Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A

Percentage Accurate: 98.4% → 98.4%

Time: 24.7s

Alternatives: 21

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = (x * exp((((y * log(z)) + ((t - 1.0d0) * log(a))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + ((t - 1.0) * Math.log(a))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + ((t - 1.0) * math.log(a))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(Float64(t - 1.0) * log(a))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + ((t - 1.0) * log(a))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[(t - 1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot e^{\left(y \cdot \log z + \log a \cdot \left(t - 1\right)\right) - b}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (* x (exp (- (+ (* y (log z)) (* (log a) (- t 1.0))) b))) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * exp((((y * log(z)) + (log(a) * (t - 1.0))) - b))) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = (x * exp((((y * log(z)) + (log(a) * (t - 1.0d0))) - b))) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.exp((((y * Math.log(z)) + (Math.log(a) * (t - 1.0))) - b))) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x * math.exp((((y * math.log(z)) + (math.log(a) * (t - 1.0))) - b))) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) + Float64(log(a) * Float64(t - 1.0))) - b))) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * exp((((y * log(z)) + (log(a) * (t - 1.0))) - b))) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] + N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Final simplification 99.0%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \log a \cdot \left(t - 1\right)\right) - b}}{y} \]

Alternative 2: 92.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+65} \lor \neg \left(y \leq 0.0017\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.85e+65) (not (<= y 0.0017)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.85e+65) || !(y <= 0.0017)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((y <= (-1.85d+65)) .or. (.not. (y <= 0.0017d0))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.85e+65) || !(y <= 0.0017)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.85e+65) or not (y <= 0.0017):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.85e+65) || !(y <= 0.0017))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.85e+65) || ~((y <= 0.0017)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.85e+65], N[Not[LessEqual[y, 0.0017]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.84999999999999997e65 or 0.00169999999999999991 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 90.7%

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

      1. mul-1-neg 90.7%

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

   4. Simplified 90.7%

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

   if -1.84999999999999997e65 < y < 0.00169999999999999991

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 97.4%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+65} \lor \neg \left(y \leq 0.0017\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \]

Alternative 3: 79.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ t_2 := x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{if}\;t \leq -9.5 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+67}:\\ \;\;\;\;\frac{a - a \cdot \frac{x \cdot \frac{y}{x}}{\frac{y}{b}}}{\frac{a \cdot a}{\frac{x}{y}}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow z y) (* y (* a (exp b))))))
        (t_2 (* x (/ (pow a (- t 1.0)) y))))
   (if (<= t -9.5e+144)
     t_2
     (if (<= t -2.5e+71)
       t_1
       (if (<= t -3e+67)
         (/ (- a (* a (/ (* x (/ y x)) (/ y b)))) (/ (* a a) (/ x y)))
         (if (<= t -1.35e-6)
           (/ (* x (/ (pow z y) a)) y)
           (if (<= t 2.65e+19) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(z, y) / (y * (a * exp(b))));
	double t_2 = x * (pow(a, (t - 1.0)) / y);
	double tmp;
	if (t <= -9.5e+144) {
		tmp = t_2;
	} else if (t <= -2.5e+71) {
		tmp = t_1;
	} else if (t <= -3e+67) {
		tmp = (a - (a * ((x * (y / x)) / (y / b)))) / ((a * a) / (x / y));
	} else if (t <= -1.35e-6) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else if (t <= 2.65e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((z ** y) / (y * (a * exp(b))))
    t_2 = x * ((a ** (t - 1.0d0)) / y)
    if (t <= (-9.5d+144)) then
        tmp = t_2
    else if (t <= (-2.5d+71)) then
        tmp = t_1
    else if (t <= (-3d+67)) then
        tmp = (a - (a * ((x * (y / x)) / (y / b)))) / ((a * a) / (x / y))
    else if (t <= (-1.35d-6)) then
        tmp = (x * ((z ** y) / a)) / y
    else if (t <= 2.65d+19) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(z, y) / (y * (a * Math.exp(b))));
	double t_2 = x * (Math.pow(a, (t - 1.0)) / y);
	double tmp;
	if (t <= -9.5e+144) {
		tmp = t_2;
	} else if (t <= -2.5e+71) {
		tmp = t_1;
	} else if (t <= -3e+67) {
		tmp = (a - (a * ((x * (y / x)) / (y / b)))) / ((a * a) / (x / y));
	} else if (t <= -1.35e-6) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else if (t <= 2.65e+19) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(z, y) / (y * (a * math.exp(b))))
	t_2 = x * (math.pow(a, (t - 1.0)) / y)
	tmp = 0
	if t <= -9.5e+144:
		tmp = t_2
	elif t <= -2.5e+71:
		tmp = t_1
	elif t <= -3e+67:
		tmp = (a - (a * ((x * (y / x)) / (y / b)))) / ((a * a) / (x / y))
	elif t <= -1.35e-6:
		tmp = (x * (math.pow(z, y) / a)) / y
	elif t <= 2.65e+19:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((z ^ y) / Float64(y * Float64(a * exp(b)))))
	t_2 = Float64(x * Float64((a ^ Float64(t - 1.0)) / y))
	tmp = 0.0
	if (t <= -9.5e+144)
		tmp = t_2;
	elseif (t <= -2.5e+71)
		tmp = t_1;
	elseif (t <= -3e+67)
		tmp = Float64(Float64(a - Float64(a * Float64(Float64(x * Float64(y / x)) / Float64(y / b)))) / Float64(Float64(a * a) / Float64(x / y)));
	elseif (t <= -1.35e-6)
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	elseif (t <= 2.65e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((z ^ y) / (y * (a * exp(b))));
	t_2 = x * ((a ^ (t - 1.0)) / y);
	tmp = 0.0;
	if (t <= -9.5e+144)
		tmp = t_2;
	elseif (t <= -2.5e+71)
		tmp = t_1;
	elseif (t <= -3e+67)
		tmp = (a - (a * ((x * (y / x)) / (y / b)))) / ((a * a) / (x / y));
	elseif (t <= -1.35e-6)
		tmp = (x * ((z ^ y) / a)) / y;
	elseif (t <= 2.65e+19)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.5e+144], t$95$2, If[LessEqual[t, -2.5e+71], t$95$1, If[LessEqual[t, -3e+67], N[(N[(a - N[(a * N[(N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision] / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(a * a), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-6], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 2.65e+19], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9.50000000000000031e144 or 2.65e19 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

      3. exp-diff 59.6%

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

      4. exp-sum 48.9%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}} \cdot \frac{x}{y} \]

      5. *-commutative 48.9%

         \[\leadsto \frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      6. exp-to-pow 48.9%

         \[\leadsto \frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      7. *-commutative 48.9%

         \[\leadsto \frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      8. exp-to-pow 48.9%

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

   3. Simplified 48.9%

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

   4. Taylor expanded in y around 0 59.7%

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

      1. associate-/l* 58.6%

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

      2. sub-neg 58.6%

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

      3. metadata-eval 58.6%

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

      4. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in b around 0 82.2%

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

   9. Simplified 82.2%

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

   if -9.50000000000000031e144 < t < -2.49999999999999986e71 or -1.34999999999999999e-6 < t < 2.65e19

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.3%

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

      2. sub-neg 98.3%

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

      3. exp-sum 83.3%

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

      4. associate-/l* 83.3%

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

      5. associate-/r/ 79.9%

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

      6. exp-neg 79.9%

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

      7. associate-*r/ 79.9%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in t around 0 86.3%

