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

Percentage Accurate: 98.3% → 98.3%

Time: 27.5s

Alternatives: 24

Speedup: 1.0×

• 21.3% 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: 98.3% 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: 98.3% 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]

Derivation

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. Final simplification 98.5%

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

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+99} \lor \neg \left(t \leq 3 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e+99) (not (<= t 3e-27)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5e+99) || !(t <= 3e-27)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - 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 ((t <= (-5d+99)) .or. (.not. (t <= 3d-27))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - 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 ((t <= -5e+99) || !(t <= 3e-27)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5e+99) or not (t <= 3e-27):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5e+99) || !(t <= 3e-27))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5e+99) || ~((t <= 3e-27)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5e+99], N[Not[LessEqual[t, 3e-27]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $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]]

Derivation

1. Split input into 2 regimes

2. if t < -5.00000000000000008e99 or 3.0000000000000001e-27 < t

   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. Taylor expanded in y around 0 91.4%

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

   if -5.00000000000000008e99 < t < 3.0000000000000001e-27

   1. Initial program 97.4%

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

   2. Taylor expanded in t around 0 95.6%

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

      1. mul-1-neg 95.6%

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

   4. Simplified 95.6%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+99} \lor \neg \left(t \leq 3 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 81.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -2e+67)
   (* x (/ (pow a t) (* y a)))
   (if (<= (+ t -1.0) 2e+69)
     (* x (/ (pow z y) (* y (* a (exp b)))))
     (/ (* x (/ (pow a t) a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -2e+67) {
		tmp = x * (pow(a, t) / (y * a));
	} else if ((t + -1.0) <= 2e+69) {
		tmp = x * (pow(z, y) / (y * (a * exp(b))));
	} else {
		tmp = (x * (pow(a, t) / a)) / 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 ((t + (-1.0d0)) <= (-2d+67)) then
        tmp = x * ((a ** t) / (y * a))
    else if ((t + (-1.0d0)) <= 2d+69) then
        tmp = x * ((z ** y) / (y * (a * exp(b))))
    else
        tmp = (x * ((a ** t) / a)) / 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 ((t + -1.0) <= -2e+67) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if ((t + -1.0) <= 2e+69) {
		tmp = x * (Math.pow(z, y) / (y * (a * Math.exp(b))));
	} else {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -2e+67:
		tmp = x * (math.pow(a, t) / (y * a))
	elif (t + -1.0) <= 2e+69:
		tmp = x * (math.pow(z, y) / (y * (a * math.exp(b))))
	else:
		tmp = (x * (math.pow(a, t) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -2e+67)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (Float64(t + -1.0) <= 2e+69)
		tmp = Float64(x * Float64((z ^ y) / Float64(y * Float64(a * exp(b)))));
	else
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -2e+67)
		tmp = x * ((a ^ t) / (y * a));
	elseif ((t + -1.0) <= 2e+69)
		tmp = x * ((z ^ y) / (y * (a * exp(b))));
	else
		tmp = (x * ((a ^ t) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+67], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 2e+69], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -1.99999999999999997e67

   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 y around 0 88.4%

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

   3. Taylor expanded in b around 0 78.8%

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

      1. expm1-log1p-u 59.1%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)\right)} \]

      2. expm1-udef 59.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)} - 1} \]

      3. associate-/l* 51.2%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t - 1\right)}}{\frac{y}{x}}}\right)} - 1 \]

      4. pow-sub 51.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{\frac{y}{x}}\right)} - 1 \]

      5. pow1 51.2%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{\color{blue}{a}}}{\frac{y}{x}}\right)} - 1 \]

   5. Applied egg-rr 51.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 51.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)\right)} \]

      2. expm1-log1p 70.9%

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

      3. associate-/r/ 78.8%

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

      4. *-commutative 78.8%

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

      5. associate-/l/ 78.8%

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

   7. Simplified 78.8%

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

   if -1.99999999999999997e67 < (-.f64 t 1) < 2.0000000000000001e69

   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/ 97.0%

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

      2. sub-neg 97.0%

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

      3. exp-sum 81.6%

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

      4. associate-/l* 81.6%

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

      5. associate-/r/ 79.5%

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

      6. exp-neg 79.5%

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

      7. associate-*r/ 79.5%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. associate-*r* 77.7%

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

      2. *-commutative 77.7%

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

      3. associate-*r* 79.0%

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

   6. Simplified 79.0%

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

   if 2.0000000000000001e69 < (-.f64 t 1)

   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 y around 0 93.0%

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

   3. Taylor expanded in b around 0 75.4%

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

      1. expm1-log1p-u 57.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)\right)}}{y} \]

      2. expm1-udef 57.4%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)} - 1}}{y} \]

      3. *-commutative 57.4%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(\color{blue}{x \cdot {a}^{\left(t - 1\right)}}\right)} - 1}{y} \]

      4. pow-sub 57.4%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1}{y} \]

      5. pow1 57.4%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)} - 1}{y} \]

   5. Applied egg-rr 57.4%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)} - 1}}{y} \]
   6. Step-by-step derivation

      1. expm1-def 57.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)\right)}}{y} \]

      2. expm1-log1p 75.4%

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

   7. Simplified 75.4%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq 2 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \end{array} \]

Alternative 4: 89.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+164} \lor \neg \left(y \leq 3.9 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e+164) (not (<= y 3.9e+59)))
   (/ (/ x (/ a (pow z y))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+164) || !(y <= 3.9e+59)) {
		tmp = (x / (a / pow(z, y))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - 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 <= (-1.25d+164)) .or. (.not. (y <= 3.9d+59))) then
        tmp = (x / (a / (z ** y))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - 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 <= -1.25e+164) || !(y <= 3.9e+59)) {
		tmp = (x / (a / Math.pow(z, y))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e+164) or not (y <= 3.9e+59):
		tmp = (x / (a / math.pow(z, y))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e+164) || !(y <= 3.9e+59))
		tmp = Float64(Float64(x / Float64(a / (z ^ y))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e+164) || ~((y <= 3.9e+59)))
		tmp = (x / (a / (z ^ y))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e+164], N[Not[LessEqual[y, 3.9e+59]], $MachinePrecision]], N[(N[(x / N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999987e164 or 3.90000000000000021e59 < 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%

