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

Percentage Accurate: 93.9% → 96.4%

Time: 17.5s

Alternatives: 15

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: 96.4% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 70.9%

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

      1. *-inverses 70.9

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

   7. Applied egg-rr 70.9%

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

4. Final simplification 98.1%

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

Alternative 2: 75.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{b \cdot b}{t}\right)}{t}, x\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -1e-74)
     1.0
     (if (<= t_1 2e+236)
       (* (- y x) (/ x (* (- y x) (+ x y))))
       (if (<= t_1 INFINITY)
         (/
          1.0
          (/
           (fma
            y
            (-
             1.0
             (/
              (fma b -1.3333333333333333 (* -0.8888888888888888 (/ (* b b) t)))
              t))
            x)
           x))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -1e-74) {
		tmp = 1.0;
	} else if (t_1 <= 2e+236) {
		tmp = (y - x) * (x / ((y - x) * (x + y)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = 1.0 / (fma(y, (1.0 - (fma(b, -1.3333333333333333, (-0.8888888888888888 * ((b * b) / t))) / t)), x) / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -1e-74)
		tmp = 1.0;
	elseif (t_1 <= 2e+236)
		tmp = Float64(Float64(y - x) * Float64(x / Float64(Float64(y - x) * Float64(x + y))));
	elseif (t_1 <= Inf)
		tmp = Float64(1.0 / Float64(fma(y, Float64(1.0 - Float64(fma(b, -1.3333333333333333, Float64(-0.8888888888888888 * Float64(Float64(b * b) / t))) / t)), x) / x));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $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]}, If[LessEqual[t$95$1, -1e-74], 1.0, If[LessEqual[t$95$1, 2e+236], N[(N[(y - x), $MachinePrecision] * N[(x / N[(N[(y - x), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(1.0 / N[(N[(y * N[(1.0 - N[(N[(b * -1.3333333333333333 + N[(-0.8888888888888888 * N[(N[(b * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 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)))))) < -9.99999999999999958e-75 or +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 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 97.4%

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

      1. *-inverses 97.4

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

   7. Applied egg-rr 97.4%

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

   if -9.99999999999999958e-75 < (-.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)))))) < 2.00000000000000011e236

   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. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 62.8

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

   5. Simplified 62.8%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 34.5

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

   8. Simplified 34.5%

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

      1. flip-+ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

      5. difference-of-squares N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

      10. --lowering--.f64 65.0

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

   10. Applied egg-rr 65.0%

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

   if 2.00000000000000011e236 < (-.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 98.5%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 73.9

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{4}{3} \cdot \frac{b}{t}}}} \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

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

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\frac{\color{blue}{b \cdot \frac{4}{3}}}{t}}} \]

      4. *-lowering-*.f64 58.6

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

   8. Simplified 58.6%

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

   9. Taylor expanded in t around -inf

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + -1 \cdot \frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \frac{x}{x + y \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)\right)}\right)} \]

       2. unsub-neg N/A

          \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 - \frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)}} \]

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

          \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 - \frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)}} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \color{blue}{\frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}}\right)} \]

       5. +-commutative N/A

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\color{blue}{\frac{-8}{9} \cdot \frac{{b}^{2}}{t} + \frac{-4}{3} \cdot b}}{t}\right)} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{-8}{9}, \frac{{b}^{2}}{t}, \frac{-4}{3} \cdot b\right)}}{t}\right)} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \color{blue}{\frac{{b}^{2}}{t}}, \frac{-4}{3} \cdot b\right)}{t}\right)} \]

       8. unpow2 N/A

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \frac{\color{blue}{b \cdot b}}{t}, \frac{-4}{3} \cdot b\right)}{t}\right)} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \frac{\color{blue}{b \cdot b}}{t}, \frac{-4}{3} \cdot b\right)}{t}\right)} \]

       10. *-commutative N/A

           \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \frac{b \cdot b}{t}, \color{blue}{b \cdot \frac{-4}{3}}\right)}{t}\right)} \]

       11. *-lowering-*.f64 74.0

           \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(-0.8888888888888888, \frac{b \cdot b}{t}, \color{blue}{b \cdot -1.3333333333333333}\right)}{t}\right)} \]

   11. Simplified 74.0%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 - \frac{\mathsf{fma}\left(-0.8888888888888888, \frac{b \cdot b}{t}, b \cdot -1.3333333333333333\right)}{t}\right)}} \]
   12. Step-by-step derivation

