;
	} else {
		tmp = x / (y * Math.exp((1.6666666666666667 * (c - b))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b - c)
	t_2 = x / (y * math.exp((-1.3333333333333333 * (c / t))))
	tmp = 0
	if c <= -3.7e+253:
		tmp = 1.0
	elif c <= -2.3e+234:
		tmp = t_2
	elif c <= -5.5e+157:
		tmp = 1.0
	elif c <= -1.36e+119:
		tmp = t_2
	elif c <= 7.8e-308:
		tmp = 1.0
	elif c <= 1.15e-175:
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))))
	elif c <= 1.1e-75:
		tmp = 1.0
	else:
		tmp = x / (y * math.exp((1.6666666666666667 * (c - b))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b - c))
	t_2 = Float64(x / Float64(y * exp(Float64(-1.3333333333333333 * Float64(c / t)))))
	tmp = 0.0
	if (c <= -3.7e+253)
		tmp = 1.0;
	elseif (c <= -2.3e+234)
		tmp = t_2;
	elseif (c <= -5.5e+157)
		tmp = 1.0;
	elseif (c <= -1.36e+119)
		tmp = t_2;
	elseif (c <= 7.8e-308)
		tmp = 1.0;
	elseif (c <= 1.15e-175)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(2.0 * Float64(t_1 * t_1))))));
	elseif (c <= 1.1e-75)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * exp(Float64(1.6666666666666667 * Float64(c - b)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b - c);
	t_2 = x / (y * exp((-1.3333333333333333 * (c / t))));
	tmp = 0.0;
	if (c <= -3.7e+253)
		tmp = 1.0;
	elseif (c <= -2.3e+234)
		tmp = t_2;
	elseif (c <= -5.5e+157)
		tmp = 1.0;
	elseif (c <= -1.36e+119)
		tmp = t_2;
	elseif (c <= 7.8e-308)
		tmp = 1.0;
	elseif (c <= 1.15e-175)
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	elseif (c <= 1.1e-75)
		tmp = 1.0;
	else
		tmp = x / (y * exp((1.6666666666666667 * (c - b))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b - c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[Exp[N[(-1.3333333333333333 * N[(c / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.7e+253], 1.0, If[LessEqual[c, -2.3e+234], t$95$2, If[LessEqual[c, -5.5e+157], 1.0, If[LessEqual[c, -1.36e+119], t$95$2, If[LessEqual[c, 7.8e-308], 1.0, If[LessEqual[c, 1.15e-175], N[(x / N[(x - N[(y * N[(-1.0 - N[(2.0 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.1e-75], 1.0, N[(x / N[(y * N[Exp[N[(1.6666666666666667 * N[(c - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -3.70000000000000029e253 or -2.3000000000000001e234 < c < -5.5000000000000003e157 or -1.35999999999999995e119 < c < 7.7999999999999999e-308 or 1.15e-175 < c < 1.10000000000000003e-75

   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 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 41.7%

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

      1. +-commutative 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in x around inf 66.4%

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

   if -3.70000000000000029e253 < c < -2.3000000000000001e234 or -5.5000000000000003e157 < c < -1.35999999999999995e119

   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 c around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 88.0%

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

   6. Taylor expanded in x around 0 81.9%

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

   if 7.7999999999999999e-308 < c < 1.15e-175

   1. Initial program 96.9%

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

   2. Taylor expanded in a around inf 63.7%

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

   3. Taylor expanded in a around 0 54.3%

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

      1. distribute-lft-out 54.3%

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

      2. unpow2 54.3%

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

      3. unpow2 54.3%

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

      4. swap-sqr 54.4%

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

      5. unpow1 54.4%

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

      6. pow-plus 54.4%

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

      7. metadata-eval 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in a around inf 54.3%

