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

Percentage Accurate: 93.9% → 96.9%

Time: 22.0s

Alternatives: 20

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\\ t_2 := \sqrt{t + a}\\ \mathbf{if}\;\frac{z \cdot t\_2}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(t\_2 \cdot \frac{z}{t} + \left(b - c\right) \cdot t\_1\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(b \cdot \left(2 \cdot \left(t\_1 + b \cdot \left(t\_1 \cdot t\_1\right)\right)\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a)))
        (t_2 (sqrt (+ t a))))
   (if (<=
        (+ (/ (* z t_2) t) (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))
        INFINITY)
     (/ x (+ x (* y (exp (* 2.0 (+ (* t_2 (/ z t)) (* (- b c) t_1)))))))
     (/ x (+ x (* y (+ (* b (* 2.0 (+ t_1 (* b (* t_1 t_1))))) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.6666666666666666 / t) + (-0.8333333333333334 - a);
	double t_2 = sqrt((t + a));
	double tmp;
	if ((((z * t_2) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * ((t_2 * (z / t)) + ((b - c) * t_1))))));
	} else {
		tmp = x / (x + (y * ((b * (2.0 * (t_1 + (b * (t_1 * t_1))))) + 1.0)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (0.6666666666666666 / t) + (-0.8333333333333334 - a);
	double t_2 = Math.sqrt((t + a));
	double tmp;
	if ((((z * t_2) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.exp((2.0 * ((t_2 * (z / t)) + ((b - c) * t_1))))));
	} else {
		tmp = x / (x + (y * ((b * (2.0 * (t_1 + (b * (t_1 * t_1))))) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = (0.6666666666666666 / t) + (-0.8333333333333334 - a)
	t_2 = math.sqrt((t + a))
	tmp = 0
	if (((z * t_2) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * ((t_2 * (z / t)) + ((b - c) * t_1))))))
	else:
		tmp = x / (x + (y * ((b * (2.0 * (t_1 + (b * (t_1 * t_1))))) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a))
	t_2 = sqrt(Float64(t + a))
	tmp = 0.0
	if (Float64(Float64(Float64(z * t_2) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0))))) <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(t_2 * Float64(z / t)) + Float64(Float64(b - c) * t_1)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(b * Float64(2.0 * Float64(t_1 + Float64(b * Float64(t_1 * t_1))))) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (0.6666666666666666 / t) + (-0.8333333333333334 - a);
	t_2 = sqrt((t + a));
	tmp = 0.0;
	if ((((z * t_2) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= Inf)
		tmp = x / (x + (y * exp((2.0 * ((t_2 * (z / t)) + ((b - c) * t_1))))));
	else
		tmp = x / (x + (y * ((b * (2.0 * (t_1 + (b * (t_1 * t_1))))) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(0.6666666666666666 / t), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(N[(z * t$95$2), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(t$95$2 * N[(z / t), $MachinePrecision]), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[(N[(b * N[(2.0 * N[(t$95$1 + N[(b * N[(t$95$1 * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $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 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < +inf.0

   1. Initial program 98.4%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   if +inf.0 < (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64))))))

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 10.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 32.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 32.2%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]

      3. distribute-lft-out N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(2 \cdot \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right), \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 70.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t} + \left(b - c\right) \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(b \cdot \left(2 \cdot \left(\left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right) + b \cdot \left(\left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right) \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)\right)\right) + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}\\ t_2 := \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{if}\;c \leq -3 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-117}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (* c (- (+ a 0.8333333333333334) (/ 0.6666666666666666 t)))))))))
        (t_2
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (*
               b
               (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))))
   (if (<= c -3e+102)
     t_1
     (if (<= c -9e-117)
       t_2
       (if (<= c 3.7e-266)
         (/ x (+ x (* y (exp (* 2.0 (* (sqrt (+ t a)) (/ z t)))))))
         (if (<= c 1.4e+35) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))));
	double t_2 = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	double tmp;
	if (c <= -3e+102) {
		tmp = t_1;
	} else if (c <= -9e-117) {
		tmp = t_2;
	} else if (c <= 3.7e-266) {
		tmp = x / (x + (y * exp((2.0 * (sqrt((t + a)) * (z / t))))));
	} else if (c <= 1.4e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (c * ((a + 0.8333333333333334d0) - (0.6666666666666666d0 / t)))))))
    t_2 = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    if (c <= (-3d+102)) then
        tmp = t_1
    else if (c <= (-9d-117)) then
        tmp = t_2
    else if (c <= 3.7d-266) then
        tmp = x / (x + (y * exp((2.0d0 * (sqrt((t + a)) * (z / t))))))
    else if (c <= 1.4d+35) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))));
	double t_2 = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	double tmp;
	if (c <= -3e+102) {
		tmp = t_1;
	} else if (c <= -9e-117) {
		tmp = t_2;
	} else if (c <= 3.7e-266) {
		tmp = x / (x + (y * Math.exp((2.0 * (Math.sqrt((t + a)) * (z / t))))));
	} else if (c <= 1.4e+35) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))))
	t_2 = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	tmp = 0
	if c <= -3e+102:
		tmp = t_1
	elif c <= -9e-117:
		tmp = t_2
	elif c <= 3.7e-266:
		tmp = x / (x + (y * math.exp((2.0 * (math.sqrt((t + a)) * (z / t))))))
	elif c <= 1.4e+35:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(Float64(a + 0.8333333333333334) - Float64(0.6666666666666666 / t))))))))
	t_2 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))))
	tmp = 0.0
	if (c <= -3e+102)
		tmp = t_1;
	elseif (c <= -9e-117)
		tmp = t_2;
	elseif (c <= 3.7e-266)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(sqrt(Float64(t + a)) * Float64(z / t)))))));
	elseif (c <= 1.4e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))));
	t_2 = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	tmp = 0.0;
	if (c <= -3e+102)
		tmp = t_1;
	elseif (c <= -9e-117)
		tmp = t_2;
	elseif (c <= 3.7e-266)
		tmp = x / (x + (y * exp((2.0 * (sqrt((t + a)) * (z / t))))));
	elseif (c <= 1.4e+35)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(N[(a + 0.8333333333333334), $MachinePrecision] - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+102], t$95$1, If[LessEqual[c, -9e-117], t$95$2, If[LessEqual[c, 3.7e-266], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.4e+35], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.9999999999999998e102 or 1.39999999999999999e35 < c

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 95.3%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 90.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 90.0%

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

   if -2.9999999999999998e102 < c < -8.99999999999999939e-117 or 3.7000000000000003e-266 < c < 1.39999999999999999e35

   1. Initial program 95.0%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 96.9%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 75.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 75.5%

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

   if -8.99999999999999939e-117 < c < 3.7000000000000003e-266

   1. Initial program 98.0%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.0%

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

   5. Taylor expanded in z around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(\frac{z}{t} \cdot \sqrt{a + t}\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{z}{t}\right), \left(\sqrt{a + t}\right)\right)\right)\right)\right)\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \left(\sqrt{a + t}\right)\right)\right)\right)\right)\right)\right) \]

      3. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{sqrt.f64}\left(\left(a + t\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{sqrt.f64}\left(\left(t + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 90.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{/.f64}\left(z, t\right), \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(t, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 90.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+102}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\sqrt{t + a} \cdot \frac{z}{t}\right)}}\\ \mathbf{elif}\;c \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (*
               b
               (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))))
   (if (<= b -6.2e+109)
     t_1
     (if (<= b 4.8e+62)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (* c (- (+ a 0.8333333333333334) (/ 0.6666666666666666 t))))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	double tmp;
	if (b <= -6.2e+109) {
		tmp = t_1;
	} else if (b <= 4.8e+62) {
		tmp = x / (x + (y * exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    if (b <= (-6.2d+109)) then
        tmp = t_1
    else if (b <= 4.8d+62) then
        tmp = x / (x + (y * exp((2.0d0 * (c * ((a + 0.8333333333333334d0) - (0.6666666666666666d0 / t)))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	double tmp;
	if (b <= -6.2e+109) {
		tmp = t_1;
	} else if (b <= 4.8e+62) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	tmp = 0
	if b <= -6.2e+109:
		tmp = t_1
	elif b <= 4.8e+62:
		tmp = x / (x + (y * math.exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))))
	tmp = 0.0
	if (b <= -6.2e+109)
		tmp = t_1;
	elseif (b <= 4.8e+62)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(Float64(a + 0.8333333333333334) - Float64(0.6666666666666666 / t))))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	tmp = 0.0;
	if (b <= -6.2e+109)
		tmp = t_1;
	elseif (b <= 4.8e+62)
		tmp = x / (x + (y * exp((2.0 * (c * ((a + 0.8333333333333334) - (0.6666666666666666 / t)))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+109], t$95$1, If[LessEqual[b, 4.8e+62], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(N[(a + 0.8333333333333334), $MachinePrecision] - N[(0.6666666666666666 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.19999999999999985e109 or 4.8e62 < b

   1. Initial program 91.7%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 93.8%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 87.9%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 87.9%

