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

Percentage Accurate: 93.4% → 96.4%

Time: 28.6s

Alternatives: 21

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: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 0.7× speedup

Math

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

FPCore

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

Java

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

Python

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

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(sqrt(Float64(a + t)) * z) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(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 = 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)
	t_1 = ((sqrt((a + t)) * 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 = 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_] := Block[{t$95$1 = N[(N[(N[(N[Sqrt[N[(a + t), $MachinePrecision]], $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(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], 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 (-.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 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in t around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. distribute-neg-in 86.2%

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

      5. metadata-eval 86.2%

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

   4. Simplified 86.2%

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

4. Final simplification 98.9%

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

Alternative 2: 96.8% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

3. Simplified 98.5%

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

4. Final simplification 98.5%

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

Alternative 3: 90.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -8e-36)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 4e-283)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
     (if (<= t 6e+122)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (+
             (* z (sqrt (/ 1.0 t)))
             (* (+ (/ -0.6666666666666666 t) 0.8333333333333334) (- c b))))))))
       (/
        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 (t <= -8e-36) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 4e-283) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 6e+122) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((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 (t <= (-8d-36)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 4d-283) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 6d+122) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) + ((((-0.6666666666666666d0) / t) + 0.8333333333333334d0) * (c - b)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((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 (t <= -8e-36) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 4e-283) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 6e+122) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -8e-36:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 4e-283:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 6e+122:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -8e-36)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 4e-283)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	elseif (t <= 6e+122)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) + Float64(Float64(Float64(-0.6666666666666666 / t) + 0.8333333333333334) * Float64(c - b))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(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 (t <= -8e-36)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 4e-283)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 6e+122)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + (((-0.6666666666666666 / t) + 0.8333333333333334) * (c - b)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -8e-36], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-283], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6e+122], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(-0.6666666666666666 / t), $MachinePrecision] + 0.8333333333333334), $MachinePrecision] * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.9999999999999995e-36

   1. Initial program 94.7%

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

   2. Taylor expanded in a around inf 94.9%

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

   if -7.9999999999999995e-36 < t < 3.99999999999999979e-283

   1. Initial program 90.2%

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

   2. Taylor expanded in t around 0 100.0%

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

   if 3.99999999999999979e-283 < t < 5.99999999999999972e122

   1. Initial program 97.5%

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

   2. Taylor expanded in a around 0 84.6%

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

      1. *-commutative 84.6%

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

      2. *-commutative 84.6%

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

      3. cancel-sign-sub-inv 84.6%

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

      4. metadata-eval 84.6%

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

      5. associate-*r/ 84.6%

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

      6. metadata-eval 84.6%

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

   4. Simplified 84.6%

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

   if 5.99999999999999972e122 < t

   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 t around inf 96.2%

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

      1. mul-1-neg 96.2%

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

      2. *-commutative 96.2%

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

      3. distribute-rgt-neg-in 96.2%

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

      4. distribute-neg-in 96.2%

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

      5. metadata-eval 96.2%

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

   4. Simplified 96.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+122}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(\frac{-0.6666666666666666}{t} + 0.8333333333333334\right) \cdot \left(c - b\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 4: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 0.8:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\frac{\left(b - c\right) \cdot 1.3333333333333333}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.02e-33)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 3.6e-178)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
     (if (<= t 4e-61)
       1.0
       (if (<= t 0.8)
         (/ x (+ x (* y (exp (/ (* (- b c) 1.3333333333333333) 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 (t <= -1.02e-33) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 3.6e-178) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 4e-61) {
		tmp = 1.0;
	} else if (t <= 0.8) {
		tmp = x / (x + (y * exp((((b - c) * 1.3333333333333333) / 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 (t <= (-1.02d-33)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 3.6d-178) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 4d-61) then
        tmp = 1.0d0
    else if (t <= 0.8d0) then
        tmp = x / (x + (y * exp((((b - c) * 1.3333333333333333d0) / 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 (t <= -1.02e-33) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 3.6e-178) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 4e-61) {
		tmp = 1.0;
	} else if (t <= 0.8) {
		tmp = x / (x + (y * Math.exp((((b - c) * 1.3333333333333333) / 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 t <= -1.02e-33:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 3.6e-178:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 4e-61:
		tmp = 1.0
	elif t <= 0.8:
		tmp = x / (x + (y * math.exp((((b - c) * 1.3333333333333333) / 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 (t <= -1.02e-33)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 3.6e-178)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	elseif (t <= 4e-61)
		tmp = 1.0;
	elseif (t <= 0.8)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(Float64(b - c) * 1.3333333333333333) / 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 (t <= -1.02e-33)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 3.6e-178)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 4e-61)
		tmp = 1.0;
	elseif (t <= 0.8)
		tmp = x / (x + (y * exp((((b - c) * 1.3333333333333333) / 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[LessEqual[t, -1.02e-33], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.6e-178], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-61], 1.0, If[LessEqual[t, 0.8], N[(x / N[(x + N[(y * N[Exp[N[(N[(N[(b - c), $MachinePrecision] * 1.3333333333333333), $MachinePrecision] / t), $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 5 regimes

2. if t < -1.02e-33

   1. Initial program 94.7%

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

   2. Taylor expanded in a around inf 94.9%

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

   if -1.02e-33 < t < 3.59999999999999994e-178

   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 t around 0 94.4%

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

   if 3.59999999999999994e-178 < t < 4.0000000000000002e-61

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 45.6%

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

      1. mul-1-neg 45.6%

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

      2. *-commutative 45.6%

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

      3. distribute-rgt-neg-in 45.6%

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

      4. distribute-neg-in 45.6%

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

      5. metadata-eval 45.6%

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

   4. Simplified 45.6%

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

   5. Taylor expanded in x around inf 78.8%

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

   if 4.0000000000000002e-61 < t < 0.80000000000000004

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 55.3%

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

   3. Taylor expanded in a around 0 66.1%

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

      1. associate-*r/ 66.1%

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

   5. Simplified 66.1%

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

   if 0.80000000000000004 < t

   1. Initial program 94.7%

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

   2. Taylor expanded in t around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. *-commutative 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