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

      1. unpow2 54.3%

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

      2. unpow2 54.3%

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

      3. swap-sqr 54.4%

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

      4. unpow2 54.4%

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

   8. Simplified 54.4%

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

      1. unpow2 54.4%

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

   10. Applied egg-rr 54.4%

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

   if 1.10000000000000003e-75 < c

   1. Initial program 91.1%

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

   2. Taylor expanded in t around inf 74.0%

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

      1. +-commutative 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-*r* 74.0%

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

      4. neg-mul-1 74.0%

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

      5. neg-sub0 74.0%

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

      6. associate--r- 74.0%

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

      7. neg-sub0 74.0%

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

      8. +-commutative 74.0%

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

      9. sub-neg 74.0%

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

   4. Simplified 74.0%

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

   5. Taylor expanded in a around 0 67.8%

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

   6. Taylor expanded in x around 0 60.1%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+253}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+157}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{-308}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-175}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(\left(a \cdot \left(b - c\right)\right) \cdot \left(a \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 1.1 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}\\ \end{array} \]

Alternative 9: 54.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b - c\right)\\ t_2 := \frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+251}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+157}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{+119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-307}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-175}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(t_1 \cdot t_1\right)\right)}\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (- b c)))
        (t_2 (/ x (* y (exp (* -1.3333333333333333 (/ c t)))))))
   (if (<= c -1.15e+251)
     1.0
     (if (<= c -2.3e+234)
       t_2
       (if (<= c -6e+157)
         1.0
         (if (<= c -1.36e+119)
           t_2
           (if (<= c 4.6e-307)
             1.0
             (if (<= c 1.08e-175)
               (/ x (- x (* y (- -1.0 (* 2.0 (* t_1 t_1))))))
               (if (<= c 9.8e-76)
                 1.0
                 (/ x (+ x (* y (exp (* c 1.6666666666666667))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b - c);
	double t_2 = x / (y * exp((-1.3333333333333333 * (c / t))));
	double tmp;
	if (c <= -1.15e+251) {
		tmp = 1.0;
	} else if (c <= -2.3e+234) {
		tmp = t_2;
	} else if (c <= -6e+157) {
		tmp = 1.0;
	} else if (c <= -1.36e+119) {
		tmp = t_2;
	} else if (c <= 4.6e-307) {
		tmp = 1.0;
	} else if (c <= 1.08e-175) {
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	} else if (c <= 9.8e-76) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((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) :: t_2
    real(8) :: tmp
    t_1 = a * (b - c)
    t_2 = x / (y * exp(((-1.3333333333333333d0) * (c / t))))
    if (c <= (-1.15d+251)) then
        tmp = 1.0d0
    else if (c <= (-2.3d+234)) then
        tmp = t_2
    else if (c <= (-6d+157)) then
        tmp = 1.0d0
    else if (c <= (-1.36d+119)) then
        tmp = t_2
    else if (c <= 4.6d-307) then
        tmp = 1.0d0
    else if (c <= 1.08d-175) then
        tmp = x / (x - (y * ((-1.0d0) - (2.0d0 * (t_1 * t_1)))))
    else if (c <= 9.8d-76) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((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 = a * (b - c);
	double t_2 = x / (y * Math.exp((-1.3333333333333333 * (c / t))));
	double tmp;
	if (c <= -1.15e+251) {
		tmp = 1.0;
	} else if (c <= -2.3e+234) {
		tmp = t_2;
	} else if (c <= -6e+157) {
		tmp = 1.0;
	} else if (c <= -1.36e+119) {
		tmp = t_2;
	} else if (c <= 4.6e-307) {
		tmp = 1.0;
	} else if (c <= 1.08e-175) {
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	} else if (c <= 9.8e-76) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b - c)
	t_2 = x / (y * math.exp((-1.3333333333333333 * (c / t))))
	tmp = 0
	if c <= -1.15e+251:
		tmp = 1.0
	elif c <= -2.3e+234:
		tmp = t_2
	elif c <= -6e+157:
		tmp = 1.0
	elif c <= -1.36e+119:
		tmp = t_2
	elif c <= 4.6e-307:
		tmp = 1.0
	elif c <= 1.08e-175:
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))))
	elif c <= 9.8e-76:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b - c))
	t_2 = Float64(x / Float64(y * exp(Float64(-1.3333333333333333 * Float64(c / t)))))
	tmp = 0.0
	if (c <= -1.15e+251)
		tmp = 1.0;
	elseif (c <= -2.3e+234)
		tmp = t_2;
	elseif (c <= -6e+157)
		tmp = 1.0;
	elseif (c <= -1.36e+119)
		tmp = t_2;
	elseif (c <= 4.6e-307)
		tmp = 1.0;
	elseif (c <= 1.08e-175)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(2.0 * Float64(t_1 * t_1))))));
	elseif (c <= 9.8e-76)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b - c);
	t_2 = x / (y * exp((-1.3333333333333333 * (c / t))));
	tmp = 0.0;
	if (c <= -1.15e+251)
		tmp = 1.0;
	elseif (c <= -2.3e+234)
		tmp = t_2;
	elseif (c <= -6e+157)
		tmp = 1.0;
	elseif (c <= -1.36e+119)
		tmp = t_2;
	elseif (c <= 4.6e-307)
		tmp = 1.0;
	elseif (c <= 1.08e-175)
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	elseif (c <= 9.8e-76)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b - c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[Exp[N[(-1.3333333333333333 * N[(c / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+251], 1.0, If[LessEqual[c, -2.3e+234], t$95$2, If[LessEqual[c, -6e+157], 1.0, If[LessEqual[c, -1.36e+119], t$95$2, If[LessEqual[c, 4.6e-307], 1.0, If[LessEqual[c, 1.08e-175], N[(x / N[(x - N[(y * N[(-1.0 - N[(2.0 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.8e-76], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.14999999999999994e251 or -2.3000000000000001e234 < c < -6.00000000000000021e157 or -1.35999999999999995e119 < c < 4.5999999999999998e-307 or 1.0799999999999999e-175 < c < 9.79999999999999944e-76