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

      1. associate-*r* 80.8%

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

      2. *-commutative 80.8%

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

      3. associate-*r* 86.3%

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

   6. Simplified 86.3%

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

   if -2.49999999999999986e71 < t < -3.0000000000000001e67

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

      6. exp-neg 100.0%

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

      7. associate-*r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 3.4%

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

      1. associate-*r* 3.4%

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

      2. *-commutative 3.4%

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

      3. associate-*r* 3.4%

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

   6. Simplified 3.4%

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

   7. Taylor expanded in y around 0 3.4%

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

   8. Taylor expanded in b around 0 3.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 3.4%

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

      2. unsub-neg 3.4%

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

      3. associate-/r* 3.4%

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

      4. *-commutative 3.4%

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

      5. *-commutative 3.4%

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

      6. times-frac 3.4%

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

   10. Simplified 3.4%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]
   11. Step-by-step derivation

       1. associate-/l/ 3.4%

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

       2. clear-num 3.4%

          \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot a}{x}}} - \frac{x}{a} \cdot \frac{b}{y} \]

       3. associate-*l/ 3.4%

          \[\leadsto \frac{1}{\frac{y \cdot a}{x}} - \color{blue}{\frac{x \cdot \frac{b}{y}}{a}} \]

       4. frac-sub 3.4%

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

       5. *-un-lft-identity 3.4%

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

       6. *-commutative 3.4%

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

       7. *-un-lft-identity 3.4%

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

       8. times-frac 3.4%

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

       9. /-rgt-identity 3.4%

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

       10. clear-num 3.4%

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

       11. un-div-inv 3.4%

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

       12. *-commutative 3.4%

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

       13. *-un-lft-identity 3.4%

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

       14. times-frac 3.4%

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

       15. /-rgt-identity 3.4%

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

   12. Applied egg-rr 3.4%

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

       1. associate-*l* 3.4%

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

       2. associate-*r/ 3.4%

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

       3. /-rgt-identity 3.4%

          \[\leadsto \frac{a - a \cdot \frac{\frac{y}{x} \cdot x}{\frac{y}{b}}}{\color{blue}{\frac{a \cdot \frac{y}{x}}{1}} \cdot a} \]

       4. associate-/l* 3.4%

          \[\leadsto \frac{a - a \cdot \frac{\frac{y}{x} \cdot x}{\frac{y}{b}}}{\color{blue}{\frac{a}{\frac{1}{\frac{y}{x}}}} \cdot a} \]

       5. associate-*l/ 100.0%

          \[\leadsto \frac{a - a \cdot \frac{\frac{y}{x} \cdot x}{\frac{y}{b}}}{\color{blue}{\frac{a \cdot a}{\frac{1}{\frac{y}{x}}}}} \]

       6. associate-/r/ 100.0%

          \[\leadsto \frac{a - a \cdot \frac{\frac{y}{x} \cdot x}{\frac{y}{b}}}{\frac{a \cdot a}{\color{blue}{\frac{1}{y} \cdot x}}} \]

       7. associate-*l/ 100.0%

          \[\leadsto \frac{a - a \cdot \frac{\frac{y}{x} \cdot x}{\frac{y}{b}}}{\frac{a \cdot a}{\color{blue}{\frac{1 \cdot x}{y}}}} \]

       8. *-lft-identity 100.0%

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

   14. Simplified 100.0%

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

   if -3.0000000000000001e67 < t < -1.34999999999999999e-6

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 79.2%

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

      1. mul-1-neg 79.2%

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

   4. Simplified 79.2%

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

   5. Taylor expanded in b around 0 72.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 72.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 72.2%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 72.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 72.2%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 72.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{+67}:\\ \;\;\;\;\frac{a - a \cdot \frac{x \cdot \frac{y}{x}}{\frac{y}{b}}}{\frac{a \cdot a}{\frac{x}{y}}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \end{array} \]

Alternative 4: 88.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+133} \lor \neg \left(y \leq 0.0017\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e+133) (not (<= y 0.0017)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (log a) (- t 1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+133) || !(y <= 0.0017)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((y <= (-3d+133)) .or. (.not. (y <= 0.0017d0))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp(((log(a) * (t - 1.0d0)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+133) || !(y <= 0.0017)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t - 1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3e+133) or not (y <= 0.0017):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t - 1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3e+133) || !(y <= 0.0017))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t - 1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3e+133) || ~((y <= 0.0017)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp(((log(a) * (t - 1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3e+133], N[Not[LessEqual[y, 0.0017]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t - 1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000007e133 or 0.00169999999999999991 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 91.6%

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

      1. mul-1-neg 91.6%

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

   4. Simplified 91.6%

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

   5. Taylor expanded in b around 0 87.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 87.0%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 87.0%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 87.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 87.0%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 87.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   if -3.00000000000000007e133 < y < 0.00169999999999999991

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in y around 0 95.0%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+133} \lor \neg \left(y \leq 0.0017\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}{y}\\ \end{array} \]

Alternative 5: 80.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+144} \lor \neg \left(t \leq 2.3 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.32e+144) (not (<= t 2.3e+20)))
   (* x (/ (pow a (- t 1.0)) y))
   (* (/ (pow z y) y) (/ x (* a (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.32e+144) || !(t <= 2.3e+20)) {
		tmp = x * (pow(a, (t - 1.0)) / y);
	} else {
		tmp = (pow(z, y) / y) * (x / (a * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((t <= (-1.32d+144)) .or. (.not. (t <= 2.3d+20))) then
        tmp = x * ((a ** (t - 1.0d0)) / y)
    else
        tmp = ((z ** y) / y) * (x / (a * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.32e+144) || !(t <= 2.3e+20)) {
		tmp = x * (Math.pow(a, (t - 1.0)) / y);
	} else {
		tmp = (Math.pow(z, y) / y) * (x / (a * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.32e+144) or not (t <= 2.3e+20):
		tmp = x * (math.pow(a, (t - 1.0)) / y)
	else:
		tmp = (math.pow(z, y) / y) * (x / (a * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.32e+144) || !(t <= 2.3e+20))
		tmp = Float64(x * Float64((a ^ Float64(t - 1.0)) / y));
	else
		tmp = Float64(Float64((z ^ y) / y) * Float64(x / Float64(a * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.32e+144) || ~((t <= 2.3e+20)))
		tmp = x * ((a ^ (t - 1.0)) / y);
	else
		tmp = ((z ^ y) / y) * (x / (a * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.32e+144], N[Not[LessEqual[t, 2.3e+20]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / y), $MachinePrecision] * N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.32e144 or 2.3e20 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

      3. exp-diff 59.6%

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

      4. exp-sum 48.9%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}} \cdot \frac{x}{y} \]

      5. *-commutative 48.9%

         \[\leadsto \frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      6. exp-to-pow 48.9%

         \[\leadsto \frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      7. *-commutative 48.9%

         \[\leadsto \frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      8. exp-to-pow 48.9%

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

   3. Simplified 48.9%

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

   4. Taylor expanded in y around 0 59.7%

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

      1. associate-/l* 58.6%

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

      2. sub-neg 58.6%

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

      3. metadata-eval 58.6%

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

      4. associate-/l* 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in b around 0 82.2%

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

   9. Simplified 82.2%

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

   if -1.32e144 < t < 2.3e20

   1. Initial program 98.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.5%

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

      2. sub-neg 98.5%

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

      3. exp-sum 83.7%

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

      4. associate-/l* 83.7%

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

      5. associate-/r/ 80.6%

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

      6. exp-neg 80.6%

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

      7. associate-*r/ 80.6%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in t around 0 82.4%

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

      1. times-frac 83.2%

         \[\leadsto \color{blue}{\frac{{z}^{y}}{y} \cdot \frac{x}{a \cdot e^{b}}} \]

