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

Percentage Accurate: 94.0% → 95.8%

Time: 22.0s

Alternatives: 17

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.0% 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: 95.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\sqrt{t + a} \cdot z}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot t_1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{y \cdot c}{t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (+
          (/ (* (sqrt (+ t a)) z) t)
          (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a 0.8333333333333334))))))
   (if (<= t_1 INFINITY)
     (/ x (+ x (* y (exp (* 2.0 t_1)))))
     (/ x (+ x (+ y (* -1.3333333333333333 (/ (* y c) t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((sqrt((t + a)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = x / (x + (y * exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((Math.sqrt((t + a)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = x / (x + (y * Math.exp((2.0 * t_1))));
	} else {
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = ((math.sqrt((t + a)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = x / (x + (y * math.exp((2.0 * t_1))))
	else:
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(sqrt(Float64(t + a)) * z) / t) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + 0.8333333333333334))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * t_1)))));
	else
		tmp = Float64(x / Float64(x + Float64(y + Float64(-1.3333333333333333 * Float64(Float64(y * c) / t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((sqrt((t + a)) * z) / t) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = x / (x + (y * exp((2.0 * t_1))));
	else
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision] * z), $MachinePrecision] / t), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y + N[(-1.3333333333333333 * N[(N[(y * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 99.6%

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

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

   1. Initial program 0.0%

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

   2. Taylor expanded in c around inf 59.6%

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

      1. associate-*r/ 59.6%

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

      2. metadata-eval 59.6%

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

      3. metadata-eval 59.6%

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

      4. associate-/r* 59.6%

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

      5. *-commutative 59.6%

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

      6. sub-neg 59.6%

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

      7. +-commutative 59.6%

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

      8. associate-+l+ 59.6%

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

      9. sub-neg 59.6%

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

      10. *-commutative 59.6%

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

      11. associate-/r* 59.6%

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

      12. metadata-eval 59.6%

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

      13. sub-neg 59.6%

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

      14. distribute-neg-frac 59.6%

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

      15. metadata-eval 59.6%

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

   4. Simplified 59.6%

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

   5. Taylor expanded in t around 0 35.4%

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

      1. associate-*r/ 35.4%

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

      2. metadata-eval 35.4%

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

      3. distribute-lft-neg-in 35.4%

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

      4. *-commutative 35.4%

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

      5. distribute-rgt-neg-in 35.4%

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

      6. metadata-eval 35.4%

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

      7. associate-*r/ 35.4%

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

   7. Simplified 35.4%

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

   8. Taylor expanded in c around 0 67.7%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + -1.3333333333333333 \cdot \frac{c \cdot y}{t}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\sqrt{t + a} \cdot z}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right) \leq \infty:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\sqrt{t + a} \cdot z}{t} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{y \cdot c}{t}\right)}\\ \end{array} \]

Alternative 2: 97.1% accurate, 0.4× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. +-commutative 94.9%

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

   2. fma-def 94.9%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 3: 95.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y \cdot {\left(e^{2}\right)}^{\left(\frac{z}{\frac{t}{\sqrt{t + a}}} + \left(b - c\right) \cdot \left(\frac{2}{t \cdot 3} - \left(a + 0.8333333333333334\right)\right)\right)}} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/
  x
  (+
   x
   (*
    y
    (pow
     (exp 2.0)
     (+
      (/ z (/ t (sqrt (+ t a))))
      (* (- b c) (- (/ 2.0 (* t 3.0)) (+ a 0.8333333333333334)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return x / (x + (y * pow(exp(2.0), ((z / (t / sqrt((t + a)))) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)))))));
}

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 / (t / sqrt((t + a)))) + ((b - c) * ((2.0d0 / (t * 3.0d0)) - (a + 0.8333333333333334d0)))))))
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.pow(Math.exp(2.0), ((z / (t / Math.sqrt((t + a)))) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)))))));
}

Python

def code(x, y, z, t, a, b, c):
	return x / (x + (y * math.pow(math.exp(2.0), ((z / (t / math.sqrt((t + a)))) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)))))))

Julia

function code(x, y, z, t, a, b, c)
	return Float64(x / Float64(x + Float64(y * (exp(2.0) ^ Float64(Float64(z / Float64(t / sqrt(Float64(t + a)))) + Float64(Float64(b - c) * Float64(Float64(2.0 / Float64(t * 3.0)) - Float64(a + 0.8333333333333334))))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = x / (x + (y * (exp(2.0) ^ ((z / (t / sqrt((t + a)))) + ((b - c) * ((2.0 / (t * 3.0)) - (a + 0.8333333333333334)))))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(x / N[(x + N[(y * N[Power[N[Exp[2.0], $MachinePrecision], N[(N[(z / N[(t / N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.9%

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

   1. exp-prod 94.9%

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

   2. associate-/l* 96.9%

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

   3. metadata-eval 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 4: 89.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.0001:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(b - c\right) \cdot \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -1.08e-11)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 7.4e-193)
     (/
      x
      (+
       x
       (*
        y
        (exp
         (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
     (if (<= t 0.0001)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (+
             (* z (sqrt (/ 1.0 t)))
             (* (- b c) (- (/ 0.6666666666666666 t) 0.8333333333333334))))))))
       (/
        x
        (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.08e-11) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 7.4e-193) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 0.0001) {
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((b - c) * ((0.6666666666666666 / t) - 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-1.08d-11)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 7.4d-193) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 0.0001d0) then
        tmp = x / (x + (y * exp((2.0d0 * ((z * sqrt((1.0d0 / t))) + ((b - c) * ((0.6666666666666666d0 / t) - 0.8333333333333334d0)))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -1.08e-11) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 7.4e-193) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 0.0001) {
		tmp = x / (x + (y * Math.exp((2.0 * ((z * Math.sqrt((1.0 / t))) + ((b - c) * ((0.6666666666666666 / t) - 0.8333333333333334)))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -1.08e-11:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 7.4e-193:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 0.0001:
		tmp = x / (x + (y * math.exp((2.0 * ((z * math.sqrt((1.0 / t))) + ((b - c) * ((0.6666666666666666 / t) - 0.8333333333333334)))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -1.08e-11)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 7.4e-193)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	elseif (t <= 0.0001)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(z * sqrt(Float64(1.0 / t))) + Float64(Float64(b - c) * Float64(Float64(0.6666666666666666 / t) - 0.8333333333333334))))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -1.08e-11)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 7.4e-193)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 0.0001)
		tmp = x / (x + (y * exp((2.0 * ((z * sqrt((1.0 / t))) + ((b - c) * ((0.6666666666666666 / t) - 0.8333333333333334)))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -1.08e-11], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.4e-193], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.0001], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(b - c), $MachinePrecision] * N[(N[(0.6666666666666666 / t), $MachinePrecision] - 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.07999999999999992e-11