   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 a around inf 58.6%

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

   3. Taylor expanded in a around 0 41.2%

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

      1. +-commutative 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in x around inf 66.2%

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

   if -1.14999999999999994e251 < c < -2.3000000000000001e234 or -6.00000000000000021e157 < c < -1.35999999999999995e119

   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 c around inf 100.0%

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

      1. cancel-sign-sub-inv 100.0%

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

      2. +-commutative 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+r+ 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 88.0%

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

   6. Taylor expanded in x around 0 81.9%

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

   if 4.5999999999999998e-307 < c < 1.0799999999999999e-175

   1. Initial program 96.9%

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

   2. Taylor expanded in a around inf 63.7%

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

   3. Taylor expanded in a around 0 54.3%

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

      1. distribute-lft-out 54.3%

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

      2. unpow2 54.3%

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

      3. unpow2 54.3%

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

      4. swap-sqr 54.4%

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

      5. unpow1 54.4%

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

      6. pow-plus 54.4%

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

      7. metadata-eval 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in a around inf 54.3%

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

      1. unpow2 54.3%

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

      2. unpow2 54.3%

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

      3. swap-sqr 54.4%

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

      4. unpow2 54.4%

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

   8. Simplified 54.4%

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

      1. unpow2 54.4%

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

   10. Applied egg-rr 54.4%

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

   if 9.79999999999999944e-76 < c

   1. Initial program 91.2%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. *-commutative 73.1%

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

      3. associate-*r* 73.1%

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

      4. neg-mul-1 73.1%

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

      5. neg-sub0 73.1%

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

      6. associate--r- 73.1%

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

      7. neg-sub0 73.1%

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

      8. +-commutative 73.1%

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

      9. sub-neg 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in a around 0 66.9%

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

   6. Taylor expanded in c around inf 60.9%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+251}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{+234}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{elif}\;c \leq -6 \cdot 10^{+157}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.36 \cdot 10^{+119}:\\ \;\;\;\;\frac{x}{y \cdot e^{-1.3333333333333333 \cdot \frac{c}{t}}}\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{-307}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.08 \cdot 10^{-175}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(\left(a \cdot \left(b - c\right)\right) \cdot \left(a \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 9.8 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 10: 78.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-235} \lor \neg \left(t \leq 4.6 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -6e-235) (not (<= t 4.6e-58)))
   (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (*
        2.0
        (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -6e-235) || !(t <= 4.6e-58)) {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (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) :: tmp
    if ((t <= (-6d-235)) .or. (.not. (t <= 4.6d-58))) then
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (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 tmp;
	if ((t <= -6e-235) || !(t <= 4.6e-58)) {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -6e-235) or not (t <= 4.6e-58):
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -6e-235) || !(t <= 4.6e-58))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -6e-235) || ~((t <= 4.6e-58)))
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	else
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -6e-235], N[Not[LessEqual[t, 4.6e-58]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9999999999999997e-235 or 4.5999999999999998e-58 < t