   6. Simplified 83.2%

      \[\leadsto \color{blue}{\frac{{z}^{y}}{y} \cdot \frac{x}{a \cdot e^{b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.32 \cdot 10^{+144} \lor \neg \left(t \leq 2.3 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{y} \cdot \frac{x}{a \cdot e^{b}}\\ \end{array} \]

Alternative 6: 81.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -52 \lor \neg \left(y \leq 2.1 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -52.0) (not (<= y 2.1e-17)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (pow a t)) (* y (* a (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -52.0) || !(y <= 2.1e-17)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * pow(a, t)) / (y * (a * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((y <= (-52.0d0)) .or. (.not. (y <= 2.1d-17))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * (a ** t)) / (y * (a * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -52.0) || !(y <= 2.1e-17)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.pow(a, t)) / (y * (a * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -52.0) or not (y <= 2.1e-17):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.pow(a, t)) / (y * (a * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -52.0) || !(y <= 2.1e-17))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * Float64(a * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -52.0) || ~((y <= 2.1e-17)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * (a ^ t)) / (y * (a * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -52.0], N[Not[LessEqual[y, 2.1e-17]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -52 or 2.09999999999999992e-17 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 88.2%

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

      1. mul-1-neg 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in b around 0 84.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 84.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 84.3%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 84.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 84.4%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 84.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   if -52 < y < 2.09999999999999992e-17

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.2%

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

      2. sub-neg 98.2%

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

      3. exp-sum 85.1%

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

      4. associate-/l* 85.1%

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

      5. associate-/r/ 81.3%

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

      6. exp-neg 81.3%

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

      7. associate-*r/ 81.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in y around 0 83.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -52 \lor \neg \left(y \leq 2.1 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]

Alternative 7: 81.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13500 \lor \neg \left(y \leq 2.1 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{\frac{y}{\frac{x}{e^{b}}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -13500.0) (not (<= y 2.1e-17)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (pow a (- t 1.0)) (/ y (/ x (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -13500.0) || !(y <= 2.1e-17)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = pow(a, (t - 1.0)) / (y / (x / exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((y <= (-13500.0d0)) .or. (.not. (y <= 2.1d-17))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (a ** (t - 1.0d0)) / (y / (x / exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -13500.0) || !(y <= 2.1e-17)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = Math.pow(a, (t - 1.0)) / (y / (x / Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -13500.0) or not (y <= 2.1e-17):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = math.pow(a, (t - 1.0)) / (y / (x / math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -13500.0) || !(y <= 2.1e-17))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64((a ^ Float64(t - 1.0)) / Float64(y / Float64(x / exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -13500.0) || ~((y <= 2.1e-17)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (a ^ (t - 1.0)) / (y / (x / exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -13500.0], N[Not[LessEqual[y, 2.1e-17]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / N[(y / N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -13500 or 2.09999999999999992e-17 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 88.2%

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

      1. mul-1-neg 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in b around 0 84.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 84.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 84.3%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 84.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 84.4%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 84.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   if -13500 < y < 2.09999999999999992e-17

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.6%

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

      2. *-commutative 90.6%

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

      3. exp-diff 78.3%

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

      4. exp-sum 78.3%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}} \cdot \frac{x}{y} \]

      5. *-commutative 78.3%

         \[\leadsto \frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      6. exp-to-pow 78.3%

         \[\leadsto \frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      7. *-commutative 78.3%

         \[\leadsto \frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      8. exp-to-pow 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in y around 0 81.3%

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

      1. associate-/l* 84.6%

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

      2. sub-neg 84.6%

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

      3. metadata-eval 84.6%

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

      4. associate-/l* 84.6%

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

   6. Simplified 84.6%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13500 \lor \neg \left(y \leq 2.1 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t - 1\right)}}{\frac{y}{\frac{x}{e^{b}}}}\\ \end{array} \]

Alternative 8: 75.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ t_2 := \frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ t_3 := \frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{if}\;y \leq -1800:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-249}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-150}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-18}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a (- t 1.0)) y)))
        (t_2 (/ (* x (/ (pow z y) a)) y))
        (t_3 (/ (/ x (* a (exp b))) y)))
   (if (<= y -1800.0)
     t_2
     (if (<= y -2.2e-249)
       t_1
       (if (<= y 3.5e-150)
         t_3
         (if (<= y 1e-67) t_1 (if (<= y 6.7e-18) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, (t - 1.0)) / y);
	double t_2 = (x * (pow(z, y) / a)) / y;
	double t_3 = (x / (a * exp(b))) / y;
	double tmp;
	if (y <= -1800.0) {
		tmp = t_2;
	} else if (y <= -2.2e-249) {
		tmp = t_1;
	} else if (y <= 3.5e-150) {
		tmp = t_3;
	} else if (y <= 1e-67) {
		tmp = t_1;
	} else if (y <= 6.7e-18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((a ** (t - 1.0d0)) / y)
    t_2 = (x * ((z ** y) / a)) / y
    t_3 = (x / (a * exp(b))) / y
    if (y <= (-1800.0d0)) then
        tmp = t_2
    else if (y <= (-2.2d-249)) then
        tmp = t_1
    else if (y <= 3.5d-150) then
        tmp = t_3
    else if (y <= 1d-67) then
        tmp = t_1
    else if (y <= 6.7d-18) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (Math.pow(a, (t - 1.0)) / y);
	double t_2 = (x * (Math.pow(z, y) / a)) / y;
	double t_3 = (x / (a * Math.exp(b))) / y;
	double tmp;
	if (y <= -1800.0) {
		tmp = t_2;
	} else if (y <= -2.2e-249) {
		tmp = t_1;
	} else if (y <= 3.5e-150) {
		tmp = t_3;
	} else if (y <= 1e-67) {
		tmp = t_1;
	} else if (y <= 6.7e-18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, (t - 1.0)) / y)
	t_2 = (x * (math.pow(z, y) / a)) / y
	t_3 = (x / (a * math.exp(b))) / y
	tmp = 0
	if y <= -1800.0:
		tmp = t_2
	elif y <= -2.2e-249:
		tmp = t_1
	elif y <= 3.5e-150:
		tmp = t_3
	elif y <= 1e-67:
		tmp = t_1
	elif y <= 6.7e-18:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ Float64(t - 1.0)) / y))
	t_2 = Float64(Float64(x * Float64((z ^ y) / a)) / y)
	t_3 = Float64(Float64(x / Float64(a * exp(b))) / y)
	tmp = 0.0
	if (y <= -1800.0)
		tmp = t_2;
	elseif (y <= -2.2e-249)
		tmp = t_1;
	elseif (y <= 3.5e-150)
		tmp = t_3;
	elseif (y <= 1e-67)
		tmp = t_1;
	elseif (y <= 6.7e-18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * ((a ^ (t - 1.0)) / y);
	t_2 = (x * ((z ^ y) / a)) / y;
	t_3 = (x / (a * exp(b))) / y;
	tmp = 0.0;
	if (y <= -1800.0)
		tmp = t_2;
	elseif (y <= -2.2e-249)
		tmp = t_1;
	elseif (y <= 3.5e-150)
		tmp = t_3;
	elseif (y <= 1e-67)
		tmp = t_1;
	elseif (y <= 6.7e-18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -1800.0], t$95$2, If[LessEqual[y, -2.2e-249], t$95$1, If[LessEqual[y, 3.5e-150], t$95$3, If[LessEqual[y, 1e-67], t$95$1, If[LessEqual[y, 6.7e-18], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1800 or 6.6999999999999998e-18 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 87.6%