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

   5. Taylor expanded in b around 0 85.5%

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

      1. *-commutative 85.5%

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

      2. exp-diff 85.5%

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

      3. *-commutative 85.5%

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

      4. exp-to-pow 85.5%

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

      5. rem-exp-log 85.5%

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

      6. associate-*r/ 85.5%

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

      7. associate-/l* 85.5%

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

   7. Simplified 85.5%

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

   if -1.24999999999999987e164 < y < 3.90000000000000021e59

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 93.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+164} \lor \neg \left(y \leq 3.9 \cdot 10^{+59}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 80.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+63} \lor \neg \left(y \leq 1.85 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.55e+63) (not (<= y 1.85e+56)))
   (/ (/ x (/ a (pow z y))) y)
   (* (/ (pow a t) a) (/ x (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.55e+63) || !(y <= 1.85e+56)) {
		tmp = (x / (a / pow(z, y))) / y;
	} else {
		tmp = (pow(a, t) / a) * (x / (y * 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 <= (-1.55d+63)) .or. (.not. (y <= 1.85d+56))) then
        tmp = (x / (a / (z ** y))) / y
    else
        tmp = ((a ** t) / a) * (x / (y * 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 <= -1.55e+63) || !(y <= 1.85e+56)) {
		tmp = (x / (a / Math.pow(z, y))) / y;
	} else {
		tmp = (Math.pow(a, t) / a) * (x / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.55e+63) or not (y <= 1.85e+56):
		tmp = (x / (a / math.pow(z, y))) / y
	else:
		tmp = (math.pow(a, t) / a) * (x / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.55e+63) || !(y <= 1.85e+56))
		tmp = Float64(Float64(x / Float64(a / (z ^ y))) / y);
	else
		tmp = Float64(Float64((a ^ t) / a) * Float64(x / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.55e+63) || ~((y <= 1.85e+56)))
		tmp = (x / (a / (z ^ y))) / y;
	else
		tmp = ((a ^ t) / a) * (x / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.55e+63], N[Not[LessEqual[y, 1.85e+56]], $MachinePrecision]], N[(N[(x / N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] * N[(x / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e63 or 1.84999999999999998e56 < 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 91.0%

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

      1. mul-1-neg 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in b around 0 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-diff 82.8%

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

      3. *-commutative 82.8%

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

      4. exp-to-pow 82.8%

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

      5. rem-exp-log 82.8%

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

      6. associate-*r/ 82.8%

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

      7. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

   if -1.55e63 < y < 1.84999999999999998e56

   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/ 96.9%

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

      2. sub-neg 96.9%

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

      3. exp-sum 80.6%

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

      4. associate-/l* 80.6%

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

      5. associate-/r/ 78.6%

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

      6. exp-neg 78.6%

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

      7. associate-*r/ 78.6%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in y around 0 78.4%

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

      1. associate-*r* 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*r* 78.4%

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

      4. times-frac 79.0%

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

   6. Simplified 79.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+63} \lor \neg \left(y \leq 1.85 \cdot 10^{+56}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y \cdot e^{b}}\\ \end{array} \]

Alternative 6: 82.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+66} \lor \neg \left(y \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4e+66) (not (<= y 1.1e+57)))
   (/ (/ x (/ a (pow z y))) y)
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -4e+66) || !(y <= 1.1e+57)) {
		tmp = (x / (a / pow(z, y))) / y;
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / exp(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 <= (-4d+66)) .or. (.not. (y <= 1.1d+57))) then
        tmp = (x / (a / (z ** y))) / y
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(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 <= -4e+66) || !(y <= 1.1e+57)) {
		tmp = (x / (a / Math.pow(z, y))) / y;
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -4e+66) or not (y <= 1.1e+57):
		tmp = (x / (a / math.pow(z, y))) / y
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -4e+66) || !(y <= 1.1e+57))
		tmp = Float64(Float64(x / Float64(a / (z ^ y))) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -4e+66) || ~((y <= 1.1e+57)))
		tmp = (x / (a / (z ^ y))) / y;
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -4e+66], N[Not[LessEqual[y, 1.1e+57]], $MachinePrecision]], N[(N[(x / N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999978e66 or 1.1e57 < 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 91.0%

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

      1. mul-1-neg 91.0%

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

   4. Simplified 91.0%

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

   5. Taylor expanded in b around 0 82.8%

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

      1. *-commutative 82.8%

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

      2. exp-diff 82.8%

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

      3. *-commutative 82.8%

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

      4. exp-to-pow 82.8%

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

      5. rem-exp-log 82.8%

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

      6. associate-*r/ 82.8%

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

      7. associate-/l* 82.8%

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

   7. Simplified 82.8%

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

   if -3.99999999999999978e66 < y < 1.1e57

   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. Taylor expanded in y around 0 95.5%