       1. clear-num N/A

          \[\leadsto \color{blue}{\frac{1}{\frac{x + y \cdot \left(1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}\right)}{x}}} \]

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

          \[\leadsto \color{blue}{\frac{1}{\frac{x + y \cdot \left(1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}\right)}{x}}} \]

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

          \[\leadsto \frac{1}{\color{blue}{\frac{x + y \cdot \left(1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}\right)}{x}}} \]

       4. +-commutative N/A

          \[\leadsto \frac{1}{\frac{\color{blue}{y \cdot \left(1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}\right) + x}}{x}} \]

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

          \[\leadsto \frac{1}{\frac{\color{blue}{\mathsf{fma}\left(y, 1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}, x\right)}}{x}} \]

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

          \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, \color{blue}{1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}}, x\right)}{x}} \]

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

          \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, 1 - \color{blue}{\frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}}, x\right)}{x}} \]

       8. +-commutative N/A

          \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\color{blue}{b \cdot \frac{-4}{3} + \frac{-8}{9} \cdot \frac{b \cdot b}{t}}}{t}, x\right)}{x}} \]

       9. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\color{blue}{\mathsf{fma}\left(b, \frac{-4}{3}, \frac{-8}{9} \cdot \frac{b \cdot b}{t}\right)}}{t}, x\right)}{x}} \]

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

           \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\mathsf{fma}\left(b, \frac{-4}{3}, \color{blue}{\frac{-8}{9} \cdot \frac{b \cdot b}{t}}\right)}{t}, x\right)}{x}} \]

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

           \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\mathsf{fma}\left(b, \frac{-4}{3}, \frac{-8}{9} \cdot \color{blue}{\frac{b \cdot b}{t}}\right)}{t}, x\right)}{x}} \]

       12. *-lowering-*.f64 75.5

           \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{\color{blue}{b \cdot b}}{t}\right)}{t}, x\right)}{x}} \]

   13. Applied egg-rr 75.5%

       \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{b \cdot b}{t}\right)}{t}, x\right)}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{1}{\frac{\mathsf{fma}\left(y, 1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{b \cdot b}{t}\right)}{t}, x\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{b \cdot b}{t}\right)}{t}, y, x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -1e-74)
     1.0
     (if (<= t_1 2e+236)
       (* (- y x) (/ x (* (- y x) (+ x y))))
       (if (<= t_1 INFINITY)
         (/
          x
          (fma
           (-
            1.0
            (/
             (fma b -1.3333333333333333 (* -0.8888888888888888 (/ (* b b) t)))
             t))
           y
           x))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -1e-74) {
		tmp = 1.0;
	} else if (t_1 <= 2e+236) {
		tmp = (y - x) * (x / ((y - x) * (x + y)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x / fma((1.0 - (fma(b, -1.3333333333333333, (-0.8888888888888888 * ((b * b) / t))) / t)), y, x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -1e-74)
		tmp = 1.0;
	elseif (t_1 <= 2e+236)
		tmp = Float64(Float64(y - x) * Float64(x / Float64(Float64(y - x) * Float64(x + y))));
	elseif (t_1 <= Inf)
		tmp = Float64(x / fma(Float64(1.0 - Float64(fma(b, -1.3333333333333333, Float64(-0.8888888888888888 * Float64(Float64(b * b) / t))) / t)), y, x));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $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]}, If[LessEqual[t$95$1, -1e-74], 1.0, If[LessEqual[t$95$1, 2e+236], N[(N[(y - x), $MachinePrecision] * N[(x / N[(N[(y - x), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(x / N[(N[(1.0 - N[(N[(b * -1.3333333333333333 + N[(-0.8888888888888888 * N[(N[(b * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 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)))))) < -9.99999999999999958e-75 or +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 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 97.4%

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

      1. *-inverses 97.4

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

   7. Applied egg-rr 97.4%

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

   if -9.99999999999999958e-75 < (-.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)))))) < 2.00000000000000011e236

   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. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 62.8

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

   5. Simplified 62.8%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 34.5

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

   8. Simplified 34.5%

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

      1. flip-+ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

      5. difference-of-squares N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

      10. --lowering--.f64 65.0

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

   10. Applied egg-rr 65.0%

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

   if 2.00000000000000011e236 < (-.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 98.5%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 73.9

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{4}{3} \cdot \frac{b}{t}}}} \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

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

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\frac{\color{blue}{b \cdot \frac{4}{3}}}{t}}} \]