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

   if -6.19999999999999985e109 < b < 4.8e62

   1. Initial program 96.3%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 77.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 77.1%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(\frac{0.6666666666666666}{t} - \left(0.8333333333333334 + a\right)\right) \cdot \left(0 - c\right)\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{+62}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\left(a + 0.8333333333333334\right) - \frac{0.6666666666666666}{t}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{if}\;b \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           x
           (*
            y
            (exp
             (*
              2.0
              (*
               b
               (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))))
   (if (<= b -6.2e+109)
     t_1
     (if (<= b 1.6e-47)
       (/ x (+ x (* y (exp (* 2.0 (* c (+ a 0.8333333333333334)))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	double tmp;
	if (b <= -6.2e+109) {
		tmp = t_1;
	} else if (b <= 1.6e-47) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + 0.8333333333333334))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    if (b <= (-6.2d+109)) then
        tmp = t_1
    else if (b <= 1.6d-47) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + 0.8333333333333334d0))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	double tmp;
	if (b <= -6.2e+109) {
		tmp = t_1;
	} else if (b <= 1.6e-47) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + 0.8333333333333334))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	tmp = 0
	if b <= -6.2e+109:
		tmp = t_1
	elif b <= 1.6e-47:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + 0.8333333333333334))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))))
	tmp = 0.0
	if (b <= -6.2e+109)
		tmp = t_1;
	elseif (b <= 1.6e-47)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	tmp = 0.0;
	if (b <= -6.2e+109)
		tmp = t_1;
	elseif (b <= 1.6e-47)
		tmp = x / (x + (y * exp((2.0 * (c * (a + 0.8333333333333334))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.2e+109], t$95$1, If[LessEqual[b, 1.6e-47], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -6.19999999999999985e109 or 1.6e-47 < b

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 93.5%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 79.7%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 79.7%

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

   if -6.19999999999999985e109 < b < 1.6e-47

   1. Initial program 97.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 99.2%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 79.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 79.6%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 70.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 70.8%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -8.6e+37)
   1.0
   (if (<= c 3.5e-153)
     (/ x (+ x (* y (exp (* 2.0 (* b (- -0.8333333333333334 a)))))))
     (if (<= c 2.35e-17)
       1.0
       (/ x (+ x (* y (exp (* c 1.6666666666666667)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -8.6e+37) {
		tmp = 1.0;
	} else if (c <= 3.5e-153) {
		tmp = x / (x + (y * exp((2.0 * (b * (-0.8333333333333334 - a))))));
	} else if (c <= 2.35e-17) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-8.6d+37)) then
        tmp = 1.0d0
    else if (c <= 3.5d-153) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((-0.8333333333333334d0) - a))))))
    else if (c <= 2.35d-17) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -8.6e+37) {
		tmp = 1.0;
	} else if (c <= 3.5e-153) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * (-0.8333333333333334 - a))))));
	} else if (c <= 2.35e-17) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -8.6e+37:
		tmp = 1.0
	elif c <= 3.5e-153:
		tmp = x / (x + (y * math.exp((2.0 * (b * (-0.8333333333333334 - a))))))
	elif c <= 2.35e-17:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -8.6e+37)
		tmp = 1.0;
	elseif (c <= 3.5e-153)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(-0.8333333333333334 - a)))))));
	elseif (c <= 2.35e-17)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -8.6e+37)
		tmp = 1.0;
	elseif (c <= 3.5e-153)
		tmp = x / (x + (y * exp((2.0 * (b * (-0.8333333333333334 - a))))));
	elseif (c <= 2.35e-17)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -8.6e+37], 1.0, If[LessEqual[c, 3.5e-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], If[LessEqual[c, 2.35e-17], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -8.5999999999999994e37 or 3.49999999999999981e-153 < c < 2.35e-17

   1. Initial program 97.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.9%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 73.6%

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

   if -8.5999999999999994e37 < c < 3.49999999999999981e-153

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 96.7%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 76.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 76.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(-1 \cdot \frac{5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{-5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) - a\right)\right)\right)\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right), a\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval 73.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\frac{-5}{6}, a\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 73.3%

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

   if 2.35e-17 < c

   1. Initial program 91.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 93.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 81.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 81.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 71.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.5%

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

   11. Taylor expanded in a around 0

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{\frac{5}{3} \cdot c}}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{\frac{5}{3} \cdot c}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{\frac{5}{3} \cdot c}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{\frac{5}{3} \cdot c}\right)}\right)\right)\right) \]

       4. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\frac{5}{3} \cdot c\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 70.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{5}{3}, c\right)\right)\right)\right)\right) \]

   13. Simplified 70.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -8.6 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-153}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{elif}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 64.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 2.0 (* b (- -0.8333333333333334 a)))))))))
   (if (<= b -2.3e+195)
     t_1
     (if (<= b 8.6e-45)
       (/ x (+ x (* y (exp (* 2.0 (* c (+ a 0.8333333333333334)))))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((2.0 * (b * (-0.8333333333333334 - a))))));
	double tmp;
	if (b <= -2.3e+195) {
		tmp = t_1;
	} else if (b <= 8.6e-45) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + 0.8333333333333334))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((2.0d0 * (b * ((-0.8333333333333334d0) - a))))))
    if (b <= (-2.3d+195)) then
        tmp = t_1
    else if (b <= 8.6d-45) then
        tmp = x / (x + (y * exp((2.0d0 * (c * (a + 0.8333333333333334d0))))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((2.0 * (b * (-0.8333333333333334 - a))))));
	double tmp;
	if (b <= -2.3e+195) {
		tmp = t_1;
	} else if (b <= 8.6e-45) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * (a + 0.8333333333333334))))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((2.0 * (b * (-0.8333333333333334 - a))))))
	tmp = 0
	if b <= -2.3e+195:
		tmp = t_1
	elif b <= 8.6e-45:
		tmp = x / (x + (y * math.exp((2.0 * (c * (a + 0.8333333333333334))))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(-0.8333333333333334 - a)))))))
	tmp = 0.0
	if (b <= -2.3e+195)
		tmp = t_1;
	elseif (b <= 8.6e-45)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334)))))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((2.0 * (b * (-0.8333333333333334 - a))))));
	tmp = 0.0;
	if (b <= -2.3e+195)
		tmp = t_1;
	elseif (b <= 8.6e-45)
		tmp = x / (x + (y * exp((2.0 * (c * (a + 0.8333333333333334))))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.3e+195], t$95$1, If[LessEqual[b, 8.6e-45], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.3000000000000001e195 or 8.5999999999999998e-45 < b

   1. Initial program 89.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 92.5%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 80.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 80.1%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(-1 \cdot \frac{5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{-5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) - a\right)\right)\right)\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right), a\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval 77.4%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\frac{-5}{6}, a\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 77.4%

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

   if -2.3000000000000001e195 < b < 8.5999999999999998e-45

   1. Initial program 98.0%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 99.3%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 76.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 76.7%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 69.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 69.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.3 \cdot 10^{+195}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{-45}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 57.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 2 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 2e-17) 1.0 (/ x (+ x (* y (exp (* c 1.6666666666666667)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2e-17) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 2d-17) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((c * 1.6666666666666667d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2e-17) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((c * 1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 2e-17:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((c * 1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 2e-17)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(c * 1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 2e-17)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((c * 1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 2e-17], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(c * 1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 2.00000000000000014e-17

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 66.8%

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

   if 2.00000000000000014e-17 < c

   1. Initial program 91.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 93.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 81.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 81.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 71.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.5%

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

   11. Taylor expanded in a around 0

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{\frac{5}{3} \cdot c}}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{\frac{5}{3} \cdot c}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{\frac{5}{3} \cdot c}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{\frac{5}{3} \cdot c}\right)}\right)\right)\right) \]

       4. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\frac{5}{3} \cdot c\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 70.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{5}{3}, c\right)\right)\right)\right)\right) \]