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf 100.0%

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

   if -1.07999999999999992e-11 < t < 7.4000000000000004e-193

   1. Initial program 93.0%

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

   2. Taylor expanded in t around 0 95.8%

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

   if 7.4000000000000004e-193 < t < 1.00000000000000005e-4

   1. Initial program 96.1%

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

   2. Taylor expanded in a around 0 86.8%

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

      1. *-commutative 86.8%

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

      2. associate-*r/ 86.9%

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

      3. metadata-eval 86.9%

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

   4. Simplified 86.9%

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

   if 1.00000000000000005e-4 < t

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-rgt-neg-in 91.7%

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

      3. +-commutative 91.7%

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

      4. distribute-neg-in 91.7%

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

      5. neg-mul-1 91.7%

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

      6. metadata-eval 91.7%

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

      7. +-commutative 91.7%

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

      8. neg-mul-1 91.7%

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

      9. sub-neg 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.08 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 7.4 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 0.0001:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}} + \left(b - c\right) \cdot \left(\frac{0.6666666666666666}{t} - 0.8333333333333334\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 5: 87.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{if}\;t \leq -2.35 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 0.66:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))))
   (if (<= t -2.35e-13)
     (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
     (if (<= t 4e-192)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (* 2.0 (/ (+ (* z (sqrt a)) (* -0.6666666666666666 (- c b))) t))))))
       (if (<= t 1.2e-50)
         t_1
         (if (<= t 1.75e-41)
           (/ x (+ x (* y (exp (* 2.0 (* z (sqrt (/ 1.0 t))))))))
           (if (<= t 1.1e-23)
             (/
              x
              (+
               x
               (*
                y
                (exp
                 (*
                  2.0
                  (*
                   b
                   (+ (/ 0.6666666666666666 t) (- -0.8333333333333334 a))))))))
             (if (<= t 0.66)
               t_1
               (/
                x
                (+
                 x
                 (*
                  y
                  (exp
                   (* 2.0 (* (- b c) (- -0.8333333333333334 a)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= -2.35e-13) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 4e-192) {
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 1.2e-50) {
		tmp = t_1;
	} else if (t <= 1.75e-41) {
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	} else if (t <= 1.1e-23) {
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) + (-0.8333333333333334 - a)))))));
	} else if (t <= 0.66) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    if (t <= (-2.35d-13)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 4d-192) then
        tmp = x / (x + (y * exp((2.0d0 * (((z * sqrt(a)) + ((-0.6666666666666666d0) * (c - b))) / t)))))
    else if (t <= 1.2d-50) then
        tmp = t_1
    else if (t <= 1.75d-41) then
        tmp = x / (x + (y * exp((2.0d0 * (z * sqrt((1.0d0 / t)))))))
    else if (t <= 1.1d-23) then
        tmp = x / (x + (y * exp((2.0d0 * (b * ((0.6666666666666666d0 / t) + ((-0.8333333333333334d0) - a)))))))
    else if (t <= 0.66d0) then
        tmp = t_1
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	double tmp;
	if (t <= -2.35e-13) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 4e-192) {
		tmp = x / (x + (y * Math.exp((2.0 * (((z * Math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	} else if (t <= 1.2e-50) {
		tmp = t_1;
	} else if (t <= 1.75e-41) {
		tmp = x / (x + (y * Math.exp((2.0 * (z * Math.sqrt((1.0 / t)))))));
	} else if (t <= 1.1e-23) {
		tmp = x / (x + (y * Math.exp((2.0 * (b * ((0.6666666666666666 / t) + (-0.8333333333333334 - a)))))));
	} else if (t <= 0.66) {
		tmp = t_1;
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	tmp = 0
	if t <= -2.35e-13:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 4e-192:
		tmp = x / (x + (y * math.exp((2.0 * (((z * math.sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))))
	elif t <= 1.2e-50:
		tmp = t_1
	elif t <= 1.75e-41:
		tmp = x / (x + (y * math.exp((2.0 * (z * math.sqrt((1.0 / t)))))))
	elif t <= 1.1e-23:
		tmp = x / (x + (y * math.exp((2.0 * (b * ((0.6666666666666666 / t) + (-0.8333333333333334 - a)))))))
	elif t <= 0.66:
		tmp = t_1
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))))
	tmp = 0.0
	if (t <= -2.35e-13)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 4e-192)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(z * sqrt(a)) + Float64(-0.6666666666666666 * Float64(c - b))) / t))))));
	elseif (t <= 1.2e-50)
		tmp = t_1;
	elseif (t <= 1.75e-41)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(z * sqrt(Float64(1.0 / t))))))));
	elseif (t <= 1.1e-23)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 / t) + Float64(-0.8333333333333334 - a))))))));
	elseif (t <= 0.66)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	tmp = 0.0;
	if (t <= -2.35e-13)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 4e-192)
		tmp = x / (x + (y * exp((2.0 * (((z * sqrt(a)) + (-0.6666666666666666 * (c - b))) / t)))));
	elseif (t <= 1.2e-50)
		tmp = t_1;
	elseif (t <= 1.75e-41)
		tmp = x / (x + (y * exp((2.0 * (z * sqrt((1.0 / t)))))));
	elseif (t <= 1.1e-23)
		tmp = x / (x + (y * exp((2.0 * (b * ((0.6666666666666666 / t) + (-0.8333333333333334 - a)))))));
	elseif (t <= 0.66)
		tmp = t_1;
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.35e-13], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-192], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(z * N[Sqrt[a], $MachinePrecision]), $MachinePrecision] + N[(-0.6666666666666666 * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-50], t$95$1, If[LessEqual[t, 1.75e-41], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(z * N[Sqrt[N[(1.0 / t), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-23], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(b * N[(N[(0.6666666666666666 / t), $MachinePrecision] + N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.66], t$95$1, N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.3500000000000001e-13

   1. Initial program 93.8%

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

   2. Taylor expanded in a around inf 100.0%

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

   if -2.3500000000000001e-13 < t < 4.0000000000000004e-192

   1. Initial program 93.0%

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

   2. Taylor expanded in t around 0 95.8%

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

   if 4.0000000000000004e-192 < t < 1.20000000000000001e-50 or 1.1e-23 < t < 0.660000000000000031

   1. Initial program 94.9%

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

   2. Taylor expanded in t around 0 67.6%

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

   3. Taylor expanded in a around 0 87.8%

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

   if 1.20000000000000001e-50 < t < 1.75e-41

   1. Initial program 100.0%

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

   2. Taylor expanded in a around 0 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   if 1.75e-41 < t < 1.1e-23

   1. Initial program 100.0%

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

   2. Taylor expanded in b around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. associate--r+ 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*r/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. metadata-eval 100.0%

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

      7. associate-+r- 100.0%

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

   4. Simplified 100.0%

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

   if 0.660000000000000031 < t

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-rgt-neg-in 91.7%

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

      3. +-commutative 91.7%

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

      4. distribute-neg-in 91.7%

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

      5. neg-mul-1 91.7%

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

      6. metadata-eval 91.7%

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

      7. +-commutative 91.7%

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

      8. neg-mul-1 91.7%

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

      9. sub-neg 91.7%

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

   4. Simplified 91.7%

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.35 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-192}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \sqrt{a} + -0.6666666666666666 \cdot \left(c - b\right)}{t}}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(z \cdot \sqrt{\frac{1}{t}}\right)}}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(b \cdot \left(\frac{0.6666666666666666}{t} + \left(-0.8333333333333334 - a\right)\right)\right)}}\\ \mathbf{elif}\;t \leq 0.66:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 6: 67.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-238}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \frac{1}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))))
   (if (<= t -7.6e-266)
     t_1
     (if (<= t 4.8e-278)
       (/ x (+ x (+ y (* -1.3333333333333333 (/ c (/ t y))))))
       (if (<= t 4e-238)
         1.0
         (if (<= t 1.3e-193)
           (* x (/ 1.0 (+ x (- y (* 2.0 (* a (* y (- b c))))))))
           (if (<= t 5e-6) 1.0 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	double tmp;
	if (t <= -7.6e-266) {
		tmp = t_1;
	} else if (t <= 4.8e-278) {
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))));
	} else if (t <= 4e-238) {
		tmp = 1.0;
	} else if (t <= 1.3e-193) {
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	} else if (t <= 5e-6) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    if (t <= (-7.6d-266)) then
        tmp = t_1
    else if (t <= 4.8d-278) then
        tmp = x / (x + (y + ((-1.3333333333333333d0) * (c / (t / y)))))
    else if (t <= 4d-238) then
        tmp = 1.0d0
    else if (t <= 1.3d-193) then
        tmp = x * (1.0d0 / (x + (y - (2.0d0 * (a * (y * (b - c)))))))
    else if (t <= 5d-6) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	double tmp;
	if (t <= -7.6e-266) {
		tmp = t_1;
	} else if (t <= 4.8e-278) {
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))));
	} else if (t <= 4e-238) {
		tmp = 1.0;
	} else if (t <= 1.3e-193) {
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	} else if (t <= 5e-6) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	tmp = 0
	if t <= -7.6e-266:
		tmp = t_1
	elif t <= 4.8e-278:
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))))
	elif t <= 4e-238:
		tmp = 1.0
	elif t <= 1.3e-193:
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))))
	elif t <= 5e-6:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))))
	tmp = 0.0
	if (t <= -7.6e-266)
		tmp = t_1;
	elseif (t <= 4.8e-278)
		tmp = Float64(x / Float64(x + Float64(y + Float64(-1.3333333333333333 * Float64(c / Float64(t / y))))));
	elseif (t <= 4e-238)
		tmp = 1.0;
	elseif (t <= 1.3e-193)
		tmp = Float64(x * Float64(1.0 / Float64(x + Float64(y - Float64(2.0 * Float64(a * Float64(y * Float64(b - c))))))));
	elseif (t <= 5e-6)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	tmp = 0.0;
	if (t <= -7.6e-266)
		tmp = t_1;
	elseif (t <= 4.8e-278)
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))));
	elseif (t <= 4e-238)
		tmp = 1.0;
	elseif (t <= 1.3e-193)
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	elseif (t <= 5e-6)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.6e-266], t$95$1, If[LessEqual[t, 4.8e-278], N[(x / N[(x + N[(y + N[(-1.3333333333333333 * N[(c / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e-238], 1.0, If[LessEqual[t, 1.3e-193], N[(x * N[(1.0 / N[(x + N[(y - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-6], 1.0, t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.59999999999999988e-266 or 5.00000000000000041e-6 < t