      4. distribute-neg-in 87.5%

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

      5. metadata-eval 87.5%

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

   4. Simplified 87.5%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(-0.8333333333333334 + \left(-a\right)\right)\right)}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.02 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 0.8:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\frac{\left(b - c\right) \cdot 1.3333333333333333}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 5: 80.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\frac{\left(b - c\right) \cdot 1.3333333333333333}{t}}}\\ \mathbf{if}\;t \leq 7 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.96 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;t \leq 0.6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (/ (* (- b c) 1.3333333333333333) t)))))))
   (if (<= t 7e-308)
     (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
     (if (<= t 1.96e-101)
       t_1
       (if (<= t 1.7e-50)
         (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))
         (if (<= t 0.6)
           t_1
           (/
            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 t_1 = x / (x + (y * exp((((b - c) * 1.3333333333333333) / t))));
	double tmp;
	if (t <= 7e-308) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.96e-101) {
		tmp = t_1;
	} else if (t <= 1.7e-50) {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	} else if (t <= 0.6) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((((b - c) * 1.3333333333333333d0) / t))))
    if (t <= 7d-308) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 1.96d-101) then
        tmp = t_1
    else if (t <= 1.7d-50) then
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    else if (t <= 0.6d0) then
        tmp = t_1
    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 t_1 = x / (x + (y * Math.exp((((b - c) * 1.3333333333333333) / t))));
	double tmp;
	if (t <= 7e-308) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 1.96e-101) {
		tmp = t_1;
	} else if (t <= 1.7e-50) {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	} else if (t <= 0.6) {
		tmp = t_1;
	} 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):
	t_1 = x / (x + (y * math.exp((((b - c) * 1.3333333333333333) / t))))
	tmp = 0
	if t <= 7e-308:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 1.96e-101:
		tmp = t_1
	elif t <= 1.7e-50:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	elif t <= 0.6:
		tmp = t_1
	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)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(Float64(b - c) * 1.3333333333333333) / t)))))
	tmp = 0.0
	if (t <= 7e-308)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 1.96e-101)
		tmp = t_1;
	elseif (t <= 1.7e-50)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	elseif (t <= 0.6)
		tmp = t_1;
	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)
	t_1 = x / (x + (y * exp((((b - c) * 1.3333333333333333) / t))));
	tmp = 0.0;
	if (t <= 7e-308)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 1.96e-101)
		tmp = t_1;
	elseif (t <= 1.7e-50)
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	elseif (t <= 0.6)
		tmp = t_1;
	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_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(N[(N[(b - c), $MachinePrecision] * 1.3333333333333333), $MachinePrecision] / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 7e-308], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.96e-101], t$95$1, If[LessEqual[t, 1.7e-50], N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.6], 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]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < 7e-308

   1. Initial program 91.2%

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

   2. Taylor expanded in a around inf 88.2%

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

   if 7e-308 < t < 1.9599999999999999e-101 or 1.70000000000000007e-50 < t < 0.599999999999999978

   1. Initial program 94.3%

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

   2. Taylor expanded in t around 0 66.3%

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

   3. Taylor expanded in a around 0 74.5%

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

      1. associate-*r/ 74.5%

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

   5. Simplified 74.5%

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

   if 1.9599999999999999e-101 < t < 1.70000000000000007e-50

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. distribute-neg-in 86.2%

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

      5. metadata-eval 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in a around 0 86.2%

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

   if 0.599999999999999978 < t

   1. Initial program 94.7%

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

   2. Taylor expanded in t around inf 87.5%

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

      1. mul-1-neg 87.5%

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

      2. *-commutative 87.5%

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

      3. distribute-rgt-neg-in 87.5%

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

      4. distribute-neg-in 87.5%

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

      5. metadata-eval 87.5%

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

   4. Simplified 87.5%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7 \cdot 10^{-308}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 1.96 \cdot 10^{-101}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\frac{\left(b - c\right) \cdot 1.3333333333333333}{t}}}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;t \leq 0.6:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\frac{\left(b - c\right) \cdot 1.3333333333333333}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 6: 53.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+221}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-196}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* b -1.6666666666666667)))))))
   (if (<= c -1.65e+221)
     1.0
     (if (<= c 9.5e-255)
       t_1
       (if (<= c 5.8e-196)
         1.0
         (if (<= c 1.3e+37)
           t_1
           (/ x (+ x (- y (* 2.0 (* a (* y (- b c)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((b * -1.6666666666666667))));
	double tmp;
	if (c <= -1.65e+221) {
		tmp = 1.0;
	} else if (c <= 9.5e-255) {
		tmp = t_1;
	} else if (c <= 5.8e-196) {
		tmp = 1.0;
	} else if (c <= 1.3e+37) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((b * (-1.6666666666666667d0)))))
    if (c <= (-1.65d+221)) then
        tmp = 1.0d0
    else if (c <= 9.5d-255) then
        tmp = t_1
    else if (c <= 5.8d-196) then
        tmp = 1.0d0
    else if (c <= 1.3d+37) then
        tmp = t_1
    else
        tmp = x / (x + (y - (2.0d0 * (a * (y * (b - c))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((b * -1.6666666666666667))));
	double tmp;
	if (c <= -1.65e+221) {
		tmp = 1.0;
	} else if (c <= 9.5e-255) {
		tmp = t_1;
	} else if (c <= 5.8e-196) {
		tmp = 1.0;
	} else if (c <= 1.3e+37) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((b * -1.6666666666666667))))
	tmp = 0
	if c <= -1.65e+221:
		tmp = 1.0
	elif c <= 9.5e-255:
		tmp = t_1
	elif c <= 5.8e-196:
		tmp = 1.0
	elif c <= 1.3e+37:
		tmp = t_1
	else:
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(b * -1.6666666666666667)))))
	tmp = 0.0
	if (c <= -1.65e+221)
		tmp = 1.0;
	elseif (c <= 9.5e-255)
		tmp = t_1;
	elseif (c <= 5.8e-196)
		tmp = 1.0;
	elseif (c <= 1.3e+37)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(a * Float64(y * Float64(b - c)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((b * -1.6666666666666667))));
	tmp = 0.0;
	if (c <= -1.65e+221)
		tmp = 1.0;
	elseif (c <= 9.5e-255)
		tmp = t_1;
	elseif (c <= 5.8e-196)
		tmp = 1.0;
	elseif (c <= 1.3e+37)
		tmp = t_1;
	else
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	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[(b * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+221], 1.0, If[LessEqual[c, 9.5e-255], t$95$1, If[LessEqual[c, 5.8e-196], 1.0, If[LessEqual[c, 1.3e+37], t$95$1, N[(x / N[(x + N[(y - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.64999999999999996e221 or 9.5000000000000003e-255 < c < 5.79999999999999974e-196