   13. Simplified 70.3%

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{1.6666666666666667 \cdot c}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{c \cdot 1.6666666666666667}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 55.8% accurate, 4.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 5.4 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+182}:\\ \;\;\;\;x \cdot \frac{-1}{y \cdot \left(-1 - b \cdot \left(a \cdot -2 + \left(-1.6666666666666667 + b \cdot \left(\left(2 + -1.3333333333333333 \cdot \left(b \cdot \left(a + 0.8333333333333334\right)\right)\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right)\right)\right)\right)\right) - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 5.4e-28)
   1.0
   (if (<= c 1.45e+182)
     (*
      x
      (/
       -1.0
       (-
        (*
         y
         (-
          -1.0
          (*
           b
           (+
            (* a -2.0)
            (+
             -1.6666666666666667
             (*
              b
              (*
               (+ 2.0 (* -1.3333333333333333 (* b (+ a 0.8333333333333334))))
               (* (+ a 0.8333333333333334) (+ a 0.8333333333333334)))))))))
        x)))
     (/
      x
      (+
       x
       (* y (+ (* c (+ 1.6666666666666667 (* c 1.3888888888888888))) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 5.4e-28) {
		tmp = 1.0;
	} else if (c <= 1.45e+182) {
		tmp = x * (-1.0 / ((y * (-1.0 - (b * ((a * -2.0) + (-1.6666666666666667 + (b * ((2.0 + (-1.3333333333333333 * (b * (a + 0.8333333333333334)))) * ((a + 0.8333333333333334) * (a + 0.8333333333333334))))))))) - x));
	} else {
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 5.4d-28) then
        tmp = 1.0d0
    else if (c <= 1.45d+182) then
        tmp = x * ((-1.0d0) / ((y * ((-1.0d0) - (b * ((a * (-2.0d0)) + ((-1.6666666666666667d0) + (b * ((2.0d0 + ((-1.3333333333333333d0) * (b * (a + 0.8333333333333334d0)))) * ((a + 0.8333333333333334d0) * (a + 0.8333333333333334d0))))))))) - x))
    else
        tmp = x / (x + (y * ((c * (1.6666666666666667d0 + (c * 1.3888888888888888d0))) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 5.4e-28) {
		tmp = 1.0;
	} else if (c <= 1.45e+182) {
		tmp = x * (-1.0 / ((y * (-1.0 - (b * ((a * -2.0) + (-1.6666666666666667 + (b * ((2.0 + (-1.3333333333333333 * (b * (a + 0.8333333333333334)))) * ((a + 0.8333333333333334) * (a + 0.8333333333333334))))))))) - x));
	} else {
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 5.4e-28:
		tmp = 1.0
	elif c <= 1.45e+182:
		tmp = x * (-1.0 / ((y * (-1.0 - (b * ((a * -2.0) + (-1.6666666666666667 + (b * ((2.0 + (-1.3333333333333333 * (b * (a + 0.8333333333333334)))) * ((a + 0.8333333333333334) * (a + 0.8333333333333334))))))))) - x))
	else:
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 5.4e-28)
		tmp = 1.0;
	elseif (c <= 1.45e+182)
		tmp = Float64(x * Float64(-1.0 / Float64(Float64(y * Float64(-1.0 - Float64(b * Float64(Float64(a * -2.0) + Float64(-1.6666666666666667 + Float64(b * Float64(Float64(2.0 + Float64(-1.3333333333333333 * Float64(b * Float64(a + 0.8333333333333334)))) * Float64(Float64(a + 0.8333333333333334) * Float64(a + 0.8333333333333334))))))))) - x)));
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(c * Float64(1.6666666666666667 + Float64(c * 1.3888888888888888))) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 5.4e-28)
		tmp = 1.0;
	elseif (c <= 1.45e+182)
		tmp = x * (-1.0 / ((y * (-1.0 - (b * ((a * -2.0) + (-1.6666666666666667 + (b * ((2.0 + (-1.3333333333333333 * (b * (a + 0.8333333333333334)))) * ((a + 0.8333333333333334) * (a + 0.8333333333333334))))))))) - x));
	else
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 5.4e-28], 1.0, If[LessEqual[c, 1.45e+182], N[(x * N[(-1.0 / N[(N[(y * N[(-1.0 - N[(b * N[(N[(a * -2.0), $MachinePrecision] + N[(-1.6666666666666667 + N[(b * N[(N[(2.0 + N[(-1.3333333333333333 * N[(b * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[(N[(c * N[(1.6666666666666667 + N[(c * 1.3888888888888888), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < 5.3999999999999998e-28

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 67.3%

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

   if 5.3999999999999998e-28 < c < 1.4499999999999999e182

   1. Initial program 98.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.2%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 57.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 57.1%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(-1 \cdot \frac{5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{-5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) - a\right)\right)\right)\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right), a\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval 55.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\frac{-5}{6}, a\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 55.8%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(-2 \cdot \left(\frac{5}{6} + a\right)\right), \color{blue}{\left(b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)}\right)\right)\right)\right)\right)\right) \]

       4. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(-2 \cdot \frac{5}{6} + -2 \cdot a\right), \left(\color{blue}{b} \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{-5}{3} + -2 \cdot a\right), \left(b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \left(-2 \cdot a\right)\right), \left(\color{blue}{b} \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \mathsf{*.f64}\left(-2, a\right)\right), \left(b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \mathsf{*.f64}\left(-2, a\right)\right), \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

       9. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \mathsf{*.f64}\left(-2, a\right)\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right)\right), \color{blue}{\left(2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)}\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 54.3%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + b \cdot \left(\left(-1.6666666666666667 + -2 \cdot a\right) + b \cdot \left(\left(-1.3333333333333333 \cdot b\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right)\right)\right) + 2 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right)\right)\right)\right)\right)}} \]
   14. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \frac{1}{\color{blue}{\frac{x + y \cdot \left(1 + b \cdot \left(\left(\frac{-5}{3} + -2 \cdot a\right) + b \cdot \left(\left(\frac{-4}{3} \cdot b\right) \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)\right)\right) + 2 \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}{x}}} \]

       2. associate-/r/ N/A

          \[\leadsto \frac{1}{x + y \cdot \left(1 + b \cdot \left(\left(\frac{-5}{3} + -2 \cdot a\right) + b \cdot \left(\left(\frac{-4}{3} \cdot b\right) \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)\right)\right) + 2 \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)} \cdot \color{blue}{x} \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{1}{x + y \cdot \left(1 + b \cdot \left(\left(\frac{-5}{3} + -2 \cdot a\right) + b \cdot \left(\left(\frac{-4}{3} \cdot b\right) \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)\right)\right) + 2 \cdot \left(\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right), \color{blue}{x}\right) \]

   15. Applied egg-rr 63.1%

       \[\leadsto \color{blue}{\frac{1}{x + y \cdot \left(1 + b \cdot \left(a \cdot -2 + \left(-1.6666666666666667 + b \cdot \left(\left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right) \cdot \left(-1.3333333333333333 \cdot \left(b \cdot \left(a + 0.8333333333333334\right)\right) + 2\right)\right)\right)\right)\right)} \cdot x} \]

   if 1.4499999999999999e182 < c

   1. Initial program 75.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 83.3%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 91.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 91.9%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 79.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 79.8%

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

   11. Taylor expanded in a around 0

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{\frac{5}{3} \cdot c}}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{\frac{5}{3} \cdot c}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{\frac{5}{3} \cdot c}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{\frac{5}{3} \cdot c}\right)}\right)\right)\right) \]

       4. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\frac{5}{3} \cdot c\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 79.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{5}{3}, c\right)\right)\right)\right)\right) \]

   13. Simplified 79.8%

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

   14. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + c \cdot \left(\frac{5}{3} + \frac{25}{18} \cdot c\right)\right)}\right)\right)\right) \]
   15. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(c \cdot \left(\frac{5}{3} + \frac{25}{18} \cdot c\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \color{blue}{\left(\frac{5}{3} + \frac{25}{18} \cdot c\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \color{blue}{\left(\frac{25}{18} \cdot c\right)}\right)\right)\right)\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \left(c \cdot \color{blue}{\frac{25}{18}}\right)\right)\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 79.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \mathsf{*.f64}\left(c, \color{blue}{\frac{25}{18}}\right)\right)\right)\right)\right)\right)\right) \]

   16. Simplified 79.8%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 5.4 \cdot 10^{-28}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.45 \cdot 10^{+182}:\\ \;\;\;\;x \cdot \frac{-1}{y \cdot \left(-1 - b \cdot \left(a \cdot -2 + \left(-1.6666666666666667 + b \cdot \left(\left(2 + -1.3333333333333333 \cdot \left(b \cdot \left(a + 0.8333333333333334\right)\right)\right) \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right)\right)\right)\right)\right) - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right) + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 55.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{+178}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(b \cdot 2\right) \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right) - \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 1.15e-27)
   1.0
   (if (<= c 2.45e+178)
     (/
      x
      (+
       x
       (*
        y
        (+
         (*
          (* b 2.0)
          (-
           (* b (* (+ a 0.8333333333333334) (+ a 0.8333333333333334)))
           (+ a 0.8333333333333334)))
         1.0))))
     (/
      x
      (+
       x
       (* y (+ (* c (+ 1.6666666666666667 (* c 1.3888888888888888))) 1.0)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.15e-27) {
		tmp = 1.0;
	} else if (c <= 2.45e+178) {
		tmp = x / (x + (y * (((b * 2.0) * ((b * ((a + 0.8333333333333334) * (a + 0.8333333333333334))) - (a + 0.8333333333333334))) + 1.0)));
	} else {
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 1.15d-27) then
        tmp = 1.0d0
    else if (c <= 2.45d+178) then
        tmp = x / (x + (y * (((b * 2.0d0) * ((b * ((a + 0.8333333333333334d0) * (a + 0.8333333333333334d0))) - (a + 0.8333333333333334d0))) + 1.0d0)))
    else
        tmp = x / (x + (y * ((c * (1.6666666666666667d0 + (c * 1.3888888888888888d0))) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.15e-27) {
		tmp = 1.0;
	} else if (c <= 2.45e+178) {
		tmp = x / (x + (y * (((b * 2.0) * ((b * ((a + 0.8333333333333334) * (a + 0.8333333333333334))) - (a + 0.8333333333333334))) + 1.0)));
	} else {
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 1.15e-27:
		tmp = 1.0
	elif c <= 2.45e+178:
		tmp = x / (x + (y * (((b * 2.0) * ((b * ((a + 0.8333333333333334) * (a + 0.8333333333333334))) - (a + 0.8333333333333334))) + 1.0)))
	else:
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 1.15e-27)
		tmp = 1.0;
	elseif (c <= 2.45e+178)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(Float64(b * 2.0) * Float64(Float64(b * Float64(Float64(a + 0.8333333333333334) * Float64(a + 0.8333333333333334))) - Float64(a + 0.8333333333333334))) + 1.0))));
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(c * Float64(1.6666666666666667 + Float64(c * 1.3888888888888888))) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 1.15e-27)
		tmp = 1.0;
	elseif (c <= 2.45e+178)
		tmp = x / (x + (y * (((b * 2.0) * ((b * ((a + 0.8333333333333334) * (a + 0.8333333333333334))) - (a + 0.8333333333333334))) + 1.0)));
	else
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 1.15e-27], 1.0, If[LessEqual[c, 2.45e+178], N[(x / N[(x + N[(y * N[(N[(N[(b * 2.0), $MachinePrecision] * N[(N[(b * N[(N[(a + 0.8333333333333334), $MachinePrecision] * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[(N[(c * N[(1.6666666666666667 + N[(c * 1.3888888888888888), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < 1.15e-27