   1. Initial program 95.9%

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

   2. Taylor expanded in t around inf 84.3%

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

      1. +-commutative 84.3%

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

      2. *-commutative 84.3%

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

      3. associate-*r* 84.3%

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

      4. neg-mul-1 84.3%

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

      5. neg-sub0 84.3%

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

      6. associate--r- 84.3%

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

      7. neg-sub0 84.3%

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

      8. +-commutative 84.3%

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

      9. sub-neg 84.3%

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

   4. Simplified 84.3%

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

   if -5.9999999999999997e-235 < t < 4.5999999999999998e-58

   1. Initial program 90.8%

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

   2. Taylor expanded in b around inf 67.8%

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

      1. associate-*r/ 67.8%

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

      2. metadata-eval 67.8%

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

      3. +-commutative 67.8%

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

   4. Simplified 67.8%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-235} \lor \neg \left(t \leq 4.6 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \]

Alternative 11: 79.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+43} \lor \neg \left(c \leq 7.5 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= c -1.42e+43) (not (<= c 7.5e+17)))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (* 2.0 (* c (+ a (+ (/ -0.6666666666666666 t) 0.8333333333333334))))))))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (*
        2.0
        (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((c <= -1.42e+43) || !(c <= 7.5e+17)) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (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) :: tmp
    if ((c <= (-1.42d+43)) .or. (.not. (c <= 7.5d+17))) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + (((-0.6666666666666666d0) / t) + 0.8333333333333334d0)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (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 tmp;
	if ((c <= -1.42e+43) || !(c <= 7.5e+17)) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (c <= -1.42e+43) or not (c <= 7.5e+17):
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((c <= -1.42e+43) || !(c <= 7.5e+17))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((c <= -1.42e+43) || ~((c <= 7.5e+17)))
		tmp = x / (x + (y * exp((2.0 * (c * (a + ((-0.6666666666666666 / t) + 0.8333333333333334)))))));
	else
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[c, -1.42e+43], N[Not[LessEqual[c, 7.5e+17]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.4199999999999999e43 or 7.5e17 < c

   1. Initial program 92.2%

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

   2. Taylor expanded in c around inf 82.3%

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

      1. cancel-sign-sub-inv 82.3%

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

      2. +-commutative 82.3%

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

      3. metadata-eval 82.3%

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

      4. associate-*r/ 82.3%

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

      5. metadata-eval 82.3%

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

      6. associate-+r+ 82.3%

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

   4. Simplified 82.3%

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

   if -1.4199999999999999e43 < c < 7.5e17

   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 b around inf 78.4%

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

      1. associate-*r/ 78.4%

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

      2. metadata-eval 78.4%

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

      3. +-commutative 78.4%

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

   4. Simplified 78.4%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.42 \cdot 10^{+43} \lor \neg \left(c \leq 7.5 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \]

Alternative 12: 76.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-234} \lor \neg \left(t \leq 2.4 \cdot 10^{-112}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -4.5e-234) (not (<= t 2.4e-112)))
   (/ x (+ x (* y (exp (* 2.0 (* (+ a 0.8333333333333334) (- c b)))))))
   (/ x (+ x (* y (exp (* 2.0 (* 0.6666666666666666 (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -4.5e-234) || !(t <= 2.4e-112)) {
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (0.6666666666666666 * (b / t))))));
	}
	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 <= (-4.5d-234)) .or. (.not. (t <= 2.4d-112))) then
        tmp = x / (x + (y * exp((2.0d0 * ((a + 0.8333333333333334d0) * (c - b))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (0.6666666666666666d0 * (b / t))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -4.5e-234) || !(t <= 2.4e-112)) {
		tmp = x / (x + (y * Math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (0.6666666666666666 * (b / t))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -4.5e-234) or not (t <= 2.4e-112):
		tmp = x / (x + (y * math.exp((2.0 * ((a + 0.8333333333333334) * (c - b))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (0.6666666666666666 * (b / t))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -4.5e-234) || !(t <= 2.4e-112))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(a + 0.8333333333333334) * Float64(c - b)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(0.6666666666666666 * Float64(b / t)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -4.5e-234) || ~((t <= 2.4e-112)))
		tmp = x / (x + (y * exp((2.0 * ((a + 0.8333333333333334) * (c - b))))));
	else
		tmp = x / (x + (y * exp((2.0 * (0.6666666666666666 * (b / t))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -4.5e-234], N[Not[LessEqual[t, 2.4e-112]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(0.6666666666666666 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.50000000000000009e-234 or 2.4000000000000001e-112 < t