   1. Initial program 96.4%

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

   2. Taylor expanded in t around inf 90.0%

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

      1. mul-1-neg 90.0%

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

      2. distribute-rgt-neg-in 90.0%

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

      3. +-commutative 90.0%

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

      4. distribute-neg-in 90.0%

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

      5. neg-mul-1 90.0%

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

      6. metadata-eval 90.0%

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

      7. +-commutative 90.0%

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

      8. neg-mul-1 90.0%

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

      9. sub-neg 90.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in a around 0 80.1%

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

   if -7.59999999999999988e-266 < t < 4.8e-278

   1. Initial program 85.0%

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

   2. Taylor expanded in c around inf 61.3%

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

      1. associate-*r/ 61.3%

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

      2. metadata-eval 61.3%

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

      3. metadata-eval 61.3%

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

      4. associate-/r* 61.3%

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

      5. *-commutative 61.3%

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

      6. sub-neg 61.3%

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

      7. +-commutative 61.3%

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

      8. associate-+l+ 61.3%

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

      9. sub-neg 61.3%

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

      10. *-commutative 61.3%

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

      11. associate-/r* 61.3%

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

      12. metadata-eval 61.3%

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

      13. sub-neg 61.3%

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

      14. distribute-neg-frac 61.3%

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

      15. metadata-eval 61.3%

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

   4. Simplified 61.3%

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

   5. Taylor expanded in t around 0 61.3%

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

      1. associate-*r/ 61.3%

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

      2. metadata-eval 61.3%

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

      3. distribute-lft-neg-in 61.3%

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

      4. *-commutative 61.3%

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

      5. distribute-rgt-neg-in 61.3%

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

      6. metadata-eval 61.3%

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

      7. associate-*r/ 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in c around 0 61.2%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + -1.3333333333333333 \cdot \frac{c \cdot y}{t}\right)}} \]
   9. Step-by-step derivation

      1. associate-/l* 61.4%

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

   10. Simplified 61.4%

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

   if 4.8e-278 < t < 4e-238 or 1.30000000000000004e-193 < t < 5.00000000000000041e-6

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 30.8%

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

      1. mul-1-neg 30.8%

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

      2. distribute-rgt-neg-in 30.8%

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

      3. +-commutative 30.8%

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

      4. distribute-neg-in 30.8%

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

      5. neg-mul-1 30.8%

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

      6. metadata-eval 30.8%

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

      7. +-commutative 30.8%

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

      8. neg-mul-1 30.8%

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

      9. sub-neg 30.8%

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

   4. Simplified 30.8%

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

   5. Taylor expanded in x around inf 66.2%

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

   if 4e-238 < t < 1.30000000000000004e-193

   1. Initial program 90.9%

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

   2. Taylor expanded in a around inf 47.2%

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

      1. div-inv 47.2%

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

      2. exp-prod 47.2%

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

   4. Applied egg-rr 47.2%

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

   5. Taylor expanded in a around 0 73.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-266}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-238}:\\ \;\;\;\;1\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \frac{1}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 7: 57.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{if}\;c \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(c \cdot a + \left(a \cdot a\right) \cdot \left(c \cdot c\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ x (+ x (* y (exp (* -2.0 (* b a))))))))
   (if (<= c -2.4e+101)
     1.0
     (if (<= c -1.65e-38)
       t_1
       (if (<= c -4.5e-82)
         1.0
         (if (<= c 6e+14)
           t_1
           (/
            x
            (- x (* y (- -1.0 (* 2.0 (+ (* c a) (* (* a a) (* c c))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * exp((-2.0 * (b * a)))));
	double tmp;
	if (c <= -2.4e+101) {
		tmp = 1.0;
	} else if (c <= -1.65e-38) {
		tmp = t_1;
	} else if (c <= -4.5e-82) {
		tmp = 1.0;
	} else if (c <= 6e+14) {
		tmp = t_1;
	} else {
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * exp(((-2.0d0) * (b * a)))))
    if (c <= (-2.4d+101)) then
        tmp = 1.0d0
    else if (c <= (-1.65d-38)) then
        tmp = t_1
    else if (c <= (-4.5d-82)) then
        tmp = 1.0d0
    else if (c <= 6d+14) then
        tmp = t_1
    else
        tmp = x / (x - (y * ((-1.0d0) - (2.0d0 * ((c * a) + ((a * a) * (c * c)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * Math.exp((-2.0 * (b * a)))));
	double tmp;
	if (c <= -2.4e+101) {
		tmp = 1.0;
	} else if (c <= -1.65e-38) {
		tmp = t_1;
	} else if (c <= -4.5e-82) {
		tmp = 1.0;
	} else if (c <= 6e+14) {
		tmp = t_1;
	} else {
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * math.exp((-2.0 * (b * a)))))
	tmp = 0
	if c <= -2.4e+101:
		tmp = 1.0
	elif c <= -1.65e-38:
		tmp = t_1
	elif c <= -4.5e-82:
		tmp = 1.0
	elif c <= 6e+14:
		tmp = t_1
	else:
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(b * a))))))
	tmp = 0.0
	if (c <= -2.4e+101)
		tmp = 1.0;
	elseif (c <= -1.65e-38)
		tmp = t_1;
	elseif (c <= -4.5e-82)
		tmp = 1.0;
	elseif (c <= 6e+14)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(2.0 * Float64(Float64(c * a) + Float64(Float64(a * a) * Float64(c * c))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * exp((-2.0 * (b * a)))));
	tmp = 0.0;
	if (c <= -2.4e+101)
		tmp = 1.0;
	elseif (c <= -1.65e-38)
		tmp = t_1;
	elseif (c <= -4.5e-82)
		tmp = 1.0;
	elseif (c <= 6e+14)
		tmp = t_1;
	else
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(b * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -2.4e+101], 1.0, If[LessEqual[c, -1.65e-38], t$95$1, If[LessEqual[c, -4.5e-82], 1.0, If[LessEqual[c, 6e+14], t$95$1, N[(x / N[(x - N[(y * N[(-1.0 - N[(2.0 * N[(N[(c * a), $MachinePrecision] + N[(N[(a * a), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -2.39999999999999988e101 or -1.6500000000000001e-38 < c < -4.4999999999999998e-82

   1. Initial program 92.9%

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

   2. Taylor expanded in t around inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-rgt-neg-in 77.5%

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

      3. +-commutative 77.5%

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

      4. distribute-neg-in 77.5%

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

      5. neg-mul-1 77.5%

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

      6. metadata-eval 77.5%

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

      7. +-commutative 77.5%

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

      8. neg-mul-1 77.5%

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

      9. sub-neg 77.5%

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

   4. Simplified 77.5%

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

   5. Taylor expanded in x around inf 67.1%

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

   if -2.39999999999999988e101 < c < -1.6500000000000001e-38 or -4.4999999999999998e-82 < c < 6e14