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.7%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 67.3%

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

   if 1.15e-27 < c < 2.4500000000000001e178

   1. Initial program 98.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.2%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 57.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 57.1%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]

      3. distribute-lft-out N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(2 \cdot \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right), \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 61.5%

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

   11. Taylor expanded in t around inf

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2} - \left(\frac{5}{6} + a\right)\right)\right)\right)}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot \left(1 + 2 \cdot \left(b \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(1 + 2 \cdot \left(b \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + 2 \cdot \left(b \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right) \]

       4. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(2 \cdot \left(b \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{2} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right) \]

       5. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \left(\left(2 \cdot b\right) \cdot \color{blue}{\left(b \cdot {\left(\frac{5}{6} + a\right)}^{2} - \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\left(2 \cdot b\right), \color{blue}{\left(b \cdot {\left(\frac{5}{6} + a\right)}^{2} - \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \left(\color{blue}{b \cdot {\left(\frac{5}{6} + a\right)}^{2}} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

       8. --lowering--.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \mathsf{\_.f64}\left(\left(b \cdot {\left(\frac{5}{6} + a\right)}^{2}\right), \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left({\left(\frac{5}{6} + a\right)}^{2}\right)\right), \left(\color{blue}{\frac{5}{6}} + a\right)\right)\right)\right)\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \left(\left(\frac{5}{6} + a\right) \cdot \left(\frac{5}{6} + a\right)\right)\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), \left(\frac{5}{6} + a\right)\right)\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

       12. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), \left(\frac{5}{6} + a\right)\right)\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

       13. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

       14. +-lowering-+.f64 56.9%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, b\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(b, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right), \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 56.9%

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

   if 2.4500000000000001e178 < c

   1. Initial program 75.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 83.3%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 91.9%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 91.9%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 79.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 79.8%

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

   11. Taylor expanded in a around 0

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{\frac{5}{3} \cdot c}}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{\frac{5}{3} \cdot c}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{\frac{5}{3} \cdot c}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{\frac{5}{3} \cdot c}\right)}\right)\right)\right) \]

       4. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\frac{5}{3} \cdot c\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 79.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{5}{3}, c\right)\right)\right)\right)\right) \]

   13. Simplified 79.8%

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

   14. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + c \cdot \left(\frac{5}{3} + \frac{25}{18} \cdot c\right)\right)}\right)\right)\right) \]
   15. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(c \cdot \left(\frac{5}{3} + \frac{25}{18} \cdot c\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \color{blue}{\left(\frac{5}{3} + \frac{25}{18} \cdot c\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \color{blue}{\left(\frac{25}{18} \cdot c\right)}\right)\right)\right)\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \left(c \cdot \color{blue}{\frac{25}{18}}\right)\right)\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 79.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \mathsf{*.f64}\left(c, \color{blue}{\frac{25}{18}}\right)\right)\right)\right)\right)\right)\right) \]

   16. Simplified 79.8%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{+178}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(\left(b \cdot 2\right) \cdot \left(b \cdot \left(\left(a + 0.8333333333333334\right) \cdot \left(a + 0.8333333333333334\right)\right) - \left(a + 0.8333333333333334\right)\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right) + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.3% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(b \cdot \left(-1.6666666666666667 + b \cdot \left(1.3888888888888888 + b \cdot -0.7716049382716049\right)\right) + 1\right)}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(c \cdot \left(y \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.6e+113)
   (/
    x
    (+
     x
     (*
      y
      (+
       (*
        b
        (+
         -1.6666666666666667
         (* b (+ 1.3888888888888888 (* b -0.7716049382716049)))))
       1.0))))
   (if (<= b -7e-108)
     1.0
     (if (<= b 6.5e-247)
       (/ x (+ (+ x y) (* 2.0 (* c (* y (+ a 0.8333333333333334))))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.6e+113) {
		tmp = x / (x + (y * ((b * (-1.6666666666666667 + (b * (1.3888888888888888 + (b * -0.7716049382716049))))) + 1.0)));
	} else if (b <= -7e-108) {
		tmp = 1.0;
	} else if (b <= 6.5e-247) {
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.6d+113)) then
        tmp = x / (x + (y * ((b * ((-1.6666666666666667d0) + (b * (1.3888888888888888d0 + (b * (-0.7716049382716049d0)))))) + 1.0d0)))
    else if (b <= (-7d-108)) then
        tmp = 1.0d0
    else if (b <= 6.5d-247) then
        tmp = x / ((x + y) + (2.0d0 * (c * (y * (a + 0.8333333333333334d0)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.6e+113) {
		tmp = x / (x + (y * ((b * (-1.6666666666666667 + (b * (1.3888888888888888 + (b * -0.7716049382716049))))) + 1.0)));
	} else if (b <= -7e-108) {
		tmp = 1.0;
	} else if (b <= 6.5e-247) {
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.6e+113:
		tmp = x / (x + (y * ((b * (-1.6666666666666667 + (b * (1.3888888888888888 + (b * -0.7716049382716049))))) + 1.0)))
	elif b <= -7e-108:
		tmp = 1.0
	elif b <= 6.5e-247:
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.6e+113)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(b * Float64(-1.6666666666666667 + Float64(b * Float64(1.3888888888888888 + Float64(b * -0.7716049382716049))))) + 1.0))));
	elseif (b <= -7e-108)
		tmp = 1.0;
	elseif (b <= 6.5e-247)
		tmp = Float64(x / Float64(Float64(x + y) + Float64(2.0 * Float64(c * Float64(y * Float64(a + 0.8333333333333334))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.6e+113)
		tmp = x / (x + (y * ((b * (-1.6666666666666667 + (b * (1.3888888888888888 + (b * -0.7716049382716049))))) + 1.0)));
	elseif (b <= -7e-108)
		tmp = 1.0;
	elseif (b <= 6.5e-247)
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.6e+113], N[(x / N[(x + N[(y * N[(N[(b * N[(-1.6666666666666667 + N[(b * N[(1.3888888888888888 + N[(b * -0.7716049382716049), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7e-108], 1.0, If[LessEqual[b, 6.5e-247], N[(x / N[(N[(x + y), $MachinePrecision] + N[(2.0 * N[(c * N[(y * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.5999999999999999e113

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 87.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 87.6%

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

   8. Taylor expanded in t around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \color{blue}{\left(-1 \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right) \]
   9. Step-by-step derivation

      1. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(-1 \cdot \frac{5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{-5}{6} + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + -1 \cdot a\right)\right)\right)\right)\right)\right)\right) \]

      4. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) - a\right)\right)\right)\right)\right)\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right), a\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval 77.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\frac{-5}{6}, a\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 77.6%

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

   11. Taylor expanded in b around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(-2 \cdot \left(\frac{5}{6} + a\right) + b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(-2 \cdot \left(\frac{5}{6} + a\right)\right), \color{blue}{\left(b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)}\right)\right)\right)\right)\right)\right) \]

       4. distribute-lft-in N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(-2 \cdot \frac{5}{6} + -2 \cdot a\right), \left(\color{blue}{b} \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       5. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{-5}{3} + -2 \cdot a\right), \left(b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       6. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \left(-2 \cdot a\right)\right), \left(\color{blue}{b} \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \mathsf{*.f64}\left(-2, a\right)\right), \left(b \cdot \left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)\right)\right)\right)\right)\right)\right)\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \mathsf{*.f64}\left(-2, a\right)\right), \mathsf{*.f64}\left(b, \color{blue}{\left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right) + 2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)}\right)\right)\right)\right)\right)\right)\right) \]

       9. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{+.f64}\left(\frac{-5}{3}, \mathsf{*.f64}\left(-2, a\right)\right), \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(\frac{-4}{3} \cdot \left(b \cdot {\left(\frac{5}{6} + a\right)}^{3}\right)\right), \color{blue}{\left(2 \cdot {\left(\frac{5}{6} + a\right)}^{2}\right)}\right)\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 72.5%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + b \cdot \left(\left(-1.6666666666666667 + -2 \cdot a\right) + b \cdot \left(\left(-1.3333333333333333 \cdot b\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right)\right)\right) + 2 \cdot \left(\left(0.8333333333333334 + a\right) \cdot \left(0.8333333333333334 + a\right)\right)\right)\right)\right)}} \]