   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 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

      4. distribute-neg-in 67.7%

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

      5. metadata-eval 67.7%

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

   4. Simplified 67.7%

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

   5. Taylor expanded in x around inf 70.9%

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

   if -1.64999999999999996e221 < c < 9.5000000000000003e-255 or 5.79999999999999974e-196 < c < 1.3e37

   1. Initial program 95.3%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in b around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. distribute-rgt-neg-in 68.2%

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

      3. distribute-neg-in 68.2%

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

      4. metadata-eval 68.2%

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

      5. sub-neg 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in a around 0 61.7%

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

   if 1.3e37 < c

   1. Initial program 91.3%

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

   2. Taylor expanded in a around inf 74.6%

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

   3. Taylor expanded in a around 0 59.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+221}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 9.5 \cdot 10^{-255}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;c \leq 5.8 \cdot 10^{-196}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \end{array} \]

Alternative 7: 67.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.6 \cdot 10^{-305} \lor \neg \left(t \leq 3.2 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (or (<= t 7.6e-305) (not (<= t 3.2e-102)))
   (/ x (+ x (* y (exp (* (- b 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 ((t <= 7.6e-305) || !(t <= 3.2e-102)) {
		tmp = x / (x + (y * exp(((b - 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 ((t <= 7.6d-305) .or. (.not. (t <= 3.2d-102))) then
        tmp = x / (x + (y * exp(((b - 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 ((t <= 7.6e-305) || !(t <= 3.2e-102)) {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (t <= 7.6e-305) or not (t <= 3.2e-102):
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if ((t <= 7.6e-305) || !(t <= 3.2e-102))
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - 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 ((t <= 7.6e-305) || ~((t <= 3.2e-102)))
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[Or[LessEqual[t, 7.6e-305], N[Not[LessEqual[t, 3.2e-102]], $MachinePrecision]], N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < 7.6e-305 or 3.19999999999999986e-102 < t

   1. Initial program 94.6%

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

   2. Taylor expanded in t around inf 82.1%

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

      1. mul-1-neg 82.1%

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

      2. *-commutative 82.1%

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

      3. distribute-rgt-neg-in 82.1%

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

      4. distribute-neg-in 82.1%

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

      5. metadata-eval 82.1%

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

   4. Simplified 82.1%

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

   5. Taylor expanded in a around 0 69.6%

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

   if 7.6e-305 < t < 3.19999999999999986e-102

   1. Initial program 91.2%

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

   2. Taylor expanded in t around inf 26.1%

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

      1. mul-1-neg 26.1%

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

      2. *-commutative 26.1%

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

      3. distribute-rgt-neg-in 26.1%

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

      4. distribute-neg-in 26.1%

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

      5. metadata-eval 26.1%

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

   4. Simplified 26.1%

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

   5. Taylor expanded in x around inf 68.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.6 \cdot 10^{-305} \lor \neg \left(t \leq 3.2 \cdot 10^{-102}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 64.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -5.5e+153)
   (/ x (+ x (* y (exp (* 2.0 (* b (- -0.8333333333333334 a)))))))
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.5e+153) {
		tmp = x / (x + (y * exp((2.0 * (b * (-0.8333333333333334 - a))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-5.5d+153)) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((-0.8333333333333334d0) - a))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -5.5e+153) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * (-0.8333333333333334 - a))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -5.5e+153:
		tmp = x / (x + (y * math.exp((2.0 * (b * (-0.8333333333333334 - a))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -5.5e+153)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(-0.8333333333333334 - a)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -5.5e+153)
		tmp = x / (x + (y * exp((2.0 * (b * (-0.8333333333333334 - a))))));
	else
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -5.5e+153], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.5000000000000003e153

   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 t around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. *-commutative 83.4%

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

      3. distribute-rgt-neg-in 83.4%

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

      4. distribute-neg-in 83.4%

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

      5. metadata-eval 83.4%

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

   4. Simplified 83.4%

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

   5. Taylor expanded in b around inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-in 83.4%

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

      3. distribute-neg-in 83.4%

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

      4. metadata-eval 83.4%

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

      5. sub-neg 83.4%

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

   7. Simplified 83.4%

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

   if -5.5000000000000003e153 < b

   1. Initial program 94.6%

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

   2. Taylor expanded in a around inf 71.8%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+153}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \end{array} \]

Alternative 9: 59.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -4.4e-13)
   (/ x (+ x (* y (exp (* b -1.6666666666666667)))))
   (if (<= b 3.5e+191) (/ x (+ x (* y (exp (* c 1.6666666666666667))))) 1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.4e-13) {
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	} else if (b <= 3.5e+191) {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-4.4d-13)) then
        tmp = x / (x + (y * exp((b * (-1.6666666666666667d0)))))
    else if (b <= 3.5d+191) then
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -4.4e-13) {
		tmp = x / (x + (y * Math.exp((b * -1.6666666666666667))));
	} else if (b <= 3.5e+191) {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -4.4e-13:
		tmp = x / (x + (y * math.exp((b * -1.6666666666666667))))
	elif b <= 3.5e+191:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -4.4e-13)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(b * -1.6666666666666667)))));
	elseif (b <= 3.5e+191)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -4.4e-13)
		tmp = x / (x + (y * exp((b * -1.6666666666666667))));
	elseif (b <= 3.5e+191)
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -4.4e-13], N[(x / N[(x + N[(y * N[Exp[N[(b * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.5e+191], N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if b < -4.39999999999999993e-13