   1. Initial program 94.7%

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

   2. Taylor expanded in a around inf 66.3%

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

   3. Taylor expanded in c around 0 67.0%

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

   if 6e14 < c

   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. Taylor expanded in a around inf 56.6%

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

   3. Taylor expanded in b around 0 54.6%

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

   4. Taylor expanded in c around 0 54.8%

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

      1. distribute-lft-out 54.8%

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

      2. *-commutative 54.8%

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

      3. *-commutative 54.8%

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

      4. unpow2 54.8%

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

      5. unpow2 54.8%

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

   6. Simplified 54.8%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+101}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{elif}\;c \leq -4.5 \cdot 10^{-82}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq 6 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(c \cdot a + \left(a \cdot a\right) \cdot \left(c \cdot c\right)\right)\right)}\\ \end{array} \]

Alternative 8: 83.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 0.02:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -6.6e-66)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 0.02)
     (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
     (/ x (+ x (* y (exp (* 2.0 (* (- b c) (- -0.8333333333333334 a))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -6.6e-66) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 0.02) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-6.6d-66)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 0.02d0) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((b - c) * ((-0.8333333333333334d0) - a))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -6.6e-66) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 0.02) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -6.6e-66:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 0.02:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -6.6e-66)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 0.02)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(b - c) * Float64(-0.8333333333333334 - a)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -6.6e-66)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 0.02)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp((2.0 * ((b - c) * (-0.8333333333333334 - a))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -6.6e-66], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.02], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(b - c), $MachinePrecision] * N[(-0.8333333333333334 - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.5999999999999998e-66

   1. Initial program 96.0%

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

   2. Taylor expanded in a around inf 96.1%

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

   if -6.5999999999999998e-66 < t < 0.0200000000000000004

   1. Initial program 93.8%

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

   2. Taylor expanded in t around 0 80.8%

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

   3. Taylor expanded in a around 0 77.9%

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

   if 0.0200000000000000004 < t

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-rgt-neg-in 91.7%

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

      3. +-commutative 91.7%

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

      4. distribute-neg-in 91.7%

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

      5. neg-mul-1 91.7%

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

      6. metadata-eval 91.7%

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

      7. +-commutative 91.7%

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

      8. neg-mul-1 91.7%

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

      9. sub-neg 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 0.02:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(b - c\right) \cdot \left(-0.8333333333333334 - a\right)\right)}}\\ \end{array} \]

Alternative 9: 77.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 0.8:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t -2e-74)
   (/ x (+ x (* y (exp (* 2.0 (* a (- c b)))))))
   (if (<= t 0.8)
     (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
     (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2e-74) {
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	} else if (t <= 0.8) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= (-2d-74)) then
        tmp = x / (x + (y * exp((2.0d0 * (a * (c - b))))))
    else if (t <= 0.8d0) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= -2e-74) {
		tmp = x / (x + (y * Math.exp((2.0 * (a * (c - b))))));
	} else if (t <= 0.8) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= -2e-74:
		tmp = x / (x + (y * math.exp((2.0 * (a * (c - b))))))
	elif t <= 0.8:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= -2e-74)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(a * Float64(c - b)))))));
	elseif (t <= 0.8)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= -2e-74)
		tmp = x / (x + (y * exp((2.0 * (a * (c - b))))));
	elseif (t <= 0.8)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, -2e-74], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(a * N[(c - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.8], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.99999999999999992e-74

   1. Initial program 96.0%

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

   2. Taylor expanded in a around inf 96.1%

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

   if -1.99999999999999992e-74 < t < 0.80000000000000004

   1. Initial program 93.8%

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

   2. Taylor expanded in t around 0 80.8%

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

   3. Taylor expanded in a around 0 77.9%

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

   if 0.80000000000000004 < t

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-rgt-neg-in 91.7%

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

      3. +-commutative 91.7%

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

      4. distribute-neg-in 91.7%

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

      5. neg-mul-1 91.7%

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

      6. metadata-eval 91.7%

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

      7. +-commutative 91.7%

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

      8. neg-mul-1 91.7%

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

      9. sub-neg 91.7%

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

   4. Simplified 91.7%

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

   5. Taylor expanded in a around 0 81.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-74}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(a \cdot \left(c - b\right)\right)}}\\ \mathbf{elif}\;t \leq 0.8:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 10: 60.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b -3.8e+104)
   (/ x (+ x (* y (exp (* -2.0 (* b a))))))
   (if (<= b 2.1e-22) (/ x (+ x (* y (exp (* 2.0 (* c a)))))) 1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.8e+104) {
		tmp = x / (x + (y * exp((-2.0 * (b * a)))));
	} else if (b <= 2.1e-22) {
		tmp = x / (x + (y * exp((2.0 * (c * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= (-3.8d+104)) then
        tmp = x / (x + (y * exp(((-2.0d0) * (b * a)))))
    else if (b <= 2.1d-22) then
        tmp = x / (x + (y * exp((2.0d0 * (c * a)))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= -3.8e+104) {
		tmp = x / (x + (y * Math.exp((-2.0 * (b * a)))));
	} else if (b <= 2.1e-22) {
		tmp = x / (x + (y * Math.exp((2.0 * (c * a)))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= -3.8e+104:
		tmp = x / (x + (y * math.exp((-2.0 * (b * a)))))
	elif b <= 2.1e-22:
		tmp = x / (x + (y * math.exp((2.0 * (c * a)))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= -3.8e+104)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(-2.0 * Float64(b * a))))));
	elseif (b <= 2.1e-22)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(c * a))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= -3.8e+104)
		tmp = x / (x + (y * exp((-2.0 * (b * a)))));
	elseif (b <= 2.1e-22)
		tmp = x / (x + (y * exp((2.0 * (c * a)))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, -3.8e+104], N[(x / N[(x + N[(y * N[Exp[N[(-2.0 * N[(b * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-22], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(c * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if b < -3.79999999999999969e104

   1. Initial program 91.3%

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

   2. Taylor expanded in a around inf 66.7%

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

   3. Taylor expanded in c around 0 64.6%

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

   if -3.79999999999999969e104 < b < 2.10000000000000008e-22

   1. Initial program 99.3%

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

   2. Taylor expanded in a around inf 62.6%

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

   3. Taylor expanded in b around 0 62.6%

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

   if 2.10000000000000008e-22 < b

   1. Initial program 88.8%

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

   2. Taylor expanded in t around inf 70.0%

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

      1. mul-1-neg 70.0%

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

      2. distribute-rgt-neg-in 70.0%

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

      3. +-commutative 70.0%

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

      4. distribute-neg-in 70.0%

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

      5. neg-mul-1 70.0%

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

      6. metadata-eval 70.0%

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

      7. +-commutative 70.0%

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

      8. neg-mul-1 70.0%

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

      9. sub-neg 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in x around inf 59.1%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{-2 \cdot \left(b \cdot a\right)}}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot a\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 76.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 0.15:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= t 0.15)
   (/ x (+ x (* y (exp (* 1.3333333333333333 (/ (- b c) t))))))
   (/ x (+ x (* y (exp (* (- b c) -1.6666666666666667)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 0.15) {
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (t <= 0.15d0) then
        tmp = x / (x + (y * exp((1.3333333333333333d0 * ((b - c) / t)))))
    else
        tmp = x / (x + (y * exp(((b - c) * (-1.6666666666666667d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (t <= 0.15) {
		tmp = x / (x + (y * Math.exp((1.3333333333333333 * ((b - c) / t)))));
	} else {
		tmp = x / (x + (y * Math.exp(((b - c) * -1.6666666666666667))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if t <= 0.15:
		tmp = x / (x + (y * math.exp((1.3333333333333333 * ((b - c) / t)))))
	else:
		tmp = x / (x + (y * math.exp(((b - c) * -1.6666666666666667))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (t <= 0.15)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(1.3333333333333333 * Float64(Float64(b - c) / t))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(Float64(b - c) * -1.6666666666666667)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (t <= 0.15)
		tmp = x / (x + (y * exp((1.3333333333333333 * ((b - c) / t)))));
	else
		tmp = x / (x + (y * exp(((b - c) * -1.6666666666666667))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[t, 0.15], N[(x / N[(x + N[(y * N[Exp[N[(1.3333333333333333 * N[(N[(b - c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(N[(b - c), $MachinePrecision] * -1.6666666666666667), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 0.149999999999999994

