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

Percentage Accurate: 93.9% → 97.3%

Time: 24.4s

Alternatives: 25

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.9% 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: 97.3% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 89.8%

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

   1. +-commutative 89.8%

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

   2. fma-def 89.8%

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

3. Simplified 96.6%

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

4. Final simplification 96.6%

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

Alternative 2: 96.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\\ t_2 := \sqrt{t + a}\\ \mathbf{if}\;\frac{t_2 \cdot z}{t} + t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{t_2}} + t_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a 0.8333333333333334))))
        (t_2 (sqrt (+ t a))))
   (if (<= (+ (/ (* t_2 z) t) t_1) INFINITY)
     (/ x (+ x (* y (pow (exp 2.0) (+ (/ z (/ t t_2)) t_1)))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334));
	double t_2 = sqrt((t + a));
	double tmp;
	if ((((t_2 * z) / t) + t_1) <= ((double) INFINITY)) {
		tmp = x / (x + (y * pow(exp(2.0), ((z / (t / t_2)) + t_1))));
	} else {
		tmp = 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 = (b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334));
	double t_2 = Math.sqrt((t + a));
	double tmp;
	if ((((t_2 * z) / t) + t_1) <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.pow(Math.exp(2.0), ((z / (t / t_2)) + t_1))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334))
	t_2 = math.sqrt((t + a))
	tmp = 0
	if (((t_2 * z) / t) + t_1) <= math.inf:
		tmp = x / (x + (y * math.pow(math.exp(2.0), ((z / (t / t_2)) + t_1))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + 0.8333333333333334)))
	t_2 = sqrt(Float64(t + a))
	tmp = 0.0
	if (Float64(Float64(Float64(t_2 * z) / t) + t_1) <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * (exp(2.0) ^ Float64(Float64(z / Float64(t / t_2)) + t_1)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334));
	t_2 = sqrt((t + a));
	tmp = 0.0;
	if ((((t_2 * z) / t) + t_1) <= Inf)
		tmp = x / (x + (y * (exp(2.0) ^ ((z / (t / t_2)) + t_1))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(N[(t$95$2 * z), $MachinePrecision] / t), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(x / N[(x + N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(z / N[(t / t$95$2), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 99.1%

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

      1. exp-prod 99.1%

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

      2. associate-/l* 99.5%

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

      3. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in a around inf 43.7%

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

   3. Taylor expanded in a around 0 31.4%

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

   4. Taylor expanded in x around inf 67.7%

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

4. Final simplification 96.5%

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

Alternative 3: 96.4% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* (sqrt (+ t a)) z) 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 = ((sqrt((t + a)) * z) / 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 = ((Math.sqrt((t + a)) * z) / 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 = ((math.sqrt((t + a)) * z) / 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(sqrt(Float64(t + a)) * z) / 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 = ((sqrt((t + a)) * z) / 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[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] * z), $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 99.1%

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

   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 43.7%

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

   3. Taylor expanded in a around 0 31.4%

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

   4. Taylor expanded in x around inf 67.7%

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

4. Final simplification 96.2%

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

Alternative 4: 79.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{-216}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a)))))))))
   (if (<= t -1.1e-216)
     t_1
     (if (<= t 1.15e-196)
       (/ x (+ x (* y (exp (* 2.0 (* (sqrt (+ t a)) (/ z t)))))))
       (if (<= t 9.2e-19)
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (* c (+ 0.8333333333333334 (- a (/ 0.6666666666666666 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 * ((b - c) * (-0.8333333333333334 - a))))));
	double tmp;
	if (t <= -1.1e-216) {
		tmp = t_1;
	} else if (t <= 1.15e-196) {
		tmp = x / (x + (y * exp((2.0 * (sqrt((t + a)) * (z / t))))));
	} else if (t <= 9.2e-19) {
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    if (t <= (-1.1d-216)) then
        tmp = t_1
    else if (t <= 1.15d-196) then
        tmp = x / (x + (y * exp((2.0d0 * (sqrt((t + a)) * (z / t))))))
    else if (t <= 9.2d-19) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (0.8333333333333334d0 + (a - (0.6666666666666666d0 / 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 * ((b - c) * (-0.8333333333333334 - a))))));
	double tmp;
	if (t <= -1.1e-216) {
		tmp = t_1;
	} else if (t <= 1.15e-196) {
		tmp = x / (x + (y * Math.exp((2.0 * (Math.sqrt((t + a)) * (z / t))))));
	} else if (t <= 9.2e-19) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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 * ((b - c) * (-0.8333333333333334 - a))))))
	tmp = 0
	if t <= -1.1e-216:
		tmp = t_1
	elif t <= 1.15e-196:
		tmp = x / (x + (y * math.exp((2.0 * (math.sqrt((t + a)) * (z / t))))))
	elif t <= 9.2e-19:
		tmp = x / (x + (y * math.exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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(b - c) * Float64(-0.8333333333333334 - a)))))))
	tmp = 0.0
	if (t <= -1.1e-216)
		tmp = t_1;
	elseif (t <= 1.15e-196)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(sqrt(Float64(t + a)) * Float64(z / t)))))));
	elseif (t <= 9.2e-19)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / 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 * ((b - c) * (-0.8333333333333334 - a))))));
	tmp = 0.0;
	if (t <= -1.1e-216)
		tmp = t_1;
	elseif (t <= 1.15e-196)
		tmp = x / (x + (y * exp((2.0 * (sqrt((t + a)) * (z / t))))));
	elseif (t <= 9.2e-19)
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.1e-216], t$95$1, If[LessEqual[t, 1.15e-196], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.2e-19], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.09999999999999995e-216 or 9.19999999999999919e-19 < t

   1. Initial program 96.3%

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

   2. Taylor expanded in t around inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-in 90.1%

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

      3. distribute-neg-in 90.1%

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

      4. metadata-eval 90.1%

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

      5. sub-neg 90.1%

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

   4. Simplified 90.1%

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

   if -1.09999999999999995e-216 < t < 1.1500000000000001e-196

   1. Initial program 63.8%

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

   2. Taylor expanded in z around inf 69.1%

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

   if 1.1500000000000001e-196 < t < 9.19999999999999919e-19

   1. Initial program 93.2%

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

   2. Taylor expanded in c around inf 69.3%

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

      1. associate--l+ 69.3%

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

      2. associate-*r/ 69.3%

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

      3. metadata-eval 69.3%

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

   4. Simplified 69.3%

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

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.1 \cdot 10^{-216}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-196}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 5: 56.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-239}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-163}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 300:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 10^{+26} \lor \neg \left(c \leq 3 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -7.2e-117)
   1.0
   (if (<= c -2.2e-283)
     (/
      x
      (-
       x
       (*
        y
        (+
         -1.0
         (*
          2.0
          (*
           b
           (+ (+ a 0.8333333333333334) (* 0.6666666666666666 (/ -1.0 t)))))))))
     (if (<= c 1.25e-239)
       1.0
       (if (<= c 5e-186)
         (/ x (* y (exp (* -2.0 (* b a)))))
         (if (<= c 6.8e-163)
           1.0
           (if (<= c 300.0)
             (/ x (+ y (+ x (* 2.0 (* a (* y (- c b)))))))
             (if (or (<= c 1e+26) (not (<= c 3e+52)))
               (/ x (* y (exp (* c 1.6666666666666667))))
               1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -7.2e-117) {
		tmp = 1.0;
	} else if (c <= -2.2e-283) {
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	} else if (c <= 1.25e-239) {
		tmp = 1.0;
	} else if (c <= 5e-186) {
		tmp = x / (y * exp((-2.0 * (b * a))));
	} else if (c <= 6.8e-163) {
		tmp = 1.0;
	} else if (c <= 300.0) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if ((c <= 1e+26) || !(c <= 3e+52)) {
		tmp = x / (y * exp((c * 1.6666666666666667)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-7.2d-117)) then
        tmp = 1.0d0
    else if (c <= (-2.2d-283)) then
        tmp = x / (x - (y * ((-1.0d0) + (2.0d0 * (b * ((a + 0.8333333333333334d0) + (0.6666666666666666d0 * ((-1.0d0) / t))))))))
    else if (c <= 1.25d-239) then
        tmp = 1.0d0
    else if (c <= 5d-186) then
        tmp = x / (y * exp(((-2.0d0) * (b * a))))
    else if (c <= 6.8d-163) then
        tmp = 1.0d0
    else if (c <= 300.0d0) then
        tmp = x / (y + (x + (2.0d0 * (a * (y * (c - b))))))
    else if ((c <= 1d+26) .or. (.not. (c <= 3d+52))) then
        tmp = x / (y * exp((c * 1.6666666666666667d0)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -7.2e-117) {
		tmp = 1.0;
	} else if (c <= -2.2e-283) {
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	} else if (c <= 1.25e-239) {
		tmp = 1.0;
	} else if (c <= 5e-186) {
		tmp = x / (y * Math.exp((-2.0 * (b * a))));
	} else if (c <= 6.8e-163) {
		tmp = 1.0;
	} else if (c <= 300.0) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if ((c <= 1e+26) || !(c <= 3e+52)) {
		tmp = x / (y * Math.exp((c * 1.6666666666666667)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -7.2e-117:
		tmp = 1.0
	elif c <= -2.2e-283:
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))))
	elif c <= 1.25e-239:
		tmp = 1.0
	elif c <= 5e-186:
		tmp = x / (y * math.exp((-2.0 * (b * a))))
	elif c <= 6.8e-163:
		tmp = 1.0
	elif c <= 300.0:
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))))
	elif (c <= 1e+26) or not (c <= 3e+52):
		tmp = x / (y * math.exp((c * 1.6666666666666667)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -7.2e-117)
		tmp = 1.0;
	elseif (c <= -2.2e-283)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 + Float64(2.0 * Float64(b * Float64(Float64(a + 0.8333333333333334) + Float64(0.6666666666666666 * Float64(-1.0 / t)))))))));
	elseif (c <= 1.25e-239)
		tmp = 1.0;
	elseif (c <= 5e-186)
		tmp = Float64(x / Float64(y * exp(Float64(-2.0 * Float64(b * a)))));
	elseif (c <= 6.8e-163)
		tmp = 1.0;
	elseif (c <= 300.0)
		tmp = Float64(x / Float64(y + Float64(x + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	elseif ((c <= 1e+26) || !(c <= 3e+52))
		tmp = Float64(x / Float64(y * exp(Float64(c * 1.6666666666666667))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -7.2e-117)
		tmp = 1.0;
	elseif (c <= -2.2e-283)
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	elseif (c <= 1.25e-239)
		tmp = 1.0;
	elseif (c <= 5e-186)
		tmp = x / (y * exp((-2.0 * (b * a))));
	elseif (c <= 6.8e-163)
		tmp = 1.0;
	elseif (c <= 300.0)
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	elseif ((c <= 1e+26) || ~((c <= 3e+52)))
		tmp = x / (y * exp((c * 1.6666666666666667)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -7.2e-117], 1.0, If[LessEqual[c, -2.2e-283], N[(x / N[(x - N[(y * N[(-1.0 + N[(2.0 * N[(b * N[(N[(a + 0.8333333333333334), $MachinePrecision] + N[(0.6666666666666666 * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-239], 1.0, If[LessEqual[c, 5e-186], N[(x / N[(y * N[Exp[N[(-2.0 * N[(b * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e-163], 1.0, If[LessEqual[c, 300.0], N[(x / N[(y + N[(x + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 1e+26], N[Not[LessEqual[c, 3e+52]], $MachinePrecision]], N[(x / N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -7.2000000000000001e-117 or -2.1999999999999998e-283 < c < 1.25e-239 or 5e-186 < c < 6.80000000000000028e-163 or 1.00000000000000005e26 < c < 3e52