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

      1. exp-diff 81.2%

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

      2. sub-neg 81.2%

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

      3. metadata-eval 81.2%

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

      4. *-commutative 81.2%

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

      5. exp-to-pow 82.3%

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

   4. Simplified 82.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+66} \lor \neg \left(y \leq 1.1 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 7: 73.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_3 := \frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-276}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (/ a (pow z y))) y))
        (t_2 (/ x (* a (* y (exp b)))))
        (t_3 (/ (* x (/ (pow a t) a)) y)))
   (if (<= b -6.8e+113)
     t_2
     (if (<= b -5.7e+35)
       (* (/ (pow z y) a) (/ x y))
       (if (<= b -5.5e-111)
         t_3
         (if (<= b 4.5e-301)
           t_1
           (if (<= b 8e-276) t_3 (if (<= b 5.2e+58) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a / pow(z, y))) / y;
	double t_2 = x / (a * (y * exp(b)));
	double t_3 = (x * (pow(a, t) / a)) / y;
	double tmp;
	if (b <= -6.8e+113) {
		tmp = t_2;
	} else if (b <= -5.7e+35) {
		tmp = (pow(z, y) / a) * (x / y);
	} else if (b <= -5.5e-111) {
		tmp = t_3;
	} else if (b <= 4.5e-301) {
		tmp = t_1;
	} else if (b <= 8e-276) {
		tmp = t_3;
	} else if (b <= 5.2e+58) {
		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) :: t_3
    real(8) :: tmp
    t_1 = (x / (a / (z ** y))) / y
    t_2 = x / (a * (y * exp(b)))
    t_3 = (x * ((a ** t) / a)) / y
    if (b <= (-6.8d+113)) then
        tmp = t_2
    else if (b <= (-5.7d+35)) then
        tmp = ((z ** y) / a) * (x / y)
    else if (b <= (-5.5d-111)) then
        tmp = t_3
    else if (b <= 4.5d-301) then
        tmp = t_1
    else if (b <= 8d-276) then
        tmp = t_3
    else if (b <= 5.2d+58) 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 / (a / Math.pow(z, y))) / y;
	double t_2 = x / (a * (y * Math.exp(b)));
	double t_3 = (x * (Math.pow(a, t) / a)) / y;
	double tmp;
	if (b <= -6.8e+113) {
		tmp = t_2;
	} else if (b <= -5.7e+35) {
		tmp = (Math.pow(z, y) / a) * (x / y);
	} else if (b <= -5.5e-111) {
		tmp = t_3;
	} else if (b <= 4.5e-301) {
		tmp = t_1;
	} else if (b <= 8e-276) {
		tmp = t_3;
	} else if (b <= 5.2e+58) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a / math.pow(z, y))) / y
	t_2 = x / (a * (y * math.exp(b)))
	t_3 = (x * (math.pow(a, t) / a)) / y
	tmp = 0
	if b <= -6.8e+113:
		tmp = t_2
	elif b <= -5.7e+35:
		tmp = (math.pow(z, y) / a) * (x / y)
	elif b <= -5.5e-111:
		tmp = t_3
	elif b <= 4.5e-301:
		tmp = t_1
	elif b <= 8e-276:
		tmp = t_3
	elif b <= 5.2e+58:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a / (z ^ y))) / y)
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_3 = Float64(Float64(x * Float64((a ^ t) / a)) / y)
	tmp = 0.0
	if (b <= -6.8e+113)
		tmp = t_2;
	elseif (b <= -5.7e+35)
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	elseif (b <= -5.5e-111)
		tmp = t_3;
	elseif (b <= 4.5e-301)
		tmp = t_1;
	elseif (b <= 8e-276)
		tmp = t_3;
	elseif (b <= 5.2e+58)
		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 / (a / (z ^ y))) / y;
	t_2 = x / (a * (y * exp(b)));
	t_3 = (x * ((a ^ t) / a)) / y;
	tmp = 0.0;
	if (b <= -6.8e+113)
		tmp = t_2;
	elseif (b <= -5.7e+35)
		tmp = ((z ^ y) / a) * (x / y);
	elseif (b <= -5.5e-111)
		tmp = t_3;
	elseif (b <= 4.5e-301)
		tmp = t_1;
	elseif (b <= 8e-276)
		tmp = t_3;
	elseif (b <= 5.2e+58)
		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[(N[(x / N[(a / N[Power[z, y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -6.8e+113], t$95$2, If[LessEqual[b, -5.7e+35], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.5e-111], t$95$3, If[LessEqual[b, 4.5e-301], t$95$1, If[LessEqual[b, 8e-276], t$95$3, If[LessEqual[b, 5.2e+58], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.80000000000000038e113 or 5.19999999999999976e58 < b

   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 94.1%

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

      1. mul-1-neg 94.1%

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

   4. Simplified 94.1%

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

   5. Taylor expanded in y around 0 87.2%

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

      1. exp-neg 87.2%

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

      2. associate-*l/ 87.2%

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

      3. *-lft-identity 87.2%

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

      4. exp-sum 87.2%

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

      5. rem-exp-log 87.2%

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

      6. *-commutative 87.2%

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

      7. associate-/r* 80.2%

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

      8. associate-/r* 80.2%

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

      9. *-commutative 80.2%

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

      10. associate-/r* 87.2%

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

   7. Simplified 87.2%

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

   if -6.80000000000000038e113 < b < -5.69999999999999993e35

   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 36.8%

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

      4. associate-/l* 36.8%

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

      5. associate-/r/ 36.8%

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

      6. exp-neg 36.8%

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

      7. associate-*r/ 36.8%

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

   3. Simplified 31.6%

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

   4. Taylor expanded in t around 0 42.3%

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

      1. associate-*r* 42.2%

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

      2. *-commutative 42.2%

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

      3. associate-*r* 42.3%

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

      4. times-frac 42.3%

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

   6. Simplified 42.3%

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

   7. Taylor expanded in b around 0 75.0%

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

   if -5.69999999999999993e35 < b < -5.4999999999999998e-111 or 4.5000000000000002e-301 < b < 8e-276

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0 88.7%

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

   3. Taylor expanded in b around 0 91.6%

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

      1. expm1-log1p-u 56.9%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)\right)}}{y} \]

      2. expm1-udef 51.7%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)} - 1}}{y} \]

      3. *-commutative 51.7%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(\color{blue}{x \cdot {a}^{\left(t - 1\right)}}\right)} - 1}{y} \]

      4. pow-sub 51.7%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1}{y} \]

      5. pow1 51.7%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)} - 1}{y} \]

   5. Applied egg-rr 51.7%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)} - 1}}{y} \]
   6. Step-by-step derivation

      1. expm1-def 56.9%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)\right)}}{y} \]

      2. expm1-log1p 91.6%

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

   7. Simplified 91.6%

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

   if -5.4999999999999998e-111 < b < 4.5000000000000002e-301 or 8e-276 < b < 5.19999999999999976e58

   1. Initial program 96.5%

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

   2. Taylor expanded in t around 0 79.9%

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

      1. mul-1-neg 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in b around 0 79.0%

