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

Percentage Accurate: 94.1% → 96.9%

Time: 18.5s

Alternatives: 10

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(N[(z * t$95$1), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(x * N[(1.0 / N[(y * N[Exp[N[(2.0 * N[(t$95$1 * N[(z / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(N[(0.6666666666666666 / t), $MachinePrecision] - a), $MachinePrecision] - 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[((-a) - 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 97.6%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 98.7%

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

   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 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. lower-*.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. lower--.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. lower-/.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. lower-+.f64 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 82.4%

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

4. Final simplification 98.0%

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

Alternative 2: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -1000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(e^{2 \cdot \left(a \cdot \left(-b\right)\right)}, y, x\right)}\\ \end{array} \end{array} \]

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 -1000000000000.0)
     1.0
     (if (<= t_1 5e+198)
       (/ x (+ x (* y (exp (* 2.0 (* c (+ a 0.8333333333333334)))))))
       (if (<= t_1 5e+296)
         (* x (pow (* (* x x) (* x x)) -0.25))
         (/ x (fma (exp (* 2.0 (* a (- b)))) y x)))))))

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 <= -1000000000000.0) {
		tmp = 1.0;
	} else if (t_1 <= 5e+198) {
		tmp = x / (x + (y * exp((2.0 * (c * (a + 0.8333333333333334))))));
	} else if (t_1 <= 5e+296) {
		tmp = x * pow(((x * x) * (x * x)), -0.25);
	} else {
		tmp = x / fma(exp((2.0 * (a * -b))), y, x);
	}
	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 <= -1000000000000.0)
		tmp = 1.0;
	elseif (t_1 <= 5e+198)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * Float64(a + 0.8333333333333334)))))));
	elseif (t_1 <= 5e+296)
		tmp = Float64(x * (Float64(Float64(x * x) * Float64(x * x)) ^ -0.25));
	else
		tmp = Float64(x / fma(exp(Float64(2.0 * Float64(a * Float64(-b)))), y, x));
	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, -1000000000000.0], 1.0, If[LessEqual[t$95$1, 5e+198], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+296], N[(x * N[Power[N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision], -0.25], $MachinePrecision]), $MachinePrecision], N[(x / N[(N[Exp[N[(2.0 * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 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)))))) < -1e12

   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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if -1e12 < (-.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)))))) < 5.00000000000000049e198

   1. Initial program 98.0%

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

   3. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 64.2

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

   5. Applied rewrites 64.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 62.3%

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

   if 5.00000000000000049e198 < (-.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)))))) < 5.0000000000000001e296

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 96.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 3.1

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

   7. Applied rewrites 3.1%

      \[\leadsto \color{blue}{\frac{1}{x}} \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 45.6%

      \[\leadsto {\left(x \cdot x\right)}^{\color{blue}{-0.5}} \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 57.0%

       \[\leadsto {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{\color{blue}{-0.25}} \cdot x \]

   if 5.0000000000000001e296 < (-.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 75.2%

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

   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. lower-*.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. lower--.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. lower-/.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. lower-+.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 64.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 64.5

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

   10. Applied rewrites 64.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -1000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.8333333333333334\right)\right)}}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(e^{2 \cdot \left(a \cdot \left(-b\right)\right)}, y, x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -100000000:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(e^{2 \cdot \left(a \cdot \left(-b\right)\right)}, y, x\right)}\\ \end{array} \end{array} \]

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 -100000000.0)
     1.0
     (if (<= t_1 4e+131)
       (/ x (+ x (* y (exp (* 2.0 (* b -0.8333333333333334))))))
       (if (<= t_1 5e+296)
         (* x (pow (* (* x x) (* x x)) -0.25))
         (/ x (fma (exp (* 2.0 (* a (- b)))) y x)))))))