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

      1. mul-1-neg 87.6%

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

   4. Simplified 87.6%

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

   5. Taylor expanded in b around 0 83.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 83.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 83.7%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 83.7%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 83.7%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 83.7%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   if -1800 < y < -2.2e-249 or 3.4999999999999998e-150 < y < 9.99999999999999943e-68

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.6%

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

      2. *-commutative 90.6%

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

      3. exp-diff 79.1%

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

      4. exp-sum 79.1%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}} \cdot \frac{x}{y} \]

      5. *-commutative 79.1%

         \[\leadsto \frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      6. exp-to-pow 79.1%

         \[\leadsto \frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      7. *-commutative 79.1%

         \[\leadsto \frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      8. exp-to-pow 80.0%

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

   3. Simplified 80.0%

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

   4. Taylor expanded in y around 0 82.5%

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

      1. associate-/l* 84.3%

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

      2. sub-neg 84.3%

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

      3. metadata-eval 84.3%

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

      4. associate-/l* 84.3%

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

   6. Simplified 84.3%

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

   7. Taylor expanded in b around 0 81.5%

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

   9. Simplified 83.2%

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

   if -2.2e-249 < y < 3.4999999999999998e-150 or 9.99999999999999943e-68 < y < 6.6999999999999998e-18

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 83.7%

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

      1. mul-1-neg 83.7%

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

   4. Simplified 83.7%

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

   5. Taylor expanded in y around 0 83.7%

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

      1. exp-neg 83.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 83.7%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 83.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 83.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 83.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 85.0%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 85.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1800:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-249}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 10^{-67}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 9: 75.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -45000000000 \lor \neg \left(t \leq 1.95 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -45000000000.0) (not (<= t 1.95e+17)))
   (* x (/ (pow a (- t 1.0)) y))
   (/ x (* y (* a (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -45000000000.0) || !(t <= 1.95e+17)) {
		tmp = x * (pow(a, (t - 1.0)) / y);
	} else {
		tmp = x / (y * (a * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((t <= (-45000000000.0d0)) .or. (.not. (t <= 1.95d+17))) then
        tmp = x * ((a ** (t - 1.0d0)) / y)
    else
        tmp = x / (y * (a * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -45000000000.0) || !(t <= 1.95e+17)) {
		tmp = x * (Math.pow(a, (t - 1.0)) / y);
	} else {
		tmp = x / (y * (a * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -45000000000.0) or not (t <= 1.95e+17):
		tmp = x * (math.pow(a, (t - 1.0)) / y)
	else:
		tmp = x / (y * (a * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -45000000000.0) || !(t <= 1.95e+17))
		tmp = Float64(x * Float64((a ^ Float64(t - 1.0)) / y));
	else
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -45000000000.0) || ~((t <= 1.95e+17)))
		tmp = x * ((a ^ (t - 1.0)) / y);
	else
		tmp = x / (y * (a * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -45000000000.0], N[Not[LessEqual[t, 1.95e+17]], $MachinePrecision]], N[(x * N[(N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e10 or 1.95e17 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 91.5%

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

      2. *-commutative 91.5%

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

      3. exp-diff 62.0%

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

      4. exp-sum 49.6%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}} \cdot \frac{x}{y} \]

      5. *-commutative 49.6%

         \[\leadsto \frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      6. exp-to-pow 49.6%

         \[\leadsto \frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      7. *-commutative 49.6%

         \[\leadsto \frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      8. exp-to-pow 49.6%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in y around 0 58.3%

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

      1. associate-/l* 56.7%

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

      2. sub-neg 56.7%

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

      3. metadata-eval 56.7%

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

      4. associate-/l* 56.7%

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

   6. Simplified 56.7%

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

   7. Taylor expanded in b around 0 75.6%

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

   9. Simplified 75.6%

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

   if -4.5e10 < t < 1.95e17

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.1%

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

      2. sub-neg 98.1%

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

      3. exp-sum 85.5%

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

      4. associate-/l* 85.5%

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

      5. associate-/r/ 81.6%

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

      6. exp-neg 81.6%

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

      7. associate-*r/ 81.6%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in t around 0 86.6%

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

      1. associate-*r* 81.9%

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

      2. *-commutative 81.9%

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

      3. associate-*r* 86.6%

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

   6. Simplified 86.6%

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

   7. Taylor expanded in y around 0 76.3%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -45000000000 \lor \neg \left(t \leq 1.95 \cdot 10^{+17}\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]

Alternative 10: 56.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-111} \lor \neg \left(b \leq 2.2 \cdot 10^{-240}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{a}}{y} \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.1e-111) (not (<= b 2.2e-240)))
   (/ x (* y (* a (exp b))))
   (- (* (/ (/ x a) y) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e-111) || !(b <= 2.2e-240)) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = -(((x / a) / y) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if ((b <= (-1.1d-111)) .or. (.not. (b <= 2.2d-240))) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = -(((x / a) / y) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.1e-111) || !(b <= 2.2e-240)) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = -(((x / a) / y) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.1e-111) or not (b <= 2.2e-240):
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = -(((x / a) / y) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.1e-111) || !(b <= 2.2e-240))
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(-Float64(Float64(Float64(x / a) / y) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.1e-111) || ~((b <= 2.2e-240)))
		tmp = x / (y * (a * exp(b)));
	else
		tmp = -(((x / a) / y) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.1e-111], N[Not[LessEqual[b, 2.2e-240]], $MachinePrecision]], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision] * b), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if b < -1.1e-111 or 2.1999999999999999e-240 < b

   1. Initial program 99.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.9%

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

      2. sub-neg 98.9%

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

      3. exp-sum 71.4%

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

      4. associate-/l* 71.4%

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

      5. associate-/r/ 68.9%

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

      6. exp-neg 68.9%

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

      7. associate-*r/ 68.9%

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

   3. Simplified 62.0%

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

   4. Taylor expanded in t around 0 69.3%

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

      1. associate-*r* 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-*r* 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in y around 0 64.9%

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

   if -1.1e-111 < b < 2.1999999999999999e-240

   1. Initial program 97.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.5%

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

      2. sub-neg 99.5%

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

      3. exp-sum 99.5%

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

      4. associate-/l* 99.5%

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

      5. associate-/r/ 99.5%

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

      6. exp-neg 99.5%

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

      7. associate-*r/ 99.5%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in t around 0 59.5%

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

      1. associate-*r* 59.5%

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

      2. *-commutative 59.5%

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

      3. associate-*r* 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in y around 0 28.4%

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

   8. Taylor expanded in b around 0 26.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 26.5%

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

      2. unsub-neg 26.5%

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

      3. associate-/r* 29.6%

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

      4. *-commutative 29.6%

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

      5. *-commutative 29.6%

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

      6. times-frac 29.4%

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

   10. Simplified 29.4%

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

   11. Taylor expanded in b around inf 39.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. mul-1-neg 39.4%

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

       2. associate-*r/ 41.9%

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

       3. associate-/r* 43.9%

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

       4. distribute-rgt-neg-in 43.9%

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

       5. distribute-frac-neg 43.9%

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

       6. distribute-frac-neg 43.9%

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

   13. Simplified 43.9%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-111} \lor \neg \left(b \leq 2.2 \cdot 10^{-240}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{a}}{y} \cdot b\\ \end{array} \]

Alternative 11: 58.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a \cdot e^{b}}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x (* a (exp b))) y))

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = (x / (a * exp(b))) / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in t around 0 80.6%