   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 t around inf 76.1%

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

      1. mul-1-neg 76.1%

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

      2. *-commutative 76.1%

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

      3. distribute-rgt-neg-in 76.1%

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

      4. distribute-neg-in 76.1%

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

      5. metadata-eval 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in b around inf 74.8%

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

      1. mul-1-neg 74.8%

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

      2. distribute-rgt-neg-in 74.8%

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

      3. distribute-neg-in 74.8%

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

      4. metadata-eval 74.8%

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

      5. sub-neg 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in a around 0 68.2%

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

   if -4.39999999999999993e-13 < b < 3.4999999999999997e191

   1. Initial program 95.7%

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

   2. Taylor expanded in t around inf 72.5%

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

      1. mul-1-neg 72.5%

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

      2. *-commutative 72.5%

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

      3. distribute-rgt-neg-in 72.5%

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

      4. distribute-neg-in 72.5%

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

      5. metadata-eval 72.5%

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

   4. Simplified 72.5%

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

   5. Taylor expanded in a around 0 59.6%

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

   6. Taylor expanded in b around 0 60.1%

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

   if 3.4999999999999997e191 < b

   1. Initial program 90.5%

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

   2. Taylor expanded in t around inf 86.2%

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

      1. mul-1-neg 86.2%

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

      2. *-commutative 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. distribute-neg-in 86.2%

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

      5. metadata-eval 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in x around inf 76.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{b \cdot -1.6666666666666667}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 63.6% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

2. Taylor expanded in a around inf 70.8%

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

3. Final simplification 70.8%

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

Alternative 11: 48.8% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \frac{y \cdot b}{t}}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+117}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 - \left(b - c\right) \cdot \left(2 \cdot a\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.45e+36)
   1.0
   (if (<= c -3.4e-247)
     (/ x (+ x (* 1.3333333333333333 (/ (* y b) t))))
     (if (<= c 1.25e-201)
       1.0
       (if (<= c 4.8e-94)
         (/ x (+ x y))
         (if (<= c 4.9e+117)
           1.0
           (/ x (* y (- 1.0 (* (- b c) (* 2.0 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.45e+36) {
		tmp = 1.0;
	} else if (c <= -3.4e-247) {
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	} else if (c <= 1.25e-201) {
		tmp = 1.0;
	} else if (c <= 4.8e-94) {
		tmp = x / (x + y);
	} else if (c <= 4.9e+117) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 - ((b - c) * (2.0 * 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 <= (-2.45d+36)) then
        tmp = 1.0d0
    else if (c <= (-3.4d-247)) then
        tmp = x / (x + (1.3333333333333333d0 * ((y * b) / t)))
    else if (c <= 1.25d-201) then
        tmp = 1.0d0
    else if (c <= 4.8d-94) then
        tmp = x / (x + y)
    else if (c <= 4.9d+117) then
        tmp = 1.0d0
    else
        tmp = x / (y * (1.0d0 - ((b - c) * (2.0d0 * 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 <= -2.45e+36) {
		tmp = 1.0;
	} else if (c <= -3.4e-247) {
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	} else if (c <= 1.25e-201) {
		tmp = 1.0;
	} else if (c <= 4.8e-94) {
		tmp = x / (x + y);
	} else if (c <= 4.9e+117) {
		tmp = 1.0;
	} else {
		tmp = x / (y * (1.0 - ((b - c) * (2.0 * a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.45e+36:
		tmp = 1.0
	elif c <= -3.4e-247:
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)))
	elif c <= 1.25e-201:
		tmp = 1.0
	elif c <= 4.8e-94:
		tmp = x / (x + y)
	elif c <= 4.9e+117:
		tmp = 1.0
	else:
		tmp = x / (y * (1.0 - ((b - c) * (2.0 * a))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.45e+36)
		tmp = 1.0;
	elseif (c <= -3.4e-247)
		tmp = Float64(x / Float64(x + Float64(1.3333333333333333 * Float64(Float64(y * b) / t))));
	elseif (c <= 1.25e-201)
		tmp = 1.0;
	elseif (c <= 4.8e-94)
		tmp = Float64(x / Float64(x + y));
	elseif (c <= 4.9e+117)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(y * Float64(1.0 - Float64(Float64(b - c) * Float64(2.0 * a)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -2.45e+36)
		tmp = 1.0;
	elseif (c <= -3.4e-247)
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	elseif (c <= 1.25e-201)
		tmp = 1.0;
	elseif (c <= 4.8e-94)
		tmp = x / (x + y);
	elseif (c <= 4.9e+117)
		tmp = 1.0;
	else
		tmp = x / (y * (1.0 - ((b - c) * (2.0 * a))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.45e+36], 1.0, If[LessEqual[c, -3.4e-247], N[(x / N[(x + N[(1.3333333333333333 * N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-201], 1.0, If[LessEqual[c, 4.8e-94], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.9e+117], 1.0, N[(x / N[(y * N[(1.0 - N[(N[(b - c), $MachinePrecision] * N[(2.0 * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.4499999999999999e36 or -3.4000000000000001e-247 < c < 1.25e-201 or 4.8e-94 < c < 4.9000000000000001e117

   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 75.8%

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

      1. mul-1-neg 75.8%

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

      2. *-commutative 75.8%

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

      3. distribute-rgt-neg-in 75.8%

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

      4. distribute-neg-in 75.8%

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

      5. metadata-eval 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in x around inf 53.5%