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 80.8%

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

      1. +-commutative 80.8%

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

      2. *-commutative 80.8%

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

      3. associate-*r* 80.8%

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

      4. neg-mul-1 80.8%

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

      5. neg-sub0 80.8%

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

      6. associate--r- 80.8%

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

      7. neg-sub0 80.8%

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

      8. +-commutative 80.8%

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

      9. sub-neg 80.8%

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

   4. Simplified 80.8%

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

   if -4.50000000000000009e-234 < t < 2.4000000000000001e-112

   1. Initial program 88.9%

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

   2. Taylor expanded in b around inf 71.8%

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

      1. associate-*r/ 71.8%

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

      2. metadata-eval 71.8%

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

      3. +-commutative 71.8%

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

   4. Simplified 71.8%

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

   5. Taylor expanded in t around 0 69.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-234} \lor \neg \left(t \leq 2.4 \cdot 10^{-112}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \end{array} \]

Alternative 13: 68.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-234} \lor \neg \left(t \leq 2.1 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.15e-234) (not (<= t 2.1e-113)))
   (/ x (+ x (* y (exp (* 1.6666666666666667 (- c b))))))
   (/ x (+ x (* y (exp (* 2.0 (* 0.6666666666666666 (/ b t)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.15e-234) || !(t <= 2.1e-113)) {
		tmp = x / (x + (y * exp((1.6666666666666667 * (c - b)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (0.6666666666666666 * (b / t))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-2.15d-234)) .or. (.not. (t <= 2.1d-113))) then
        tmp = x / (x + (y * exp((1.6666666666666667d0 * (c - b)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (0.6666666666666666d0 * (b / t))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.15e-234) || !(t <= 2.1e-113)) {
		tmp = x / (x + (y * Math.exp((1.6666666666666667 * (c - b)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (0.6666666666666666 * (b / t))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.15e-234) or not (t <= 2.1e-113):
		tmp = x / (x + (y * math.exp((1.6666666666666667 * (c - b)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (0.6666666666666666 * (b / t))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.15e-234) || !(t <= 2.1e-113))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.6666666666666667 * Float64(c - b))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(0.6666666666666666 * Float64(b / t)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.15e-234) || ~((t <= 2.1e-113)))
		tmp = x / (x + (y * exp((1.6666666666666667 * (c - b)))));
	else
		tmp = x / (x + (y * exp((2.0 * (0.6666666666666666 * (b / t))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.15e-234], N[Not[LessEqual[t, 2.1e-113]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(1.6666666666666667 * N[(c - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(0.6666666666666666 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.15e-234 or 2.1e-113 < t

   1. Initial program 96.2%

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

   2. Taylor expanded in t around inf 80.8%

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

      1. +-commutative 80.8%

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

      2. *-commutative 80.8%

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

      3. associate-*r* 80.8%

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

      4. neg-mul-1 80.8%

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

      5. neg-sub0 80.8%

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

      6. associate--r- 80.8%

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

      7. neg-sub0 80.8%

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

      8. +-commutative 80.8%

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

      9. sub-neg 80.8%

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

   4. Simplified 80.8%

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

   5. Taylor expanded in a around 0 71.0%

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

   if -2.15e-234 < t < 2.1e-113

   1. Initial program 88.9%

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

   2. Taylor expanded in b around inf 71.8%

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

      1. associate-*r/ 71.8%

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

      2. metadata-eval 71.8%

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

      3. +-commutative 71.8%

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

   4. Simplified 71.8%

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

   5. Taylor expanded in t around 0 69.1%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{-234} \lor \neg \left(t \leq 2.1 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(0.6666666666666666 \cdot \frac{b}{t}\right)}}\\ \end{array} \]