   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 62.8%

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

   3. Taylor expanded in a around 0 33.0%

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

   4. Taylor expanded in x around inf 73.8%

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

   if -7.2000000000000001e-117 < c < -2.1999999999999998e-283

   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 b around inf 83.1%

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

      1. *-commutative 83.1%

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

      2. associate--r+ 83.1%

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

      3. sub-neg 83.1%

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

      4. associate-*r/ 83.1%

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

      5. metadata-eval 83.1%

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

      6. metadata-eval 83.1%

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

      7. associate-+r- 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in b around 0 60.5%

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

   if 1.25e-239 < c < 5e-186

   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 70.9%

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

   3. Taylor expanded in x around 0 70.9%

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

   4. Taylor expanded in c around 0 70.9%

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

   if 6.80000000000000028e-163 < c < 300

   1. Initial program 85.4%

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

   2. Taylor expanded in a around inf 69.2%

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

   3. Taylor expanded in a around 0 68.9%

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

   if 300 < c < 1.00000000000000005e26 or 3e52 < c

   1. Initial program 80.7%

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

   2. Taylor expanded in t around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. distribute-rgt-neg-in 82.8%

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

      3. distribute-neg-in 82.8%

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

      4. metadata-eval 82.8%

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

      5. sub-neg 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in a around 0 78.1%

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

   6. Taylor expanded in b around 0 73.4%

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

   7. Taylor expanded in x around 0 73.4%

      \[\leadsto \color{blue}{\frac{x}{e^{1.6666666666666667 \cdot c} \cdot y}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.2 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.2 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-239}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 5 \cdot 10^{-186}:\\ \;\;\;\;\frac{x}{y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{-163}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 300:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 10^{+26} \lor \neg \left(c \leq 3 \cdot 10^{+52}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 79.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{if}\;t \leq -2 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-168}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a)))))))))
   (if (<= t -2e-304)
     t_1
     (if (<= t 4.2e-168)
       1.0
       (if (<= t 5e-19)
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (* c (+ 0.8333333333333334 (- a (/ 0.6666666666666666 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 * ((b - c) * (-0.8333333333333334 - a))))));
	double tmp;
	if (t <= -2e-304) {
		tmp = t_1;
	} else if (t <= 4.2e-168) {
		tmp = 1.0;
	} else if (t <= 5e-19) {
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    if (t <= (-2d-304)) then
        tmp = t_1
    else if (t <= 4.2d-168) then
        tmp = 1.0d0
    else if (t <= 5d-19) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (0.8333333333333334d0 + (a - (0.6666666666666666d0 / 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 * ((b - c) * (-0.8333333333333334 - a))))));
	double tmp;
	if (t <= -2e-304) {
		tmp = t_1;
	} else if (t <= 4.2e-168) {
		tmp = 1.0;
	} else if (t <= 5e-19) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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 * ((b - c) * (-0.8333333333333334 - a))))))
	tmp = 0
	if t <= -2e-304:
		tmp = t_1
	elif t <= 4.2e-168:
		tmp = 1.0
	elif t <= 5e-19:
		tmp = x / (x + (y * math.exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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(b - c) * Float64(-0.8333333333333334 - a)))))))
	tmp = 0.0
	if (t <= -2e-304)
		tmp = t_1;
	elseif (t <= 4.2e-168)
		tmp = 1.0;
	elseif (t <= 5e-19)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / 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 * ((b - c) * (-0.8333333333333334 - a))))));
	tmp = 0.0;
	if (t <= -2e-304)
		tmp = t_1;
	elseif (t <= 4.2e-168)
		tmp = 1.0;
	elseif (t <= 5e-19)
		tmp = x / (x + (y * exp((2.0 * (c * (0.8333333333333334 + (a - (0.6666666666666666 / 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[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2e-304], t$95$1, If[LessEqual[t, 4.2e-168], 1.0, If[LessEqual[t, 5e-19], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999994e-304 or 5.0000000000000004e-19 < t

   1. Initial program 92.8%

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

   2. Taylor expanded in t around inf 87.7%

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

      1. mul-1-neg 87.7%

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

      2. distribute-rgt-neg-in 87.7%

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

      3. distribute-neg-in 87.7%

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

      4. metadata-eval 87.7%

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

      5. sub-neg 87.7%

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

   4. Simplified 87.7%

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

   if -1.99999999999999994e-304 < t < 4.19999999999999988e-168

   1. Initial program 70.3%

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

   2. Taylor expanded in a around inf 39.9%

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

   3. Taylor expanded in a around 0 32.4%

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

   4. Taylor expanded in x around inf 68.6%

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

   if 4.19999999999999988e-168 < t < 5.0000000000000004e-19

   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 c around inf 72.1%

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

      1. associate--l+ 72.1%

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

      2. associate-*r/ 72.1%

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

      3. metadata-eval 72.1%

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

   4. Simplified 72.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-304}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-168}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 7: 75.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+136} \lor \neg \left(b \leq 0.25\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\left(-0.8333333333333334 - a\right) + \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= b -1e+136) (not (<= b 0.25)))
   (/
    x
    (+
     x
     (*
      y
      (exp
       (* 2.0 (* b (+ (- -0.8333333333333334 a) (/ 0.6666666666666666 t))))))))
   (/ x (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1e+136) || !(b <= 0.25)) {
		tmp = x / (x + (y * exp((2.0 * (b * ((-0.8333333333333334 - a) + (0.6666666666666666 / t)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b <= (-1d+136)) .or. (.not. (b <= 0.25d0))) then
        tmp = x / (x + (y * exp((2.0d0 * (b * (((-0.8333333333333334d0) - a) + (0.6666666666666666d0 / t)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b <= -1e+136) || !(b <= 0.25)) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((-0.8333333333333334 - a) + (0.6666666666666666 / t)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b <= -1e+136) or not (b <= 0.25):
		tmp = x / (x + (y * math.exp((2.0 * (b * ((-0.8333333333333334 - a) + (0.6666666666666666 / t)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((b <= -1e+136) || !(b <= 0.25))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(-0.8333333333333334 - a) + Float64(0.6666666666666666 / t))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b <= -1e+136) || ~((b <= 0.25)))
		tmp = x / (x + (y * exp((2.0 * (b * ((-0.8333333333333334 - a) + (0.6666666666666666 / t)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[b, -1e+136], N[Not[LessEqual[b, 0.25]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(-0.8333333333333334 - a), $MachinePrecision] + N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.00000000000000006e136 or 0.25 < b

   1. Initial program 85.1%

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

   2. Taylor expanded in b around inf 84.6%

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

      1. *-commutative 84.6%

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

      2. associate--r+ 84.6%

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

      3. sub-neg 84.6%

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

      4. associate-*r/ 84.6%

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

      5. metadata-eval 84.6%

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

      6. metadata-eval 84.6%

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

      7. associate-+r- 84.6%

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

   4. Simplified 84.6%

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

   if -1.00000000000000006e136 < b < 0.25

   1. Initial program 93.3%

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

   2. Taylor expanded in t around inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-rgt-neg-in 76.7%

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

      3. distribute-neg-in 76.7%

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

      4. metadata-eval 76.7%

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

      5. sub-neg 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+136} \lor \neg \left(b \leq 0.25\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\left(-0.8333333333333334 - a\right) + \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 8: 56.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-159}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 240:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+28} \lor \neg \left(c \leq 2.8 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.25e-116)
   1.0
   (if (<= c -2.15e-283)
     (/
      x
      (-
       x
       (*
        y
        (+
         -1.0
         (*
          2.0
          (*
           b
           (+ (+ a 0.8333333333333334) (* 0.6666666666666666 (/ -1.0 t)))))))))
     (if (<= c 2.4e-159)
       1.0
       (if (<= c 240.0)
         (/ x (+ y (+ x (* 2.0 (* a (* y (- c b)))))))
         (if (or (<= c 2e+28) (not (<= c 2.8e+53)))
           (/ x (* y (exp (* c 1.6666666666666667))))
           1.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.25e-116) {
		tmp = 1.0;
	} else if (c <= -2.15e-283) {
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	} else if (c <= 2.4e-159) {
		tmp = 1.0;
	} else if (c <= 240.0) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if ((c <= 2e+28) || !(c <= 2.8e+53)) {
		tmp = x / (y * exp((c * 1.6666666666666667)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-2.25d-116)) then
        tmp = 1.0d0
    else if (c <= (-2.15d-283)) then
        tmp = x / (x - (y * ((-1.0d0) + (2.0d0 * (b * ((a + 0.8333333333333334d0) + (0.6666666666666666d0 * ((-1.0d0) / t))))))))
    else if (c <= 2.4d-159) then
        tmp = 1.0d0
    else if (c <= 240.0d0) then
        tmp = x / (y + (x + (2.0d0 * (a * (y * (c - b))))))
    else if ((c <= 2d+28) .or. (.not. (c <= 2.8d+53))) then
        tmp = x / (y * exp((c * 1.6666666666666667d0)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.25e-116) {
		tmp = 1.0;
	} else if (c <= -2.15e-283) {
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	} else if (c <= 2.4e-159) {
		tmp = 1.0;
	} else if (c <= 240.0) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if ((c <= 2e+28) || !(c <= 2.8e+53)) {
		tmp = x / (y * Math.exp((c * 1.6666666666666667)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.25e-116:
		tmp = 1.0
	elif c <= -2.15e-283:
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))))
	elif c <= 2.4e-159:
		tmp = 1.0
	elif c <= 240.0:
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))))
	elif (c <= 2e+28) or not (c <= 2.8e+53):
		tmp = x / (y * math.exp((c * 1.6666666666666667)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.25e-116)
		tmp = 1.0;
	elseif (c <= -2.15e-283)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 + Float64(2.0 * Float64(b * Float64(Float64(a + 0.8333333333333334) + Float64(0.6666666666666666 * Float64(-1.0 / t)))))))));
	elseif (c <= 2.4e-159)
		tmp = 1.0;
	elseif (c <= 240.0)
		tmp = Float64(x / Float64(y + Float64(x + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	elseif ((c <= 2e+28) || !(c <= 2.8e+53))
		tmp = Float64(x / Float64(y * exp(Float64(c * 1.6666666666666667))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -2.25e-116)
		tmp = 1.0;
	elseif (c <= -2.15e-283)
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	elseif (c <= 2.4e-159)
		tmp = 1.0;
	elseif (c <= 240.0)
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	elseif ((c <= 2e+28) || ~((c <= 2.8e+53)))
		tmp = x / (y * exp((c * 1.6666666666666667)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.25e-116], 1.0, If[LessEqual[c, -2.15e-283], N[(x / N[(x - N[(y * N[(-1.0 + N[(2.0 * N[(b * N[(N[(a + 0.8333333333333334), $MachinePrecision] + N[(0.6666666666666666 * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e-159], 1.0, If[LessEqual[c, 240.0], N[(x / N[(y + N[(x + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[c, 2e+28], N[Not[LessEqual[c, 2.8e+53]], $MachinePrecision]], N[(x / N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.25000000000000006e-116 or -2.15000000000000001e-283 < c < 2.39999999999999997e-159 or 1.99999999999999992e28 < c < 2.8e53