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

   if -2.4499999999999999e36 < c < -3.4000000000000001e-247

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 53.8%

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

   3. Taylor expanded in t around inf 41.5%

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

   4. Taylor expanded in b around inf 58.3%

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

   if 1.25e-201 < c < 4.8e-94

   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 57.8%

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

   3. Taylor expanded in a around 0 53.6%

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

      1. +-commutative 53.6%

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

   5. Simplified 53.6%

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

   if 4.9000000000000001e117 < c

   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 79.6%

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

   3. Taylor expanded in a around 0 74.5%

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

   4. Taylor expanded in y around inf 69.5%

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

      1. associate-*r* 69.5%

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

   6. Simplified 69.5%

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

4. Final simplification 56.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.4 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \frac{y \cdot b}{t}}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 4.9 \cdot 10^{+117}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 - \left(b - c\right) \cdot \left(2 \cdot a\right)\right)}\\ \end{array} \]

Alternative 12: 50.2% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \frac{y \cdot b}{t}}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+112}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot c\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -2.05e+37)
   1.0
   (if (<= c -4.5e-244)
     (/ x (+ x (* 1.3333333333333333 (/ (* y b) t))))
     (if (<= c 1.25e-201)
       1.0
       (if (<= c 3.3e-93)
         (/ x (+ x y))
         (if (<= c 3e+112) 1.0 (/ x (+ x (+ y (* 2.0 (* a (* y c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.05e+37) {
		tmp = 1.0;
	} else if (c <= -4.5e-244) {
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	} else if (c <= 1.25e-201) {
		tmp = 1.0;
	} else if (c <= 3.3e-93) {
		tmp = x / (x + y);
	} else if (c <= 3e+112) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (y * c)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-2.05d+37)) then
        tmp = 1.0d0
    else if (c <= (-4.5d-244)) then
        tmp = x / (x + (1.3333333333333333d0 * ((y * b) / t)))
    else if (c <= 1.25d-201) then
        tmp = 1.0d0
    else if (c <= 3.3d-93) then
        tmp = x / (x + y)
    else if (c <= 3d+112) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + (2.0d0 * (a * (y * c)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -2.05e+37) {
		tmp = 1.0;
	} else if (c <= -4.5e-244) {
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	} else if (c <= 1.25e-201) {
		tmp = 1.0;
	} else if (c <= 3.3e-93) {
		tmp = x / (x + y);
	} else if (c <= 3e+112) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (y * c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -2.05e+37:
		tmp = 1.0
	elif c <= -4.5e-244:
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)))
	elif c <= 1.25e-201:
		tmp = 1.0
	elif c <= 3.3e-93:
		tmp = x / (x + y)
	elif c <= 3e+112:
		tmp = 1.0
	else:
		tmp = x / (x + (y + (2.0 * (a * (y * c)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -2.05e+37)
		tmp = 1.0;
	elseif (c <= -4.5e-244)
		tmp = Float64(x / Float64(x + Float64(1.3333333333333333 * Float64(Float64(y * b) / t))));
	elseif (c <= 1.25e-201)
		tmp = 1.0;
	elseif (c <= 3.3e-93)
		tmp = Float64(x / Float64(x + y));
	elseif (c <= 3e+112)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(a * Float64(y * c))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -2.05e+37)
		tmp = 1.0;
	elseif (c <= -4.5e-244)
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	elseif (c <= 1.25e-201)
		tmp = 1.0;
	elseif (c <= 3.3e-93)
		tmp = x / (x + y);
	elseif (c <= 3e+112)
		tmp = 1.0;
	else
		tmp = x / (x + (y + (2.0 * (a * (y * c)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -2.05e+37], 1.0, If[LessEqual[c, -4.5e-244], N[(x / N[(x + N[(1.3333333333333333 * N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.25e-201], 1.0, If[LessEqual[c, 3.3e-93], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+112], 1.0, N[(x / N[(x + N[(y + N[(2.0 * N[(a * N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.0499999999999999e37 or -4.5000000000000002e-244 < c < 1.25e-201 or 3.3000000000000001e-93 < c < 2.99999999999999979e112

   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 75.8%

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

      1. mul-1-neg 75.8%

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

      2. *-commutative 75.8%

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

      3. distribute-rgt-neg-in 75.8%

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

      4. distribute-neg-in 75.8%

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

      5. metadata-eval 75.8%

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

   4. Simplified 75.8%

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

   5. Taylor expanded in x around inf 53.5%

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

   if -2.0499999999999999e37 < c < -4.5000000000000002e-244

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 53.8%

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

   3. Taylor expanded in t around inf 41.5%

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

   4. Taylor expanded in b around inf 58.3%

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

   if 1.25e-201 < c < 3.3000000000000001e-93

   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 57.8%

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

   3. Taylor expanded in a around 0 53.6%

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

      1. +-commutative 53.6%

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

   5. Simplified 53.6%

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

   if 2.99999999999999979e112 < c

   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 79.6%

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

   3. Taylor expanded in a around 0 74.5%

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

   4. Taylor expanded in c around inf 72.0%

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

      1. *-commutative 72.0%

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

   6. Simplified 72.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.05 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \frac{y \cdot b}{t}}\\ \mathbf{elif}\;c \leq 1.25 \cdot 10^{-201}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{-93}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+112}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot c\right)\right)\right)}\\ \end{array} \]

Alternative 13: 49.9% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b - c}{t}\right)}\\ \mathbf{if}\;c \leq -3.4 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot c\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= c -3.4e+36)
     1.0
     (if (<= c -4.2e-243)
       t_1
       (if (<= c 1.5e-195)
         1.0
         (if (<= c 1.75e-31)
           t_1
           (if (<= c 4.2e+114)
             1.0
             (/ x (+ x (+ y (* 2.0 (* a (* y c)))))))))))))