   1. Initial program 94.2%

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

   2. Taylor expanded in t around 0 78.0%

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

   3. Taylor expanded in a around 0 77.0%

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

   if 0.149999999999999994 < t

   1. Initial program 95.8%

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

   2. Taylor expanded in t around inf 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-rgt-neg-in 91.7%

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

      3. +-commutative 91.7%

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

      4. distribute-neg-in 91.7%

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

      5. neg-mul-1 91.7%

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

      6. metadata-eval 91.7%

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

      7. +-commutative 91.7%

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

      8. neg-mul-1 91.7%

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

      9. sub-neg 91.7%

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

   4. Simplified 91.7%

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

   5. Taylor expanded in a around 0 81.0%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.15:\\ \;\;\;\;\frac{x}{x + y \cdot e^{1.3333333333333333 \cdot \frac{b - c}{t}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(b - c\right) \cdot -1.6666666666666667}}\\ \end{array} \]

Alternative 12: 51.3% accurate, 7.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{if}\;c \leq -1.15 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-97}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(c \cdot a + \left(a \cdot a\right) \cdot \left(c \cdot c\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           x
           (*
            y
            (+
             (*
              2.0
              (*
               b
               (- (* 0.6666666666666666 (/ 1.0 t)) (+ a 0.8333333333333334))))
             1.0))))))
   (if (<= c -1.15e+100)
     1.0
     (if (<= c -2.9e-37)
       t_1
       (if (<= c -1.15e-97)
         1.0
         (if (<= c -2.4e-174)
           t_1
           (if (<= c 2.5e-76)
             1.0
             (/
              x
              (-
               x
               (* y (- -1.0 (* 2.0 (+ (* c a) (* (* a a) (* c c)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)));
	double tmp;
	if (c <= -1.15e+100) {
		tmp = 1.0;
	} else if (c <= -2.9e-37) {
		tmp = t_1;
	} else if (c <= -1.15e-97) {
		tmp = 1.0;
	} else if (c <= -2.4e-174) {
		tmp = t_1;
	} else if (c <= 2.5e-76) {
		tmp = 1.0;
	} else {
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * ((2.0d0 * (b * ((0.6666666666666666d0 * (1.0d0 / t)) - (a + 0.8333333333333334d0)))) + 1.0d0)))
    if (c <= (-1.15d+100)) then
        tmp = 1.0d0
    else if (c <= (-2.9d-37)) then
        tmp = t_1
    else if (c <= (-1.15d-97)) then
        tmp = 1.0d0
    else if (c <= (-2.4d-174)) then
        tmp = t_1
    else if (c <= 2.5d-76) then
        tmp = 1.0d0
    else
        tmp = x / (x - (y * ((-1.0d0) - (2.0d0 * ((c * a) + ((a * a) * (c * c)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)));
	double tmp;
	if (c <= -1.15e+100) {
		tmp = 1.0;
	} else if (c <= -2.9e-37) {
		tmp = t_1;
	} else if (c <= -1.15e-97) {
		tmp = 1.0;
	} else if (c <= -2.4e-174) {
		tmp = t_1;
	} else if (c <= 2.5e-76) {
		tmp = 1.0;
	} else {
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)))
	tmp = 0
	if c <= -1.15e+100:
		tmp = 1.0
	elif c <= -2.9e-37:
		tmp = t_1
	elif c <= -1.15e-97:
		tmp = 1.0
	elif c <= -2.4e-174:
		tmp = t_1
	elif c <= 2.5e-76:
		tmp = 1.0
	else:
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 * Float64(1.0 / t)) - Float64(a + 0.8333333333333334)))) + 1.0))))
	tmp = 0.0
	if (c <= -1.15e+100)
		tmp = 1.0;
	elseif (c <= -2.9e-37)
		tmp = t_1;
	elseif (c <= -1.15e-97)
		tmp = 1.0;
	elseif (c <= -2.4e-174)
		tmp = t_1;
	elseif (c <= 2.5e-76)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x - Float64(y * Float64(-1.0 - Float64(2.0 * Float64(Float64(c * a) + Float64(Float64(a * a) * Float64(c * c))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)));
	tmp = 0.0;
	if (c <= -1.15e+100)
		tmp = 1.0;
	elseif (c <= -2.9e-37)
		tmp = t_1;
	elseif (c <= -1.15e-97)
		tmp = 1.0;
	elseif (c <= -2.4e-174)
		tmp = t_1;
	elseif (c <= 2.5e-76)
		tmp = 1.0;
	else
		tmp = x / (x - (y * (-1.0 - (2.0 * ((c * a) + ((a * a) * (c * c)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[(N[(2.0 * N[(b * N[(N[(0.6666666666666666 * N[(1.0 / t), $MachinePrecision]), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.15e+100], 1.0, If[LessEqual[c, -2.9e-37], t$95$1, If[LessEqual[c, -1.15e-97], 1.0, If[LessEqual[c, -2.4e-174], t$95$1, If[LessEqual[c, 2.5e-76], 1.0, N[(x / N[(x - N[(y * N[(-1.0 - N[(2.0 * N[(N[(c * a), $MachinePrecision] + N[(N[(a * a), $MachinePrecision] * N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.14999999999999995e100 or -2.90000000000000005e-37 < c < -1.14999999999999997e-97 or -2.4e-174 < c < 2.4999999999999999e-76

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 70.4%

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

      1. mul-1-neg 70.4%

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

      2. distribute-rgt-neg-in 70.4%

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

      3. +-commutative 70.4%

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

      4. distribute-neg-in 70.4%

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

      5. neg-mul-1 70.4%

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

      6. metadata-eval 70.4%

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

      7. +-commutative 70.4%

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

      8. neg-mul-1 70.4%

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

      9. sub-neg 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in x around inf 62.5%

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

   if -1.14999999999999995e100 < c < -2.90000000000000005e-37 or -1.14999999999999997e-97 < c < -2.4e-174

   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. Taylor expanded in b around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate--r+ 77.8%

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

      3. sub-neg 77.8%

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

      4. associate-*r/ 77.8%

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

      5. metadata-eval 77.8%

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

      6. metadata-eval 77.8%

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

      7. associate-+r- 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in b around 0 63.9%

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

   if 2.4999999999999999e-76 < c

   1. Initial program 97.2%

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

   2. Taylor expanded in a around inf 59.1%

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

   3. Taylor expanded in b around 0 55.0%

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

   4. Taylor expanded in c around 0 57.8%

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

      1. distribute-lft-out 57.8%

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

      2. *-commutative 57.8%

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

      3. *-commutative 57.8%

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

      4. unpow2 57.8%

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

      5. unpow2 57.8%

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

   6. Simplified 57.8%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.15 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.9 \cdot 10^{-37}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{elif}\;c \leq -1.15 \cdot 10^{-97}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -2.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{elif}\;c \leq 2.5 \cdot 10^{-76}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x - y \cdot \left(-1 - 2 \cdot \left(c \cdot a + \left(a \cdot a\right) \cdot \left(c \cdot c\right)\right)\right)}\\ \end{array} \]