   14. Taylor expanded in a around 0

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot \left(1 + b \cdot \left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) - \frac{5}{3}\right)\right)}} \]
   15. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot \left(1 + b \cdot \left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) - \frac{5}{3}\right)\right)\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot \left(1 + b \cdot \left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) - \frac{5}{3}\right)\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) - \frac{5}{3}\right)\right)}\right)\right)\right) \]

       4. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) - \frac{5}{3}\right)\right)}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) - \frac{5}{3}\right)}\right)\right)\right)\right)\right) \]

       6. sub-neg N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{5}{3}\right)\right)}\right)\right)\right)\right)\right)\right) \]

       7. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right) + \frac{-5}{3}\right)\right)\right)\right)\right)\right) \]

       8. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\left(b \cdot \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right)\right), \color{blue}{\frac{-5}{3}}\right)\right)\right)\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \left(\frac{25}{18} + \frac{-125}{162} \cdot b\right)\right), \frac{-5}{3}\right)\right)\right)\right)\right)\right) \]

       10. +-lowering-+.f64 N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{25}{18}, \left(\frac{-125}{162} \cdot b\right)\right)\right), \frac{-5}{3}\right)\right)\right)\right)\right)\right) \]

       11. *-commutative N/A

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{25}{18}, \left(b \cdot \frac{-125}{162}\right)\right)\right), \frac{-5}{3}\right)\right)\right)\right)\right)\right) \]

       12. *-lowering-*.f64 72.7%

           \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\mathsf{*.f64}\left(b, \mathsf{+.f64}\left(\frac{25}{18}, \mathsf{*.f64}\left(b, \frac{-125}{162}\right)\right)\right), \frac{-5}{3}\right)\right)\right)\right)\right)\right) \]

   16. Simplified 72.7%

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot \left(1 + b \cdot \left(b \cdot \left(1.3888888888888888 + b \cdot -0.7716049382716049\right) + -1.6666666666666667\right)\right)}} \]

   if -2.5999999999999999e113 < b < -6.9999999999999997e-108 or 6.4999999999999996e-247 < b

   1. Initial program 93.6%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 94.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 67.6%

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

   if -6.9999999999999997e-108 < b < 6.4999999999999996e-247

   1. Initial program 95.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.4%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 78.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.3%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 72.3%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(x + y\right) + \color{blue}{2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{2} \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right) \]

       7. +-lowering-+.f64 62.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 62.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(b \cdot \left(-1.6666666666666667 + b \cdot \left(1.3888888888888888 + b \cdot -0.7716049382716049\right)\right) + 1\right)}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-247}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(c \cdot \left(y \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 53.6% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x \cdot 0.5}{a \cdot \left(a \cdot \left(b \cdot b\right)\right)}}{y}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(c \cdot \left(y \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.9e+113)
   (/ (/ (* x 0.5) (* a (* a (* b b)))) y)
   (if (<= b -2.8e-108)
     1.0
     (if (<= b 1.25e-246)
       (/ x (+ (+ x y) (* 2.0 (* c (* y (+ a 0.8333333333333334))))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.9e+113) {
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	} else if (b <= -2.8e-108) {
		tmp = 1.0;
	} else if (b <= 1.25e-246) {
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.9d+113)) then
        tmp = ((x * 0.5d0) / (a * (a * (b * b)))) / y
    else if (b <= (-2.8d-108)) then
        tmp = 1.0d0
    else if (b <= 1.25d-246) then
        tmp = x / ((x + y) + (2.0d0 * (c * (y * (a + 0.8333333333333334d0)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.9e+113) {
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	} else if (b <= -2.8e-108) {
		tmp = 1.0;
	} else if (b <= 1.25e-246) {
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.9e+113:
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y
	elif b <= -2.8e-108:
		tmp = 1.0
	elif b <= 1.25e-246:
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.9e+113)
		tmp = Float64(Float64(Float64(x * 0.5) / Float64(a * Float64(a * Float64(b * b)))) / y);
	elseif (b <= -2.8e-108)
		tmp = 1.0;
	elseif (b <= 1.25e-246)
		tmp = Float64(x / Float64(Float64(x + y) + Float64(2.0 * Float64(c * Float64(y * Float64(a + 0.8333333333333334))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.9e+113)
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	elseif (b <= -2.8e-108)
		tmp = 1.0;
	elseif (b <= 1.25e-246)
		tmp = x / ((x + y) + (2.0 * (c * (y * (a + 0.8333333333333334)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.9e+113], N[(N[(N[(x * 0.5), $MachinePrecision] / N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -2.8e-108], 1.0, If[LessEqual[b, 1.25e-246], N[(x / N[(N[(x + y), $MachinePrecision] + N[(2.0 * N[(c * N[(y * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.89999999999999984e113

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 87.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 87.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]

      3. distribute-lft-out N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(2 \cdot \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right), \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 72.7%

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

   11. Taylor expanded in a around inf

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

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left({a}^{2} \cdot \left({b}^{2} \cdot y\right)\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(\color{blue}{{a}^{2}} \cdot \left({b}^{2} \cdot y\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\left({a}^{2}\right), \color{blue}{\left({b}^{2} \cdot y\right)}\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\left(a \cdot a\right), \left(\color{blue}{{b}^{2}} \cdot y\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \left(\color{blue}{{b}^{2}} \cdot y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{y}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\left(b \cdot b\right), y\right)\right)\right) \]

       9. *-lowering-*.f64 51.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), y\right)\right)\right) \]

   13. Simplified 51.9%

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

       1. associate-*r* N/A

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

       2. associate-/r* N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{2} \cdot x}{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right), \color{blue}{y}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \left(a \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       10. *-lowering-*.f64 72.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   15. Applied egg-rr 72.6%

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

   if -2.89999999999999984e113 < b < -2.8e-108 or 1.2499999999999999e-246 < b

   1. Initial program 93.6%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 94.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 67.6%

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

   if -2.8e-108 < b < 1.2499999999999999e-246

   1. Initial program 95.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.4%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 78.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.3%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 72.3%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(x + y\right) + \color{blue}{2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{2} \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right) \]

       7. +-lowering-+.f64 62.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 62.1%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x \cdot 0.5}{a \cdot \left(a \cdot \left(b \cdot b\right)\right)}}{y}\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + 2 \cdot \left(c \cdot \left(y \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 54.5% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x \cdot 0.5}{a \cdot \left(a \cdot \left(b \cdot b\right)\right)}}{y}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.8e+113)
   (/ (/ (* x 0.5) (* a (* a (* b b)))) y)
   (if (<= b -8.2e-108)
     1.0
     (if (<= b -1.2e-238)
       (/
        x
        (+
         x
         (* y (+ (* c (+ 1.6666666666666667 (* c 1.3888888888888888))) 1.0))))
       1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.8e+113) {
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	} else if (b <= -8.2e-108) {
		tmp = 1.0;
	} else if (b <= -1.2e-238) {
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.8d+113)) then
        tmp = ((x * 0.5d0) / (a * (a * (b * b)))) / y
    else if (b <= (-8.2d-108)) then
        tmp = 1.0d0
    else if (b <= (-1.2d-238)) then
        tmp = x / (x + (y * ((c * (1.6666666666666667d0 + (c * 1.3888888888888888d0))) + 1.0d0)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.8e+113) {
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	} else if (b <= -8.2e-108) {
		tmp = 1.0;
	} else if (b <= -1.2e-238) {
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.8e+113:
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y
	elif b <= -8.2e-108:
		tmp = 1.0
	elif b <= -1.2e-238:
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.8e+113)
		tmp = Float64(Float64(Float64(x * 0.5) / Float64(a * Float64(a * Float64(b * b)))) / y);
	elseif (b <= -8.2e-108)
		tmp = 1.0;
	elseif (b <= -1.2e-238)
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(c * Float64(1.6666666666666667 + Float64(c * 1.3888888888888888))) + 1.0))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.8e+113)
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	elseif (b <= -8.2e-108)
		tmp = 1.0;
	elseif (b <= -1.2e-238)
		tmp = x / (x + (y * ((c * (1.6666666666666667 + (c * 1.3888888888888888))) + 1.0)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.8e+113], N[(N[(N[(x * 0.5), $MachinePrecision] / N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -8.2e-108], 1.0, If[LessEqual[b, -1.2e-238], N[(x / N[(x + N[(y * N[(N[(c * N[(1.6666666666666667 + N[(c * 1.3888888888888888), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.79999999999999998e113

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 87.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 87.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]

      3. distribute-lft-out N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(2 \cdot \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right), \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 72.7%

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

   11. Taylor expanded in a around inf

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

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left({a}^{2} \cdot \left({b}^{2} \cdot y\right)\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(\color{blue}{{a}^{2}} \cdot \left({b}^{2} \cdot y\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\left({a}^{2}\right), \color{blue}{\left({b}^{2} \cdot y\right)}\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\left(a \cdot a\right), \left(\color{blue}{{b}^{2}} \cdot y\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \left(\color{blue}{{b}^{2}} \cdot y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{y}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\left(b \cdot b\right), y\right)\right)\right) \]