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

   1. mul-1-neg 80.6%

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

4. Simplified 80.6%

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

5. Taylor expanded in y around 0 58.1%

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

   1. exp-neg 58.1%

      \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

   2. associate-*l/ 58.1%

      \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

   3. *-lft-identity 58.1%

      \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

   4. +-commutative 58.1%

      \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

   5. exp-sum 58.1%

      \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

   6. rem-exp-log 58.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

7. Simplified 58.6%

   \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

8. Final simplification 58.6%

   \[\leadsto \frac{\frac{x}{a \cdot e^{b}}}{y} \]

Alternative 12: 34.5% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{a \cdot \left(x - y \cdot \left(x \cdot \frac{b}{y}\right)\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 4.5e-239)
   (/ 1.0 (* a (/ y x)))
   (if (<= a 6.8e-63)
     (/ (* a (- x (* y (* x (/ b y))))) (* y (* a a)))
     (if (<= a 8e+249)
       (/ x (* a (* y (+ 1.0 b))))
       (/ (- (/ x y) (/ x (/ y b))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4.5e-239) {
		tmp = 1.0 / (a * (y / x));
	} else if (a <= 6.8e-63) {
		tmp = (a * (x - (y * (x * (b / y))))) / (y * (a * a));
	} else if (a <= 8e+249) {
		tmp = x / (a * (y * (1.0 + b)));
	} else {
		tmp = ((x / y) - (x / (y / b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= 4.5d-239) then
        tmp = 1.0d0 / (a * (y / x))
    else if (a <= 6.8d-63) then
        tmp = (a * (x - (y * (x * (b / y))))) / (y * (a * a))
    else if (a <= 8d+249) then
        tmp = x / (a * (y * (1.0d0 + b)))
    else
        tmp = ((x / y) - (x / (y / b))) / 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 tmp;
	if (a <= 4.5e-239) {
		tmp = 1.0 / (a * (y / x));
	} else if (a <= 6.8e-63) {
		tmp = (a * (x - (y * (x * (b / y))))) / (y * (a * a));
	} else if (a <= 8e+249) {
		tmp = x / (a * (y * (1.0 + b)));
	} else {
		tmp = ((x / y) - (x / (y / b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 4.5e-239:
		tmp = 1.0 / (a * (y / x))
	elif a <= 6.8e-63:
		tmp = (a * (x - (y * (x * (b / y))))) / (y * (a * a))
	elif a <= 8e+249:
		tmp = x / (a * (y * (1.0 + b)))
	else:
		tmp = ((x / y) - (x / (y / b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 4.5e-239)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (a <= 6.8e-63)
		tmp = Float64(Float64(a * Float64(x - Float64(y * Float64(x * Float64(b / y))))) / Float64(y * Float64(a * a)));
	elseif (a <= 8e+249)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	else
		tmp = Float64(Float64(Float64(x / y) - Float64(x / Float64(y / b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 4.5e-239)
		tmp = 1.0 / (a * (y / x));
	elseif (a <= 6.8e-63)
		tmp = (a * (x - (y * (x * (b / y))))) / (y * (a * a));
	elseif (a <= 8e+249)
		tmp = x / (a * (y * (1.0 + b)));
	else
		tmp = ((x / y) - (x / (y / b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 4.5e-239], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-63], N[(N[(a * N[(x - N[(y * N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e+249], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] - N[(x / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 4.50000000000000013e-239

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

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

      2. *-commutative 89.1%

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

      3. exp-diff 74.8%

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

      4. exp-sum 67.5%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}} \cdot \frac{x}{y} \]

      5. *-commutative 67.5%

         \[\leadsto \frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      6. exp-to-pow 67.5%

         \[\leadsto \frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      7. *-commutative 67.5%

         \[\leadsto \frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      8. exp-to-pow 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in y around 0 57.8%

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

      1. associate-/l* 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. associate-/l* 67.8%

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

   6. Simplified 67.8%

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

   7. Taylor expanded in b around 0 65.0%

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

   9. Simplified 61.5%

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

   10. Taylor expanded in t around 0 43.4%

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

       1. *-commutative 43.4%

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

   12. Simplified 43.4%

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

       1. associate-*l/ 43.4%

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

       2. times-frac 53.7%

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

       3. associate-/r/ 54.6%

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

       4. associate-/l* 44.4%

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

       5. *-commutative 44.4%

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

       6. *-un-lft-identity 44.4%

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

       7. times-frac 58.0%

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

       8. /-rgt-identity 58.0%

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

   14. Applied egg-rr 58.0%

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

   if 4.50000000000000013e-239 < a < 6.79999999999999997e-63

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.5%

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

      2. sub-neg 98.5%

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

      3. exp-sum 75.6%

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

      4. associate-/l* 75.6%

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

      5. associate-/r/ 68.5%

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

      6. exp-neg 68.5%

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

      7. associate-*r/ 68.5%

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

   3. Simplified 61.5%

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

   4. Taylor expanded in t around 0 74.6%

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

      1. associate-*r* 64.6%

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

      2. *-commutative 64.6%

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

      3. associate-*r* 74.6%

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

   6. Simplified 74.6%

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

   7. Taylor expanded in y around 0 61.1%

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

   8. Taylor expanded in b around 0 26.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 26.1%

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

      2. unsub-neg 26.1%

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

      3. associate-/r* 28.9%

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

      4. *-commutative 28.9%

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

      5. *-commutative 28.9%

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

      6. times-frac 26.1%

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

   10. Simplified 26.1%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]
   11. Step-by-step derivation

       1. associate-/l/ 26.1%

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

       2. associate-*l/ 27.7%

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

       3. frac-sub 27.3%

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

       4. *-commutative 27.3%

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

       5. clear-num 27.3%

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

       6. un-div-inv 27.4%

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

       7. *-commutative 27.4%

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

   12. Applied egg-rr 27.4%

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

       1. *-commutative 27.4%

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

       2. associate-*l* 35.8%

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

       3. distribute-lft-out-- 35.8%

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

       4. associate-/r/ 35.8%

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

       5. associate-*l/ 35.8%

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

       6. associate-*r/ 35.8%

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

       7. *-commutative 35.8%

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

       8. associate-*r* 42.6%

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

   14. Simplified 42.6%

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

   if 6.79999999999999997e-63 < a < 7.9999999999999994e249

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 78.7%

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

      1. mul-1-neg 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in y around 0 56.1%

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

      1. exp-neg 56.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 56.1%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 56.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 56.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 56.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 56.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 56.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 38.9%

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

   9. Taylor expanded in a around 0 40.1%

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

   if 7.9999999999999994e249 < a

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 74.2%

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

      4. associate-/l* 74.2%

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

      5. associate-/r/ 74.2%

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

      6. exp-neg 74.2%

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

      7. associate-*r/ 74.2%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around 0 59.3%

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

      1. associate-*r* 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*r* 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in y around 0 59.6%

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

   8. Taylor expanded in b around 0 39.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 39.6%

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

      2. unsub-neg 39.6%

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

      3. associate-/r* 39.7%

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

      4. *-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. times-frac 46.7%

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

   10. Simplified 46.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]
   11. Step-by-step derivation

       1. associate-/l/ 43.3%

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

       2. associate-/r* 40.0%

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

       3. associate-*l/ 57.0%

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

       4. sub-div 57.0%

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

       5. clear-num 57.0%

          \[\leadsto \frac{\frac{x}{y} - x \cdot \color{blue}{\frac{1}{\frac{y}{b}}}}{a} \]

       6. un-div-inv 57.0%

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

   12. Applied egg-rr 57.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{a \cdot \left(x - y \cdot \left(x \cdot \frac{b}{y}\right)\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \end{array} \]