   1. Initial program 92.4%

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

   2. Taylor expanded in a around inf 63.4%

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

   3. Taylor expanded in a around 0 32.3%

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

   4. Taylor expanded in x around inf 69.9%

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

   if -2.25000000000000006e-116 < c < -2.15000000000000001e-283

   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 b around inf 83.1%

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

      1. *-commutative 83.1%

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

      2. associate--r+ 83.1%

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

      3. sub-neg 83.1%

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

      4. associate-*r/ 83.1%

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

      5. metadata-eval 83.1%

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

      6. metadata-eval 83.1%

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

      7. associate-+r- 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in b around 0 60.5%

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

   if 2.39999999999999997e-159 < c < 240

   1. Initial program 85.4%

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

   2. Taylor expanded in a around inf 69.2%

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

   3. Taylor expanded in a around 0 68.9%

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

   if 240 < c < 1.99999999999999992e28 or 2.8e53 < c

   1. Initial program 80.7%

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

   2. Taylor expanded in t around inf 82.8%

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

      1. mul-1-neg 82.8%

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

      2. distribute-rgt-neg-in 82.8%

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

      3. distribute-neg-in 82.8%

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

      4. metadata-eval 82.8%

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

      5. sub-neg 82.8%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in a around 0 78.1%

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

   6. Taylor expanded in b around 0 73.4%

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

   7. Taylor expanded in x around 0 73.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.25 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.15 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-159}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 240:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+28} \lor \neg \left(c \leq 2.8 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 61.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-267}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b}{t}}}\\ \mathbf{elif}\;c \leq 420:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* b -0.8333333333333334))))))))
   (if (<= c -4.4e-117)
     1.0
     (if (<= c 1.15e-267)
       t_1
       (if (<= c 2e-182)
         (/ x (+ x (* y (exp (* 1.3333333333333333 (/ b t))))))
         (if (<= c 420.0) t_1 (/ 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 * (b * -0.8333333333333334)))));
	double tmp;
	if (c <= -4.4e-117) {
		tmp = 1.0;
	} else if (c <= 1.15e-267) {
		tmp = t_1;
	} else if (c <= 2e-182) {
		tmp = x / (x + (y * exp((1.3333333333333333 * (b / t)))));
	} else if (c <= 420.0) {
		tmp = t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (b * (-0.8333333333333334d0))))))
    if (c <= (-4.4d-117)) then
        tmp = 1.0d0
    else if (c <= 1.15d-267) then
        tmp = t_1
    else if (c <= 2d-182) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * (b / t)))))
    else if (c <= 420.0d0) then
        tmp = t_1
    else
        tmp = 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 * (b * -0.8333333333333334)))));
	double tmp;
	if (c <= -4.4e-117) {
		tmp = 1.0;
	} else if (c <= 1.15e-267) {
		tmp = t_1;
	} else if (c <= 2e-182) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * (b / t)))));
	} else if (c <= 420.0) {
		tmp = t_1;
	} else {
		tmp = 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 * (b * -0.8333333333333334)))))
	tmp = 0
	if c <= -4.4e-117:
		tmp = 1.0
	elif c <= 1.15e-267:
		tmp = t_1
	elif c <= 2e-182:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * (b / t)))))
	elif c <= 420.0:
		tmp = t_1
	else:
		tmp = 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(b * -0.8333333333333334))))))
	tmp = 0.0
	if (c <= -4.4e-117)
		tmp = 1.0;
	elseif (c <= 1.15e-267)
		tmp = t_1;
	elseif (c <= 2e-182)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(b / t))))));
	elseif (c <= 420.0)
		tmp = t_1;
	else
		tmp = 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 * (b * -0.8333333333333334)))));
	tmp = 0.0;
	if (c <= -4.4e-117)
		tmp = 1.0;
	elseif (c <= 1.15e-267)
		tmp = t_1;
	elseif (c <= 2e-182)
		tmp = x / (x + (y * exp((1.3333333333333333 * (b / t)))));
	elseif (c <= 420.0)
		tmp = t_1;
	else
		tmp = 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[(b * -0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.4e-117], 1.0, If[LessEqual[c, 1.15e-267], t$95$1, If[LessEqual[c, 2e-182], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 420.0], t$95$1, N[(x / N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -4.4000000000000002e-117

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf 62.0%

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

   3. Taylor expanded in a around 0 30.0%

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

   4. Taylor expanded in x around inf 72.8%

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

   if -4.4000000000000002e-117 < c < 1.15000000000000003e-267 or 2.0000000000000001e-182 < c < 420

   1. Initial program 92.3%

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

   2. Taylor expanded in t around inf 81.7%

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

      1. mul-1-neg 81.7%

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

      2. distribute-rgt-neg-in 81.7%

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

      3. distribute-neg-in 81.7%

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

      4. metadata-eval 81.7%

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

      5. sub-neg 81.7%

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

   4. Simplified 81.7%

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

   5. Taylor expanded in a around 0 75.6%

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

   6. Taylor expanded in b around inf 75.6%

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

   if 1.15000000000000003e-267 < c < 2.0000000000000001e-182

   1. Initial program 94.1%

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

   2. Taylor expanded in b around inf 71.5%

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

      1. *-commutative 71.5%

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

      2. associate--r+ 71.5%

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

      3. sub-neg 71.5%

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

      4. associate-*r/ 71.5%

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

      5. metadata-eval 71.5%

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

      6. metadata-eval 71.5%

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

      7. associate-+r- 71.5%

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

   4. Simplified 71.5%

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

   5. Taylor expanded in t around 0 60.6%

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

      1. associate-*r/ 60.6%

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

      2. associate-*l/ 60.6%

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

      3. *-commutative 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in y around 0 60.6%

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

   if 420 < c

   1. Initial program 79.0%

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

   2. Taylor expanded in t around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. distribute-neg-in 76.8%

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

      4. metadata-eval 76.8%

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

      5. sub-neg 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in a around 0 72.7%

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

   6. Taylor expanded in b around 0 65.9%

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

   7. Taylor expanded in x around 0 65.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.4 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{-267}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-182}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b}{t}}}\\ \mathbf{elif}\;c \leq 420:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 10: 66.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -4 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot 0.8333333333333334\right)}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= a -4e+32)
     t_1
     (if (<= a 2e-249)
       (/ x (+ x (* y (exp (* 2.0 (* b -0.8333333333333334))))))
       (if (<= a 1.7e-61)
         (/ x (+ x (* y (exp (* 2.0 (* c 0.8333333333333334))))))
         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 * (c - b))))));
	double tmp;
	if (a <= -4e+32) {
		tmp = t_1;
	} else if (a <= 2e-249) {
		tmp = x / (x + (y * exp((2.0 * (b * -0.8333333333333334)))));
	} else if (a <= 1.7e-61) {
		tmp = x / (x + (y * exp((2.0 * (c * 0.8333333333333334)))));
	} 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 * (c - b))))))
    if (a <= (-4d+32)) then
        tmp = t_1
    else if (a <= 2d-249) then
        tmp = x / (x + (y * exp((2.0d0 * (b * (-0.8333333333333334d0))))))
    else if (a <= 1.7d-61) then
        tmp = x / (x + (y * exp((2.0d0 * (c * 0.8333333333333334d0)))))
    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 * (c - b))))));
	double tmp;
	if (a <= -4e+32) {
		tmp = t_1;
	} else if (a <= 2e-249) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * -0.8333333333333334)))));
	} else if (a <= 1.7e-61) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * 0.8333333333333334)))));
	} 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 * (c - b))))))
	tmp = 0
	if a <= -4e+32:
		tmp = t_1
	elif a <= 2e-249:
		tmp = x / (x + (y * math.exp((2.0 * (b * -0.8333333333333334)))))
	elif a <= 1.7e-61:
		tmp = x / (x + (y * math.exp((2.0 * (c * 0.8333333333333334)))))
	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(a * Float64(c - b)))))))
	tmp = 0.0
	if (a <= -4e+32)
		tmp = t_1;
	elseif (a <= 2e-249)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * -0.8333333333333334))))));
	elseif (a <= 1.7e-61)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * 0.8333333333333334))))));
	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 * (c - b))))));
	tmp = 0.0;
	if (a <= -4e+32)
		tmp = t_1;
	elseif (a <= 2e-249)
		tmp = x / (x + (y * exp((2.0 * (b * -0.8333333333333334)))));
	elseif (a <= 1.7e-61)
		tmp = x / (x + (y * exp((2.0 * (c * 0.8333333333333334)))));
	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[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+32], t$95$1, If[LessEqual[a, 2e-249], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * -0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-61], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * 0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.00000000000000021e32 or 1.6999999999999999e-61 < a