Alternative 13: 50.9% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{if}\;c \leq -3.3 \cdot 10^{+99}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-98}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1
         (/
          x
          (+
           x
           (*
            y
            (+
             (*
              2.0
              (*
               b
               (- (* 0.6666666666666666 (/ 1.0 t)) (+ a 0.8333333333333334))))
             1.0))))))
   (if (<= c -3.3e+99)
     1.0
     (if (<= c -7.6e-36)
       t_1
       (if (<= c -1.7e-98)
         1.0
         (if (<= c -1.65e-176)
           t_1
           (if (<= c 2e-16)
             1.0
             (* x (/ 1.0 (+ x (- y (* 2.0 (* a (* y (- b c)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)));
	double tmp;
	if (c <= -3.3e+99) {
		tmp = 1.0;
	} else if (c <= -7.6e-36) {
		tmp = t_1;
	} else if (c <= -1.7e-98) {
		tmp = 1.0;
	} else if (c <= -1.65e-176) {
		tmp = t_1;
	} else if (c <= 2e-16) {
		tmp = 1.0;
	} else {
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + (y * ((2.0d0 * (b * ((0.6666666666666666d0 * (1.0d0 / t)) - (a + 0.8333333333333334d0)))) + 1.0d0)))
    if (c <= (-3.3d+99)) then
        tmp = 1.0d0
    else if (c <= (-7.6d-36)) then
        tmp = t_1
    else if (c <= (-1.7d-98)) then
        tmp = 1.0d0
    else if (c <= (-1.65d-176)) then
        tmp = t_1
    else if (c <= 2d-16) then
        tmp = 1.0d0
    else
        tmp = x * (1.0d0 / (x + (y - (2.0d0 * (a * (y * (b - c)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)));
	double tmp;
	if (c <= -3.3e+99) {
		tmp = 1.0;
	} else if (c <= -7.6e-36) {
		tmp = t_1;
	} else if (c <= -1.7e-98) {
		tmp = 1.0;
	} else if (c <= -1.65e-176) {
		tmp = t_1;
	} else if (c <= 2e-16) {
		tmp = 1.0;
	} else {
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)))
	tmp = 0
	if c <= -3.3e+99:
		tmp = 1.0
	elif c <= -7.6e-36:
		tmp = t_1
	elif c <= -1.7e-98:
		tmp = 1.0
	elif c <= -1.65e-176:
		tmp = t_1
	elif c <= 2e-16:
		tmp = 1.0
	else:
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(b * Float64(Float64(0.6666666666666666 * Float64(1.0 / t)) - Float64(a + 0.8333333333333334)))) + 1.0))))
	tmp = 0.0
	if (c <= -3.3e+99)
		tmp = 1.0;
	elseif (c <= -7.6e-36)
		tmp = t_1;
	elseif (c <= -1.7e-98)
		tmp = 1.0;
	elseif (c <= -1.65e-176)
		tmp = t_1;
	elseif (c <= 2e-16)
		tmp = 1.0;
	else
		tmp = Float64(x * Float64(1.0 / Float64(x + Float64(y - Float64(2.0 * Float64(a * Float64(y * Float64(b - c))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = x / (x + (y * ((2.0 * (b * ((0.6666666666666666 * (1.0 / t)) - (a + 0.8333333333333334)))) + 1.0)));
	tmp = 0.0;
	if (c <= -3.3e+99)
		tmp = 1.0;
	elseif (c <= -7.6e-36)
		tmp = t_1;
	elseif (c <= -1.7e-98)
		tmp = 1.0;
	elseif (c <= -1.65e-176)
		tmp = t_1;
	elseif (c <= 2e-16)
		tmp = 1.0;
	else
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(x / N[(x + N[(y * N[(N[(2.0 * N[(b * N[(N[(0.6666666666666666 * N[(1.0 / t), $MachinePrecision]), $MachinePrecision] - N[(a + 0.8333333333333334), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.3e+99], 1.0, If[LessEqual[c, -7.6e-36], t$95$1, If[LessEqual[c, -1.7e-98], 1.0, If[LessEqual[c, -1.65e-176], t$95$1, If[LessEqual[c, 2e-16], 1.0, N[(x * N[(1.0 / N[(x + N[(y - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.2999999999999999e99 or -7.59999999999999942e-36 < c < -1.7000000000000001e-98 or -1.65000000000000006e-176 < c < 2e-16

   1. Initial program 94.7%

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

   2. Taylor expanded in t around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. distribute-rgt-neg-in 69.7%

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

      3. +-commutative 69.7%

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

      4. distribute-neg-in 69.7%

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

      5. neg-mul-1 69.7%

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

      6. metadata-eval 69.7%

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

      7. +-commutative 69.7%

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

      8. neg-mul-1 69.7%

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

      9. sub-neg 69.7%

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

   4. Simplified 69.7%

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

   5. Taylor expanded in x around inf 62.5%

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

   if -3.2999999999999999e99 < c < -7.59999999999999942e-36 or -1.7000000000000001e-98 < c < -1.65000000000000006e-176

   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. Taylor expanded in b around inf 77.8%

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

      1. *-commutative 77.8%

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

      2. associate--r+ 77.8%

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

      3. sub-neg 77.8%

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

      4. associate-*r/ 77.8%

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

      5. metadata-eval 77.8%

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

      6. metadata-eval 77.8%

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

      7. associate-+r- 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in b around 0 63.9%

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

   if 2e-16 < c

   1. Initial program 98.3%

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

   2. Taylor expanded in a around inf 56.7%

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

      1. div-inv 56.6%

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

      2. exp-prod 56.6%

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

   4. Applied egg-rr 56.6%

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

   5. Taylor expanded in a around 0 50.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{+99}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -7.6 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-98}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.65 \cdot 10^{-176}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(b \cdot \left(0.6666666666666666 \cdot \frac{1}{t} - \left(a + 0.8333333333333334\right)\right)\right) + 1\right)}\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \end{array} \]

Alternative 14: 52.6% accurate, 10.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-174} \lor \neg \left(c \leq 1.15 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{1}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -9.5e-100)
   1.0
   (if (or (<= c -1.95e-174) (not (<= c 1.15e-13)))
     (* x (/ 1.0 (+ x (- y (* 2.0 (* a (* y (- b c))))))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.5e-100) {
		tmp = 1.0;
	} else if ((c <= -1.95e-174) || !(c <= 1.15e-13)) {
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-9.5d-100)) then
        tmp = 1.0d0
    else if ((c <= (-1.95d-174)) .or. (.not. (c <= 1.15d-13))) then
        tmp = x * (1.0d0 / (x + (y - (2.0d0 * (a * (y * (b - c)))))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -9.5e-100) {
		tmp = 1.0;
	} else if ((c <= -1.95e-174) || !(c <= 1.15e-13)) {
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -9.5e-100:
		tmp = 1.0
	elif (c <= -1.95e-174) or not (c <= 1.15e-13):
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -9.5e-100)
		tmp = 1.0;
	elseif ((c <= -1.95e-174) || !(c <= 1.15e-13))
		tmp = Float64(x * Float64(1.0 / Float64(x + Float64(y - Float64(2.0 * Float64(a * Float64(y * Float64(b - c))))))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -9.5e-100)
		tmp = 1.0;
	elseif ((c <= -1.95e-174) || ~((c <= 1.15e-13)))
		tmp = x * (1.0 / (x + (y - (2.0 * (a * (y * (b - c)))))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -9.5e-100], 1.0, If[Or[LessEqual[c, -1.95e-174], N[Not[LessEqual[c, 1.15e-13]], $MachinePrecision]], N[(x * N[(1.0 / N[(x + N[(y - N[(2.0 * N[(a * N[(y * N[(b - c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if c < -9.4999999999999992e-100 or -1.9499999999999999e-174 < c < 1.1499999999999999e-13

   1. Initial program 93.8%

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

   2. Taylor expanded in t around inf 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-rgt-neg-in 71.6%

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

      3. +-commutative 71.6%

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

      4. distribute-neg-in 71.6%

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

      5. neg-mul-1 71.6%

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

      6. metadata-eval 71.6%

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

      7. +-commutative 71.6%

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

      8. neg-mul-1 71.6%

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

      9. sub-neg 71.6%

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

   4. Simplified 71.6%

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

   5. Taylor expanded in x around inf 60.0%

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

   if -9.4999999999999992e-100 < c < -1.9499999999999999e-174 or 1.1499999999999999e-13 < c