      4. *-lowering-*.f64 58.6

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

   8. Simplified 58.6%

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

   9. Taylor expanded in t around -inf

      \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 + -1 \cdot \frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)}} \]
   10. Step-by-step derivation

       1. mul-1-neg N/A

          \[\leadsto \frac{x}{x + y \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(\frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)\right)}\right)} \]

       2. unsub-neg N/A

          \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 - \frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)}} \]

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

          \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 - \frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}\right)}} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \color{blue}{\frac{\frac{-4}{3} \cdot b + \frac{-8}{9} \cdot \frac{{b}^{2}}{t}}{t}}\right)} \]

       5. +-commutative N/A

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\color{blue}{\frac{-8}{9} \cdot \frac{{b}^{2}}{t} + \frac{-4}{3} \cdot b}}{t}\right)} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\color{blue}{\mathsf{fma}\left(\frac{-8}{9}, \frac{{b}^{2}}{t}, \frac{-4}{3} \cdot b\right)}}{t}\right)} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \color{blue}{\frac{{b}^{2}}{t}}, \frac{-4}{3} \cdot b\right)}{t}\right)} \]

       8. unpow2 N/A

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \frac{\color{blue}{b \cdot b}}{t}, \frac{-4}{3} \cdot b\right)}{t}\right)} \]

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

          \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \frac{\color{blue}{b \cdot b}}{t}, \frac{-4}{3} \cdot b\right)}{t}\right)} \]

       10. *-commutative N/A

           \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(\frac{-8}{9}, \frac{b \cdot b}{t}, \color{blue}{b \cdot \frac{-4}{3}}\right)}{t}\right)} \]

       11. *-lowering-*.f64 74.0

           \[\leadsto \frac{x}{x + y \cdot \left(1 - \frac{\mathsf{fma}\left(-0.8888888888888888, \frac{b \cdot b}{t}, \color{blue}{b \cdot -1.3333333333333333}\right)}{t}\right)} \]

   11. Simplified 74.0%

       \[\leadsto \frac{x}{x + y \cdot \color{blue}{\left(1 - \frac{\mathsf{fma}\left(-0.8888888888888888, \frac{b \cdot b}{t}, b \cdot -1.3333333333333333\right)}{t}\right)}} \]
   12. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \frac{x}{\color{blue}{y \cdot \left(1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}\right) + x}} \]

       2. *-commutative N/A

          \[\leadsto \frac{x}{\color{blue}{\left(1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}\right) \cdot y} + x} \]

       3. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}, y, x\right)}} \]

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

          \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{1 - \frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}}, y, x\right)} \]

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

          \[\leadsto \frac{x}{\mathsf{fma}\left(1 - \color{blue}{\frac{\frac{-8}{9} \cdot \frac{b \cdot b}{t} + b \cdot \frac{-4}{3}}{t}}, y, x\right)} \]

       6. +-commutative N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(1 - \frac{\color{blue}{b \cdot \frac{-4}{3} + \frac{-8}{9} \cdot \frac{b \cdot b}{t}}}{t}, y, x\right)} \]

       7. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{x}{\mathsf{fma}\left(1 - \frac{\color{blue}{\mathsf{fma}\left(b, \frac{-4}{3}, \frac{-8}{9} \cdot \frac{b \cdot b}{t}\right)}}{t}, y, x\right)} \]

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

          \[\leadsto \frac{x}{\mathsf{fma}\left(1 - \frac{\mathsf{fma}\left(b, \frac{-4}{3}, \color{blue}{\frac{-8}{9} \cdot \frac{b \cdot b}{t}}\right)}{t}, y, x\right)} \]

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

          \[\leadsto \frac{x}{\mathsf{fma}\left(1 - \frac{\mathsf{fma}\left(b, \frac{-4}{3}, \frac{-8}{9} \cdot \color{blue}{\frac{b \cdot b}{t}}\right)}{t}, y, x\right)} \]

       10. *-lowering-*.f64 74.0

           \[\leadsto \frac{x}{\mathsf{fma}\left(1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{\color{blue}{b \cdot b}}{t}\right)}{t}, y, x\right)} \]