   1. Initial program 87.1%

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

   2. Taylor expanded in a around inf 75.7%

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

   if -4.00000000000000021e32 < a < 2.00000000000000011e-249

   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 t around inf 72.9%

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

      1. mul-1-neg 72.9%

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

      2. distribute-rgt-neg-in 72.9%

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

      3. distribute-neg-in 72.9%

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

      4. metadata-eval 72.9%

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

      5. sub-neg 72.9%

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

   4. Simplified 72.9%

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

   5. Taylor expanded in a around 0 71.2%

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

   6. Taylor expanded in b around inf 66.8%

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

   if 2.00000000000000011e-249 < a < 1.6999999999999999e-61

   1. Initial program 88.7%

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

   2. Taylor expanded in t around inf 71.4%

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

      1. mul-1-neg 71.4%

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

      2. distribute-rgt-neg-in 71.4%

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

      3. distribute-neg-in 71.4%

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

      4. metadata-eval 71.4%

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

      5. sub-neg 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in a around 0 71.4%

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

   6. Taylor expanded in b around 0 71.6%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-249}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-61}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot 0.8333333333333334\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 11: 71.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{if}\;a \leq -35000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b}{t}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))
   (if (<= a -35000000.0)
     t_1
     (if (<= a 1.65e-7)
       (/ x (+ x (* y (exp (* 2.0 (* (- b c) -0.8333333333333334))))))
       (if (<= a 2.85e+16)
         (/ x (+ x (* y (exp (* 1.3333333333333333 (/ b 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 * (c - b))))));
	double tmp;
	if (a <= -35000000.0) {
		tmp = t_1;
	} else if (a <= 1.65e-7) {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * -0.8333333333333334)))));
	} else if (a <= 2.85e+16) {
		tmp = x / (x + (y * exp((1.3333333333333333 * (b / 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 * (c - b))))))
    if (a <= (-35000000.0d0)) then
        tmp = t_1
    else if (a <= 1.65d-7) then
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * (-0.8333333333333334d0))))))
    else if (a <= 2.85d+16) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * (b / t)))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	double tmp;
	if (a <= -35000000.0) {
		tmp = t_1;
	} else if (a <= 1.65e-7) {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * -0.8333333333333334)))));
	} else if (a <= 2.85e+16) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * (b / 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 * (c - b))))))
	tmp = 0
	if a <= -35000000.0:
		tmp = t_1
	elif a <= 1.65e-7:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * -0.8333333333333334)))))
	elif a <= 2.85e+16:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * (b / 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(a * Float64(c - b)))))))
	tmp = 0.0
	if (a <= -35000000.0)
		tmp = t_1;
	elseif (a <= 1.65e-7)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * -0.8333333333333334))))));
	elseif (a <= 2.85e+16)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(b / 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 * (c - b))))));
	tmp = 0.0;
	if (a <= -35000000.0)
		tmp = t_1;
	elseif (a <= 1.65e-7)
		tmp = x / (x + (y * exp((2.0 * ((b - c) * -0.8333333333333334)))));
	elseif (a <= 2.85e+16)
		tmp = x / (x + (y * exp((1.3333333333333333 * (b / 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[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -35000000.0], t$95$1, If[LessEqual[a, 1.65e-7], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * -0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.85e+16], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.5e7 or 2.85e16 < a

   1. Initial program 88.3%

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

   2. Taylor expanded in a around inf 81.1%

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

   if -3.5e7 < a < 1.6500000000000001e-7

   1. Initial program 93.0%

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

   2. Taylor expanded in t around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-rgt-neg-in 70.6%

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

      3. distribute-neg-in 70.6%

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

      4. metadata-eval 70.6%

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

      5. sub-neg 70.6%

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

   4. Simplified 70.6%

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

   5. Taylor expanded in a around 0 70.6%

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

   if 1.6500000000000001e-7 < a < 2.85e16

   1. Initial program 76.9%

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

   2. Taylor expanded in b around inf 77.7%

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

      1. *-commutative 77.7%

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

      2. associate--r+ 77.7%

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

      3. sub-neg 77.7%

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

      4. associate-*r/ 77.7%

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

      5. metadata-eval 77.7%

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

      6. metadata-eval 77.7%

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

      7. associate-+r- 77.7%

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

   4. Simplified 77.7%

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

   5. Taylor expanded in t around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. associate-*l/ 77.7%

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

      3. *-commutative 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in y around 0 77.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -35000000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{+16}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 12: 75.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-307} \lor \neg \left(t \leq 6.9 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t -2.9e-307) (not (<= t 6.9e-133)))
   (/ x (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a)))))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.9e-307) || !(t <= 6.9e-133)) {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((t <= (-2.9d-307)) .or. (.not. (t <= 6.9d-133))) then
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((t <= -2.9e-307) || !(t <= 6.9e-133)) {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= -2.9e-307) or not (t <= 6.9e-133):
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= -2.9e-307) || !(t <= 6.9e-133))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((t <= -2.9e-307) || ~((t <= 6.9e-133)))
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, -2.9e-307], N[Not[LessEqual[t, 6.9e-133]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -2.9e-307 or 6.9000000000000001e-133 < t

   1. Initial program 93.2%

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

   2. Taylor expanded in t around inf 83.1%

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

      1. mul-1-neg 83.1%

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

      2. distribute-rgt-neg-in 83.1%

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

      3. distribute-neg-in 83.1%

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

      4. metadata-eval 83.1%

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

      5. sub-neg 83.1%

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

   4. Simplified 83.1%

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

   if -2.9e-307 < t < 6.9000000000000001e-133

   1. Initial program 76.0%

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

   2. Taylor expanded in a around inf 36.2%

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

   3. Taylor expanded in a around 0 30.6%

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

   4. Taylor expanded in x around inf 63.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-307} \lor \neg \left(t \leq 6.9 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 61.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 650000000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -4.5e-116)
   1.0
   (if (<= c 650000000.0)
     (/ x (+ x (* y (exp (* 2.0 (* b -0.8333333333333334))))))
     (/ x (* y (exp (* c 1.6666666666666667)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -4.5e-116) {
		tmp = 1.0;
	} else if (c <= 650000000.0) {
		tmp = x / (x + (y * exp((2.0 * (b * -0.8333333333333334)))));
	} else {
		tmp = 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) :: tmp
    if (c <= (-4.5d-116)) then
        tmp = 1.0d0
    else if (c <= 650000000.0d0) then
        tmp = x / (x + (y * exp((2.0d0 * (b * (-0.8333333333333334d0))))))
    else
        tmp = 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 tmp;
	if (c <= -4.5e-116) {
		tmp = 1.0;
	} else if (c <= 650000000.0) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * -0.8333333333333334)))));
	} else {
		tmp = x / (y * Math.exp((c * 1.6666666666666667)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -4.5e-116:
		tmp = 1.0
	elif c <= 650000000.0:
		tmp = x / (x + (y * math.exp((2.0 * (b * -0.8333333333333334)))))
	else:
		tmp = x / (y * math.exp((c * 1.6666666666666667)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -4.5e-116)
		tmp = 1.0;
	elseif (c <= 650000000.0)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * -0.8333333333333334))))));
	else
		tmp = 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)
	tmp = 0.0;
	if (c <= -4.5e-116)
		tmp = 1.0;
	elseif (c <= 650000000.0)
		tmp = x / (x + (y * exp((2.0 * (b * -0.8333333333333334)))));
	else
		tmp = x / (y * exp((c * 1.6666666666666667)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -4.5e-116], 1.0, If[LessEqual[c, 650000000.0], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * -0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.50000000000000012e-116

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf 62.0%

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

   3. Taylor expanded in a around 0 30.0%

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

   4. Taylor expanded in x around inf 72.8%

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

   if -4.50000000000000012e-116 < c < 6.5e8

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

      3. distribute-neg-in 76.9%

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

      4. metadata-eval 76.9%

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

      5. sub-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in a around 0 67.9%

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

   6. Taylor expanded in b around inf 67.9%

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

   if 6.5e8 < c

   1. Initial program 79.0%

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

   2. Taylor expanded in t around inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-in 76.8%

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

      3. distribute-neg-in 76.8%

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

      4. metadata-eval 76.8%

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

      5. sub-neg 76.8%

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

   4. Simplified 76.8%

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

   5. Taylor expanded in a around 0 72.7%

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

   6. Taylor expanded in b around 0 65.9%

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

   7. Taylor expanded in x around 0 65.9%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.5 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 650000000:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 14: 62.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -8.6e-116)
   1.0
   (if (<= c 2.05e+42)
     (/ x (+ x (* y (exp (* -2.0 (* b a))))))
     (/ x (* y (exp (* c 1.6666666666666667)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -8.6e-116) {
		tmp = 1.0;
	} else if (c <= 2.05e+42) {
		tmp = x / (x + (y * exp((-2.0 * (b * a)))));
	} else {
		tmp = 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) :: tmp
    if (c <= (-8.6d-116)) then
        tmp = 1.0d0
    else if (c <= 2.05d+42) then
        tmp = x / (x + (y * exp(((-2.0d0) * (b * a)))))
    else
        tmp = 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 tmp;
	if (c <= -8.6e-116) {
		tmp = 1.0;
	} else if (c <= 2.05e+42) {
		tmp = x / (x + (y * Math.exp((-2.0 * (b * a)))));
	} else {
		tmp = x / (y * Math.exp((c * 1.6666666666666667)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -8.6e-116:
		tmp = 1.0
	elif c <= 2.05e+42:
		tmp = x / (x + (y * math.exp((-2.0 * (b * a)))))
	else:
		tmp = x / (y * math.exp((c * 1.6666666666666667)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -8.6e-116)
		tmp = 1.0;
	elseif (c <= 2.05e+42)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(b * a))))));
	else
		tmp = 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)
	tmp = 0.0;
	if (c <= -8.6e-116)
		tmp = 1.0;
	elseif (c <= 2.05e+42)
		tmp = x / (x + (y * exp((-2.0 * (b * a)))));
	else
		tmp = x / (y * exp((c * 1.6666666666666667)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -8.6e-116], 1.0, If[LessEqual[c, 2.05e+42], N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(b * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.5999999999999994e-116

   1. Initial program 95.5%

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

   2. Taylor expanded in a around inf 62.0%

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

   3. Taylor expanded in a around 0 30.0%

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

   4. Taylor expanded in x around inf 72.8%

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

   if -8.5999999999999994e-116 < c < 2.05e42

   1. Initial program 91.4%

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

   2. Taylor expanded in a around inf 70.0%

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

   3. Taylor expanded in c around 0 70.0%

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

   if 2.05e42 < c

   1. Initial program 78.8%

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

   2. Taylor expanded in t around inf 77.8%

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

      1. mul-1-neg 77.8%

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

      2. distribute-rgt-neg-in 77.8%

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

      3. distribute-neg-in 77.8%

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

      4. metadata-eval 77.8%

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

      5. sub-neg 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in a around 0 73.0%