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 <= -100000000.0) {
		tmp = 1.0;
	} else if (t_1 <= 4e+131) {
		tmp = x / (x + (y * exp((2.0 * (b * -0.8333333333333334)))));
	} else if (t_1 <= 5e+296) {
		tmp = x * pow(((x * x) * (x * x)), -0.25);
	} else {
		tmp = x / fma(exp((2.0 * (a * -b))), y, x);
	}
	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 <= -100000000.0)
		tmp = 1.0;
	elseif (t_1 <= 4e+131)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * -0.8333333333333334))))));
	elseif (t_1 <= 5e+296)
		tmp = Float64(x * (Float64(Float64(x * x) * Float64(x * x)) ^ -0.25));
	else
		tmp = Float64(x / fma(exp(Float64(2.0 * Float64(a * Float64(-b)))), y, x));
	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, -100000000.0], 1.0, If[LessEqual[t$95$1, 4e+131], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * -0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+296], N[(x * N[Power[N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision], -0.25], $MachinePrecision]), $MachinePrecision], N[(x / N[(N[Exp[N[(2.0 * N[(a * (-b)), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 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)))))) < -1e8

   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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if -1e8 < (-.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)))))) < 3.9999999999999996e131

   1. Initial program 97.3%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   2. 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. lower-*.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. lower--.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. lower-/.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. lower-+.f64 74.9

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 69.6%

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

   9. Taylor expanded in a around 0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{-5}{6} \cdot b\right)}} \]
   10. Step-by-step derivation

   11. Applied rewrites 67.9%

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

   if 3.9999999999999996e131 < (-.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)))))) < 5.0000000000000001e296

   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. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 3.1

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

   7. Applied rewrites 3.1%

      \[\leadsto \color{blue}{\frac{1}{x}} \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 36.9%

      \[\leadsto {\left(x \cdot x\right)}^{\color{blue}{-0.5}} \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 47.2%

       \[\leadsto {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{\color{blue}{-0.25}} \cdot x \]

   if 5.0000000000000001e296 < (-.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 75.2%

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

   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. lower-*.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. lower--.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. lower-/.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. lower-+.f64 74.2

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

   5. Applied rewrites 74.2%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 64.5%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 64.5

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

   10. Applied rewrites 64.5%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 4 \cdot 10^{+131}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+296}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(e^{2 \cdot \left(a \cdot \left(-b\right)\right)}, y, x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 0:\\ \;\;\;\;x \cdot {\left(x \cdot x\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

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))))))))))
      0.0)
   (* x (pow (* x x) -0.5))
   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)))))))))) <= 0.0) {
		tmp = x * pow((x * x), -0.5);
	} 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)))))))))) <= 0.0d0) then
        tmp = x * ((x * x) ** (-0.5d0))
    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)))))))))) <= 0.0) {
		tmp = x * Math.pow((x * x), -0.5);
	} 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)))))))))) <= 0.0:
		tmp = x * math.pow((x * x), -0.5)
	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)))))))))) <= 0.0)
		tmp = Float64(x * (Float64(x * x) ^ -0.5));
	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)))))))))) <= 0.0)
		tmp = x * ((x * x) ^ -0.5);
	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], 0.0], N[(x * N[Power[N[(x * x), $MachinePrecision], -0.5], $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))))))))))) < 0.0

   1. Initial program 95.7%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 97.4%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 6.6

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

   7. Applied rewrites 6.6%

      \[\leadsto \color{blue}{\frac{1}{x}} \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 29.1%

      \[\leadsto {\left(x \cdot x\right)}^{\color{blue}{-0.5}} \cdot x \]

   if 0.0 < (/.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 91.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 89.3%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\right)}} \leq 0:\\ \;\;\;\;x \cdot {\left(x \cdot x\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right)\\ \mathbf{if}\;t\_1 \leq -100000000:\\ \;\;\;\;1\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(e^{2 \cdot \left(a \cdot c\right)}, y, x\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \end{array} \end{array} \]