Alternative 13: 34.8% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{-202}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-64}:\\ \;\;\;\;\frac{a \cdot \left(\frac{x}{y} - x \cdot \frac{b}{y}\right)}{a \cdot a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1e-202)
   (/ 1.0 (* a (/ y x)))
   (if (<= a 2.4e-64)
     (/ (* a (- (/ x y) (* x (/ b y)))) (* a a))
     (if (<= a 8.5e+249)
       (/ x (* a (* y (+ 1.0 b))))
       (/ (- (/ x y) (/ x (/ y b))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-202) {
		tmp = 1.0 / (a * (y / x));
	} else if (a <= 2.4e-64) {
		tmp = (a * ((x / y) - (x * (b / y)))) / (a * a);
	} else if (a <= 8.5e+249) {
		tmp = x / (a * (y * (1.0 + b)));
	} else {
		tmp = ((x / y) - (x / (y / b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= 1d-202) then
        tmp = 1.0d0 / (a * (y / x))
    else if (a <= 2.4d-64) then
        tmp = (a * ((x / y) - (x * (b / y)))) / (a * a)
    else if (a <= 8.5d+249) then
        tmp = x / (a * (y * (1.0d0 + b)))
    else
        tmp = ((x / y) - (x / (y / b))) / 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 tmp;
	if (a <= 1e-202) {
		tmp = 1.0 / (a * (y / x));
	} else if (a <= 2.4e-64) {
		tmp = (a * ((x / y) - (x * (b / y)))) / (a * a);
	} else if (a <= 8.5e+249) {
		tmp = x / (a * (y * (1.0 + b)));
	} else {
		tmp = ((x / y) - (x / (y / b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1e-202:
		tmp = 1.0 / (a * (y / x))
	elif a <= 2.4e-64:
		tmp = (a * ((x / y) - (x * (b / y)))) / (a * a)
	elif a <= 8.5e+249:
		tmp = x / (a * (y * (1.0 + b)))
	else:
		tmp = ((x / y) - (x / (y / b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1e-202)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (a <= 2.4e-64)
		tmp = Float64(Float64(a * Float64(Float64(x / y) - Float64(x * Float64(b / y)))) / Float64(a * a));
	elseif (a <= 8.5e+249)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	else
		tmp = Float64(Float64(Float64(x / y) - Float64(x / Float64(y / b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1e-202)
		tmp = 1.0 / (a * (y / x));
	elseif (a <= 2.4e-64)
		tmp = (a * ((x / y) - (x * (b / y)))) / (a * a);
	elseif (a <= 8.5e+249)
		tmp = x / (a * (y * (1.0 + b)));
	else
		tmp = ((x / y) - (x / (y / b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1e-202], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.4e-64], N[(N[(a * N[(N[(x / y), $MachinePrecision] - N[(x * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.5e+249], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] - N[(x / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < 1e-202

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*l/ 92.2%

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

      2. *-commutative 92.2%

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

      3. exp-diff 76.8%

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

      4. exp-sum 71.5%

         \[\leadsto \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}} \cdot \frac{x}{y} \]

      5. *-commutative 71.5%

         \[\leadsto \frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      6. exp-to-pow 71.5%

         \[\leadsto \frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}} \cdot \frac{x}{y} \]

      7. *-commutative 71.5%

         \[\leadsto \frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}} \cdot \frac{x}{y} \]

      8. exp-to-pow 71.8%

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

   3. Simplified 71.8%

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

   4. Taylor expanded in y around 0 64.6%

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

      1. associate-/l* 69.4%

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

      2. sub-neg 69.4%

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

      3. metadata-eval 69.4%

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

      4. associate-/l* 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in b around 0 64.8%

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

   9. Simplified 59.9%

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

   10. Taylor expanded in t around 0 36.9%

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

       1. *-commutative 36.9%

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

   12. Simplified 36.9%

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

       1. associate-*l/ 36.9%

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

       2. times-frac 46.7%

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

       3. associate-/r/ 47.4%

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

       4. associate-/l* 37.6%

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

       5. *-commutative 37.6%

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

       6. *-un-lft-identity 37.6%

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

       7. times-frac 49.8%

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

       8. /-rgt-identity 49.8%

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

   14. Applied egg-rr 49.8%

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

   if 1e-202 < a < 2.39999999999999998e-64

   1. Initial program 99.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.2%

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

      2. sub-neg 98.2%

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

      3. exp-sum 74.4%

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

      4. associate-/l* 74.4%

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

      5. associate-/r/ 69.4%

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

      6. exp-neg 69.4%

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

      7. associate-*r/ 69.4%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in t around 0 73.3%

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

      1. associate-*r* 64.7%

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

      2. *-commutative 64.7%

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

      3. associate-*r* 73.3%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in y around 0 63.8%

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

   8. Taylor expanded in b around 0 27.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 27.1%

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

      2. unsub-neg 27.1%

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

      3. associate-/r* 28.8%

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

      4. *-commutative 28.8%

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

      5. *-commutative 28.8%

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

      6. times-frac 27.3%

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

   10. Simplified 27.3%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]
   11. Step-by-step derivation

       1. associate-/l/ 27.2%

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

       2. associate-/r* 28.8%

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

       3. associate-*l/ 30.6%

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

       4. frac-sub 41.7%

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

       5. clear-num 41.7%

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

       6. un-div-inv 41.7%

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

   12. Applied egg-rr 41.7%

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

       1. *-commutative 41.7%

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

       2. distribute-lft-out-- 41.7%

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

       3. associate-/r/ 40.0%

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

       4. associate-*l/ 43.3%

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

       5. associate-*r/ 41.7%

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

   14. Simplified 41.7%

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

   if 2.39999999999999998e-64 < a < 8.49999999999999933e249

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 78.7%

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

      1. mul-1-neg 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in y around 0 56.1%

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

      1. exp-neg 56.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 56.1%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 56.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 56.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 56.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 56.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 56.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 38.9%

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

   9. Taylor expanded in a around 0 40.1%

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

   if 8.49999999999999933e249 < a

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 74.2%

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

      4. associate-/l* 74.2%

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

      5. associate-/r/ 74.2%

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

      6. exp-neg 74.2%

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

      7. associate-*r/ 74.2%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around 0 59.3%

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

      1. associate-*r* 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*r* 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in y around 0 59.6%

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

   8. Taylor expanded in b around 0 39.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 39.6%

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

      2. unsub-neg 39.6%

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

      3. associate-/r* 39.7%

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

      4. *-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. times-frac 46.7%

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

   10. Simplified 46.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]
   11. Step-by-step derivation

       1. associate-/l/ 43.3%

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

       2. associate-/r* 40.0%

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

       3. associate-*l/ 57.0%

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

       4. sub-div 57.0%

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

       5. clear-num 57.0%

          \[\leadsto \frac{\frac{x}{y} - x \cdot \color{blue}{\frac{1}{\frac{y}{b}}}}{a} \]

       6. un-div-inv 57.0%

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

   12. Applied egg-rr 57.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{-202}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-64}:\\ \;\;\;\;\frac{a \cdot \left(\frac{x}{y} - x \cdot \frac{b}{y}\right)}{a \cdot a}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \end{array} \]