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

   6. Taylor expanded in b around 0 68.2%

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

   7. Taylor expanded in x around 0 68.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.05 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]

Alternative 15: 51.0% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+221}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(2 \cdot c\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -9e-116)
   1.0
   (if (<= c -7.5e-259)
     (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))
     (if (<= c 2.6e-161)
       1.0
       (if (<= c 1.4e+117)
         (/ x (+ y (+ x (* 2.0 (* a (* y (- c b)))))))
         (if (<= c 2e+221)
           1.0
           (/
            x
            (+
             x
             (*
              y
              (+
               (*
                (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t)))
                (* 2.0 c))
               1.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9e-116) {
		tmp = 1.0;
	} else if (c <= -7.5e-259) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 2.6e-161) {
		tmp = 1.0;
	} else if (c <= 1.4e+117) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if (c <= 2e+221) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-9d-116)) then
        tmp = 1.0d0
    else if (c <= (-7.5d-259)) then
        tmp = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    else if (c <= 2.6d-161) then
        tmp = 1.0d0
    else if (c <= 1.4d+117) then
        tmp = x / (y + (x + (2.0d0 * (a * (y * (c - b))))))
    else if (c <= 2d+221) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * (((0.8333333333333334d0 + (a - (0.6666666666666666d0 / t))) * (2.0d0 * c)) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9e-116) {
		tmp = 1.0;
	} else if (c <= -7.5e-259) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 2.6e-161) {
		tmp = 1.0;
	} else if (c <= 1.4e+117) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if (c <= 2e+221) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -9e-116:
		tmp = 1.0
	elif c <= -7.5e-259:
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	elif c <= 2.6e-161:
		tmp = 1.0
	elif c <= 1.4e+117:
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))))
	elif c <= 2e+221:
		tmp = 1.0
	else:
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -9e-116)
		tmp = 1.0;
	elseif (c <= -7.5e-259)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))));
	elseif (c <= 2.6e-161)
		tmp = 1.0;
	elseif (c <= 1.4e+117)
		tmp = Float64(x / Float64(y + Float64(x + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	elseif (c <= 2e+221)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t))) * Float64(2.0 * c)) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -9e-116)
		tmp = 1.0;
	elseif (c <= -7.5e-259)
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	elseif (c <= 2.6e-161)
		tmp = 1.0;
	elseif (c <= 1.4e+117)
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	elseif (c <= 2e+221)
		tmp = 1.0;
	else
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -9e-116], 1.0, If[LessEqual[c, -7.5e-259], N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.6e-161], 1.0, If[LessEqual[c, 1.4e+117], N[(x / N[(y + N[(x + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e+221], 1.0, N[(x / N[(x + N[(y * N[(N[(N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 * c), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.00000000000000023e-116 or -7.50000000000000052e-259 < c < 2.59999999999999995e-161 or 1.39999999999999999e117 < c < 2.0000000000000001e221

   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 a around inf 61.7%

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

   3. Taylor expanded in a around 0 30.1%

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

   4. Taylor expanded in x around inf 64.2%

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

   if -9.00000000000000023e-116 < c < -7.50000000000000052e-259

   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 b around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. associate--r+ 83.5%

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

      3. sub-neg 83.5%

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

      4. associate-*r/ 83.5%

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

      5. metadata-eval 83.5%

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

      6. metadata-eval 83.5%

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

      7. associate-+r- 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in t around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*l/ 56.8%

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

      3. *-commutative 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in b around 0 63.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1.3333333333333333 \cdot \frac{b}{t} + 1\right)}} \]

   if 2.59999999999999995e-161 < c < 1.39999999999999999e117

   1. Initial program 81.3%

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

   2. Taylor expanded in a around inf 67.8%

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

   3. Taylor expanded in a around 0 58.9%

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

   if 2.0000000000000001e221 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in 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. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in c around 0 74.6%

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

      1. associate-*r* 74.6%

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

      2. associate--l+ 74.6%

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

      3. associate-*r/ 74.6%

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

      4. metadata-eval 74.6%

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

   7. Simplified 74.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + \left(2 \cdot c\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -7.5 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+221}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(2 \cdot c\right) + 1\right)}\\ \end{array} \]

Alternative 16: 51.2% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+216}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(2 \cdot c\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.6e-116)
   1.0
   (if (<= c -1.95e-283)
     (/
      x
      (-
       x
       (*
        y
        (+
         -1.0
         (*
          2.0
          (*
           b
           (+ (+ a 0.8333333333333334) (* 0.6666666666666666 (/ -1.0 t)))))))))
     (if (<= c 2.5e-160)
       1.0
       (if (<= c 3.8e+117)
         (/ x (+ y (+ x (* 2.0 (* a (* y (- c b)))))))
         (if (<= c 5.8e+216)
           1.0
           (/
            x
            (+
             x
             (*
              y
              (+
               (*
                (+ 0.8333333333333334 (- a (/ 0.6666666666666666 t)))
                (* 2.0 c))
               1.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.6e-116) {
		tmp = 1.0;
	} else if (c <= -1.95e-283) {
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	} else if (c <= 2.5e-160) {
		tmp = 1.0;
	} else if (c <= 3.8e+117) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if (c <= 5.8e+216) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-2.6d-116)) then
        tmp = 1.0d0
    else if (c <= (-1.95d-283)) then
        tmp = x / (x - (y * ((-1.0d0) + (2.0d0 * (b * ((a + 0.8333333333333334d0) + (0.6666666666666666d0 * ((-1.0d0) / t))))))))
    else if (c <= 2.5d-160) then
        tmp = 1.0d0
    else if (c <= 3.8d+117) then
        tmp = x / (y + (x + (2.0d0 * (a * (y * (c - b))))))
    else if (c <= 5.8d+216) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * (((0.8333333333333334d0 + (a - (0.6666666666666666d0 / t))) * (2.0d0 * c)) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.6e-116) {
		tmp = 1.0;
	} else if (c <= -1.95e-283) {
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	} else if (c <= 2.5e-160) {
		tmp = 1.0;
	} else if (c <= 3.8e+117) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if (c <= 5.8e+216) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.6e-116:
		tmp = 1.0
	elif c <= -1.95e-283:
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))))
	elif c <= 2.5e-160:
		tmp = 1.0
	elif c <= 3.8e+117:
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))))
	elif c <= 5.8e+216:
		tmp = 1.0
	else:
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.6e-116)
		tmp = 1.0;
	elseif (c <= -1.95e-283)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 + Float64(2.0 * Float64(b * Float64(Float64(a + 0.8333333333333334) + Float64(0.6666666666666666 * Float64(-1.0 / t)))))))));
	elseif (c <= 2.5e-160)
		tmp = 1.0;
	elseif (c <= 3.8e+117)
		tmp = Float64(x / Float64(y + Float64(x + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	elseif (c <= 5.8e+216)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(Float64(0.8333333333333334 + Float64(a - Float64(0.6666666666666666 / t))) * Float64(2.0 * c)) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -2.6e-116)
		tmp = 1.0;
	elseif (c <= -1.95e-283)
		tmp = x / (x - (y * (-1.0 + (2.0 * (b * ((a + 0.8333333333333334) + (0.6666666666666666 * (-1.0 / t))))))));
	elseif (c <= 2.5e-160)
		tmp = 1.0;
	elseif (c <= 3.8e+117)
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	elseif (c <= 5.8e+216)
		tmp = 1.0;
	else
		tmp = x / (x + (y * (((0.8333333333333334 + (a - (0.6666666666666666 / t))) * (2.0 * c)) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.6e-116], 1.0, If[LessEqual[c, -1.95e-283], N[(x / N[(x - N[(y * N[(-1.0 + N[(2.0 * N[(b * N[(N[(a + 0.8333333333333334), $MachinePrecision] + N[(0.6666666666666666 * N[(-1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.5e-160], 1.0, If[LessEqual[c, 3.8e+117], N[(x / N[(y + N[(x + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.8e+216], 1.0, N[(x / N[(x + N[(y * N[(N[(N[(0.8333333333333334 + N[(a - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(2.0 * c), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.6e-116 or -1.9500000000000001e-283 < c < 2.49999999999999997e-160 or 3.8000000000000002e117 < c < 5.8000000000000002e216

   1. Initial program 91.9%

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

   2. Taylor expanded in a around inf 61.7%

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

   3. Taylor expanded in a around 0 29.7%

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

   4. Taylor expanded in x around inf 64.9%

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

   if -2.6e-116 < c < -1.9500000000000001e-283

   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 b around inf 83.1%

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

      1. *-commutative 83.1%

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

      2. associate--r+ 83.1%

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

      3. sub-neg 83.1%

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

      4. associate-*r/ 83.1%

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

      5. metadata-eval 83.1%

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

      6. metadata-eval 83.1%

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

      7. associate-+r- 83.1%

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

   4. Simplified 83.1%

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

   5. Taylor expanded in b around 0 60.5%

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

   if 2.49999999999999997e-160 < c < 3.8000000000000002e117

   1. Initial program 81.3%

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

   2. Taylor expanded in a around inf 67.8%

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

   3. Taylor expanded in a around 0 58.9%

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

   if 5.8000000000000002e216 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in 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. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in c around 0 74.6%

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

      1. associate-*r* 74.6%

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

      2. associate--l+ 74.6%

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

      3. associate-*r/ 74.6%

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

      4. metadata-eval 74.6%

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

   7. Simplified 74.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + \left(2 \cdot c\right) \cdot \left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 + 2 \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) + 0.6666666666666666 \cdot \frac{-1}{t}\right)\right)\right)}\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{+216}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(0.8333333333333334 + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(2 \cdot c\right) + 1\right)}\\ \end{array} \]