   1. Initial program 97.5%

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

   2. Taylor expanded in a around inf 58.5%

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

      1. div-inv 58.5%

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

      2. exp-prod 58.5%

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

   4. Applied egg-rr 58.5%

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

   5. Taylor expanded in a around 0 50.1%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{-100}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -1.95 \cdot 10^{-174} \lor \neg \left(c \leq 1.15 \cdot 10^{-13}\right):\\ \;\;\;\;x \cdot \frac{1}{x + \left(y - 2 \cdot \left(a \cdot \left(y \cdot \left(b - c\right)\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 15: 52.7% accurate, 12.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot a\right) + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= c -1.6e-99)
   1.0
   (if (<= c -3.8e-168)
     (/ x (+ x (+ y (* -1.3333333333333333 (/ c (/ t y))))))
     (if (<= c 8.5e-73) 1.0 (/ x (+ x (* y (+ (* 2.0 (* c a)) 1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.6e-99) {
		tmp = 1.0;
	} else if (c <= -3.8e-168) {
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))));
	} else if (c <= 8.5e-73) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * ((2.0 * (c * a)) + 1.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (c <= (-1.6d-99)) then
        tmp = 1.0d0
    else if (c <= (-3.8d-168)) then
        tmp = x / (x + (y + ((-1.3333333333333333d0) * (c / (t / y)))))
    else if (c <= 8.5d-73) then
        tmp = 1.0d0
    else
        tmp = x / (x + (y * ((2.0d0 * (c * a)) + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (c <= -1.6e-99) {
		tmp = 1.0;
	} else if (c <= -3.8e-168) {
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))));
	} else if (c <= 8.5e-73) {
		tmp = 1.0;
	} else {
		tmp = x / (x + (y * ((2.0 * (c * a)) + 1.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if c <= -1.6e-99:
		tmp = 1.0
	elif c <= -3.8e-168:
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))))
	elif c <= 8.5e-73:
		tmp = 1.0
	else:
		tmp = x / (x + (y * ((2.0 * (c * a)) + 1.0)))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (c <= -1.6e-99)
		tmp = 1.0;
	elseif (c <= -3.8e-168)
		tmp = Float64(x / Float64(x + Float64(y + Float64(-1.3333333333333333 * Float64(c / Float64(t / y))))));
	elseif (c <= 8.5e-73)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + Float64(y * Float64(Float64(2.0 * Float64(c * a)) + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (c <= -1.6e-99)
		tmp = 1.0;
	elseif (c <= -3.8e-168)
		tmp = x / (x + (y + (-1.3333333333333333 * (c / (t / y)))));
	elseif (c <= 8.5e-73)
		tmp = 1.0;
	else
		tmp = x / (x + (y * ((2.0 * (c * a)) + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[c, -1.6e-99], 1.0, If[LessEqual[c, -3.8e-168], N[(x / N[(x + N[(y + N[(-1.3333333333333333 * N[(c / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 8.5e-73], 1.0, N[(x / N[(x + N[(y * N[(N[(2.0 * N[(c * a), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.6e-99 or -3.8e-168 < c < 8.4999999999999996e-73

   1. Initial program 93.9%

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

   2. Taylor expanded in t around inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-rgt-neg-in 72.3%

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

      3. +-commutative 72.3%

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

      4. distribute-neg-in 72.3%

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

      5. neg-mul-1 72.3%

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

      6. metadata-eval 72.3%

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

      7. +-commutative 72.3%

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

      8. neg-mul-1 72.3%

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

      9. sub-neg 72.3%

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

   4. Simplified 72.3%

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

   5. Taylor expanded in x around inf 59.8%

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

   if -1.6e-99 < c < -3.8e-168

   1. Initial program 95.2%

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

   2. Taylor expanded in c around inf 54.1%

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

      1. associate-*r/ 54.1%

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

      2. metadata-eval 54.1%

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

      3. metadata-eval 54.1%

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

      4. associate-/r* 54.1%

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

      5. *-commutative 54.1%

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

      6. sub-neg 54.1%

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

      7. +-commutative 54.1%

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

      8. associate-+l+ 54.1%

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

      9. sub-neg 54.1%

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

      10. *-commutative 54.1%

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

      11. associate-/r* 54.1%

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

      12. metadata-eval 54.1%

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

      13. sub-neg 54.1%

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

      14. distribute-neg-frac 54.1%

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

      15. metadata-eval 54.1%

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

   4. Simplified 54.1%

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

   5. Taylor expanded in t around 0 49.5%

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

      1. associate-*r/ 49.5%

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

      2. metadata-eval 49.5%

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

      3. distribute-lft-neg-in 49.5%

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

      4. *-commutative 49.5%

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

      5. distribute-rgt-neg-in 49.5%

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

      6. metadata-eval 49.5%

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

      7. associate-*r/ 49.5%

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

   7. Simplified 49.5%

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

   8. Taylor expanded in c around 0 49.5%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + -1.3333333333333333 \cdot \frac{c \cdot y}{t}\right)}} \]
   9. Step-by-step derivation

      1. associate-/l* 49.5%

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

   10. Simplified 49.5%

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

   if 8.4999999999999996e-73 < c

   1. Initial program 97.2%

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

   2. Taylor expanded in a around inf 59.1%

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

   3. Taylor expanded in b around 0 55.0%

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

   4. Taylor expanded in c around 0 49.7%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;1\\ \mathbf{elif}\;c \leq -3.8 \cdot 10^{-168}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{c}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;c \leq 8.5 \cdot 10^{-73}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot \left(2 \cdot \left(c \cdot a\right) + 1\right)}\\ \end{array} \]

Alternative 16: 50.6% accurate, 13.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.65 \cdot 10^{-253}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{y \cdot c}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (if (<= b 1.65e-253)
   1.0
   (if (<= b 3.1e-22)
     (/ x (+ x (+ y (* -1.3333333333333333 (/ (* y c) t)))))
     1.0)))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= 1.65e-253) {
		tmp = 1.0;
	} else if (b <= 3.1e-22) {
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: tmp
    if (b <= 1.65d-253) then
        tmp = 1.0d0
    else if (b <= 3.1d-22) then
        tmp = x / (x + (y + ((-1.3333333333333333d0) * ((y * c) / t))))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (b <= 1.65e-253) {
		tmp = 1.0;
	} else if (b <= 3.1e-22) {
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	tmp = 0
	if b <= 1.65e-253:
		tmp = 1.0
	elif b <= 3.1e-22:
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (b <= 1.65e-253)
		tmp = 1.0;
	elseif (b <= 3.1e-22)
		tmp = Float64(x / Float64(x + Float64(y + Float64(-1.3333333333333333 * Float64(Float64(y * c) / t)))));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	tmp = 0.0;
	if (b <= 1.65e-253)
		tmp = 1.0;
	elseif (b <= 3.1e-22)
		tmp = x / (x + (y + (-1.3333333333333333 * ((y * c) / t))));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[b, 1.65e-253], 1.0, If[LessEqual[b, 3.1e-22], N[(x / N[(x + N[(y + N[(-1.3333333333333333 * N[(N[(y * c), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if b < 1.65e-253 or 3.10000000000000013e-22 < b

   1. Initial program 93.7%

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

   2. Taylor expanded in t around inf 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-rgt-neg-in 71.0%

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

      3. +-commutative 71.0%

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

      4. distribute-neg-in 71.0%

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

      5. neg-mul-1 71.0%

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

      6. metadata-eval 71.0%

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

      7. +-commutative 71.0%

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

      8. neg-mul-1 71.0%

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

      9. sub-neg 71.0%

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

   4. Simplified 71.0%

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

   5. Taylor expanded in x around inf 52.7%

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

   if 1.65e-253 < b < 3.10000000000000013e-22

   1. Initial program 100.0%

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

   2. Taylor expanded in c around inf 74.4%

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

      1. associate-*r/ 74.4%

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

      2. metadata-eval 74.4%

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

      3. metadata-eval 74.4%

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

      4. associate-/r* 74.4%

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

      5. *-commutative 74.4%

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

      6. sub-neg 74.4%

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

      7. +-commutative 74.4%

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

      8. associate-+l+ 74.4%

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

      9. sub-neg 74.4%

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

      10. *-commutative 74.4%

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

      11. associate-/r* 74.4%

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

      12. metadata-eval 74.4%

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

      13. sub-neg 74.4%

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

      14. distribute-neg-frac 74.4%

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

      15. metadata-eval 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in t around 0 60.8%