Alternative 14: 38.9% accurate, 16.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a} + x \cdot \frac{b \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 1.55e+142)
   (/ (+ (/ (- x (* x b)) a) (* x (/ (* b b) a))) y)
   (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.55e+142) {
		tmp = (((x - (x * b)) / a) + (x * ((b * b) / a))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (y <= 1.55d+142) then
        tmp = (((x - (x * b)) / a) + (x * ((b * b) / a))) / y
    else
        tmp = x / (a * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= 1.55e+142) {
		tmp = (((x - (x * b)) / a) + (x * ((b * b) / a))) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= 1.55e+142:
		tmp = (((x - (x * b)) / a) + (x * ((b * b) / a))) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= 1.55e+142)
		tmp = Float64(Float64(Float64(Float64(x - Float64(x * b)) / a) + Float64(x * Float64(Float64(b * b) / a))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= 1.55e+142)
		tmp = (((x - (x * b)) / a) + (x * ((b * b) / a))) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, 1.55e+142], N[(N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] + N[(x * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.55e142

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 77.3%

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

      1. mul-1-neg 77.3%

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

   4. Simplified 77.3%

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

   5. Taylor expanded in y around 0 60.4%

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

      1. exp-neg 60.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 60.4%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 60.4%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 60.4%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 60.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 61.0%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 61.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 34.1%

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

   9. Taylor expanded in b around 0 42.9%

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

       1. +-commutative 42.9%

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

       2. +-commutative 42.9%

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

       3. mul-1-neg 42.9%

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

       4. sub-neg 42.9%

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

       5. *-commutative 42.9%

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

       6. div-sub 43.8%

          \[\leadsto \frac{\color{blue}{\frac{x - x \cdot b}{a}} + \frac{{b}^{2} \cdot x}{a}}{y} \]

       7. associate-/l* 38.1%

          \[\leadsto \frac{\frac{x - x \cdot b}{a} + \color{blue}{\frac{{b}^{2}}{\frac{a}{x}}}}{y} \]

       8. associate-/r/ 43.3%

          \[\leadsto \frac{\frac{x - x \cdot b}{a} + \color{blue}{\frac{{b}^{2}}{a} \cdot x}}{y} \]

       9. unpow2 43.3%

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

   11. Simplified 43.3%

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

   if 1.55e142 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 97.7%

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

      1. mul-1-neg 97.7%

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

   4. Simplified 97.7%

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

   5. Taylor expanded in y around 0 46.7%

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

      1. exp-neg 46.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 46.7%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 46.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 46.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 46.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 46.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 46.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 33.3%

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

   9. Taylor expanded in a around 0 44.5%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.55 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a} + x \cdot \frac{b \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 15: 35.2% accurate, 20.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 3.1e-50)
   (/ (/ (- x (* x b)) a) y)
   (if (<= a 9.2e+249)
     (/ x (* a (* y (+ 1.0 b))))
     (/ (- (/ x y) (/ x (/ y b))) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 3.1e-50) {
		tmp = ((x - (x * b)) / a) / y;
	} else if (a <= 9.2e+249) {
		tmp = x / (a * (y * (1.0 + b)));
	} else {
		tmp = ((x / y) - (x / (y / b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= 3.1d-50) then
        tmp = ((x - (x * b)) / a) / y
    else if (a <= 9.2d+249) then
        tmp = x / (a * (y * (1.0d0 + b)))
    else
        tmp = ((x / y) - (x / (y / b))) / 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 tmp;
	if (a <= 3.1e-50) {
		tmp = ((x - (x * b)) / a) / y;
	} else if (a <= 9.2e+249) {
		tmp = x / (a * (y * (1.0 + b)));
	} else {
		tmp = ((x / y) - (x / (y / b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 3.1e-50:
		tmp = ((x - (x * b)) / a) / y
	elif a <= 9.2e+249:
		tmp = x / (a * (y * (1.0 + b)))
	else:
		tmp = ((x / y) - (x / (y / b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 3.1e-50)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / a) / y);
	elseif (a <= 9.2e+249)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	else
		tmp = Float64(Float64(Float64(x / y) - Float64(x / Float64(y / b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 3.1e-50)
		tmp = ((x - (x * b)) / a) / y;
	elseif (a <= 9.2e+249)
		tmp = x / (a * (y * (1.0 + b)));
	else
		tmp = ((x / y) - (x / (y / b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 3.1e-50], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[a, 9.2e+249], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] - N[(x / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < 3.1000000000000002e-50

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 85.5%

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

      1. mul-1-neg 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in y around 0 60.8%

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

      1. exp-neg 60.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 60.8%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 60.8%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 60.8%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 60.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 60.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 60.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 26.6%

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

   9. Taylor expanded in b around 0 26.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   10. Step-by-step derivation

       1. associate-/r* 31.3%

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

       2. mul-1-neg 31.3%

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

       3. *-commutative 31.3%

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

       4. *-commutative 31.3%

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

       5. times-frac 29.4%

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

       6. distribute-lft-neg-in 29.4%

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

       7. cancel-sign-sub-inv 29.4%

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

       8. associate-/r* 29.4%

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

       9. times-frac 26.6%

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

       10. div-sub 35.6%

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

       11. associate-/r* 41.0%

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

   11. Simplified 41.0%

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

   if 3.1000000000000002e-50 < a < 9.1999999999999993e249

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in y around 0 55.1%

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

      1. exp-neg 55.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 55.1%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 55.1%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 55.1%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 55.1%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 55.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 55.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 37.3%

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

   9. Taylor expanded in a around 0 39.2%

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

   if 9.1999999999999993e249 < a

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 74.2%

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

      4. associate-/l* 74.2%

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

      5. associate-/r/ 74.2%

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

      6. exp-neg 74.2%

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

      7. associate-*r/ 74.2%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in t around 0 59.3%

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

      1. associate-*r* 59.3%

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

      2. *-commutative 59.3%

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

      3. associate-*r* 59.3%

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

   6. Simplified 59.3%

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

   7. Taylor expanded in y around 0 59.6%

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

   8. Taylor expanded in b around 0 39.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 39.6%

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

      2. unsub-neg 39.6%

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

      3. associate-/r* 39.7%

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

      4. *-commutative 39.7%

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

      5. *-commutative 39.7%

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

      6. times-frac 46.7%

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

   10. Simplified 46.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]
   11. Step-by-step derivation

       1. associate-/l/ 43.3%

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

       2. associate-/r* 40.0%

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

       3. associate-*l/ 57.0%

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

       4. sub-div 57.0%

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

       5. clear-num 57.0%

          \[\leadsto \frac{\frac{x}{y} - x \cdot \color{blue}{\frac{1}{\frac{y}{b}}}}{a} \]

       6. un-div-inv 57.0%

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

   12. Applied egg-rr 57.0%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 3.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \end{array} \]

Alternative 16: 35.0% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 9.5e-50) (/ (/ x a) y) (/ x (* a (* y (+ 1.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 9.5e-50) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= 9.5d-50) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * (1.0d0 + b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 9.5e-50) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * (1.0 + b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 9.5e-50:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * (1.0 + b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 9.5e-50)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 9.5e-50)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * (1.0 + b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 9.5e-50], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.4999999999999993e-50

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 84.7%

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

      1. mul-1-neg 84.7%

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

   4. Simplified 84.7%

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

   5. Taylor expanded in b around 0 67.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 67.0%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 67.0%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 67.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 67.2%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 67.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   8. Taylor expanded in y around 0 31.7%

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

      1. *-commutative 31.7%

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

      2. associate-/r* 38.2%

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

   10. Simplified 38.2%

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

   if 9.4999999999999993e-50 < a

   1. Initial program 98.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 77.8%

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

      1. mul-1-neg 77.8%

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

   4. Simplified 77.8%

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

   5. Taylor expanded in y around 0 56.7%

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

      1. exp-neg 56.7%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 56.7%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 56.7%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 56.7%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 56.7%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 57.5%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 57.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 39.2%

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

   9. Taylor expanded in a around 0 39.5%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 9.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b\right)\right)}\\ \end{array} \]