Alternative 17: 49.0% accurate, 8.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;c \leq -3.8 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-161}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+116} \lor \neg \left(c \leq 9.4 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{x}{y - 2 \cdot \left(y \cdot \left(\left(b - c\right) \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))))
   (if (<= c -3.8e-116)
     1.0
     (if (<= c -1.7e-260)
       t_1
       (if (<= c 1.7e-161)
         1.0
         (if (<= c 4.8e+27)
           t_1
           (if (<= c 1.15e+54)
             1.0
             (if (or (<= c 4.7e+116) (not (<= c 9.4e+219)))
               (/ x (- y (* 2.0 (* y (* (- b c) a)))))
               1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -3.8e-116) {
		tmp = 1.0;
	} else if (c <= -1.7e-260) {
		tmp = t_1;
	} else if (c <= 1.7e-161) {
		tmp = 1.0;
	} else if (c <= 4.8e+27) {
		tmp = t_1;
	} else if (c <= 1.15e+54) {
		tmp = 1.0;
	} else if ((c <= 4.7e+116) || !(c <= 9.4e+219)) {
		tmp = x / (y - (2.0 * (y * ((b - c) * a))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    if (c <= (-3.8d-116)) then
        tmp = 1.0d0
    else if (c <= (-1.7d-260)) then
        tmp = t_1
    else if (c <= 1.7d-161) then
        tmp = 1.0d0
    else if (c <= 4.8d+27) then
        tmp = t_1
    else if (c <= 1.15d+54) then
        tmp = 1.0d0
    else if ((c <= 4.7d+116) .or. (.not. (c <= 9.4d+219))) then
        tmp = x / (y - (2.0d0 * (y * ((b - c) * a))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -3.8e-116) {
		tmp = 1.0;
	} else if (c <= -1.7e-260) {
		tmp = t_1;
	} else if (c <= 1.7e-161) {
		tmp = 1.0;
	} else if (c <= 4.8e+27) {
		tmp = t_1;
	} else if (c <= 1.15e+54) {
		tmp = 1.0;
	} else if ((c <= 4.7e+116) || !(c <= 9.4e+219)) {
		tmp = x / (y - (2.0 * (y * ((b - c) * a))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	tmp = 0
	if c <= -3.8e-116:
		tmp = 1.0
	elif c <= -1.7e-260:
		tmp = t_1
	elif c <= 1.7e-161:
		tmp = 1.0
	elif c <= 4.8e+27:
		tmp = t_1
	elif c <= 1.15e+54:
		tmp = 1.0
	elif (c <= 4.7e+116) or not (c <= 9.4e+219):
		tmp = x / (y - (2.0 * (y * ((b - c) * a))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))))
	tmp = 0.0
	if (c <= -3.8e-116)
		tmp = 1.0;
	elseif (c <= -1.7e-260)
		tmp = t_1;
	elseif (c <= 1.7e-161)
		tmp = 1.0;
	elseif (c <= 4.8e+27)
		tmp = t_1;
	elseif (c <= 1.15e+54)
		tmp = 1.0;
	elseif ((c <= 4.7e+116) || !(c <= 9.4e+219))
		tmp = Float64(x / Float64(y - Float64(2.0 * Float64(y * Float64(Float64(b - c) * a)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	tmp = 0.0;
	if (c <= -3.8e-116)
		tmp = 1.0;
	elseif (c <= -1.7e-260)
		tmp = t_1;
	elseif (c <= 1.7e-161)
		tmp = 1.0;
	elseif (c <= 4.8e+27)
		tmp = t_1;
	elseif (c <= 1.15e+54)
		tmp = 1.0;
	elseif ((c <= 4.7e+116) || ~((c <= 9.4e+219)))
		tmp = x / (y - (2.0 * (y * ((b - c) * a))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.8e-116], 1.0, If[LessEqual[c, -1.7e-260], t$95$1, If[LessEqual[c, 1.7e-161], 1.0, If[LessEqual[c, 4.8e+27], t$95$1, If[LessEqual[c, 1.15e+54], 1.0, If[Or[LessEqual[c, 4.7e+116], N[Not[LessEqual[c, 9.4e+219]], $MachinePrecision]], N[(x / N[(y - N[(2.0 * N[(y * N[(N[(b - c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.8000000000000001e-116 or -1.6999999999999999e-260 < c < 1.69999999999999991e-161 or 4.79999999999999995e27 < c < 1.14999999999999997e54 or 4.7000000000000003e116 < c < 9.40000000000000027e219

   1. Initial program 90.8%

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

   2. Taylor expanded in a around inf 60.8%

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

   3. Taylor expanded in a around 0 31.5%

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

   4. Taylor expanded in x around inf 65.5%

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

   if -3.8000000000000001e-116 < c < -1.6999999999999999e-260 or 1.69999999999999991e-161 < c < 4.79999999999999995e27

   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 b around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate--r+ 83.0%

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

      3. sub-neg 83.0%

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

      4. associate-*r/ 83.0%

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

      5. metadata-eval 83.0%

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

      6. metadata-eval 83.0%

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

      7. associate-+r- 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in t around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. associate-*l/ 53.5%

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

      3. *-commutative 53.5%

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

   7. Simplified 53.5%

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

   8. Taylor expanded in b around 0 58.4%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1.3333333333333333 \cdot \frac{b}{t} + 1\right)}} \]

   if 1.14999999999999997e54 < c < 4.7000000000000003e116 or 9.40000000000000027e219 < c

   1. Initial program 80.8%

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

   2. Taylor expanded in a around inf 81.3%

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

   3. Taylor expanded in a around 0 56.6%

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

   4. Taylor expanded in x around 0 59.5%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.8 \cdot 10^{-116}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 1.7 \cdot 10^{-161}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 1.15 \cdot 10^{+54}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.7 \cdot 10^{+116} \lor \neg \left(c \leq 9.4 \cdot 10^{+219}\right):\\ \;\;\;\;\frac{x}{y - 2 \cdot \left(y \cdot \left(\left(b - c\right) \cdot a\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 18: 51.0% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-261}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-162}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+115} \lor \neg \left(c \leq 7.6 \cdot 10^{+216}\right):\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -9.2e-117)
   1.0
   (if (<= c -1.9e-261)
     (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))
     (if (<= c 2.3e-162)
       1.0
       (if (or (<= c 4.2e+115) (not (<= c 7.6e+216)))
         (/ x (+ x (* y (+ (* 2.0 (* a (- c b))) 1.0))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.2e-117) {
		tmp = 1.0;
	} else if (c <= -1.9e-261) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 2.3e-162) {
		tmp = 1.0;
	} else if ((c <= 4.2e+115) || !(c <= 7.6e+216)) {
		tmp = x / (x + (y * ((2.0 * (a * (c - b))) + 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-9.2d-117)) then
        tmp = 1.0d0
    else if (c <= (-1.9d-261)) then
        tmp = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    else if (c <= 2.3d-162) then
        tmp = 1.0d0
    else if ((c <= 4.2d+115) .or. (.not. (c <= 7.6d+216))) then
        tmp = x / (x + (y * ((2.0d0 * (a * (c - b))) + 1.0d0)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.2e-117) {
		tmp = 1.0;
	} else if (c <= -1.9e-261) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 2.3e-162) {
		tmp = 1.0;
	} else if ((c <= 4.2e+115) || !(c <= 7.6e+216)) {
		tmp = x / (x + (y * ((2.0 * (a * (c - b))) + 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -9.2e-117:
		tmp = 1.0
	elif c <= -1.9e-261:
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	elif c <= 2.3e-162:
		tmp = 1.0
	elif (c <= 4.2e+115) or not (c <= 7.6e+216):
		tmp = x / (x + (y * ((2.0 * (a * (c - b))) + 1.0)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -9.2e-117)
		tmp = 1.0;
	elseif (c <= -1.9e-261)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))));
	elseif (c <= 2.3e-162)
		tmp = 1.0;
	elseif ((c <= 4.2e+115) || !(c <= 7.6e+216))
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(a * Float64(c - b))) + 1.0))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -9.2e-117)
		tmp = 1.0;
	elseif (c <= -1.9e-261)
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	elseif (c <= 2.3e-162)
		tmp = 1.0;
	elseif ((c <= 4.2e+115) || ~((c <= 7.6e+216)))
		tmp = x / (x + (y * ((2.0 * (a * (c - b))) + 1.0)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -9.2e-117], 1.0, If[LessEqual[c, -1.9e-261], N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e-162], 1.0, If[Or[LessEqual[c, 4.2e+115], N[Not[LessEqual[c, 7.6e+216]], $MachinePrecision]], N[(x / N[(x + N[(y * N[(N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.19999999999999978e-117 or -1.9e-261 < c < 2.2999999999999998e-162 or 4.20000000000000007e115 < c < 7.60000000000000029e216

   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 a around inf 61.7%

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

   3. Taylor expanded in a around 0 30.1%

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

   4. Taylor expanded in x around inf 64.2%

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

   if -9.19999999999999978e-117 < c < -1.9e-261

   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 b around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. associate--r+ 83.5%

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

      3. sub-neg 83.5%

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

      4. associate-*r/ 83.5%

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

      5. metadata-eval 83.5%

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

      6. metadata-eval 83.5%

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

      7. associate-+r- 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in t around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*l/ 56.8%

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

      3. *-commutative 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in b around 0 63.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1.3333333333333333 \cdot \frac{b}{t} + 1\right)}} \]

   if 2.2999999999999998e-162 < c < 4.20000000000000007e115 or 7.60000000000000029e216 < c

   1. Initial program 80.8%

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

   2. Taylor expanded in a around inf 72.2%

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

   3. Taylor expanded in a around 0 57.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.9 \cdot 10^{-261}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{-162}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+115} \lor \neg \left(c \leq 7.6 \cdot 10^{+216}\right):\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 19: 50.6% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.8 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+222}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -9.8e-117)
   1.0
   (if (<= c -2.6e-258)
     (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))
     (if (<= c 1.35e-160)
       1.0
       (if (<= c 3.9e+115)
         (/ x (+ y (+ x (* 2.0 (* a (* y (- c b)))))))
         (if (<= c 4.6e+222)
           1.0
           (/ x (+ x (* y (+ (* 2.0 (* a (- c b))) 1.0))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.8e-117) {
		tmp = 1.0;
	} else if (c <= -2.6e-258) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 1.35e-160) {
		tmp = 1.0;
	} else if (c <= 3.9e+115) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if (c <= 4.6e+222) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * ((2.0 * (a * (c - 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 (c <= (-9.8d-117)) then
        tmp = 1.0d0
    else if (c <= (-2.6d-258)) then
        tmp = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    else if (c <= 1.35d-160) then
        tmp = 1.0d0
    else if (c <= 3.9d+115) then
        tmp = x / (y + (x + (2.0d0 * (a * (y * (c - b))))))
    else if (c <= 4.6d+222) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * ((2.0d0 * (a * (c - 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 (c <= -9.8e-117) {
		tmp = 1.0;
	} else if (c <= -2.6e-258) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	} else if (c <= 1.35e-160) {
		tmp = 1.0;
	} else if (c <= 3.9e+115) {
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	} else if (c <= 4.6e+222) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * ((2.0 * (a * (c - b))) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -9.8e-117:
		tmp = 1.0
	elif c <= -2.6e-258:
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	elif c <= 1.35e-160:
		tmp = 1.0
	elif c <= 3.9e+115:
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))))
	elif c <= 4.6e+222:
		tmp = 1.0
	else:
		tmp = x / (x + (y * ((2.0 * (a * (c - b))) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -9.8e-117)
		tmp = 1.0;
	elseif (c <= -2.6e-258)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))));
	elseif (c <= 1.35e-160)
		tmp = 1.0;
	elseif (c <= 3.9e+115)
		tmp = Float64(x / Float64(y + Float64(x + Float64(2.0 * Float64(a * Float64(y * Float64(c - b)))))));
	elseif (c <= 4.6e+222)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(a * Float64(c - b))) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -9.8e-117)
		tmp = 1.0;
	elseif (c <= -2.6e-258)
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	elseif (c <= 1.35e-160)
		tmp = 1.0;
	elseif (c <= 3.9e+115)
		tmp = x / (y + (x + (2.0 * (a * (y * (c - b))))));
	elseif (c <= 4.6e+222)
		tmp = 1.0;
	else
		tmp = x / (x + (y * ((2.0 * (a * (c - b))) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -9.8e-117], 1.0, If[LessEqual[c, -2.6e-258], N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e-160], 1.0, If[LessEqual[c, 3.9e+115], N[(x / N[(y + N[(x + N[(2.0 * N[(a * N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.6e+222], 1.0, N[(x / N[(x + N[(y * N[(N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.7999999999999995e-117 or -2.60000000000000018e-258 < c < 1.35000000000000005e-160 or 3.90000000000000006e115 < c < 4.60000000000000021e222