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

      1. associate-*r/ 60.8%

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

      2. metadata-eval 60.8%

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

      3. distribute-lft-neg-in 60.8%

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

      4. *-commutative 60.8%

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

      5. distribute-rgt-neg-in 60.8%

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

      6. metadata-eval 60.8%

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

      7. associate-*r/ 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in c around 0 57.2%

      \[\leadsto \frac{x}{x + \color{blue}{\left(y + -1.3333333333333333 \cdot \frac{c \cdot y}{t}\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.65 \cdot 10^{-253}:\\ \;\;\;\;1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{x + \left(y + -1.3333333333333333 \cdot \frac{y \cdot c}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 17: 51.4% accurate, 231.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

2. Taylor expanded in t around inf 69.8%

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

   1. mul-1-neg 69.8%

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

   2. distribute-rgt-neg-in 69.8%

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

   3. +-commutative 69.8%

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

   4. distribute-neg-in 69.8%

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

   5. neg-mul-1 69.8%

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

   6. metadata-eval 69.8%

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

   7. +-commutative 69.8%

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

   8. neg-mul-1 69.8%

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

   9. sub-neg 69.8%

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

4. Simplified 69.8%

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

5. Taylor expanded in x around inf 50.4%

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

6. Final simplification 50.4%

   \[\leadsto 1 \]

Developer target: 94.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \sqrt{t + a}\\ t_2 := a - \frac{5}{6}\\ \mathbf{if}\;t < -2.118326644891581 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\left(a \cdot c + 0.8333333333333334 \cdot c\right) - a \cdot b\right)}}\\ \mathbf{elif}\;t < 5.196588770651547 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{t_1 \cdot \left(\left(3 \cdot t\right) \cdot t_2\right) - \left(\left(\frac{5}{6} + a\right) \cdot \left(3 \cdot t\right) - 2\right) \cdot \left(t_2 \cdot \left(\left(b - c\right) \cdot t\right)\right)}{\left(\left(t \cdot t\right) \cdot 3\right) \cdot t_2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{t_1}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* z (sqrt (+ t a)))) (t_2 (- a (/ 5.0 6.0))))
   (if (< t -2.118326644891581e-50)
     (/
      x
      (+
       x
       (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b)))))))
     (if (< t 5.196588770651547e-123)
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (/
             (-
              (* t_1 (* (* 3.0 t) t_2))
              (*
               (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0)
               (* t_2 (* (- b c) t))))
             (* (* (* t t) 3.0) t_2)))))))
       (/
        x
        (+
         x
         (*
          y
          (exp
           (*
            2.0
            (-
             (/ t_1 t)
             (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z * sqrt((t + a))
    t_2 = a - (5.0d0 / 6.0d0)
    if (t < (-2.118326644891581d-50)) then
        tmp = x / (x + (y * exp((2.0d0 * (((a * c) + (0.8333333333333334d0 * c)) - (a * b))))))
    else if (t < 5.196588770651547d-123) then
        tmp = x / (x + (y * exp((2.0d0 * (((t_1 * ((3.0d0 * t) * t_2)) - (((((5.0d0 / 6.0d0) + a) * (3.0d0 * t)) - 2.0d0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0d0) * t_2))))))
    else
        tmp = x / (x + (y * exp((2.0d0 * ((t_1 / t) - ((b - c) * ((a + (5.0d0 / 6.0d0)) - (2.0d0 / (t * 3.0d0)))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = z * Math.sqrt((t + a));
	double t_2 = a - (5.0 / 6.0);
	double tmp;
	if (t < -2.118326644891581e-50) {
		tmp = x / (x + (y * Math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	} else if (t < 5.196588770651547e-123) {
		tmp = x / (x + (y * Math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	} else {
		tmp = x / (x + (y * Math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	t_1 = z * math.sqrt((t + a))
	t_2 = a - (5.0 / 6.0)
	tmp = 0
	if t < -2.118326644891581e-50:
		tmp = x / (x + (y * math.exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))))
	elif t < 5.196588770651547e-123:
		tmp = x / (x + (y * math.exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))))
	else:
		tmp = x / (x + (y * math.exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))))
	return tmp

Julia

function code(x, y, z, t, a, b, c)
	t_1 = Float64(z * sqrt(Float64(t + a)))
	t_2 = Float64(a - Float64(5.0 / 6.0))
	tmp = 0.0
	if (t < -2.118326644891581e-50)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(a * c) + Float64(0.8333333333333334 * c)) - Float64(a * b)))))));
	elseif (t < 5.196588770651547e-123)
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(Float64(t_1 * Float64(Float64(3.0 * t) * t_2)) - Float64(Float64(Float64(Float64(Float64(5.0 / 6.0) + a) * Float64(3.0 * t)) - 2.0) * Float64(t_2 * Float64(Float64(b - c) * t)))) / Float64(Float64(Float64(t * t) * 3.0) * t_2)))))));
	else
		tmp = Float64(x / Float64(x + Float64(y * exp(Float64(2.0 * Float64(Float64(t_1 / t) - Float64(Float64(b - c) * Float64(Float64(a + Float64(5.0 / 6.0)) - Float64(2.0 / Float64(t * 3.0))))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = z * sqrt((t + a));
	t_2 = a - (5.0 / 6.0);
	tmp = 0.0;
	if (t < -2.118326644891581e-50)
		tmp = x / (x + (y * exp((2.0 * (((a * c) + (0.8333333333333334 * c)) - (a * b))))));
	elseif (t < 5.196588770651547e-123)
		tmp = x / (x + (y * exp((2.0 * (((t_1 * ((3.0 * t) * t_2)) - (((((5.0 / 6.0) + a) * (3.0 * t)) - 2.0) * (t_2 * ((b - c) * t)))) / (((t * t) * 3.0) * t_2))))));
	else
		tmp = x / (x + (y * exp((2.0 * ((t_1 / t) - ((b - c) * ((a + (5.0 / 6.0)) - (2.0 / (t * 3.0)))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(z * N[Sqrt[N[(t + a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a - N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -2.118326644891581e-50], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(a * c), $MachinePrecision] + N[(0.8333333333333334 * c), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[t, 5.196588770651547e-123], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(N[(t$95$1 * N[(N[(3.0 * t), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(N[(N[(5.0 / 6.0), $MachinePrecision] + a), $MachinePrecision] * N[(3.0 * t), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision] * N[(t$95$2 * N[(N[(b - c), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * t), $MachinePrecision] * 3.0), $MachinePrecision] * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + N[(y * N[Exp[N[(2.0 * N[(N[(t$95$1 / t), $MachinePrecision] - N[(N[(b - c), $MachinePrecision] * N[(N[(a + N[(5.0 / 6.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / N[(t * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, I"
  :precision binary64

  :herbie-target
  (if (< t -2.118326644891581e-50) (/ x (+ x (* y (exp (* 2.0 (- (+ (* a c) (* 0.8333333333333334 c)) (* a b))))))) (if (< t 5.196588770651547e-123) (/ x (+ x (* y (exp (* 2.0 (/ (- (* (* z (sqrt (+ t a))) (* (* 3.0 t) (- a (/ 5.0 6.0)))) (* (- (* (+ (/ 5.0 6.0) a) (* 3.0 t)) 2.0) (* (- a (/ 5.0 6.0)) (* (- b c) t)))) (* (* (* t t) 3.0) (- a (/ 5.0 6.0))))))))) (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0))))))))))))

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