Alternative 17: 36.2% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 10^{-49}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1e-49) (/ (/ x a) y) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-49) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= 1d-49) then
        tmp = (x / a) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1e-49) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1e-49:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1e-49)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1e-49)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1e-49], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 9.99999999999999936e-50

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 84.7%

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

      1. mul-1-neg 84.7%

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

   4. Simplified 84.7%

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

   5. Taylor expanded in b around 0 67.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 67.0%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 67.0%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 67.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 67.2%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 67.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   8. Taylor expanded in y around 0 31.7%

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

      1. *-commutative 31.7%

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

      2. associate-/r* 38.2%

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

   10. Simplified 38.2%

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

   if 9.99999999999999936e-50 < a

   1. Initial program 98.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.2%

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

      2. sub-neg 99.2%

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

      3. exp-sum 76.8%

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

      4. associate-/l* 76.8%

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

      5. associate-/r/ 76.8%

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

      6. exp-neg 76.8%

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

      7. associate-*r/ 76.8%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in t around 0 61.8%

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

      1. associate-*r* 59.8%

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

      2. *-commutative 59.8%

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

      3. associate-*r* 61.8%

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

   6. Simplified 61.8%

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

   7. Taylor expanded in y around 0 57.1%

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

   8. Taylor expanded in b around 0 40.1%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 10^{-49}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 18: 37.2% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2.6e-50) (/ (/ (- x (* x b)) a) y) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.6e-50) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: tmp
    if (a <= 2.6d-50) then
        tmp = ((x - (x * b)) / a) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.6e-50) {
		tmp = ((x - (x * b)) / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2.6e-50:
		tmp = ((x - (x * b)) / a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2.6e-50)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / a) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2.6e-50)
		tmp = ((x - (x * b)) / a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2.6e-50], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.6000000000000001e-50

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 85.5%

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

      1. mul-1-neg 85.5%

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

   4. Simplified 85.5%

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

   5. Taylor expanded in y around 0 60.8%

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

      1. exp-neg 60.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 60.8%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 60.8%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. +-commutative 60.8%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      5. exp-sum 60.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      6. rem-exp-log 60.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

   7. Simplified 60.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   8. Taylor expanded in b around 0 26.6%

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

   9. Taylor expanded in b around 0 26.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   10. Step-by-step derivation

       1. associate-/r* 31.3%

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

       2. mul-1-neg 31.3%

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

       3. *-commutative 31.3%

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

       4. *-commutative 31.3%

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

       5. times-frac 29.4%

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

       6. distribute-lft-neg-in 29.4%

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

       7. cancel-sign-sub-inv 29.4%

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

       8. associate-/r* 29.4%

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

       9. times-frac 26.6%

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

       10. div-sub 35.6%

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

       11. associate-/r* 41.0%

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

   11. Simplified 41.0%

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

   if 2.6000000000000001e-50 < a

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.2%

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

      2. sub-neg 99.2%

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

      3. exp-sum 76.3%

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

      4. associate-/l* 76.3%

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

      5. associate-/r/ 76.3%

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

      6. exp-neg 76.3%

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

      7. associate-*r/ 76.3%

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

   3. Simplified 67.3%

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

   4. Taylor expanded in t around 0 61.4%

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

      1. associate-*r* 59.4%

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

      2. *-commutative 59.4%

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

      3. associate-*r* 61.4%

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

   6. Simplified 61.4%

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

   7. Taylor expanded in y around 0 56.8%

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

   8. Taylor expanded in b around 0 39.8%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{\frac{x - x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 19: 32.1% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;y \leq 5.8 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-t_1 \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y))) (if (<= y 5.8e+15) t_1 (- (* t_1 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (y <= 5.8e+15) {
		tmp = t_1;
	} else {
		tmp = -(t_1 * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x / a) / y
    if (y <= 5.8d+15) then
        tmp = t_1
    else
        tmp = -(t_1 * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double tmp;
	if (y <= 5.8e+15) {
		tmp = t_1;
	} else {
		tmp = -(t_1 * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	tmp = 0
	if y <= 5.8e+15:
		tmp = t_1
	else:
		tmp = -(t_1 * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (y <= 5.8e+15)
		tmp = t_1;
	else
		tmp = Float64(-Float64(t_1 * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	tmp = 0.0;
	if (y <= 5.8e+15)
		tmp = t_1;
	else
		tmp = -(t_1 * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, 5.8e+15], t$95$1, (-N[(t$95$1 * b), $MachinePrecision])]]

Derivation

1. Split input into 2 regimes

2. if y < 5.8e15

   1. Initial program 98.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 76.1%

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

      1. mul-1-neg 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in b around 0 55.1%

      \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
   6. Step-by-step derivation

      1. div-exp 55.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      2. *-commutative 55.1%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      3. exp-to-pow 55.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      4. rem-exp-log 55.8%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   7. Simplified 55.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

   8. Taylor expanded in y around 0 35.5%

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

      1. *-commutative 35.5%

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

      2. associate-/r* 37.5%

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

   10. Simplified 37.5%

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

   if 5.8e15 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 73.9%

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

      4. associate-/l* 73.9%

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

      5. associate-/r/ 73.9%

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

      6. exp-neg 73.9%

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

      7. associate-*r/ 73.9%

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

   3. Simplified 55.1%

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

   4. Taylor expanded in t around 0 66.8%

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

      1. associate-*r* 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*r* 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in y around 0 45.3%

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

   8. Taylor expanded in b around 0 21.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. mul-1-neg 21.6%

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

      2. unsub-neg 21.6%

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

      3. associate-/r* 24.2%

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

      4. *-commutative 24.2%

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

      5. *-commutative 24.2%

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

      6. times-frac 20.1%

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

   10. Simplified 20.1%

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

   11. Taylor expanded in b around inf 32.5%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. mul-1-neg 32.5%

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

       2. associate-*r/ 35.6%

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

       3. associate-/r* 35.4%

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

       4. distribute-rgt-neg-in 35.4%

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

       5. distribute-frac-neg 35.4%

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

       6. distribute-frac-neg 35.4%

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

   13. Simplified 35.4%

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

4. Final simplification 36.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;-\frac{\frac{x}{a}}{y} \cdot b\\ \end{array} \]

Alternative 20: 31.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = x / (y * a)
end function

Java

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

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in t around 0 80.6%

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

   1. mul-1-neg 80.6%

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

4. Simplified 80.6%

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

5. Taylor expanded in b around 0 63.0%

   \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
6. Step-by-step derivation

   1. div-exp 62.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

   2. *-commutative 62.9%

      \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

   3. exp-to-pow 62.9%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

   4. rem-exp-log 63.5%

      \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

7. Simplified 63.5%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

8. Taylor expanded in y around 0 32.5%

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

9. Final simplification 32.5%

   \[\leadsto \frac{x}{y \cdot a} \]

Alternative 21: 31.4% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = (x / a) / y
end function

Java

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

Python

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

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 99.0%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in t around 0 80.6%

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

   1. mul-1-neg 80.6%

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

4. Simplified 80.6%

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

5. Taylor expanded in b around 0 63.0%

   \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
6. Step-by-step derivation

   1. div-exp 62.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

   2. *-commutative 62.9%

      \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

   3. exp-to-pow 62.9%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

   4. rem-exp-log 63.5%

      \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

7. Simplified 63.5%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

8. Taylor expanded in y around 0 32.5%

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

   1. *-commutative 32.5%

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

   2. associate-/r* 35.0%

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

10. Simplified 35.0%

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

11. Final simplification 35.0%

    \[\leadsto \frac{\frac{x}{a}}{y} \]

Developer target: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023192 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))