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 -100000000.0)
     1.0
     (if (<= t_1 5e+198)
       (/ x (fma (exp (* 2.0 (* a c))) y x))
       (* x (pow (* (* x x) (* x x)) -0.25))))))

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 <= -100000000.0) {
		tmp = 1.0;
	} else if (t_1 <= 5e+198) {
		tmp = x / fma(exp((2.0 * (a * c))), y, x);
	} else {
		tmp = x * pow(((x * x) * (x * x)), -0.25);
	}
	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 <= -100000000.0)
		tmp = 1.0;
	elseif (t_1 <= 5e+198)
		tmp = Float64(x / fma(exp(Float64(2.0 * Float64(a * c))), y, x));
	else
		tmp = Float64(x * (Float64(Float64(x * x) * Float64(x * x)) ^ -0.25));
	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, -100000000.0], 1.0, If[LessEqual[t$95$1, 5e+198], N[(x / N[(N[Exp[N[(2.0 * N[(a * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * y + x), $MachinePrecision]), $MachinePrecision], N[(x * N[Power[N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision], -0.25], $MachinePrecision]), $MachinePrecision]]]]

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)))))) < -1e8

   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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if -1e8 < (-.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)))))) < 5.00000000000000049e198

   1. Initial program 97.9%

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

   3. Taylor expanded in c around inf

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

      1. lower-*.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. associate-+l+ N/A

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

      5. sub-neg N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. lower-+.f64 N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. lower-/.f64 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 45.2%

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

      1. lift-+.f64 N/A

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

   10. Applied rewrites 45.2%

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

   11. Taylor expanded in a around inf

       \[\leadsto \frac{x}{\mathsf{fma}\left(e^{2 \cdot \left(a \cdot \color{blue}{c}\right)}, y, x\right)} \]
   12. Step-by-step derivation

   13. Applied rewrites 55.3%

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

   if 5.00000000000000049e198 < (-.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 82.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 90.6%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 9.9

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

   7. Applied rewrites 9.9%

      \[\leadsto \color{blue}{\frac{1}{x}} \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 34.8%

      \[\leadsto {\left(x \cdot x\right)}^{\color{blue}{-0.5}} \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 48.3%

       \[\leadsto {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{\color{blue}{-0.25}} \cdot x \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 5 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(e^{2 \cdot \left(a \cdot c\right)}, y, x\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (+
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))
      -100000000.0)
   1.0
   (/
    x
    (+
     x
     (*
      y
      (exp
       (*
        2.0
        (* b (- (/ 0.6666666666666666 t) (+ a 0.8333333333333334))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0))))) <= (-100000000.0d0)) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) - (a + 0.8333333333333334d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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))))) <= -100000000.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) - Float64(a + 0.8333333333333334))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) - (a + 0.8333333333333334)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], -100000000.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.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)))))) < -1e8

   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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if -1e8 < (-.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 88.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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. lower-*.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. lower--.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. lower-/.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. lower-+.f64 66.7

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

   5. Applied rewrites 66.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\left(-a\right) - 0.8333333333333334\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (+
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))
      -100000000.0)
   1.0
   (/ x (+ x (* y (exp (* 2.0 (* b (- (- a) 0.8333333333333334)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * (b * (-a - 0.8333333333333334))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0))))) <= (-100000000.0d0)) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * (b * (-a - 0.8333333333333334d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (b * (-a - 0.8333333333333334))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * (b * (-a - 0.8333333333333334))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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))))) <= -100000000.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(-a) - 0.8333333333333334)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((2.0 * (b * (-a - 0.8333333333333334))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], -100000000.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[((-a) - 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -1e8