   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 a around inf 61.7%

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

   3. Taylor expanded in a around 0 30.1%

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

   4. Taylor expanded in x around inf 64.2%

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

   if -9.7999999999999995e-117 < c < -2.60000000000000018e-258

   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 b around inf 83.5%

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

      1. *-commutative 83.5%

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

      2. associate--r+ 83.5%

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

      3. sub-neg 83.5%

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

      4. associate-*r/ 83.5%

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

      5. metadata-eval 83.5%

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

      6. metadata-eval 83.5%

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

      7. associate-+r- 83.5%

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

   4. Simplified 83.5%

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

   5. Taylor expanded in t around 0 56.8%

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

      1. associate-*r/ 56.8%

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

      2. associate-*l/ 56.8%

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

      3. *-commutative 56.8%

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

   7. Simplified 56.8%

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

   8. Taylor expanded in b around 0 63.6%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1.3333333333333333 \cdot \frac{b}{t} + 1\right)}} \]

   if 1.35000000000000005e-160 < c < 3.90000000000000006e115

   1. Initial program 81.3%

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

   2. Taylor expanded in a around inf 67.8%

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

   3. Taylor expanded in a around 0 58.9%

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

   if 4.60000000000000021e222 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in a around inf 84.7%

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

   3. Taylor expanded in a around 0 59.3%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + 2 \cdot \left(a \cdot \left(c - b\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.8 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{+115}:\\ \;\;\;\;\frac{x}{y + \left(x + 2 \cdot \left(a \cdot \left(y \cdot \left(c - b\right)\right)\right)\right)}\\ \mathbf{elif}\;c \leq 4.6 \cdot 10^{+222}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(a \cdot \left(c - b\right)\right) + 1\right)}\\ \end{array} \]

Alternative 20: 49.9% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{if}\;c \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.16 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+218}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{y \cdot \left(c \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ b t))))))))
   (if (<= c -7.6e-117)
     1.0
     (if (<= c -1.55e-260)
       t_1
       (if (<= c 7.5e-160)
         1.0
         (if (<= c 2.16e+27)
           t_1
           (if (<= c 1.5e+218) 1.0 (/ (* x 0.5) (* y (* c a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -7.6e-117) {
		tmp = 1.0;
	} else if (c <= -1.55e-260) {
		tmp = t_1;
	} else if (c <= 7.5e-160) {
		tmp = 1.0;
	} else if (c <= 2.16e+27) {
		tmp = t_1;
	} else if (c <= 1.5e+218) {
		tmp = 1.0;
	} else {
		tmp = (x * 0.5) / (y * (c * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * (b / t)))))
    if (c <= (-7.6d-117)) then
        tmp = 1.0d0
    else if (c <= (-1.55d-260)) then
        tmp = t_1
    else if (c <= 7.5d-160) then
        tmp = 1.0d0
    else if (c <= 2.16d+27) then
        tmp = t_1
    else if (c <= 1.5d+218) then
        tmp = 1.0d0
    else
        tmp = (x * 0.5d0) / (y * (c * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	double tmp;
	if (c <= -7.6e-117) {
		tmp = 1.0;
	} else if (c <= -1.55e-260) {
		tmp = t_1;
	} else if (c <= 7.5e-160) {
		tmp = 1.0;
	} else if (c <= 2.16e+27) {
		tmp = t_1;
	} else if (c <= 1.5e+218) {
		tmp = 1.0;
	} else {
		tmp = (x * 0.5) / (y * (c * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))))
	tmp = 0
	if c <= -7.6e-117:
		tmp = 1.0
	elif c <= -1.55e-260:
		tmp = t_1
	elif c <= 7.5e-160:
		tmp = 1.0
	elif c <= 2.16e+27:
		tmp = t_1
	elif c <= 1.5e+218:
		tmp = 1.0
	else:
		tmp = (x * 0.5) / (y * (c * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(b / t))))))
	tmp = 0.0
	if (c <= -7.6e-117)
		tmp = 1.0;
	elseif (c <= -1.55e-260)
		tmp = t_1;
	elseif (c <= 7.5e-160)
		tmp = 1.0;
	elseif (c <= 2.16e+27)
		tmp = t_1;
	elseif (c <= 1.5e+218)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x * 0.5) / Float64(y * Float64(c * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * (b / t)))));
	tmp = 0.0;
	if (c <= -7.6e-117)
		tmp = 1.0;
	elseif (c <= -1.55e-260)
		tmp = t_1;
	elseif (c <= 7.5e-160)
		tmp = 1.0;
	elseif (c <= 2.16e+27)
		tmp = t_1;
	elseif (c <= 1.5e+218)
		tmp = 1.0;
	else
		tmp = (x * 0.5) / (y * (c * a));
	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[(-1.0 - N[(1.3333333333333333 * N[(b / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.6e-117], 1.0, If[LessEqual[c, -1.55e-260], t$95$1, If[LessEqual[c, 7.5e-160], 1.0, If[LessEqual[c, 2.16e+27], t$95$1, If[LessEqual[c, 1.5e+218], 1.0, N[(N[(x * 0.5), $MachinePrecision] / N[(y * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.59999999999999945e-117 or -1.54999999999999991e-260 < c < 7.50000000000000023e-160 or 2.16e27 < c < 1.5e218

   1. Initial program 90.3%

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

   2. Taylor expanded in a around inf 61.9%

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

   3. Taylor expanded in a around 0 33.5%

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

   4. Taylor expanded in x around inf 62.4%

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

   if -7.59999999999999945e-117 < c < -1.54999999999999991e-260 or 7.50000000000000023e-160 < c < 2.16e27

   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 b around inf 83.0%

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

      1. *-commutative 83.0%

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

      2. associate--r+ 83.0%

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

      3. sub-neg 83.0%

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

      4. associate-*r/ 83.0%

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

      5. metadata-eval 83.0%

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

      6. metadata-eval 83.0%

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

      7. associate-+r- 83.0%

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

   4. Simplified 83.0%

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

   5. Taylor expanded in t around 0 53.5%

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

      1. associate-*r/ 53.5%

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

      2. associate-*l/ 53.5%

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

      3. *-commutative 53.5%

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

   7. Simplified 53.5%

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

   8. Taylor expanded in b around 0 58.4%

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1.3333333333333333 \cdot \frac{b}{t} + 1\right)}} \]

   if 1.5e218 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in a around inf 84.7%

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

   3. Taylor expanded in a around 0 54.5%

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

   4. Taylor expanded in c around inf 49.4%

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

      1. associate-*r/ 49.4%

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

      2. *-commutative 49.4%

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

      3. associate-*r* 54.2%

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

   6. Simplified 54.2%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.6 \cdot 10^{-117}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.55 \cdot 10^{-260}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 7.5 \cdot 10^{-160}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.16 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b}{t}\right)}\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{+218}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{y \cdot \left(c \cdot a\right)}\\ \end{array} \]

Alternative 21: 49.6% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.6 \cdot 10^{-86}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+27}:\\ \;\;\;\;0.5 \cdot \frac{\frac{x}{a}}{y \cdot \left(c - b\right)}\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+221}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{y \cdot \left(c \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -9.6e-86)
   1.0
   (if (<= c -1.1e-258)
     (/ x (+ x y))
     (if (<= c 3.3e-22)
       1.0
       (if (<= c 2.2e+27)
         (* 0.5 (/ (/ x a) (* y (- c b))))
         (if (<= c 1.3e+221) 1.0 (/ (* x 0.5) (* y (* c a)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.6e-86) {
		tmp = 1.0;
	} else if (c <= -1.1e-258) {
		tmp = x / (x + y);
	} else if (c <= 3.3e-22) {
		tmp = 1.0;
	} else if (c <= 2.2e+27) {
		tmp = 0.5 * ((x / a) / (y * (c - b)));
	} else if (c <= 1.3e+221) {
		tmp = 1.0;
	} else {
		tmp = (x * 0.5) / (y * (c * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-9.6d-86)) then
        tmp = 1.0d0
    else if (c <= (-1.1d-258)) then
        tmp = x / (x + y)
    else if (c <= 3.3d-22) then
        tmp = 1.0d0
    else if (c <= 2.2d+27) then
        tmp = 0.5d0 * ((x / a) / (y * (c - b)))
    else if (c <= 1.3d+221) then
        tmp = 1.0d0
    else
        tmp = (x * 0.5d0) / (y * (c * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.6e-86) {
		tmp = 1.0;
	} else if (c <= -1.1e-258) {
		tmp = x / (x + y);
	} else if (c <= 3.3e-22) {
		tmp = 1.0;
	} else if (c <= 2.2e+27) {
		tmp = 0.5 * ((x / a) / (y * (c - b)));
	} else if (c <= 1.3e+221) {
		tmp = 1.0;
	} else {
		tmp = (x * 0.5) / (y * (c * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -9.6e-86:
		tmp = 1.0
	elif c <= -1.1e-258:
		tmp = x / (x + y)
	elif c <= 3.3e-22:
		tmp = 1.0
	elif c <= 2.2e+27:
		tmp = 0.5 * ((x / a) / (y * (c - b)))
	elif c <= 1.3e+221:
		tmp = 1.0
	else:
		tmp = (x * 0.5) / (y * (c * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -9.6e-86)
		tmp = 1.0;
	elseif (c <= -1.1e-258)
		tmp = Float64(x / Float64(x + y));
	elseif (c <= 3.3e-22)
		tmp = 1.0;
	elseif (c <= 2.2e+27)
		tmp = Float64(0.5 * Float64(Float64(x / a) / Float64(y * Float64(c - b))));
	elseif (c <= 1.3e+221)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x * 0.5) / Float64(y * Float64(c * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -9.6e-86)
		tmp = 1.0;
	elseif (c <= -1.1e-258)
		tmp = x / (x + y);
	elseif (c <= 3.3e-22)
		tmp = 1.0;
	elseif (c <= 2.2e+27)
		tmp = 0.5 * ((x / a) / (y * (c - b)));
	elseif (c <= 1.3e+221)
		tmp = 1.0;
	else
		tmp = (x * 0.5) / (y * (c * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -9.6e-86], 1.0, If[LessEqual[c, -1.1e-258], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e-22], 1.0, If[LessEqual[c, 2.2e+27], N[(0.5 * N[(N[(x / a), $MachinePrecision] / N[(y * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.3e+221], 1.0, N[(N[(x * 0.5), $MachinePrecision] / N[(y * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -9.60000000000000053e-86 or -1.10000000000000008e-258 < c < 3.3000000000000001e-22 or 2.1999999999999999e27 < c < 1.30000000000000002e221