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

      1. *-commutative 79.0%

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

      2. exp-diff 79.0%

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

      3. *-commutative 79.0%

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

      4. exp-to-pow 79.0%

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

      5. rem-exp-log 80.3%

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

      6. associate-*r/ 80.3%

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

      7. associate-/l* 80.3%

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

   7. Simplified 80.3%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -5.7 \cdot 10^{+35}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-301}:\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-276}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{x}{\frac{a}{{z}^{y}}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8: 43.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y + y \cdot b\right)}\\ t_2 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -6 \cdot 10^{+99}:\\ \;\;\;\;\left(t_2 - \frac{x}{a} \cdot \frac{b}{y}\right) + t_2 \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 125000000000 \lor \neg \left(b \leq 2.8 \cdot 10^{+98}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{b}}{y} \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (+ y (* y b))))) (t_2 (/ (/ x a) y)))
   (if (<= b -6e+99)
     (+ (- t_2 (* (/ x a) (/ b y))) (* t_2 (* 0.5 (* b b))))
     (if (<= b -1.05e+73)
       t_1
       (if (<= b -9.4e-20)
         (/ (- x (* x b)) (* y a))
         (if (<= b 9.5e-54)
           (/ 1.0 (* y (/ a x)))
           (if (or (<= b 125000000000.0) (not (<= b 2.8e+98)))
             t_1
             (* (/ (exp b) y) (/ x a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (y * b)));
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -6e+99) {
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)));
	} else if (b <= -1.05e+73) {
		tmp = t_1;
	} else if (b <= -9.4e-20) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 9.5e-54) {
		tmp = 1.0 / (y * (a / x));
	} else if ((b <= 125000000000.0) || !(b <= 2.8e+98)) {
		tmp = t_1;
	} else {
		tmp = (exp(b) / y) * (x / 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (a * (y + (y * b)))
    t_2 = (x / a) / y
    if (b <= (-6d+99)) then
        tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5d0 * (b * b)))
    else if (b <= (-1.05d+73)) then
        tmp = t_1
    else if (b <= (-9.4d-20)) then
        tmp = (x - (x * b)) / (y * a)
    else if (b <= 9.5d-54) then
        tmp = 1.0d0 / (y * (a / x))
    else if ((b <= 125000000000.0d0) .or. (.not. (b <= 2.8d+98))) then
        tmp = t_1
    else
        tmp = (exp(b) / y) * (x / 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 t_1 = x / (a * (y + (y * b)));
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -6e+99) {
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)));
	} else if (b <= -1.05e+73) {
		tmp = t_1;
	} else if (b <= -9.4e-20) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 9.5e-54) {
		tmp = 1.0 / (y * (a / x));
	} else if ((b <= 125000000000.0) || !(b <= 2.8e+98)) {
		tmp = t_1;
	} else {
		tmp = (Math.exp(b) / y) * (x / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y + (y * b)))
	t_2 = (x / a) / y
	tmp = 0
	if b <= -6e+99:
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)))
	elif b <= -1.05e+73:
		tmp = t_1
	elif b <= -9.4e-20:
		tmp = (x - (x * b)) / (y * a)
	elif b <= 9.5e-54:
		tmp = 1.0 / (y * (a / x))
	elif (b <= 125000000000.0) or not (b <= 2.8e+98):
		tmp = t_1
	else:
		tmp = (math.exp(b) / y) * (x / a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y + Float64(y * b))))
	t_2 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -6e+99)
		tmp = Float64(Float64(t_2 - Float64(Float64(x / a) * Float64(b / y))) + Float64(t_2 * Float64(0.5 * Float64(b * b))));
	elseif (b <= -1.05e+73)
		tmp = t_1;
	elseif (b <= -9.4e-20)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	elseif (b <= 9.5e-54)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	elseif ((b <= 125000000000.0) || !(b <= 2.8e+98))
		tmp = t_1;
	else
		tmp = Float64(Float64(exp(b) / y) * Float64(x / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y + (y * b)));
	t_2 = (x / a) / y;
	tmp = 0.0;
	if (b <= -6e+99)
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)));
	elseif (b <= -1.05e+73)
		tmp = t_1;
	elseif (b <= -9.4e-20)
		tmp = (x - (x * b)) / (y * a);
	elseif (b <= 9.5e-54)
		tmp = 1.0 / (y * (a / x));
	elseif ((b <= 125000000000.0) || ~((b <= 2.8e+98)))
		tmp = t_1;
	else
		tmp = (exp(b) / y) * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -6e+99], N[(N[(t$95$2 - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.05e+73], t$95$1, If[LessEqual[b, -9.4e-20], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-54], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 125000000000.0], N[Not[LessEqual[b, 2.8e+98]], $MachinePrecision]], t$95$1, N[(N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.00000000000000029e99

   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 97.9%

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

      1. mul-1-neg 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in y around 0 91.4%

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

      1. exp-neg 91.4%

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

      2. associate-*l/ 91.4%

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

      3. *-lft-identity 91.4%

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

      4. exp-sum 91.4%

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

      5. rem-exp-log 91.4%

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

      6. *-commutative 91.4%

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

      7. associate-/r* 84.9%

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

      8. associate-/r* 84.9%

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

      9. *-commutative 84.9%

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

      10. associate-/r* 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in b around 0 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) + \left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}\right)} \]
   9. Step-by-step derivation

      1. +-commutative 54.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right)} \]

      2. +-commutative 54.6%

         \[\leadsto \color{blue}{\left(\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      3. mul-1-neg 54.6%

         \[\leadsto \left(\frac{x}{y \cdot a} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      4. unsub-neg 54.6%

         \[\leadsto \color{blue}{\left(\frac{x}{y \cdot a} - \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      5. *-commutative 54.6%

         \[\leadsto \left(\frac{x}{\color{blue}{a \cdot y}} - \frac{b \cdot x}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      6. associate-/r* 54.6%

         \[\leadsto \left(\color{blue}{\frac{\frac{x}{a}}{y}} - \frac{b \cdot x}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      7. *-commutative 54.6%

         \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{\color{blue}{x \cdot b}}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      8. times-frac 52.5%

         \[\leadsto \left(\frac{\frac{x}{a}}{y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      9. mul-1-neg 52.5%

         \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{\left(-{b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right)} \]

      10. *-commutative 52.5%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\color{blue}{\left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right) \cdot {b}^{2}}\right) \]