   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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if -1e8 < (-.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 88.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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. lower-*.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. lower--.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. lower-/.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. lower-+.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 57.3%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\left(-a\right) - 0.8333333333333334\right)\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (+
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))
      -100000000.0)
   1.0
   (/ x (+ x (* y (exp (* 2.0 (* b -0.8333333333333334))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * exp((2.0 * (b * -0.8333333333333334)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0))))) <= (-100000000.0d0)) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * exp((2.0d0 * (b * (-0.8333333333333334d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * (b * -0.8333333333333334)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0:
		tmp = 1.0
	else:
		tmp = x / (x + (y * math.exp((2.0 * (b * -0.8333333333333334)))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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))))) <= -100000000.0)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * -0.8333333333333334))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= -100000000.0)
		tmp = 1.0;
	else
		tmp = x / (x + (y * exp((2.0 * (b * -0.8333333333333334)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], -100000000.0], 1.0, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * -0.8333333333333334), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < -1e8

   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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 99.2%

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

   if -1e8 < (-.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 88.1%

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}} \]
   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. lower-*.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. lower--.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. lower-/.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. lower-+.f64 66.7

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

   5. Applied rewrites 66.7%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 57.3%

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

   9. Taylor expanded in a around 0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{-5}{6} \cdot b\right)}} \]
   10. Step-by-step derivation

   11. Applied rewrites 49.8%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq -100000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot -0.8333333333333334\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 1.34 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<=
      (+
       (/ (* z (sqrt (+ t a))) t)
       (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a (/ 5.0 6.0)))))
      1.34e+60)
   1.0
   (* x (pow (* (* x x) (* x x)) -0.25))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= 1.34e+60) {
		tmp = 1.0;
	} else {
		tmp = x * pow(((x * x) * (x * x)), -0.25);
	}
	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 ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + (5.0d0 / 6.0d0))))) <= 1.34d+60) then
        tmp = 1.0d0
    else
        tmp = x * (((x * x) * (x * x)) ** (-0.25d0))
    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 ((((z * Math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= 1.34e+60) {
		tmp = 1.0;
	} else {
		tmp = x * Math.pow(((x * x) * (x * x)), -0.25);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if (((z * math.sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= 1.34e+60:
		tmp = 1.0
	else:
		tmp = x * math.pow(((x * x) * (x * x)), -0.25)
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (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))))) <= 1.34e+60)
		tmp = 1.0;
	else
		tmp = Float64(x * (Float64(Float64(x * x) * Float64(x * x)) ^ -0.25));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if ((((z * sqrt((t + a))) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + (5.0 / 6.0))))) <= 1.34e+60)
		tmp = 1.0;
	else
		tmp = x * (((x * x) * (x * x)) ^ -0.25);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[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], 1.34e+60], 1.0, N[(x * N[Power[N[(N[(x * x), $MachinePrecision] * N[(x * x), $MachinePrecision]), $MachinePrecision], -0.25], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (/.f64 (*.f64 z (sqrt.f64 (+.f64 t a))) t) (*.f64 (-.f64 b c) (-.f64 (+.f64 a (/.f64 #s(literal 5 binary64) #s(literal 6 binary64))) (/.f64 #s(literal 2 binary64) (*.f64 t #s(literal 3 binary64)))))) < 1.3400000000000001e60

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 89.7%

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

   if 1.3400000000000001e60 < (-.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 87.0%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

   4. Applied rewrites 93.0%

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

   5. Taylor expanded in y around 0

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

      1. lower-/.f64 8.2

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

   7. Applied rewrites 8.2%

      \[\leadsto \color{blue}{\frac{1}{x}} \cdot x \]
   8. Step-by-step derivation

   9. Applied rewrites 29.2%

      \[\leadsto {\left(x \cdot x\right)}^{\color{blue}{-0.5}} \cdot x \]
   10. Step-by-step derivation

   11. Applied rewrites 43.5%

       \[\leadsto {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{\color{blue}{-0.25}} \cdot x \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \sqrt{t + a}}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + \frac{5}{6}\right)\right) \leq 1.34 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot {\left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right)}^{-0.25}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.7% 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 93.4%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 53.4%

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

Developer Target 1: 95.5% 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 2024233 
(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)))))))))))