       9. *-lowering-*.f64 51.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), y\right)\right)\right) \]

   13. Simplified 51.9%

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

       1. associate-*r* N/A

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

       2. associate-/r* N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{2} \cdot x}{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right), \color{blue}{y}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \left(a \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       10. *-lowering-*.f64 72.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   15. Applied egg-rr 72.6%

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

   if -2.79999999999999998e113 < b < -8.20000000000000074e-108 or -1.1999999999999999e-238 < b

   1. Initial program 93.6%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 95.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 65.1%

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

   if -8.20000000000000074e-108 < b < -1.1999999999999999e-238

   1. Initial program 96.8%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 78.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.1%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 81.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 81.6%

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

   11. Taylor expanded in a around 0

       \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{\frac{5}{3} \cdot c}}} \]
   12. Step-by-step derivation

       1. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{\frac{5}{3} \cdot c}\right)}\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{\frac{5}{3} \cdot c}\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{\frac{5}{3} \cdot c}\right)}\right)\right)\right) \]

       4. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\frac{5}{3} \cdot c\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 78.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{5}{3}, c\right)\right)\right)\right)\right) \]

   13. Simplified 78.7%

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

   14. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + c \cdot \left(\frac{5}{3} + \frac{25}{18} \cdot c\right)\right)}\right)\right)\right) \]
   15. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(c \cdot \left(\frac{5}{3} + \frac{25}{18} \cdot c\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \color{blue}{\left(\frac{5}{3} + \frac{25}{18} \cdot c\right)}\right)\right)\right)\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \color{blue}{\left(\frac{25}{18} \cdot c\right)}\right)\right)\right)\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \left(c \cdot \color{blue}{\frac{25}{18}}\right)\right)\right)\right)\right)\right)\right) \]

       5. *-lowering-*.f64 69.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{3}, \mathsf{*.f64}\left(c, \color{blue}{\frac{25}{18}}\right)\right)\right)\right)\right)\right)\right) \]

   16. Simplified 69.4%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x \cdot 0.5}{a \cdot \left(a \cdot \left(b \cdot b\right)\right)}}{y}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(c \cdot \left(1.6666666666666667 + c \cdot 1.3888888888888888\right) + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 53.6% accurate, 8.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x \cdot 0.5}{a \cdot \left(a \cdot \left(b \cdot b\right)\right)}}{y}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -2.8e+113)
   (/ (/ (* x 0.5) (* a (* a (* b b)))) y)
   (if (<= b -7e-108)
     1.0
     (if (<= b 2.8e-246) (/ x (+ (+ x y) (* (* a 2.0) (* c y)))) 1.0))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.8e+113) {
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	} else if (b <= -7e-108) {
		tmp = 1.0;
	} else if (b <= 2.8e-246) {
		tmp = x / ((x + y) + ((a * 2.0) * (c * y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-2.8d+113)) then
        tmp = ((x * 0.5d0) / (a * (a * (b * b)))) / y
    else if (b <= (-7d-108)) then
        tmp = 1.0d0
    else if (b <= 2.8d-246) then
        tmp = x / ((x + y) + ((a * 2.0d0) * (c * y)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -2.8e+113) {
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	} else if (b <= -7e-108) {
		tmp = 1.0;
	} else if (b <= 2.8e-246) {
		tmp = x / ((x + y) + ((a * 2.0) * (c * y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -2.8e+113:
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y
	elif b <= -7e-108:
		tmp = 1.0
	elif b <= 2.8e-246:
		tmp = x / ((x + y) + ((a * 2.0) * (c * y)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -2.8e+113)
		tmp = Float64(Float64(Float64(x * 0.5) / Float64(a * Float64(a * Float64(b * b)))) / y);
	elseif (b <= -7e-108)
		tmp = 1.0;
	elseif (b <= 2.8e-246)
		tmp = Float64(x / Float64(Float64(x + y) + Float64(Float64(a * 2.0) * Float64(c * y))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -2.8e+113)
		tmp = ((x * 0.5) / (a * (a * (b * b)))) / y;
	elseif (b <= -7e-108)
		tmp = 1.0;
	elseif (b <= 2.8e-246)
		tmp = x / ((x + y) + ((a * 2.0) * (c * y)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -2.8e+113], N[(N[(N[(x * 0.5), $MachinePrecision] / N[(a * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -7e-108], 1.0, If[LessEqual[b, 2.8e-246], N[(x / N[(N[(x + y), $MachinePrecision] + N[(N[(a * 2.0), $MachinePrecision] * N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.79999999999999998e113

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 87.6%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 87.6%

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

   8. Taylor expanded in b around 0

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right) \]
   9. Step-by-step derivation

      1. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(b \cdot \left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \color{blue}{\left(2 \cdot \left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right) + 2 \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]

      3. distribute-lft-out N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \left(2 \cdot \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2} + \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(b, \mathsf{*.f64}\left(2, \mathsf{+.f64}\left(\left(b \cdot {\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}^{2}\right), \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right)\right)\right) \]

   10. Simplified 72.7%

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

   11. Taylor expanded in a around inf

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

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left({a}^{2} \cdot \left({b}^{2} \cdot y\right)\right)}\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \left(\color{blue}{{a}^{2}} \cdot \left({b}^{2} \cdot y\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\left({a}^{2}\right), \color{blue}{\left({b}^{2} \cdot y\right)}\right)\right) \]

       5. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\left(a \cdot a\right), \left(\color{blue}{{b}^{2}} \cdot y\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \left(\color{blue}{{b}^{2}} \cdot y\right)\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\left({b}^{2}\right), \color{blue}{y}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\left(b \cdot b\right), y\right)\right)\right) \]

       9. *-lowering-*.f64 51.9%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{2}, x\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(a, a\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(b, b\right), y\right)\right)\right) \]

   13. Simplified 51.9%

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

       1. associate-*r* N/A

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

       2. associate-/r* N/A

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

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{\frac{1}{2} \cdot x}{\left(a \cdot a\right) \cdot \left(b \cdot b\right)}\right), \color{blue}{y}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\left(a \cdot a\right) \cdot \left(b \cdot b\right)\right)\right), y\right) \]

       7. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(a \cdot \left(a \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       8. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \left(a \cdot \left(b \cdot b\right)\right)\right)\right), y\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \left(b \cdot b\right)\right)\right)\right), y\right) \]

       10. *-lowering-*.f64 72.6%

           \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(a, \mathsf{*.f64}\left(b, b\right)\right)\right)\right), y\right) \]

   15. Applied egg-rr 72.6%

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

   if -2.79999999999999998e113 < b < -6.9999999999999997e-108 or 2.7999999999999999e-246 < b

   1. Initial program 93.6%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 94.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 67.6%

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

   if -6.9999999999999997e-108 < b < 2.7999999999999999e-246

   1. Initial program 95.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 98.4%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 78.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 78.3%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 72.3%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 72.3%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(x + y\right) + \color{blue}{2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{2} \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right) \]

       7. +-lowering-+.f64 62.1%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 62.1%

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

   14. Taylor expanded in a around inf

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \left(a \cdot \left(c \cdot y\right)\right)\right)}\right)\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\left(2 \cdot a\right) \cdot \color{blue}{\left(c \cdot y\right)}\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(2 \cdot a\right), \color{blue}{\left(c \cdot y\right)}\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, a\right), \left(\color{blue}{c} \cdot y\right)\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, a\right), \left(y \cdot \color{blue}{c}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 60.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, a\right), \mathsf{*.f64}\left(y, \color{blue}{c}\right)\right)\right)\right) \]

   16. Simplified 60.4%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{x \cdot 0.5}{a \cdot \left(a \cdot \left(b \cdot b\right)\right)}}{y}\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.8% accurate, 10.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y \cdot \left(a + 0.8333333333333334\right)\right) \cdot \left(c \cdot 2\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 2.35e-17)
   1.0
   (if (<= c 1.6e+34)
     (* (/ x (- (* x x) (* y y))) (- x y))
     (/ x (* (* y (+ a 0.8333333333333334)) (* c 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2.35e-17) {
		tmp = 1.0;
	} else if (c <= 1.6e+34) {
		tmp = (x / ((x * x) - (y * y))) * (x - y);
	} else {
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 2.35d-17) then
        tmp = 1.0d0
    else if (c <= 1.6d+34) then
        tmp = (x / ((x * x) - (y * y))) * (x - y)
    else
        tmp = x / ((y * (a + 0.8333333333333334d0)) * (c * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2.35e-17) {
		tmp = 1.0;
	} else if (c <= 1.6e+34) {
		tmp = (x / ((x * x) - (y * y))) * (x - y);
	} else {
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 2.35e-17:
		tmp = 1.0
	elif c <= 1.6e+34:
		tmp = (x / ((x * x) - (y * y))) * (x - y)
	else:
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 2.35e-17)
		tmp = 1.0;
	elseif (c <= 1.6e+34)
		tmp = Float64(Float64(x / Float64(Float64(x * x) - Float64(y * y))) * Float64(x - y));
	else
		tmp = Float64(x / Float64(Float64(y * Float64(a + 0.8333333333333334)) * Float64(c * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 2.35e-17)
		tmp = 1.0;
	elseif (c <= 1.6e+34)
		tmp = (x / ((x * x) - (y * y))) * (x - y);
	else
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 2.35e-17], 1.0, If[LessEqual[c, 1.6e+34], N[(N[(x / N[(N[(x * x), $MachinePrecision] - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision] * N[(c * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < 2.35e-17