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 - c) / t)))));
	double tmp;
	if (c <= -3.4e+36) {
		tmp = 1.0;
	} else if (c <= -4.2e-243) {
		tmp = t_1;
	} else if (c <= 1.5e-195) {
		tmp = 1.0;
	} else if (c <= 1.75e-31) {
		tmp = t_1;
	} else if (c <= 4.2e+114) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (y * c)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * ((b - c) / t)))))
    if (c <= (-3.4d+36)) then
        tmp = 1.0d0
    else if (c <= (-4.2d-243)) then
        tmp = t_1
    else if (c <= 1.5d-195) then
        tmp = 1.0d0
    else if (c <= 1.75d-31) then
        tmp = t_1
    else if (c <= 4.2d+114) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y + (2.0d0 * (a * (y * c)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (c <= -3.4e+36) {
		tmp = 1.0;
	} else if (c <= -4.2e-243) {
		tmp = t_1;
	} else if (c <= 1.5e-195) {
		tmp = 1.0;
	} else if (c <= 1.75e-31) {
		tmp = t_1;
	} else if (c <= 4.2e+114) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y + (2.0 * (a * (y * c)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x - (y * (-1.0 - (1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if c <= -3.4e+36:
		tmp = 1.0
	elif c <= -4.2e-243:
		tmp = t_1
	elif c <= 1.5e-195:
		tmp = 1.0
	elif c <= 1.75e-31:
		tmp = t_1
	elif c <= 4.2e+114:
		tmp = 1.0
	else:
		tmp = x / (x + (y + (2.0 * (a * (y * c)))))
	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(Float64(b - c) / t))))))
	tmp = 0.0
	if (c <= -3.4e+36)
		tmp = 1.0;
	elseif (c <= -4.2e-243)
		tmp = t_1;
	elseif (c <= 1.5e-195)
		tmp = 1.0;
	elseif (c <= 1.75e-31)
		tmp = t_1;
	elseif (c <= 4.2e+114)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(2.0 * Float64(a * Float64(y * c))))));
	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 - c) / t)))));
	tmp = 0.0;
	if (c <= -3.4e+36)
		tmp = 1.0;
	elseif (c <= -4.2e-243)
		tmp = t_1;
	elseif (c <= 1.5e-195)
		tmp = 1.0;
	elseif (c <= 1.75e-31)
		tmp = t_1;
	elseif (c <= 4.2e+114)
		tmp = 1.0;
	else
		tmp = x / (x + (y + (2.0 * (a * (y * c)))));
	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[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.4e+36], 1.0, If[LessEqual[c, -4.2e-243], t$95$1, If[LessEqual[c, 1.5e-195], 1.0, If[LessEqual[c, 1.75e-31], t$95$1, If[LessEqual[c, 4.2e+114], 1.0, N[(x / N[(x + N[(y + N[(2.0 * N[(a * N[(y * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.3999999999999998e36 or -4.2000000000000002e-243 < c < 1.5e-195 or 1.74999999999999993e-31 < c < 4.2000000000000001e114

   1. Initial program 92.4%

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

   2. Taylor expanded in t around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. *-commutative 73.6%

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

      3. distribute-rgt-neg-in 73.6%

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

      4. distribute-neg-in 73.6%

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

      5. metadata-eval 73.6%

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

   4. Simplified 73.6%

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

   5. Taylor expanded in x around inf 57.4%

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

   if -3.3999999999999998e36 < c < -4.2000000000000002e-243 or 1.5e-195 < c < 1.74999999999999993e-31

   1. Initial program 98.8%

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

   2. Taylor expanded in t around 0 49.5%

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

   3. Taylor expanded in t around inf 37.6%

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

   4. Taylor expanded in a around 0 56.5%

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

   if 4.2000000000000001e114 < c

   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 79.6%

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

   3. Taylor expanded in a around 0 74.5%

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

   4. Taylor expanded in c around inf 72.0%

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

      1. *-commutative 72.0%

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

   6. Simplified 72.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.4 \cdot 10^{+36}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -4.2 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b - c}{t}\right)}\\ \mathbf{elif}\;c \leq 1.5 \cdot 10^{-195}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b - c}{t}\right)}\\ \mathbf{elif}\;c \leq 4.2 \cdot 10^{+114}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + 2 \cdot \left(a \cdot \left(y \cdot c\right)\right)\right)}\\ \end{array} \]

Alternative 14: 53.7% accurate, 10.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;b - c \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b - c}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= (- b c) -2e-56)
   (/ x (+ x (- y (* 2.0 (* a (* y (- b c)))))))
   (if (<= (- b c) 5e+50)
     (/ x (- x (* y (- -1.0 (* 1.3333333333333333 (/ (- b c) t))))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -2e-56) {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	} else if ((b - c) <= 5e+50) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((b - c) <= (-2d-56)) then
        tmp = x / (x + (y - (2.0d0 * (a * (y * (b - c))))))
    else if ((b - c) <= 5d+50) then
        tmp = x / (x - (y * ((-1.0d0) - (1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((b - c) <= -2e-56) {
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	} else if ((b - c) <= 5e+50) {
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (b - c) <= -2e-56:
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))))
	elif (b - c) <= 5e+50:
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (Float64(b - c) <= -2e-56)
		tmp = Float64(x / Float64(x + Float64(y - Float64(2.0 * Float64(a * Float64(y * Float64(b - c)))))));
	elseif (Float64(b - c) <= 5e+50)
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((b - c) <= -2e-56)
		tmp = x / (x + (y - (2.0 * (a * (y * (b - c))))));
	elseif ((b - c) <= 5e+50)
		tmp = x / (x - (y * (-1.0 - (1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[N[(b - c), $MachinePrecision], -2e-56], N[(x / N[(x + N[(y - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(b - c), $MachinePrecision], 5e+50], N[(x / N[(x - N[(y * N[(-1.0 - N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 b c) < -2.0000000000000001e-56

   1. Initial program 95.1%

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

   2. Taylor expanded in a around inf 67.4%

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

   3. Taylor expanded in a around 0 51.3%

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

   if -2.0000000000000001e-56 < (-.f64 b c) < 5e50

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 60.1%

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

   3. Taylor expanded in t around inf 40.3%

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

   4. Taylor expanded in a around 0 61.0%

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

   if 5e50 < (-.f64 b c)