      11. distribute-rgt-out 76.4%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\color{blue}{\left(\frac{x}{y \cdot a} \cdot \left(0.5 + -1\right)\right)} \cdot {b}^{2}\right) \]

      12. metadata-eval 76.4%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\left(\frac{x}{y \cdot a} \cdot \color{blue}{-0.5}\right) \cdot {b}^{2}\right) \]

      13. *-commutative 76.4%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\color{blue}{\left(-0.5 \cdot \frac{x}{y \cdot a}\right)} \cdot {b}^{2}\right) \]

   10. Simplified 78.6%

       \[\leadsto \color{blue}{\left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \frac{\frac{x}{a}}{y} \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)} \]

   if -6.00000000000000029e99 < b < -1.0500000000000001e73 or 9.4999999999999994e-54 < b < 1.25e11 or 2.8000000000000001e98 < b

   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 89.2%

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

      1. mul-1-neg 89.2%

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

   4. Simplified 89.2%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. exp-neg 70.6%

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

      2. associate-*l/ 70.6%

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

      3. *-lft-identity 70.6%

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

      4. exp-sum 70.6%

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

      5. rem-exp-log 70.6%

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

      6. *-commutative 70.6%

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

      7. associate-/r* 64.2%

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

      8. associate-/r* 64.2%

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

      9. *-commutative 64.2%

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

      10. associate-/r* 75.0%

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

   7. Simplified 75.0%

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

   8. Taylor expanded in b around 0 51.6%

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

   if -1.0500000000000001e73 < b < -9.4000000000000003e-20

   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 64.4%

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

      1. mul-1-neg 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in y around 0 58.8%

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

      1. exp-neg 58.8%

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

      2. associate-*l/ 58.8%

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

      3. *-lft-identity 58.8%

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

      4. exp-sum 58.8%

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

      5. rem-exp-log 59.5%

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

      6. *-commutative 59.5%

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

      7. associate-/r* 53.5%

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

      8. associate-/r* 53.5%

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

      9. *-commutative 53.5%

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

      10. associate-/r* 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in b around 0 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

      5. associate-/r* 54.5%

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

      6. *-commutative 54.5%

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

      7. times-frac 54.5%

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

   10. Simplified 54.5%

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

       1. associate-/l/ 54.5%

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

       2. frac-times 65.6%

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

       3. *-commutative 65.6%

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

       4. sub-div 65.6%

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

       5. *-commutative 65.6%

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

   12. Applied egg-rr 65.6%

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

   if -9.4000000000000003e-20 < b < 9.4999999999999994e-54

   1. Initial program 97.6%

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

      1. associate-*r/ 96.1%

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

      2. sub-neg 96.1%

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

      3. exp-sum 96.1%

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

      4. associate-/l* 96.1%

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

      5. associate-/r/ 96.1%

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

      6. exp-neg 96.1%

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

      7. associate-*r/ 96.1%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*r* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 38.9%

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

      1. associate-/r* 38.1%

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

      2. *-commutative 38.1%

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

      3. associate-/r* 38.1%

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

      4. associate-/r* 38.1%

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

      5. *-commutative 38.1%

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

      6. associate-/r* 38.1%

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

      7. exp-neg 38.1%

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

   9. Simplified 38.1%

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

   10. Taylor expanded in b around 0 38.9%

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

       1. associate-/r* 38.1%

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

   12. Simplified 38.1%

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

       1. associate-*r/ 41.8%

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

       2. div-inv 41.8%

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

       3. div-inv 41.7%

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

       4. clear-num 41.8%

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

       5. frac-times 41.8%

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

       6. metadata-eval 41.8%

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

   14. Applied egg-rr 41.8%

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

   if 1.25e11 < b < 2.8000000000000001e98

   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 76.6%

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

      1. mul-1-neg 76.6%

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

   4. Simplified 76.6%

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

   5. Taylor expanded in y around 0 53.1%

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

      1. exp-neg 53.1%

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

      2. associate-*l/ 53.1%

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

      3. *-lft-identity 53.1%

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

      4. exp-sum 53.1%

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

      5. rem-exp-log 53.1%

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

      6. *-commutative 53.1%

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

      7. associate-/r* 53.1%

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

      8. associate-/r* 53.1%

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

      9. *-commutative 53.1%

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

      10. associate-/r* 53.1%

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

   7. Simplified 53.1%

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

      1. *-un-lft-identity 53.1%

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

      2. *-commutative 53.1%

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

      3. times-frac 53.1%

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

      4. metadata-eval 53.1%

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

      5. *-commutative 53.1%

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

      6. frac-times 53.1%

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

      7. exp-neg 53.1%

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

      8. div-inv 53.1%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 43.5%

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

      11. sqr-neg 43.5%

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

      12. sqrt-unprod 43.5%

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

      13. add-sqr-sqrt 43.5%

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

   9. Applied egg-rr 43.5%

      \[\leadsto \color{blue}{\frac{e^{b}}{y} \cdot \frac{x}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+99}:\\ \;\;\;\;\left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \frac{\frac{x}{a}}{y} \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-54}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 125000000000 \lor \neg \left(b \leq 2.8 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{b}}{y} \cdot \frac{x}{a}\\ \end{array} \]