   13. Applied egg-rr 74.0%

       \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{b \cdot b}{t}\right)}{t}, y, x\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(1 - \frac{\mathsf{fma}\left(b, -1.3333333333333333, -0.8888888888888888 \cdot \frac{b \cdot b}{t}\right)}{t}, y, x\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\\ \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(b, 2 \cdot \mathsf{fma}\left(b, t\_1 \cdot t\_1, t\_1\right), 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a))))
   (if (<=
        (/
         x
         (+
          x
          (*
           y
           (exp
            (*
             2.0
             (+
              (/ (* z (sqrt (+ t a))) t)
              (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
        4e-168)
     (/ x (+ x (* y (fma b (* 2.0 (fma b (* t_1 t_1) t_1)) 1.0))))
     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 tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = x / (x + (y * fma(b, (2.0 * fma(b, (t_1 * t_1), t_1)), 1.0)));
	} else {
		tmp = 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))
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(x / Float64(x + Float64(y * fma(b, Float64(2.0 * fma(b, Float64(t_1 * t_1), t_1)), 1.0))));
	else
		tmp = 1.0;
	end
	return 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]}, If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(x / N[(x + N[(y * N[(b * N[(2.0 * N[(b * N[(t$95$1 * t$95$1), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

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

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

   8. Simplified 77.6%

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

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(b, 2 \cdot \mathsf{fma}\left(b, \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right) \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right), \frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right), 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right), 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -1e-74)
     1.0
     (if (<= t_1 2e+236)
       (* (- y x) (/ x (* (- y x) (+ x y))))
       (if (<= t_1 INFINITY)
         (/
          x
          (+
           x
           (*
            y
            (fma
             2.0
             (* b (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a)))
             1.0))))
         1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -1e-74) {
		tmp = 1.0;
	} else if (t_1 <= 2e+236) {
		tmp = (y - x) * (x / ((y - x) * (x + y)));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * fma(2.0, (b * ((0.6666666666666666 / t) + (-0.8333333333333334 - a))), 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -1e-74)
		tmp = 1.0;
	elseif (t_1 <= 2e+236)
		tmp = Float64(Float64(y - x) * Float64(x / Float64(Float64(y - x) * Float64(x + y))));
	elseif (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * fma(2.0, Float64(b * Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a))), 1.0))));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $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]}, If[LessEqual[t$95$1, -1e-74], 1.0, If[LessEqual[t$95$1, 2e+236], N[(N[(y - x), $MachinePrecision] * N[(x / N[(N[(y - x), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(y * N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 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)))))) < -9.99999999999999958e-75 or +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 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. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 97.4%

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

      1. *-inverses 97.4

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

   7. Applied egg-rr 97.4%

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

   if -9.99999999999999958e-75 < (-.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)))))) < 2.00000000000000011e236

   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. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 62.8

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

   5. Simplified 62.8%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 34.5

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

   8. Simplified 34.5%

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

      1. flip-+ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

      5. difference-of-squares N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

      10. --lowering--.f64 65.0

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

   10. Applied egg-rr 65.0%

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

   if 2.00000000000000011e236 < (-.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 98.5%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 73.9

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

   5. Simplified 73.9%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

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

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

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

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

      4. sub-neg N/A

         \[\leadsto \frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} + \left(\mathsf{neg}\left(\left(\frac{5}{6} + a\right)\right)\right)\right)}, 1\right)} \]

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

         \[\leadsto \frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \color{blue}{\left(\frac{2}{3} \cdot \frac{1}{t} + \left(\mathsf{neg}\left(\left(\frac{5}{6} + a\right)\right)\right)\right)}, 1\right)} \]

      6. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \left(\color{blue}{\frac{\frac{2}{3} \cdot 1}{t}} + \left(\mathsf{neg}\left(\left(\frac{5}{6} + a\right)\right)\right)\right), 1\right)} \]

      7. metadata-eval N/A

         \[\leadsto \frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \left(\frac{\color{blue}{\frac{2}{3}}}{t} + \left(\mathsf{neg}\left(\left(\frac{5}{6} + a\right)\right)\right)\right), 1\right)} \]

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

         \[\leadsto \frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \left(\color{blue}{\frac{\frac{2}{3}}{t}} + \left(\mathsf{neg}\left(\left(\frac{5}{6} + a\right)\right)\right)\right), 1\right)} \]

      9. distribute-neg-in N/A

         \[\leadsto \frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \left(\frac{\frac{2}{3}}{t} + \color{blue}{\left(\left(\mathsf{neg}\left(\frac{5}{6}\right)\right) + \left(\mathsf{neg}\left(a\right)\right)\right)}\right), 1\right)} \]