Alternative 14: 66.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-235} \lor \neg \left(t \leq 1.2 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.25e-235) (not (<= t 1.2e-84)))
   (/ x (+ x (* y (exp (* 1.6666666666666667 (- c b))))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.25e-235) || !(t <= 1.2e-84)) {
		tmp = x / (x + (y * exp((1.6666666666666667 * (c - b)))));
	} 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 <= (-2.25d-235)) .or. (.not. (t <= 1.2d-84))) then
        tmp = x / (x + (y * exp((1.6666666666666667d0 * (c - b)))))
    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 <= -2.25e-235) || !(t <= 1.2e-84)) {
		tmp = x / (x + (y * Math.exp((1.6666666666666667 * (c - b)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.25e-235) or not (t <= 1.2e-84):
		tmp = x / (x + (y * math.exp((1.6666666666666667 * (c - b)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.25e-235) || !(t <= 1.2e-84))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.6666666666666667 * Float64(c - b))))));
	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 <= -2.25e-235) || ~((t <= 1.2e-84)))
		tmp = x / (x + (y * exp((1.6666666666666667 * (c - b)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.25e-235], N[Not[LessEqual[t, 1.2e-84]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(1.6666666666666667 * N[(c - b), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -2.2499999999999999e-235 or 1.20000000000000009e-84 < t

   1. Initial program 96.1%

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

   2. Taylor expanded in t around inf 81.9%

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

      1. +-commutative 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-*r* 81.9%

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

      4. neg-mul-1 81.9%

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

      5. neg-sub0 81.9%

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

      6. associate--r- 81.9%

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

      7. neg-sub0 81.9%

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

      8. +-commutative 81.9%

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

      9. sub-neg 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in a around 0 71.8%

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

   if -2.2499999999999999e-235 < t < 1.20000000000000009e-84

   1. Initial program 89.6%

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

   2. Taylor expanded in a around inf 32.5%

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

   3. Taylor expanded in a around 0 30.4%

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

      1. +-commutative 30.4%

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

   5. Simplified 30.4%

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

   6. Taylor expanded in x around inf 50.9%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-235} \lor \neg \left(t \leq 1.2 \cdot 10^{-84}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot \left(c - b\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15: 53.8% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b - c\right)\\ \mathbf{if}\;b \leq -7 \cdot 10^{+34} \lor \neg \left(b \leq -6.2 \cdot 10^{-109}\right) \land b \leq 1.9 \cdot 10^{-234}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(t_1 \cdot t_1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* a (- b c))))
   (if (or (<= b -7e+34) (and (not (<= b -6.2e-109)) (<= b 1.9e-234)))
     (/ x (- x (* y (- -1.0 (* 2.0 (* t_1 t_1))))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b - c);
	double tmp;
	if ((b <= -7e+34) || (!(b <= -6.2e-109) && (b <= 1.9e-234))) {
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b - c)
    if ((b <= (-7d+34)) .or. (.not. (b <= (-6.2d-109))) .and. (b <= 1.9d-234)) then
        tmp = x / (x - (y * ((-1.0d0) - (2.0d0 * (t_1 * t_1)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = a * (b - c);
	double tmp;
	if ((b <= -7e+34) || (!(b <= -6.2e-109) && (b <= 1.9e-234))) {
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = a * (b - c)
	tmp = 0
	if (b <= -7e+34) or (not (b <= -6.2e-109) and (b <= 1.9e-234)):
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(a * Float64(b - c))
	tmp = 0.0
	if ((b <= -7e+34) || (!(b <= -6.2e-109) && (b <= 1.9e-234)))
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(2.0 * Float64(t_1 * t_1))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = a * (b - c);
	tmp = 0.0;
	if ((b <= -7e+34) || (~((b <= -6.2e-109)) && (b <= 1.9e-234)))
		tmp = x / (x - (y * (-1.0 - (2.0 * (t_1 * t_1)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(a * N[(b - c), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[b, -7e+34], And[N[Not[LessEqual[b, -6.2e-109]], $MachinePrecision], LessEqual[b, 1.9e-234]]], N[(x / N[(x - N[(y * N[(-1.0 - N[(2.0 * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if b < -6.99999999999999996e34 or -6.1999999999999999e-109 < b < 1.89999999999999992e-234