   1. Initial program 90.6%

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

   2. Taylor expanded in a around inf 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 36.3%

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

   4. Taylor expanded in x around inf 60.7%

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

   if -9.60000000000000053e-86 < c < -1.10000000000000008e-258

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 64.3%

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

   3. Taylor expanded in a around 0 50.5%

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

   if 3.3000000000000001e-22 < c < 2.1999999999999999e27

   1. Initial program 70.0%

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

   2. Taylor expanded in a around inf 81.2%

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

   3. Taylor expanded in a around 0 52.1%

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

   4. Taylor expanded in a around inf 33.1%

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

      1. associate-*r* 33.1%

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

      2. *-commutative 33.1%

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

      3. associate-*r* 42.5%

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

      4. associate-/r* 61.6%

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

   6. Simplified 61.6%

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

   if 1.30000000000000002e221 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in a around inf 84.7%

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

   3. Taylor expanded in a around 0 54.5%

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

   4. Taylor expanded in c around inf 49.4%

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

      1. associate-*r/ 49.4%

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

      2. *-commutative 49.4%

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

      3. associate-*r* 54.2%

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

   6. Simplified 54.2%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{\left(c \cdot a\right) \cdot y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.6 \cdot 10^{-86}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+27}:\\ \;\;\;\;0.5 \cdot \frac{\frac{x}{a}}{y \cdot \left(c - b\right)}\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+221}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{y \cdot \left(c \cdot a\right)}\\ \end{array} \]

Alternative 22: 50.5% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{-84}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+217}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{\frac{x}{c}}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1.12e-84)
   1.0
   (if (<= c -2.5e-258)
     (/ x (+ x y))
     (if (<= c 1.95e+217) 1.0 (* 0.5 (/ (/ x c) (* y a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.12e-84) {
		tmp = 1.0;
	} else if (c <= -2.5e-258) {
		tmp = x / (x + y);
	} else if (c <= 1.95e+217) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * ((x / c) / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-1.12d-84)) then
        tmp = 1.0d0
    else if (c <= (-2.5d-258)) then
        tmp = x / (x + y)
    else if (c <= 1.95d+217) then
        tmp = 1.0d0
    else
        tmp = 0.5d0 * ((x / c) / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.12e-84) {
		tmp = 1.0;
	} else if (c <= -2.5e-258) {
		tmp = x / (x + y);
	} else if (c <= 1.95e+217) {
		tmp = 1.0;
	} else {
		tmp = 0.5 * ((x / c) / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1.12e-84:
		tmp = 1.0
	elif c <= -2.5e-258:
		tmp = x / (x + y)
	elif c <= 1.95e+217:
		tmp = 1.0
	else:
		tmp = 0.5 * ((x / c) / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1.12e-84)
		tmp = 1.0;
	elseif (c <= -2.5e-258)
		tmp = Float64(x / Float64(x + y));
	elseif (c <= 1.95e+217)
		tmp = 1.0;
	else
		tmp = Float64(0.5 * Float64(Float64(x / c) / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -1.12e-84)
		tmp = 1.0;
	elseif (c <= -2.5e-258)
		tmp = x / (x + y);
	elseif (c <= 1.95e+217)
		tmp = 1.0;
	else
		tmp = 0.5 * ((x / c) / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1.12e-84], 1.0, If[LessEqual[c, -2.5e-258], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.95e+217], 1.0, N[(0.5 * N[(N[(x / c), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.12000000000000007e-84 or -2.4999999999999999e-258 < c < 1.94999999999999997e217

   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 64.6%

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

   3. Taylor expanded in a around 0 37.1%

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

   4. Taylor expanded in x around inf 58.3%

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

   if -1.12000000000000007e-84 < c < -2.4999999999999999e-258

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 64.3%

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

   3. Taylor expanded in a around 0 50.5%

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

   if 1.94999999999999997e217 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in a around inf 84.7%

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

   3. Taylor expanded in a around 0 54.5%

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

   4. Taylor expanded in a around inf 59.2%

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

      1. associate-*r* 54.4%

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

      2. *-commutative 54.4%

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

      3. associate-*r* 54.5%

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

      4. associate-/r* 47.3%

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

   6. Simplified 47.3%

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

   7. Taylor expanded in c around inf 49.4%

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

      1. *-commutative 49.4%

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

      2. associate-/r* 46.8%

         \[\leadsto \color{blue}{\frac{\frac{x}{c}}{y \cdot a}} \cdot 0.5 \]

   9. Simplified 46.8%

      \[\leadsto \color{blue}{\frac{\frac{x}{c}}{y \cdot a} \cdot 0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{-84}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-258}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 1.95 \cdot 10^{+217}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{\frac{x}{c}}{y \cdot a}\\ \end{array} \]

Alternative 23: 51.0% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.92 \cdot 10^{-87}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+217}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{y \cdot \left(c \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1.92e-87)
   1.0
   (if (<= c -1.2e-259)
     (/ x (+ x y))
     (if (<= c 2.3e+217) 1.0 (/ (* x 0.5) (* y (* c a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.92e-87) {
		tmp = 1.0;
	} else if (c <= -1.2e-259) {
		tmp = x / (x + y);
	} else if (c <= 2.3e+217) {
		tmp = 1.0;
	} else {
		tmp = (x * 0.5) / (y * (c * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-1.92d-87)) then
        tmp = 1.0d0
    else if (c <= (-1.2d-259)) then
        tmp = x / (x + y)
    else if (c <= 2.3d+217) then
        tmp = 1.0d0
    else
        tmp = (x * 0.5d0) / (y * (c * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.92e-87) {
		tmp = 1.0;
	} else if (c <= -1.2e-259) {
		tmp = x / (x + y);
	} else if (c <= 2.3e+217) {
		tmp = 1.0;
	} else {
		tmp = (x * 0.5) / (y * (c * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1.92e-87:
		tmp = 1.0
	elif c <= -1.2e-259:
		tmp = x / (x + y)
	elif c <= 2.3e+217:
		tmp = 1.0
	else:
		tmp = (x * 0.5) / (y * (c * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1.92e-87)
		tmp = 1.0;
	elseif (c <= -1.2e-259)
		tmp = Float64(x / Float64(x + y));
	elseif (c <= 2.3e+217)
		tmp = 1.0;
	else
		tmp = Float64(Float64(x * 0.5) / Float64(y * Float64(c * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -1.92e-87)
		tmp = 1.0;
	elseif (c <= -1.2e-259)
		tmp = x / (x + y);
	elseif (c <= 2.3e+217)
		tmp = 1.0;
	else
		tmp = (x * 0.5) / (y * (c * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1.92e-87], 1.0, If[LessEqual[c, -1.2e-259], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.3e+217], 1.0, N[(N[(x * 0.5), $MachinePrecision] / N[(y * N[(c * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.92e-87 or -1.2e-259 < c < 2.2999999999999999e217

   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 64.6%

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

   3. Taylor expanded in a around 0 37.1%

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

   4. Taylor expanded in x around inf 58.3%

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

   if -1.92e-87 < c < -1.2e-259

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 64.3%

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

   3. Taylor expanded in a around 0 50.5%

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

   if 2.2999999999999999e217 < c

   1. Initial program 79.3%

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

   2. Taylor expanded in a around inf 84.7%

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

   3. Taylor expanded in a around 0 54.5%

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

   4. Taylor expanded in c around inf 49.4%

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

      1. associate-*r/ 49.4%

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

      2. *-commutative 49.4%

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

      3. associate-*r* 54.2%

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

   6. Simplified 54.2%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.92 \cdot 10^{-87}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.2 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 2.3 \cdot 10^{+217}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{y \cdot \left(c \cdot a\right)}\\ \end{array} \]

Alternative 24: 50.2% accurate, 25.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -7.8 \cdot 10^{-86}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-261}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -7.8e-86) 1.0 (if (<= c -4e-261) (/ x (+ x y)) 1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -7.8e-86) {
		tmp = 1.0;
	} else if (c <= -4e-261) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-7.8d-86)) then
        tmp = 1.0d0
    else if (c <= (-4d-261)) then
        tmp = x / (x + y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -7.8e-86) {
		tmp = 1.0;
	} else if (c <= -4e-261) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -7.8e-86:
		tmp = 1.0
	elif c <= -4e-261:
		tmp = x / (x + y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -7.8e-86)
		tmp = 1.0;
	elseif (c <= -4e-261)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -7.8e-86)
		tmp = 1.0;
	elseif (c <= -4e-261)
		tmp = x / (x + y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -7.8e-86], 1.0, If[LessEqual[c, -4e-261], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if c < -7.8000000000000003e-86 or -3.99999999999999994e-261 < c

   1. Initial program 88.7%

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

   2. Taylor expanded in a around inf 66.3%

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

   3. Taylor expanded in a around 0 38.6%

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

   4. Taylor expanded in x around inf 54.9%

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

   if -7.8000000000000003e-86 < c < -3.99999999999999994e-261

   1. Initial program 97.1%

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

   2. Taylor expanded in a around inf 64.3%

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

   3. Taylor expanded in a around 0 50.5%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.8 \cdot 10^{-86}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4 \cdot 10^{-261}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 25: 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 89.8%

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

2. Taylor expanded in a around inf 66.0%

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

3. Taylor expanded in a around 0 41.4%

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

4. Taylor expanded in x around inf 52.0%

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

5. Final simplification 52.0%

   \[\leadsto 1 \]

Developer target: 95.1% 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 2023192 
(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)))))))))))