      10. unsub-neg N/A

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

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

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

      12. metadata-eval 70.6

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

   8. Simplified 70.6%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -1 \cdot 10^{-74}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 2 \cdot 10^{+236}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(2, b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right), 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-97}:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+247}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \frac{x}{y}, y\right)}\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{0.75 \cdot \left(t \cdot x\right)}{b \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* z (sqrt (+ t a))) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))))
   (if (<= t_1 -5e-97)
     1.0
     (if (<= t_1 2e+247)
       (/ x (fma y (/ x y) y))
       (if (<= t_1 INFINITY) (/ (* 0.75 (* t x)) (* b y)) 1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))));
	double tmp;
	if (t_1 <= -5e-97) {
		tmp = 1.0;
	} else if (t_1 <= 2e+247) {
		tmp = x / fma(y, (x / y), y);
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = (0.75 * (t * x)) / (b * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(z * sqrt(Float64(t + a))) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))
	tmp = 0.0
	if (t_1 <= -5e-97)
		tmp = 1.0;
	elseif (t_1 <= 2e+247)
		tmp = Float64(x / fma(y, Float64(x / y), y));
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(0.75 * Float64(t * x)) / Float64(b * y));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $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]}, If[LessEqual[t$95$1, -5e-97], 1.0, If[LessEqual[t$95$1, 2e+247], N[(x / N[(y * N[(x / y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(0.75 * N[(t * x), $MachinePrecision]), $MachinePrecision] / N[(b * y), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 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)))))) < -4.9999999999999995e-97 or +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 92.7%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.4%

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

      1. *-inverses 97.4

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

   7. Applied egg-rr 97.4%

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

   if -4.9999999999999995e-97 < (-.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)))))) < 1.9999999999999999e247

   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. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 62.3

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

   5. Simplified 62.3%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 29.0

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

   8. Simplified 29.0%

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

   9. Taylor expanded in y around inf

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

       1. +-commutative N/A

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

       2. distribute-lft-in N/A

          \[\leadsto \frac{x}{\color{blue}{y \cdot \frac{x}{y} + y \cdot 1}} \]

       3. *-rgt-identity N/A

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

       4. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, \frac{x}{y}, y\right)}} \]

       5. /-lowering-/.f64 41.6

          \[\leadsto \frac{x}{\mathsf{fma}\left(y, \color{blue}{\frac{x}{y}}, y\right)} \]

   11. Simplified 41.6%

       \[\leadsto \frac{x}{\color{blue}{\mathsf{fma}\left(y, \frac{x}{y}, y\right)}} \]

   if 1.9999999999999999e247 < (-.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. Add Preprocessing

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 73.7

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{4}{3} \cdot \frac{b}{t}}}} \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

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

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\frac{\color{blue}{b \cdot \frac{4}{3}}}{t}}} \]

      4. *-lowering-*.f64 60.7

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

   8. Simplified 60.7%

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

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + \frac{4}{3} \cdot \frac{b \cdot y}{t}\right)}} \]
   10. Step-by-step derivation

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

          \[\leadsto \frac{x}{\color{blue}{x + \left(y + \frac{4}{3} \cdot \frac{b \cdot y}{t}\right)}} \]

       2. +-commutative N/A

          \[\leadsto \frac{x}{x + \color{blue}{\left(\frac{4}{3} \cdot \frac{b \cdot y}{t} + y\right)}} \]

       3. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(\frac{4}{3}, \frac{b \cdot y}{t}, y\right)}} \]

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

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(\frac{4}{3}, \color{blue}{\frac{b \cdot y}{t}}, y\right)} \]

       5. *-commutative N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(\frac{4}{3}, \frac{\color{blue}{y \cdot b}}{t}, y\right)} \]

       6. *-lowering-*.f64 54.9

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

   11. Simplified 54.9%

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

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{3}{4} \cdot \frac{t \cdot x}{b \cdot y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \color{blue}{\frac{\frac{3}{4} \cdot \left(t \cdot x\right)}{b \cdot y}} \]

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

          \[\leadsto \color{blue}{\frac{\frac{3}{4} \cdot \left(t \cdot x\right)}{b \cdot y}} \]

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

          \[\leadsto \frac{\color{blue}{\frac{3}{4} \cdot \left(t \cdot x\right)}}{b \cdot y} \]

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

          \[\leadsto \frac{\frac{3}{4} \cdot \color{blue}{\left(t \cdot x\right)}}{b \cdot y} \]