   1. Initial program 97.3%

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

   2. Taylor expanded in a around inf 58.4%

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

   3. Taylor expanded in a around 0 51.5%

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

      1. distribute-lft-out 51.5%

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

      2. unpow2 51.5%

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

      3. unpow2 51.5%

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

      4. swap-sqr 54.1%

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

      5. unpow1 54.1%

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

      6. pow-plus 54.1%

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

      7. metadata-eval 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in a around inf 51.6%

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

      1. unpow2 51.6%

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

      2. unpow2 51.6%

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

      3. swap-sqr 54.2%

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

      4. unpow2 54.2%

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

   8. Simplified 54.2%

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

      1. unpow2 54.2%

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

   10. Applied egg-rr 54.2%

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

   if -6.99999999999999996e34 < b < -6.1999999999999999e-109 or 1.89999999999999992e-234 < b

   1. Initial program 91.8%

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

   2. Taylor expanded in a around inf 57.0%

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

   3. Taylor expanded in a around 0 34.2%

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

      1. +-commutative 34.2%

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

   5. Simplified 34.2%

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

   6. Taylor expanded in x around inf 56.3%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+34} \lor \neg \left(b \leq -6.2 \cdot 10^{-109}\right) \land b \leq 1.9 \cdot 10^{-234}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(\left(a \cdot \left(b - c\right)\right) \cdot \left(a \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 16: 51.6% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.55 \cdot 10^{+179}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + -2 \cdot \left(a \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 2.55e+179) 1.0 (/ x (+ x (+ y (* -2.0 (* a (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 2.55e+179) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (-2.0 * (a * (y * 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 (y <= 2.55d+179) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + ((-2.0d0) * (a * (y * b)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 2.55e+179) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (-2.0 * (a * (y * b)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 2.55e+179:
		tmp = 1.0
	else:
		tmp = x / (x + (y + (-2.0 * (a * (y * b)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 2.55e+179)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(-2.0 * Float64(a * Float64(y * b))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 2.55e+179)
		tmp = 1.0;
	else
		tmp = x / (x + (y + (-2.0 * (a * (y * b)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 2.55e+179], 1.0, N[(x / N[(x + N[(y + N[(-2.0 * N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5500000000000001e179

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 58.6%

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

   3. Taylor expanded in a around 0 36.1%

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

      1. +-commutative 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in x around inf 50.6%

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

   if 2.5500000000000001e179 < y

   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 a around inf 47.2%

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

   3. Taylor expanded in c around 0 51.6%

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

   4. Taylor expanded in a around 0 60.5%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.55 \cdot 10^{+179}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + -2 \cdot \left(a \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]

Alternative 17: 51.0% accurate, 17.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.3 \cdot 10^{+181}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-2 \cdot \left(a \cdot b\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 6.3e+181) 1.0 (/ x (* y (+ (* -2.0 (* a b)) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 6.3e+181) {
		tmp = 1.0;
	} else {
		tmp = x / (y * ((-2.0 * (a * b)) + 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 (y <= 6.3d+181) then
        tmp = 1.0d0
    else
        tmp = x / (y * (((-2.0d0) * (a * b)) + 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 (y <= 6.3e+181) {
		tmp = 1.0;
	} else {
		tmp = x / (y * ((-2.0 * (a * b)) + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 6.3e+181:
		tmp = 1.0
	else:
		tmp = x / (y * ((-2.0 * (a * b)) + 1.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 6.3e+181)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * Float64(Float64(-2.0 * Float64(a * b)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 6.3e+181)
		tmp = 1.0;
	else
		tmp = x / (y * ((-2.0 * (a * b)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 6.3e+181], 1.0, N[(x / N[(y * N[(N[(-2.0 * N[(a * b), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.3000000000000003e181

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 58.6%

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

   3. Taylor expanded in a around 0 36.1%

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

      1. +-commutative 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in x around inf 50.6%