   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 t around inf 79.9%

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

      1. mul-1-neg 79.9%

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

      2. *-commutative 79.9%

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

      3. distribute-rgt-neg-in 79.9%

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

      4. distribute-neg-in 79.9%

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

      5. metadata-eval 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in x around inf 64.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b - c \leq -2 \cdot 10^{-56}:\\ \;\;\;\;\frac{x}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;b - c \leq 5 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 1.3333333333333333 \cdot \frac{b - c}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15: 50.2% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+222}:\\ \;\;\;\;0.5 \cdot \frac{x}{\left(c - b\right) \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \frac{y \cdot b}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.08e+222)
   (* 0.5 (/ x (* (- c b) (* y a))))
   (if (<= y 3.5e+196) 1.0 (/ x (+ x (* 1.3333333333333333 (/ (* y b) t)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.08e+222) {
		tmp = 0.5 * (x / ((c - b) * (y * a)));
	} else if (y <= 3.5e+196) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-1.08d+222)) then
        tmp = 0.5d0 * (x / ((c - b) * (y * a)))
    else if (y <= 3.5d+196) then
        tmp = 1.0d0
    else
        tmp = x / (x + (1.3333333333333333d0 * ((y * b) / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.08e+222) {
		tmp = 0.5 * (x / ((c - b) * (y * a)));
	} else if (y <= 3.5e+196) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.08e+222:
		tmp = 0.5 * (x / ((c - b) * (y * a)))
	elif y <= 3.5e+196:
		tmp = 1.0
	else:
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.08e+222)
		tmp = Float64(0.5 * Float64(x / Float64(Float64(c - b) * Float64(y * a))));
	elseif (y <= 3.5e+196)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(1.3333333333333333 * Float64(Float64(y * b) / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -1.08e+222)
		tmp = 0.5 * (x / ((c - b) * (y * a)));
	elseif (y <= 3.5e+196)
		tmp = 1.0;
	else
		tmp = x / (x + (1.3333333333333333 * ((y * b) / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -1.08e+222], N[(0.5 * N[(x / N[(N[(c - b), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+196], 1.0, N[(x / N[(x + N[(1.3333333333333333 * N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e222

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 61.3%

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

   3. Taylor expanded in a around 0 66.7%

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

   4. Taylor expanded in a around inf 61.9%

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

      1. associate-*r* 67.7%

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

   6. Simplified 67.7%

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

   if -1.08e222 < y < 3.4999999999999998e196

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around inf 49.7%

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

   if 3.4999999999999998e196 < y

   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 0 50.5%

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

   3. Taylor expanded in t around inf 46.7%

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

   4. Taylor expanded in b around inf 63.0%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+222}:\\ \;\;\;\;0.5 \cdot \frac{x}{\left(c - b\right) \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1.3333333333333333 \cdot \frac{y \cdot b}{t}}\\ \end{array} \]

Alternative 16: 49.4% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+222}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+213}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.75 \cdot \frac{t}{\frac{y \cdot b}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.1e+222)
   (* -0.5 (/ x (* a (* y b))))
   (if (<= y 1.3e+213) 1.0 (* 0.75 (/ t (/ (* y b) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.1e+222) {
		tmp = -0.5 * (x / (a * (y * b)));
	} else if (y <= 1.3e+213) {
		tmp = 1.0;
	} else {
		tmp = 0.75 * (t / ((y * b) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-1.1d+222)) then
        tmp = (-0.5d0) * (x / (a * (y * b)))
    else if (y <= 1.3d+213) then
        tmp = 1.0d0
    else
        tmp = 0.75d0 * (t / ((y * b) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.1e+222) {
		tmp = -0.5 * (x / (a * (y * b)));
	} else if (y <= 1.3e+213) {
		tmp = 1.0;
	} else {
		tmp = 0.75 * (t / ((y * b) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.1e+222:
		tmp = -0.5 * (x / (a * (y * b)))
	elif y <= 1.3e+213:
		tmp = 1.0
	else:
		tmp = 0.75 * (t / ((y * b) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.1e+222)
		tmp = Float64(-0.5 * Float64(x / Float64(a * Float64(y * b))));
	elseif (y <= 1.3e+213)
		tmp = 1.0;
	else
		tmp = Float64(0.75 * Float64(t / Float64(Float64(y * b) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -1.1e+222)
		tmp = -0.5 * (x / (a * (y * b)));
	elseif (y <= 1.3e+213)
		tmp = 1.0;
	else
		tmp = 0.75 * (t / ((y * b) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -1.1e+222], N[(-0.5 * N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e+213], 1.0, N[(0.75 * N[(t / N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1000000000000001e222

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 61.3%

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

   3. Taylor expanded in a around 0 66.7%

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

   4. Taylor expanded in b around inf 56.5%

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

   if -1.1000000000000001e222 < y < 1.29999999999999999e213

   1. Initial program 94.5%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around inf 49.3%

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

   if 1.29999999999999999e213 < y

   1. Initial program 90.9%

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

   2. Taylor expanded in t around 0 50.4%

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

   3. Taylor expanded in t around inf 46.0%

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

   4. Taylor expanded in b around inf 51.9%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+222}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+213}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.75 \cdot \frac{t}{\frac{y \cdot b}{x}}\\ \end{array} \]