       5. *-lowering-*.f64 47.8

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

   14. Simplified 47.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -5 \cdot 10^{-97}:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 2 \cdot 10^{+247}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(y, \frac{x}{y}, y\right)}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq \infty:\\ \;\;\;\;\frac{0.75 \cdot \left(t \cdot x\right)}{b \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(a, \mathsf{fma}\left(2, a \cdot \left(b \cdot b\right), b \cdot -2\right), 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (/ x (+ x (* y (fma a (fma 2.0 (* a (* b b)) (* b -2.0)) 1.0))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = x / (x + (y * fma(a, fma(2.0, (a * (b * b)), (b * -2.0)), 1.0)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(x / Float64(x + Float64(y * fma(a, fma(2.0, Float64(a * Float64(b * b)), Float64(b * -2.0)), 1.0))));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(x / N[(x + N[(y * N[(a * N[(2.0 * N[(a * N[(b * b), $MachinePrecision]), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in a around inf

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

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

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 52.6

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

   8. Simplified 52.6%

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

   9. Taylor expanded in a around 0

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

       1. +-commutative N/A

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

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

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

       3. +-commutative N/A

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

       4. accelerator-lowering-fma.f64 N/A

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

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

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

       6. unpow2 N/A

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

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

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

       8. *-lowering-*.f64 58.4

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

   11. Simplified 58.4%

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

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + y \cdot \mathsf{fma}\left(a, \mathsf{fma}\left(2, a \cdot \left(b \cdot b\right), b \cdot -2\right), 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(t, x + y, 1.3333333333333333 \cdot \left(b \cdot y\right)\right)}{t}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (/ x (/ (fma t (+ x y) (* 1.3333333333333333 (* b y))) t))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = x / (fma(t, (x + y), (1.3333333333333333 * (b * y))) / t);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(x / Float64(fma(t, Float64(x + y), Float64(1.3333333333333333 * Float64(b * y))) / t));
	else
		tmp = 1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(x / N[(N[(t * N[(x + y), $MachinePrecision] + N[(1.3333333333333333 * N[(b * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{4}{3} \cdot \frac{b}{t}}}} \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

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

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\frac{\color{blue}{b \cdot \frac{4}{3}}}{t}}} \]

      4. *-lowering-*.f64 50.4

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

   8. Simplified 50.4%

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

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + \frac{4}{3} \cdot \frac{b \cdot y}{t}\right)}} \]
   10. Step-by-step derivation

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

          \[\leadsto \frac{x}{\color{blue}{x + \left(y + \frac{4}{3} \cdot \frac{b \cdot y}{t}\right)}} \]

       2. +-commutative N/A

          \[\leadsto \frac{x}{x + \color{blue}{\left(\frac{4}{3} \cdot \frac{b \cdot y}{t} + y\right)}} \]

       3. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(\frac{4}{3}, \frac{b \cdot y}{t}, y\right)}} \]

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

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(\frac{4}{3}, \color{blue}{\frac{b \cdot y}{t}}, y\right)} \]

       5. *-commutative N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(\frac{4}{3}, \frac{\color{blue}{y \cdot b}}{t}, y\right)} \]

       6. *-lowering-*.f64 45.0

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

   11. Simplified 45.0%

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

   12. Taylor expanded in t around 0

       \[\leadsto \frac{x}{\color{blue}{\frac{\frac{4}{3} \cdot \left(b \cdot y\right) + t \cdot \left(x + y\right)}{t}}} \]
   13. Step-by-step derivation

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

          \[\leadsto \frac{x}{\color{blue}{\frac{\frac{4}{3} \cdot \left(b \cdot y\right) + t \cdot \left(x + y\right)}{t}}} \]

       2. +-commutative N/A

          \[\leadsto \frac{x}{\frac{\color{blue}{t \cdot \left(x + y\right) + \frac{4}{3} \cdot \left(b \cdot y\right)}}{t}} \]

       3. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{x}{\frac{\color{blue}{\mathsf{fma}\left(t, x + y, \frac{4}{3} \cdot \left(b \cdot y\right)\right)}}{t}} \]

       4. +-commutative N/A

          \[\leadsto \frac{x}{\frac{\mathsf{fma}\left(t, \color{blue}{y + x}, \frac{4}{3} \cdot \left(b \cdot y\right)\right)}{t}} \]

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

          \[\leadsto \frac{x}{\frac{\mathsf{fma}\left(t, \color{blue}{y + x}, \frac{4}{3} \cdot \left(b \cdot y\right)\right)}{t}} \]

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

          \[\leadsto \frac{x}{\frac{\mathsf{fma}\left(t, y + x, \color{blue}{\frac{4}{3} \cdot \left(b \cdot y\right)}\right)}{t}} \]