Alternative 9: 71.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;\frac{x \cdot \frac{e^{b}}{y}}{a}\\ \mathbf{elif}\;b \leq -50000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x \cdot y}{y} - a \cdot \left(b \cdot \frac{x}{a}\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))) (t_2 (* x (/ (pow a t) (* y a)))))
   (if (<= b -7.2e+103)
     t_1
     (if (<= b -1.05e+73)
       (/ (* x (/ (exp b) y)) a)
       (if (<= b -50000.0)
         t_2
         (if (<= b -3.2e-13)
           (/ (- (/ (* x y) y) (* a (* b (/ x a)))) (* y a))
           (if (<= b 4.7e+39) t_2 t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double t_2 = x * (pow(a, t) / (y * a));
	double tmp;
	if (b <= -7.2e+103) {
		tmp = t_1;
	} else if (b <= -1.05e+73) {
		tmp = (x * (exp(b) / y)) / a;
	} else if (b <= -50000.0) {
		tmp = t_2;
	} else if (b <= -3.2e-13) {
		tmp = (((x * y) / y) - (a * (b * (x / a)))) / (y * a);
	} else if (b <= 4.7e+39) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	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 / (a * (y * exp(b)))
    t_2 = x * ((a ** t) / (y * a))
    if (b <= (-7.2d+103)) then
        tmp = t_1
    else if (b <= (-1.05d+73)) then
        tmp = (x * (exp(b) / y)) / a
    else if (b <= (-50000.0d0)) then
        tmp = t_2
    else if (b <= (-3.2d-13)) then
        tmp = (((x * y) / y) - (a * (b * (x / a)))) / (y * a)
    else if (b <= 4.7d+39) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * Math.exp(b)));
	double t_2 = x * (Math.pow(a, t) / (y * a));
	double tmp;
	if (b <= -7.2e+103) {
		tmp = t_1;
	} else if (b <= -1.05e+73) {
		tmp = (x * (Math.exp(b) / y)) / a;
	} else if (b <= -50000.0) {
		tmp = t_2;
	} else if (b <= -3.2e-13) {
		tmp = (((x * y) / y) - (a * (b * (x / a)))) / (y * a);
	} else if (b <= 4.7e+39) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = x * (math.pow(a, t) / (y * a))
	tmp = 0
	if b <= -7.2e+103:
		tmp = t_1
	elif b <= -1.05e+73:
		tmp = (x * (math.exp(b) / y)) / a
	elif b <= -50000.0:
		tmp = t_2
	elif b <= -3.2e-13:
		tmp = (((x * y) / y) - (a * (b * (x / a)))) / (y * a)
	elif b <= 4.7e+39:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = Float64(x * Float64((a ^ t) / Float64(y * a)))
	tmp = 0.0
	if (b <= -7.2e+103)
		tmp = t_1;
	elseif (b <= -1.05e+73)
		tmp = Float64(Float64(x * Float64(exp(b) / y)) / a);
	elseif (b <= -50000.0)
		tmp = t_2;
	elseif (b <= -3.2e-13)
		tmp = Float64(Float64(Float64(Float64(x * y) / y) - Float64(a * Float64(b * Float64(x / a)))) / Float64(y * a));
	elseif (b <= 4.7e+39)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	t_2 = x * ((a ^ t) / (y * a));
	tmp = 0.0;
	if (b <= -7.2e+103)
		tmp = t_1;
	elseif (b <= -1.05e+73)
		tmp = (x * (exp(b) / y)) / a;
	elseif (b <= -50000.0)
		tmp = t_2;
	elseif (b <= -3.2e-13)
		tmp = (((x * y) / y) - (a * (b * (x / a)))) / (y * a);
	elseif (b <= 4.7e+39)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+103], t$95$1, If[LessEqual[b, -1.05e+73], N[(N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -50000.0], t$95$2, If[LessEqual[b, -3.2e-13], N[(N[(N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision] - N[(a * N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.7e+39], t$95$2, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.20000000000000033e103 or 4.6999999999999999e39 < b

   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 94.4%

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

      1. mul-1-neg 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. associate-*l/ 87.0%

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

      3. *-lft-identity 87.0%

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

      4. exp-sum 87.0%

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

      5. rem-exp-log 87.0%

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

      6. *-commutative 87.0%

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

      7. associate-/r* 80.4%

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

      8. associate-/r* 80.4%

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

      9. *-commutative 80.4%

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

      10. associate-/r* 87.0%

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

   7. Simplified 87.0%

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

   if -7.20000000000000033e103 < b < -1.0500000000000001e73

   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 11.1%

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

      4. associate-/l* 11.1%

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

      5. associate-/r/ 11.1%

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

      6. exp-neg 11.1%

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

      7. associate-*r/ 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in t around 0 22.4%

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

      1. associate-*r* 22.2%

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

      2. *-commutative 22.2%

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

      3. associate-*r* 22.4%

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

   6. Simplified 22.4%

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

   7. Taylor expanded in y around 0 23.4%

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

      1. associate-/r* 23.4%

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

      2. *-commutative 23.4%

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

      3. associate-/r* 23.4%

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

      4. associate-/r* 23.4%

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

      5. *-commutative 23.4%

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

      6. associate-/r* 23.4%

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

      7. exp-neg 23.4%

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

   9. Simplified 23.4%

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

       1. associate-*r/ 23.4%

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

       2. add-sqr-sqrt 23.4%

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

       3. sqrt-unprod 23.4%

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

       4. sqr-neg 23.4%

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

       5. sqrt-unprod 0.0%

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

       6. add-sqr-sqrt 78.1%

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

   11. Applied egg-rr 78.1%

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

   if -1.0500000000000001e73 < b < -5e4 or -3.2e-13 < b < 4.6999999999999999e39

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 72.4%

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

   3. Taylor expanded in b around 0 72.1%

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

      1. expm1-log1p-u 48.3%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)\right)} \]

      2. expm1-udef 48.1%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)} - 1} \]

      3. associate-/l* 40.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t - 1\right)}}{\frac{y}{x}}}\right)} - 1 \]

      4. pow-sub 40.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{\frac{y}{x}}\right)} - 1 \]

      5. pow1 40.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{\color{blue}{a}}}{\frac{y}{x}}\right)} - 1 \]

   5. Applied egg-rr 40.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 42.0%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)\right)} \]