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

   if 6.3000000000000003e181 < y

   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 a around inf 47.2%

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

   3. Taylor expanded in c around 0 51.6%

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

   4. Taylor expanded in a around 0 60.5%

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

   5. Taylor expanded in y around inf 56.2%

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

      1. *-commutative 56.2%

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

   7. Simplified 56.2%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.3 \cdot 10^{+181}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(-2 \cdot \left(a \cdot b\right) + 1\right)}\\ \end{array} \]

Alternative 18: 51.2% accurate, 17.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.7 \cdot 10^{+175}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y \cdot b\right) \cdot \left(a \cdot -2\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 5.7e+175) 1.0 (/ x (+ x (* (* y b) (* a -2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 5.7e+175) {
		tmp = 1.0;
	} else {
		tmp = x / (x + ((y * b) * (a * -2.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= 5.7d+175) then
        tmp = 1.0d0
    else
        tmp = x / (x + ((y * b) * (a * (-2.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 5.7e+175) {
		tmp = 1.0;
	} else {
		tmp = x / (x + ((y * b) * (a * -2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 5.7e+175:
		tmp = 1.0
	else:
		tmp = x / (x + ((y * b) * (a * -2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 5.7e+175)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(Float64(y * b) * Float64(a * -2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 5.7e+175)
		tmp = 1.0;
	else
		tmp = x / (x + ((y * b) * (a * -2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 5.7e+175], 1.0, N[(x / N[(x + N[(N[(y * b), $MachinePrecision] * N[(a * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.70000000000000024e175

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 58.8%

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

   3. Taylor expanded in a around 0 36.3%

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

      1. +-commutative 36.3%

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

   5. Simplified 36.3%

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

   6. Taylor expanded in x around inf 50.4%

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

   if 5.70000000000000024e175 < y

   1. Initial program 95.8%

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

   2. Taylor expanded in a around inf 45.3%

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

   3. Taylor expanded in c around 0 49.5%

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

   4. Taylor expanded in a around 0 57.9%

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

   5. Taylor expanded in a around inf 61.2%

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

      1. associate-*r* 61.2%

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

   7. Simplified 61.2%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.7 \cdot 10^{+175}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y \cdot b\right) \cdot \left(a \cdot -2\right)}\\ \end{array} \]

Alternative 19: 50.5% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+183}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 4.1e+183) 1.0 (* -0.5 (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 4.1e+183) {
		tmp = 1.0;
	} else {
		tmp = -0.5 * (x / (a * (y * 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 (y <= 4.1d+183) then
        tmp = 1.0d0
    else
        tmp = (-0.5d0) * (x / (a * (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 4.1e+183) {
		tmp = 1.0;
	} else {
		tmp = -0.5 * (x / (a * (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 4.1e+183:
		tmp = 1.0
	else:
		tmp = -0.5 * (x / (a * (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 4.1e+183)
		tmp = 1.0;
	else
		tmp = Float64(-0.5 * Float64(x / Float64(a * Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 4.1e+183)
		tmp = 1.0;
	else
		tmp = -0.5 * (x / (a * (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 4.1e+183], 1.0, N[(-0.5 * N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.10000000000000015e183

   1. Initial program 94.0%

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

   2. Taylor expanded in a around inf 58.6%

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

   3. Taylor expanded in a around 0 36.1%

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

      1. +-commutative 36.1%

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

   5. Simplified 36.1%

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

   6. Taylor expanded in x around inf 50.6%

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

   if 4.10000000000000015e183 < y

   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 a around inf 47.2%

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

   3. Taylor expanded in c around 0 51.6%

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

   4. Taylor expanded in a around 0 60.5%

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

   5. Taylor expanded in a around inf 55.0%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+183}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 20: 51.6% 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 94.2%

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

2. Taylor expanded in a around inf 57.6%

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

3. Taylor expanded in a around 0 36.0%

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

   1. +-commutative 36.0%

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

5. Simplified 36.0%

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

6. Taylor expanded in x around inf 48.8%

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

7. Final simplification 48.8%

   \[\leadsto 1 \]

Developer target: 95.4% 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 2023334 
(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)))))))))))