       7. *-lowering-*.f64 56.4

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

   14. Simplified 56.4%

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

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{\frac{\mathsf{fma}\left(t, x + y, 1.3333333333333333 \cdot \left(b \cdot y\right)\right)}{t}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (* (- y x) (/ x (* (- y x) (+ x y))))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = (y - x) * (x / ((y - x) * (x + y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 4d-168) then
        tmp = (y - x) * (x / ((y - x) * (x + y)))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = (y - x) * (x / ((y - x) * (x + y)));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168:
		tmp = (y - x) * (x / ((y - x) * (x + y)))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(Float64(y - x) * Float64(x / Float64(Float64(y - x) * Float64(x + y))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168)
		tmp = (y - x) * (x / ((y - x) * (x + y)));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(N[(y - x), $MachinePrecision] * N[(x / N[(N[(y - x), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 21.5

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

   8. Simplified 21.5%

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

      1. flip-+ N/A

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

      2. associate-/r/ N/A

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

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

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

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

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

      5. difference-of-squares N/A

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

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

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

      7. +-commutative N/A

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

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

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

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

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

      10. --lowering--.f64 52.5

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

   10. Applied egg-rr 52.5%

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

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\left(y - x\right) \cdot \frac{x}{\left(y - x\right) \cdot \left(x + y\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{0.75 \cdot \left(t \cdot x\right)}{b \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (/ (* 0.75 (* t x)) (* b y))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = (0.75 * (t * x)) / (b * 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 ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 4d-168) then
        tmp = (0.75d0 * (t * x)) / (b * 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 ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = (0.75 * (t * x)) / (b * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168:
		tmp = (0.75 * (t * x)) / (b * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(Float64(0.75 * Float64(t * x)) / Float64(b * 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 ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168)
		tmp = (0.75 * (t * x)) / (b * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(N[(0.75 * N[(t * x), $MachinePrecision]), $MachinePrecision] / N[(b * y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0

      \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{4}{3} \cdot \frac{b}{t}}}} \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

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

         \[\leadsto \frac{x}{x + y \cdot e^{\color{blue}{\frac{\frac{4}{3} \cdot b}{t}}}} \]

      3. *-commutative N/A

         \[\leadsto \frac{x}{x + y \cdot e^{\frac{\color{blue}{b \cdot \frac{4}{3}}}{t}}} \]

      4. *-lowering-*.f64 50.4

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

   8. Simplified 50.4%

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

   9. Taylor expanded in b around 0

      \[\leadsto \frac{x}{\color{blue}{x + \left(y + \frac{4}{3} \cdot \frac{b \cdot y}{t}\right)}} \]
   10. Step-by-step derivation

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

          \[\leadsto \frac{x}{\color{blue}{x + \left(y + \frac{4}{3} \cdot \frac{b \cdot y}{t}\right)}} \]

       2. +-commutative N/A

          \[\leadsto \frac{x}{x + \color{blue}{\left(\frac{4}{3} \cdot \frac{b \cdot y}{t} + y\right)}} \]

       3. accelerator-lowering-fma.f64 N/A

          \[\leadsto \frac{x}{x + \color{blue}{\mathsf{fma}\left(\frac{4}{3}, \frac{b \cdot y}{t}, y\right)}} \]

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

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(\frac{4}{3}, \color{blue}{\frac{b \cdot y}{t}}, y\right)} \]

       5. *-commutative N/A

          \[\leadsto \frac{x}{x + \mathsf{fma}\left(\frac{4}{3}, \frac{\color{blue}{y \cdot b}}{t}, y\right)} \]

       6. *-lowering-*.f64 45.0

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

   11. Simplified 45.0%

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

   12. Taylor expanded in b around inf

       \[\leadsto \color{blue}{\frac{3}{4} \cdot \frac{t \cdot x}{b \cdot y}} \]
   13. Step-by-step derivation

       1. associate-*r/ N/A

          \[\leadsto \color{blue}{\frac{\frac{3}{4} \cdot \left(t \cdot x\right)}{b \cdot y}} \]

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

          \[\leadsto \color{blue}{\frac{\frac{3}{4} \cdot \left(t \cdot x\right)}{b \cdot y}} \]

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

          \[\leadsto \frac{\color{blue}{\frac{3}{4} \cdot \left(t \cdot x\right)}}{b \cdot y} \]

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

          \[\leadsto \frac{\frac{3}{4} \cdot \color{blue}{\left(t \cdot x\right)}}{b \cdot y} \]