      2. expm1-log1p 65.0%

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

      3. associate-/r/ 72.5%

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

      4. *-commutative 72.5%

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

      5. associate-/l/ 67.3%

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

   7. Simplified 67.3%

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

   if -5e4 < b < -3.2e-13

   1. Initial program 96.5%

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

   2. Taylor expanded in t around 0 47.3%

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

      1. mul-1-neg 47.3%

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

   4. Simplified 47.3%

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

   5. Taylor expanded in y around 0 23.3%

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

      1. exp-neg 23.3%

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

      2. associate-*l/ 23.3%

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

      3. *-lft-identity 23.3%

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

      4. exp-sum 23.5%

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

      5. rem-exp-log 26.4%

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

      6. *-commutative 26.4%

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

      7. associate-/r* 26.4%

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

      8. associate-/r* 26.4%

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

      9. *-commutative 26.4%

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

      10. associate-/r* 26.7%

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

   7. Simplified 26.7%

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

   8. Taylor expanded in b around 0 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. *-commutative 50.8%

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

      5. associate-/r* 50.9%

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

      6. *-commutative 50.9%

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

      7. times-frac 50.9%

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

   10. Simplified 50.9%

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

       1. associate-/l/ 50.9%

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

       2. associate-/r* 50.9%

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

       3. associate-*r/ 50.9%

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

       4. frac-sub 50.8%

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

   12. Applied egg-rr 50.8%

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

       1. associate-*l/ 74.6%

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

   14. Simplified 74.6%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+73}:\\ \;\;\;\;\frac{x \cdot \frac{e^{b}}{y}}{a}\\ \mathbf{elif}\;b \leq -50000:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x \cdot y}{y} - a \cdot \left(b \cdot \frac{x}{a}\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+39}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 10: 71.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{t}}{y \cdot a}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_3 := \frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-301}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-275}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+41}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a t) (* y a))))
        (t_2 (/ x (* a (* y (exp b)))))
        (t_3 (* (/ (pow z y) a) (/ x y))))
   (if (<= b -1.25e+104)
     t_2
     (if (<= b -5.5e-111)
       t_1
       (if (<= b 1.05e-301)
         t_3
         (if (<= b 3.8e-275) t_1 (if (<= b 3.2e+41) 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) / (y * a));
	double t_2 = x / (a * (y * exp(b)));
	double t_3 = (pow(z, y) / a) * (x / y);
	double tmp;
	if (b <= -1.25e+104) {
		tmp = t_2;
	} else if (b <= -5.5e-111) {
		tmp = t_1;
	} else if (b <= 1.05e-301) {
		tmp = t_3;
	} else if (b <= 3.8e-275) {
		tmp = t_1;
	} else if (b <= 3.2e+41) {
		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) / (y * a))
    t_2 = x / (a * (y * exp(b)))
    t_3 = ((z ** y) / a) * (x / y)
    if (b <= (-1.25d+104)) then
        tmp = t_2
    else if (b <= (-5.5d-111)) then
        tmp = t_1
    else if (b <= 1.05d-301) then
        tmp = t_3
    else if (b <= 3.8d-275) then
        tmp = t_1
    else if (b <= 3.2d+41) 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) / (y * a));
	double t_2 = x / (a * (y * Math.exp(b)));
	double t_3 = (Math.pow(z, y) / a) * (x / y);
	double tmp;
	if (b <= -1.25e+104) {
		tmp = t_2;
	} else if (b <= -5.5e-111) {
		tmp = t_1;
	} else if (b <= 1.05e-301) {
		tmp = t_3;
	} else if (b <= 3.8e-275) {
		tmp = t_1;
	} else if (b <= 3.2e+41) {
		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) / (y * a))
	t_2 = x / (a * (y * math.exp(b)))
	t_3 = (math.pow(z, y) / a) * (x / y)
	tmp = 0
	if b <= -1.25e+104:
		tmp = t_2
	elif b <= -5.5e-111:
		tmp = t_1
	elif b <= 1.05e-301:
		tmp = t_3
	elif b <= 3.8e-275:
		tmp = t_1
	elif b <= 3.2e+41:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ t) / Float64(y * a)))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_3 = Float64(Float64((z ^ y) / a) * Float64(x / y))
	tmp = 0.0
	if (b <= -1.25e+104)
		tmp = t_2;
	elseif (b <= -5.5e-111)
		tmp = t_1;
	elseif (b <= 1.05e-301)
		tmp = t_3;
	elseif (b <= 3.8e-275)
		tmp = t_1;
	elseif (b <= 3.2e+41)
		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) / (y * a));
	t_2 = x / (a * (y * exp(b)));
	t_3 = ((z ^ y) / a) * (x / y);
	tmp = 0.0;
	if (b <= -1.25e+104)
		tmp = t_2;
	elseif (b <= -5.5e-111)
		tmp = t_1;
	elseif (b <= 1.05e-301)
		tmp = t_3;
	elseif (b <= 3.8e-275)
		tmp = t_1;
	elseif (b <= 3.2e+41)
		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, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+104], t$95$2, If[LessEqual[b, -5.5e-111], t$95$1, If[LessEqual[b, 1.05e-301], t$95$3, If[LessEqual[b, 3.8e-275], t$95$1, If[LessEqual[b, 3.2e+41], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.2499999999999999e104 or 3.2000000000000001e41 < b

   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 94.4%

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

      1. mul-1-neg 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. associate-*l/ 87.0%

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

      3. *-lft-identity 87.0%

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

      4. exp-sum 87.0%

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

      5. rem-exp-log 87.0%

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

      6. *-commutative 87.0%

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

      7. associate-/r* 80.4%

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

      8. associate-/r* 80.4%

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

      9. *-commutative 80.4%

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

      10. associate-/r* 87.0%

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

   7. Simplified 87.0%

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

   if -1.2499999999999999e104 < b < -5.4999999999999998e-111 or 1.0499999999999999e-301 < b < 3.79999999999999972e-275

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 79.5%

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

   3. Taylor expanded in b around 0 76.4%

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

      1. expm1-log1p-u 53.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)\right)} \]

      2. expm1-udef 55.5%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)} - 1} \]

      3. associate-/l* 46.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t - 1\right)}}{\frac{y}{x}}}\right)} - 1 \]

      4. pow-sub 46.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{\frac{y}{x}}\right)} - 1 \]

      5. pow1 46.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{\color{blue}{a}}}{\frac{y}{x}}\right)} - 1 \]

   5. Applied egg-rr 46.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 44.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)\right)} \]

      2. expm1-log1p 65.3%

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

      3. associate-/r/ 79.9%

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

      4. *-commutative 79.9%

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

      5. associate-/l/ 74.2%

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

   7. Simplified 74.2%

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

   if -5.4999999999999998e-111 < b < 1.0499999999999999e-301 or 3.79999999999999972e-275 < b < 3.2000000000000001e41