Alternative 17: 49.7% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+222}:\\ \;\;\;\;0.5 \cdot \frac{x}{\left(c - b\right) \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+213}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.75 \cdot \frac{t}{\frac{y \cdot b}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -1.55e+222)
   (* 0.5 (/ x (* (- c b) (* y a))))
   (if (<= y 1.2e+213) 1.0 (* 0.75 (/ t (/ (* y b) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.55e+222) {
		tmp = 0.5 * (x / ((c - b) * (y * a)));
	} else if (y <= 1.2e+213) {
		tmp = 1.0;
	} else {
		tmp = 0.75 * (t / ((y * b) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-1.55d+222)) then
        tmp = 0.5d0 * (x / ((c - b) * (y * a)))
    else if (y <= 1.2d+213) then
        tmp = 1.0d0
    else
        tmp = 0.75d0 * (t / ((y * b) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -1.55e+222) {
		tmp = 0.5 * (x / ((c - b) * (y * a)));
	} else if (y <= 1.2e+213) {
		tmp = 1.0;
	} else {
		tmp = 0.75 * (t / ((y * b) / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -1.55e+222:
		tmp = 0.5 * (x / ((c - b) * (y * a)))
	elif y <= 1.2e+213:
		tmp = 1.0
	else:
		tmp = 0.75 * (t / ((y * b) / x))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -1.55e+222)
		tmp = Float64(0.5 * Float64(x / Float64(Float64(c - b) * Float64(y * a))));
	elseif (y <= 1.2e+213)
		tmp = 1.0;
	else
		tmp = Float64(0.75 * Float64(t / Float64(Float64(y * b) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -1.55e+222)
		tmp = 0.5 * (x / ((c - b) * (y * a)));
	elseif (y <= 1.2e+213)
		tmp = 1.0;
	else
		tmp = 0.75 * (t / ((y * b) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -1.55e+222], N[(0.5 * N[(x / N[(N[(c - b), $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+213], 1.0, N[(0.75 * N[(t / N[(N[(y * b), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5499999999999999e222

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 61.3%

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

   3. Taylor expanded in a around 0 66.7%

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

   4. Taylor expanded in a around inf 61.9%

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

      1. associate-*r* 67.7%

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

   6. Simplified 67.7%

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

   if -1.5499999999999999e222 < y < 1.2e213

   1. Initial program 94.5%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around inf 49.3%

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

   if 1.2e213 < y

   1. Initial program 90.9%

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

   2. Taylor expanded in t around 0 50.4%

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

   3. Taylor expanded in t around inf 46.0%

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

   4. Taylor expanded in b around inf 51.9%

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

      1. associate-/l* 65.1%

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

   6. Simplified 65.1%

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

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+222}:\\ \;\;\;\;0.5 \cdot \frac{x}{\left(c - b\right) \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+213}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0.75 \cdot \frac{t}{\frac{y \cdot b}{x}}\\ \end{array} \]

Alternative 18: 48.8% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+222}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y -3.4e+222)
   (* -0.5 (/ x (* a (* y b))))
   (if (<= y 2.7e+196) 1.0 (/ x (+ x y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.4e+222) {
		tmp = -0.5 * (x / (a * (y * b)));
	} else if (y <= 2.7e+196) {
		tmp = 1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= (-3.4d+222)) then
        tmp = (-0.5d0) * (x / (a * (y * b)))
    else if (y <= 2.7d+196) then
        tmp = 1.0d0
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= -3.4e+222) {
		tmp = -0.5 * (x / (a * (y * b)));
	} else if (y <= 2.7e+196) {
		tmp = 1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= -3.4e+222:
		tmp = -0.5 * (x / (a * (y * b)))
	elif y <= 2.7e+196:
		tmp = 1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= -3.4e+222)
		tmp = Float64(-0.5 * Float64(x / Float64(a * Float64(y * b))));
	elseif (y <= 2.7e+196)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= -3.4e+222)
		tmp = -0.5 * (x / (a * (y * b)));
	elseif (y <= 2.7e+196)
		tmp = 1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, -3.4e+222], N[(-0.5 * N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e+196], 1.0, N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.40000000000000016e222

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 61.3%

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

   3. Taylor expanded in a around 0 66.7%

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

   4. Taylor expanded in b around inf 56.5%

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

   if -3.40000000000000016e222 < y < 2.69999999999999995e196

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around inf 49.7%

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

   if 2.69999999999999995e196 < y

   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 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 55.8%

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

      1. +-commutative 55.8%

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

   5. Simplified 55.8%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+222}:\\ \;\;\;\;-0.5 \cdot \frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]

Alternative 19: 49.8% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= y 5e+196) 1.0 (/ x (+ x y))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 5e+196) {
		tmp = 1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= 5d+196) then
        tmp = 1.0d0
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 5e+196) {
		tmp = 1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 5e+196:
		tmp = 1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 5e+196)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 5e+196)
		tmp = 1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 5e+196], 1.0, N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.9999999999999998e196

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around inf 47.8%

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

   if 4.9999999999999998e196 < y

   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 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 55.8%

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

      1. +-commutative 55.8%

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

   5. Simplified 55.8%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]

Alternative 20: 49.5% accurate, 45.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c) :precision binary64 (if (<= y 6e+196) 1.0 (/ x y)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 6e+196) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (y <= 6d+196) then
        tmp = 1.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (y <= 6e+196) {
		tmp = 1.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if y <= 6e+196:
		tmp = 1.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (y <= 6e+196)
		tmp = 1.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (y <= 6e+196)
		tmp = 1.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[y, 6e+196], 1.0, N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.9999999999999997e196

   1. Initial program 94.4%

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

   2. Taylor expanded in t around inf 73.1%

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

      1. mul-1-neg 73.1%

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

      2. *-commutative 73.1%

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

      3. distribute-rgt-neg-in 73.1%

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

      4. distribute-neg-in 73.1%

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

      5. metadata-eval 73.1%

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

   4. Simplified 73.1%

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

   5. Taylor expanded in x around inf 47.8%

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

   if 5.9999999999999997e196 < y

   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 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 55.8%

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

      1. +-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in x around 0 48.7%

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

4. Final simplification 47.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6 \cdot 10^{+196}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 21: 51.5% accurate, 231.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

2. Taylor expanded in t around inf 74.7%

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

   1. mul-1-neg 74.7%

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

   2. *-commutative 74.7%

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

   3. distribute-rgt-neg-in 74.7%

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

   4. distribute-neg-in 74.7%

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

   5. metadata-eval 74.7%

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

4. Simplified 74.7%

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

5. Taylor expanded in x around inf 45.1%

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

6. Final simplification 45.1%

   \[\leadsto 1 \]

Developer target: 94.7% 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 2023310 
(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)))))))))))