       5. *-lowering-*.f64 33.1

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

   14. Simplified 33.1%

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

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{0.75 \cdot \left(t \cdot x\right)}{b \cdot y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{1}{\frac{x + y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (/ 1.0 (/ (+ x y) x))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = 1.0 / ((x + y) / x);
	} 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 ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 4d-168) then
        tmp = 1.0d0 / ((x + y) / x)
    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 ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = 1.0 / ((x + y) / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168:
		tmp = 1.0 / ((x + y) / x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(1.0 / Float64(Float64(x + y) / x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168)
		tmp = 1.0 / ((x + y) / x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(1.0 / N[(N[(x + y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 21.5

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

   8. Simplified 21.5%

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

      1. clear-num N/A

         \[\leadsto \color{blue}{\frac{1}{\frac{y + x}{x}}} \]

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

         \[\leadsto \color{blue}{\frac{1}{\frac{y + x}{x}}} \]

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

         \[\leadsto \frac{1}{\color{blue}{\frac{y + x}{x}}} \]

      4. +-commutative N/A

         \[\leadsto \frac{1}{\frac{\color{blue}{x + y}}{x}} \]

      5. +-lowering-+.f64 23.6

         \[\leadsto \frac{1}{\frac{\color{blue}{x + y}}{x}} \]

   10. Applied egg-rr 23.6%

       \[\leadsto \color{blue}{\frac{1}{\frac{x + y}{x}}} \]

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{1}{\frac{x + y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (/ 1.0 (/ y x))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = 1.0 / (y / x);
	} 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 ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 4d-168) then
        tmp = 1.0d0 / (y / x)
    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 ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = 1.0 / (y / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168:
		tmp = 1.0 / (y / x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(1.0 / Float64(y / x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168)
		tmp = 1.0 / (y / x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 21.5

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

   8. Simplified 21.5%

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

   9. Taylor expanded in x around 0

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

       1. /-lowering-/.f64 20.2

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

   11. Simplified 20.2%

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

       1. clear-num N/A

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

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

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

       3. /-lowering-/.f64 22.3

          \[\leadsto \frac{1}{\color{blue}{\frac{y}{x}}} \]

   13. Applied egg-rr 22.3%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{1}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (/ x (+ x y))
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 4d-168) then
        tmp = x / (x + y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = x / (x + y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168:
		tmp = x / (x + y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(x / Float64(x + y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168)
		tmp = x / (x + y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 21.5

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

   8. Simplified 21.5%

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

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (/
       x
       (+
        x
        (*
         y
         (exp
          (*
           2.0
           (+
            (/ (* z (sqrt (+ t a))) t)
            (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0))))))))))
      4e-168)
   (/ x y)
   1.0))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((x / (x + (y * exp((2.0d0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0)))))))))) <= 4d-168) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (x / (x + (y * math.exp((2.0 * (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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(2.0 / Float64(t * 3.0)) - Float64(a + Float64(5.0 / 6.0)))))))))) <= 4e-168)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((x / (x + (y * exp((2.0 * (((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0)))))))))) <= 4e-168)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e-168], N[(x / y), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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))))))))))) < 4.0000000000000002e-168

   1. Initial program 99.1%

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

   3. Taylor expanded in b around inf

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

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

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

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

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

      3. associate-*r/ N/A

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

      4. metadata-eval N/A

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

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

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

      6. +-commutative N/A

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

      7. +-lowering-+.f64 68.1

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

   5. Simplified 68.1%

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

   6. Taylor expanded in b around 0

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

      1. +-commutative N/A

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

      2. +-lowering-+.f64 21.5

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

   8. Simplified 21.5%

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

   9. Taylor expanded in x around 0

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

       1. /-lowering-/.f64 20.2

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

   11. Simplified 20.2%

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

   if 4.0000000000000002e-168 < (/.f64 x (+.f64 x (*.f64 y (exp.f64 (*.f64 #s(literal 2 binary64) (-.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 92.8%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 97.5%

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

      1. *-inverses 97.5

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

   7. Applied egg-rr 97.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 4 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.1% accurate, 198.0× 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 95.3%

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

3. Taylor expanded in x around inf

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

5. Simplified 59.9%

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

   1. *-inverses 59.9

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

7. Applied egg-rr 59.9%

   \[\leadsto \color{blue}{1} \]
8. Add Preprocessing

Developer Target 1: 94.9% accurate, 0.7× 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 2024204 
(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)))))))))))