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 66.8%

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

   if 2.35e-17 < c < 1.5999999999999999e34

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 68.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 68.2%

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

   8. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right) \]

      2. +-lowering-+.f64 43.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 43.1%

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

       1. flip-+ N/A

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

       2. associate-/r/ N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{x \cdot x - y \cdot y}\right), \color{blue}{\left(x - y\right)}\right) \]

       4. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \left(x \cdot x - y \cdot y\right)\right), \left(\color{blue}{x} - y\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\left(x \cdot x\right), \left(y \cdot y\right)\right)\right), \left(x - y\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, x\right), \left(y \cdot y\right)\right)\right), \left(x - y\right)\right) \]

       7. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{*.f64}\left(y, y\right)\right)\right), \left(x - y\right)\right) \]

       8. --lowering--.f64 61.4%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, \mathsf{\_.f64}\left(\mathsf{*.f64}\left(x, x\right), \mathsf{*.f64}\left(y, y\right)\right)\right), \mathsf{\_.f64}\left(x, \color{blue}{y}\right)\right) \]

   12. Applied egg-rr 61.4%

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

   if 1.5999999999999999e34 < c

   1. Initial program 88.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 92.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 84.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 84.6%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 70.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 70.8%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(x + y\right) + \color{blue}{2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{2} \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right) \]

       7. +-lowering-+.f64 57.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 57.3%

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

   14. Taylor expanded in c around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(2 \cdot c\right) \cdot \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(2 \cdot c\right), \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \left(\color{blue}{y} \cdot \left(\frac{5}{6} + a\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \mathsf{*.f64}\left(y, \left(a + \color{blue}{\frac{5}{6}}\right)\right)\right)\right) \]

       6. +-lowering-+.f64 51.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \color{blue}{\frac{5}{6}}\right)\right)\right)\right) \]

   16. Simplified 51.0%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{x \cdot x - y \cdot y} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y \cdot \left(a + 0.8333333333333334\right)\right) \cdot \left(c \cdot 2\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.7% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 2.05 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{y \cdot \left(\frac{x}{y} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y \cdot \left(a + 0.8333333333333334\right)\right) \cdot \left(c \cdot 2\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 2.05e-17)
   1.0
   (if (<= c 3.1e+32)
     (/ x (* y (+ (/ x y) 1.0)))
     (/ x (* (* y (+ a 0.8333333333333334)) (* c 2.0))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2.05e-17) {
		tmp = 1.0;
	} else if (c <= 3.1e+32) {
		tmp = x / (y * ((x / y) + 1.0));
	} else {
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 2.05d-17) then
        tmp = 1.0d0
    else if (c <= 3.1d+32) then
        tmp = x / (y * ((x / y) + 1.0d0))
    else
        tmp = x / ((y * (a + 0.8333333333333334d0)) * (c * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2.05e-17) {
		tmp = 1.0;
	} else if (c <= 3.1e+32) {
		tmp = x / (y * ((x / y) + 1.0));
	} else {
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 2.05e-17:
		tmp = 1.0
	elif c <= 3.1e+32:
		tmp = x / (y * ((x / y) + 1.0))
	else:
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 2.05e-17)
		tmp = 1.0;
	elseif (c <= 3.1e+32)
		tmp = Float64(x / Float64(y * Float64(Float64(x / y) + 1.0)));
	else
		tmp = Float64(x / Float64(Float64(y * Float64(a + 0.8333333333333334)) * Float64(c * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 2.05e-17)
		tmp = 1.0;
	elseif (c <= 3.1e+32)
		tmp = x / (y * ((x / y) + 1.0));
	else
		tmp = x / ((y * (a + 0.8333333333333334)) * (c * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 2.05e-17], 1.0, If[LessEqual[c, 3.1e+32], N[(x / N[(y * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(y * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision] * N[(c * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < 2.05e-17

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 66.8%

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

   if 2.05e-17 < c < 3.09999999999999993e32

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 68.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 68.2%

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

   8. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right) \]

      2. +-lowering-+.f64 43.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 43.1%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(y \cdot \left(1 + \frac{x}{y}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + \frac{x}{y}\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

       3. /-lowering-/.f64 56.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   13. Simplified 56.0%

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

   if 3.09999999999999993e32 < c

   1. Initial program 88.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 92.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 84.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 84.6%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 70.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 70.8%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(x + y\right) + \color{blue}{2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{2} \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right) \]

       7. +-lowering-+.f64 57.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 57.3%

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

   14. Taylor expanded in c around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(2 \cdot c\right) \cdot \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\left(2 \cdot c\right), \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \left(\color{blue}{y} \cdot \left(\frac{5}{6} + a\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right) \]

       5. +-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \mathsf{*.f64}\left(y, \left(a + \color{blue}{\frac{5}{6}}\right)\right)\right)\right) \]

       6. +-lowering-+.f64 51.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, c\right), \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(a, \color{blue}{\frac{5}{6}}\right)\right)\right)\right) \]

   16. Simplified 51.0%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.05 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 3.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{y \cdot \left(\frac{x}{y} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(y \cdot \left(a + 0.8333333333333334\right)\right) \cdot \left(c \cdot 2\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.2% accurate, 11.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 2.35e-17)
   1.0
   (/ x (- x (* y (- -1.0 (* 2.0 (* c (+ a 0.8333333333333334)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2.35e-17) {
		tmp = 1.0;
	} else {
		tmp = x / (x - (y * (-1.0 - (2.0 * (c * (a + 0.8333333333333334))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= 2.35d-17) then
        tmp = 1.0d0
    else
        tmp = x / (x - (y * ((-1.0d0) - (2.0d0 * (c * (a + 0.8333333333333334d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2.35e-17) {
		tmp = 1.0;
	} else {
		tmp = x / (x - (y * (-1.0 - (2.0 * (c * (a + 0.8333333333333334))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 2.35e-17:
		tmp = 1.0
	else:
		tmp = x / (x - (y * (-1.0 - (2.0 * (c * (a + 0.8333333333333334))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 2.35e-17)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 2.35e-17)
		tmp = 1.0;
	else
		tmp = x / (x - (y * (-1.0 - (2.0 * (c * (a + 0.8333333333333334))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 2.35e-17], 1.0, N[(x / N[(x - N[(y * N[(-1.0 - N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 2.35e-17

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 66.8%

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

   if 2.35e-17 < c

   1. Initial program 91.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 93.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 81.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 81.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 71.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.5%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + 2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]
   12. Step-by-step derivation

       1. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right)\right) \]

       4. +-lowering-+.f64 56.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right)\right) \]

   13. Simplified 56.3%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.1% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot \left(\frac{x}{y} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{a \cdot \left(c \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 2.35e-17)
   1.0
   (if (<= c 1.16e+29)
     (/ x (* y (+ (/ x y) 1.0)))
     (/ (* x 0.5) (* a (* c y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 2.35e-17) {
		tmp = 1.0;
	} else if (c <= 1.16e+29) {
		tmp = x / (y * ((x / y) + 1.0));
	} else {
		tmp = (x * 0.5) / (a * (c * 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 (c <= 2.35d-17) then
        tmp = 1.0d0
    else if (c <= 1.16d+29) then
        tmp = x / (y * ((x / y) + 1.0d0))
    else
        tmp = (x * 0.5d0) / (a * (c * 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 (c <= 2.35e-17) {
		tmp = 1.0;
	} else if (c <= 1.16e+29) {
		tmp = x / (y * ((x / y) + 1.0));
	} else {
		tmp = (x * 0.5) / (a * (c * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 2.35e-17:
		tmp = 1.0
	elif c <= 1.16e+29:
		tmp = x / (y * ((x / y) + 1.0))
	else:
		tmp = (x * 0.5) / (a * (c * y))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 2.35e-17)
		tmp = 1.0;
	elseif (c <= 1.16e+29)
		tmp = Float64(x / Float64(y * Float64(Float64(x / y) + 1.0)));
	else
		tmp = Float64(Float64(x * 0.5) / Float64(a * Float64(c * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 2.35e-17)
		tmp = 1.0;
	elseif (c <= 1.16e+29)
		tmp = x / (y * ((x / y) + 1.0));
	else
		tmp = (x * 0.5) / (a * (c * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 2.35e-17], 1.0, If[LessEqual[c, 1.16e+29], N[(x / N[(y * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] / N[(a * N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < 2.35e-17

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 66.8%

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

   if 2.35e-17 < c < 1.16e29

   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. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 68.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 68.2%

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

   8. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right) \]

      2. +-lowering-+.f64 43.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 43.1%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(y \cdot \left(1 + \frac{x}{y}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + \frac{x}{y}\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

       3. /-lowering-/.f64 56.0%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   13. Simplified 56.0%

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

   if 1.16e29 < c

   1. Initial program 88.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 92.1%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 84.6%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 84.6%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 70.8%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 70.8%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(x + y\right) + \color{blue}{2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{2} \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right) \]

       7. +-lowering-+.f64 57.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 57.3%

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

   14. Taylor expanded in a around inf

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

       1. associate-*r/ N/A

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

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{2} \cdot x\right), \color{blue}{\left(a \cdot \left(c \cdot y\right)\right)}\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \frac{1}{2}\right), \left(\color{blue}{a} \cdot \left(c \cdot y\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\color{blue}{a} \cdot \left(c \cdot y\right)\right)\right) \]

       5. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \left(\left(c \cdot y\right) \cdot \color{blue}{a}\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(\left(c \cdot y\right), \color{blue}{a}\right)\right) \]

       7. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(\left(y \cdot c\right), a\right)\right) \]

       8. *-lowering-*.f64 49.5%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(x, \frac{1}{2}\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, c\right), a\right)\right) \]

   16. Simplified 49.5%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 2.35 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 1.16 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y \cdot \left(\frac{x}{y} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.5}{a \cdot \left(c \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 48.5% accurate, 12.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{y \cdot \left(\frac{x}{y} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.5e-54) 1.0 (if (<= t 4e-289) (/ x (* y (+ (/ x y) 1.0))) 1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.5e-54) {
		tmp = 1.0;
	} else if (t <= 4e-289) {
		tmp = x / (y * ((x / y) + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.5d-54)) then
        tmp = 1.0d0
    else if (t <= 4d-289) then
        tmp = x / (y * ((x / y) + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.5e-54) {
		tmp = 1.0;
	} else if (t <= 4e-289) {
		tmp = x / (y * ((x / y) + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.5e-54:
		tmp = 1.0
	elif t <= 4e-289:
		tmp = x / (y * ((x / y) + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.5e-54)
		tmp = 1.0;
	elseif (t <= 4e-289)
		tmp = Float64(x / Float64(y * Float64(Float64(x / y) + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.5e-54)
		tmp = 1.0;
	elseif (t <= 4e-289)
		tmp = x / (y * ((x / y) + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.5e-54], 1.0, If[LessEqual[t, 4e-289], N[(x / N[(y * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000005e-54 or 4e-289 < t

   1. Initial program 95.2%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.6%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 59.5%

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

   if -1.50000000000000005e-54 < t < 4e-289

   1. Initial program 92.0%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 92.0%

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

   5. Taylor expanded in b around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(b \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. +-lowering-+.f64 67.1%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(b, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 67.1%

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

   8. Taylor expanded in b around 0

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y\right)}\right) \]

      2. +-lowering-+.f64 46.2%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{y}\right)\right) \]

   10. Simplified 46.2%

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

   11. Taylor expanded in y around inf

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(y \cdot \left(1 + \frac{x}{y}\right)\right)}\right) \]
   12. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(1 + \frac{x}{y}\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \color{blue}{\left(\frac{x}{y}\right)}\right)\right)\right) \]

       3. /-lowering-/.f64 59.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right)\right)\right) \]

   13. Simplified 59.7%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-289}:\\ \;\;\;\;\frac{x}{y \cdot \left(\frac{x}{y} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 52.5% accurate, 12.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq 1.9 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c 1.9e-17) 1.0 (/ x (+ (+ x y) (* (* a 2.0) (* c y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= 1.9e-17) {
		tmp = 1.0;
	} else {
		tmp = x / ((x + y) + ((a * 2.0) * (c * 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 (c <= 1.9d-17) then
        tmp = 1.0d0
    else
        tmp = x / ((x + y) + ((a * 2.0d0) * (c * 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 (c <= 1.9e-17) {
		tmp = 1.0;
	} else {
		tmp = x / ((x + y) + ((a * 2.0) * (c * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= 1.9e-17:
		tmp = 1.0
	else:
		tmp = x / ((x + y) + ((a * 2.0) * (c * y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= 1.9e-17)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(Float64(x + y) + Float64(Float64(a * 2.0) * Float64(c * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= 1.9e-17)
		tmp = 1.0;
	else
		tmp = x / ((x + y) + ((a * 2.0) * (c * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, 1.9e-17], 1.0, N[(x / N[(N[(x + y), $MachinePrecision] + N[(N[(a * 2.0), $MachinePrecision] * N[(c * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < 1.9000000000000001e-17

   1. Initial program 96.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   6. Step-by-step derivation

   7. Simplified 66.8%

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

   if 1.9000000000000001e-17 < c

   1. Initial program 91.1%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

      4. count-2 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

      5. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

   3. Simplified 93.6%

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

   5. Taylor expanded in c around inf

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \color{blue}{\left(-1 \cdot \left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right)\right)\right)\right) \]
   6. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(c \cdot \left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\mathsf{neg}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot c\right)\right)\right)\right)\right)\right)\right) \]

      3. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right) \cdot \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t} - \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{2}{3} \cdot \frac{1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3} \cdot 1}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\left(\frac{\frac{2}{3}}{t}\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \left(\frac{5}{6} + a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(\mathsf{neg}\left(c\right)\right)\right)\right)\right)\right)\right)\right) \]

      10. neg-sub0 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \left(0 - c\right)\right)\right)\right)\right)\right)\right) \]

      11. --lowering--.f64 81.4%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{2}{3}, t\right), \mathsf{+.f64}\left(\frac{5}{6}, a\right)\right), \mathsf{\_.f64}\left(0, c\right)\right)\right)\right)\right)\right)\right) \]

   7. Simplified 81.4%

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

   8. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}}} \]
   9. Step-by-step derivation

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)}\right)}\right)\right)\right) \]

      4. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(2 \cdot \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(c \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \left(\left(\frac{5}{6} + a\right) \cdot c\right)\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\frac{5}{6} + a\right), c\right)\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 71.5%

         \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{+.f64}\left(\frac{5}{6}, a\right), c\right)\right)\right)\right)\right)\right) \]

   10. Simplified 71.5%

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

   11. Taylor expanded in c around 0

       \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + \left(y + 2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)}\right) \]
   12. Step-by-step derivation

       1. associate-+r+ N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\left(x + y\right) + \color{blue}{2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right) \]

       2. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\left(x + y\right), \color{blue}{\left(2 \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\color{blue}{2} \cdot \left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)\right)\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \color{blue}{\left(c \cdot \left(y \cdot \left(\frac{5}{6} + a\right)\right)\right)}\right)\right)\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \color{blue}{\left(y \cdot \left(\frac{5}{6} + a\right)\right)}\right)\right)\right)\right) \]

       6. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \color{blue}{\left(\frac{5}{6} + a\right)}\right)\right)\right)\right)\right) \]

       7. +-lowering-+.f64 53.8%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(c, \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\frac{5}{6}, \color{blue}{a}\right)\right)\right)\right)\right)\right) \]

   13. Simplified 53.8%

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

   14. Taylor expanded in a around inf

       \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \color{blue}{\left(2 \cdot \left(a \cdot \left(c \cdot y\right)\right)\right)}\right)\right) \]
   15. Step-by-step derivation

       1. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\left(2 \cdot a\right) \cdot \color{blue}{\left(c \cdot y\right)}\right)\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(2 \cdot a\right), \color{blue}{\left(c \cdot y\right)}\right)\right)\right) \]

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, a\right), \left(\color{blue}{c} \cdot y\right)\right)\right)\right) \]

       4. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, a\right), \left(y \cdot \color{blue}{c}\right)\right)\right)\right) \]

       5. *-lowering-*.f64 54.7%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(\mathsf{+.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, a\right), \mathsf{*.f64}\left(y, \color{blue}{c}\right)\right)\right)\right) \]

   16. Simplified 54.7%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq 1.9 \cdot 10^{-17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(x + y\right) + \left(a \cdot 2\right) \cdot \left(c \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.7% accurate, 231.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right) \]

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \color{blue}{\left(y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \color{blue}{\left(e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)}\right)\right)\right) \]

   4. count-2 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \left(e^{\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}\right)\right)\right)\right) \]

   5. exp-lowering-exp.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(x, \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(y, \mathsf{exp.f64}\left(\left(\left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) + \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)\right)\right)\right)\right)\right) \]

3. Simplified 96.5%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
6. Step-by-step derivation

7. Simplified 56.1%

   \[\leadsto \color{blue}{1} \]
8. Add Preprocessing

Developer Target 1: 95.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ t_2 := a - \frac{5}{6}\\ \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{t\_1 \cdot \left(\left(3 \cdot t\right) \cdot t\_2\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(t\_2 \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot t\_2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{t\_1}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -2118326644891581/100000000000000000000000000000000000000000000000000000000000000000) (/ x (+ x (* y (exp (* 2 (- (+ (* a c) (* 4166666666666667/5000000000000000 c)) (* a b))))))) (if (< t 5196588770651547/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (+ x (* y (exp (* 2 (/ (- (* (* z (sqrt (+ t a))) (* (* 3 t) (- a (/ 5 6)))) (* (- (* (+ (/ 5 6) a) (* 3 t)) 2) (* (- a (/ 5 6)) (* (- b c) t)))) (* (* (* t t) 3) (- a (/ 5 6))))))))) (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))))

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