   1. Initial program 96.4%

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

      1. associate-*r/ 95.6%

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

      2. sub-neg 95.6%

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

      3. exp-sum 91.4%

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

      4. associate-/l* 91.4%

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

      5. associate-/r/ 91.4%

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

      6. exp-neg 91.4%

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

      7. associate-*r/ 91.4%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in t around 0 69.8%

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

      1. associate-*r* 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 69.8%

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

      4. times-frac 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in b around 0 75.6%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+104}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{-111}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-301}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 11: 71.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x \cdot \frac{e^{b}}{y}}{a}\\ \mathbf{elif}\;b \leq -1020000000:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))))
   (if (<= b -7.5e+103)
     t_1
     (if (<= b -6.6e+72)
       (/ (* x (/ (exp b) y)) a)
       (if (<= b -1020000000.0)
         (* x (/ (pow a t) (* y a)))
         (if (<= b 1.25e+40) (* (/ (pow a t) a) (/ x y)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -7.5e+103) {
		tmp = t_1;
	} else if (b <= -6.6e+72) {
		tmp = (x * (exp(b) / y)) / a;
	} else if (b <= -1020000000.0) {
		tmp = x * (pow(a, t) / (y * a));
	} else if (b <= 1.25e+40) {
		tmp = (pow(a, t) / a) * (x / y);
	} else {
		tmp = t_1;
	}
	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 * exp(b)))
    if (b <= (-7.5d+103)) then
        tmp = t_1
    else if (b <= (-6.6d+72)) then
        tmp = (x * (exp(b) / y)) / a
    else if (b <= (-1020000000.0d0)) then
        tmp = x * ((a ** t) / (y * a))
    else if (b <= 1.25d+40) then
        tmp = ((a ** t) / a) * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -7.5e+103) {
		tmp = t_1;
	} else if (b <= -6.6e+72) {
		tmp = (x * (Math.exp(b) / y)) / a;
	} else if (b <= -1020000000.0) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if (b <= 1.25e+40) {
		tmp = (Math.pow(a, t) / a) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -7.5e+103:
		tmp = t_1
	elif b <= -6.6e+72:
		tmp = (x * (math.exp(b) / y)) / a
	elif b <= -1020000000.0:
		tmp = x * (math.pow(a, t) / (y * a))
	elif b <= 1.25e+40:
		tmp = (math.pow(a, t) / a) * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -7.5e+103)
		tmp = t_1;
	elseif (b <= -6.6e+72)
		tmp = Float64(Float64(x * Float64(exp(b) / y)) / a);
	elseif (b <= -1020000000.0)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (b <= 1.25e+40)
		tmp = Float64(Float64((a ^ t) / a) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -7.5e+103)
		tmp = t_1;
	elseif (b <= -6.6e+72)
		tmp = (x * (exp(b) / y)) / a;
	elseif (b <= -1020000000.0)
		tmp = x * ((a ^ t) / (y * a));
	elseif (b <= 1.25e+40)
		tmp = ((a ^ t) / a) * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+103], t$95$1, If[LessEqual[b, -6.6e+72], N[(N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -1020000000.0], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+40], N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.49999999999999922e103 or 1.25000000000000001e40 < b

   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 94.4%

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

      1. mul-1-neg 94.4%

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

   4. Simplified 94.4%

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

   5. Taylor expanded in y around 0 87.0%

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

      1. exp-neg 87.0%

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

      2. associate-*l/ 87.0%

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

      3. *-lft-identity 87.0%

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

      4. exp-sum 87.0%

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

      5. rem-exp-log 87.0%

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

      6. *-commutative 87.0%

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

      7. associate-/r* 80.4%

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

      8. associate-/r* 80.4%

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

      9. *-commutative 80.4%

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

      10. associate-/r* 87.0%

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

   7. Simplified 87.0%

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

   if -7.49999999999999922e103 < b < -6.6e72

   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 11.1%

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

      4. associate-/l* 11.1%

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

      5. associate-/r/ 11.1%

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

      6. exp-neg 11.1%

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

      7. associate-*r/ 11.1%

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

   3. Simplified 11.1%

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

   4. Taylor expanded in t around 0 22.4%

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

      1. associate-*r* 22.2%

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

      2. *-commutative 22.2%

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

      3. associate-*r* 22.4%

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

   6. Simplified 22.4%

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

   7. Taylor expanded in y around 0 23.4%

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

      1. associate-/r* 23.4%

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

      2. *-commutative 23.4%

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

      3. associate-/r* 23.4%

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

      4. associate-/r* 23.4%

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

      5. *-commutative 23.4%

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

      6. associate-/r* 23.4%

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

      7. exp-neg 23.4%

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

   9. Simplified 23.4%

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

       1. associate-*r/ 23.4%

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

       2. add-sqr-sqrt 23.4%

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

       3. sqrt-unprod 23.4%

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

       4. sqr-neg 23.4%

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

       5. sqrt-unprod 0.0%

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

       6. add-sqr-sqrt 78.1%

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

   11. Applied egg-rr 78.1%

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

   if -6.6e72 < b < -1.02e9

   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 y around 0 84.9%

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

   3. Taylor expanded in b around 0 70.7%

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

      1. expm1-log1p-u 39.4%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)\right)} \]

      2. expm1-udef 54.0%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{{a}^{\left(t - 1\right)} \cdot x}{y}\right)} - 1} \]

      3. associate-/l* 46.3%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{{a}^{\left(t - 1\right)}}{\frac{y}{x}}}\right)} - 1 \]

      4. pow-sub 46.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\color{blue}{\frac{{a}^{t}}{{a}^{1}}}}{\frac{y}{x}}\right)} - 1 \]

      5. pow1 46.3%

         \[\leadsto e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{\color{blue}{a}}}{\frac{y}{x}}\right)} - 1 \]

   5. Applied egg-rr 46.3%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 31.8%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{{a}^{t}}{a}}{\frac{y}{x}}\right)\right)} \]

      2. expm1-log1p 63.0%

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

      3. associate-/r/ 92.5%

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

      4. *-commutative 92.5%

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

      5. associate-/l/ 92.5%

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

   7. Simplified 92.5%

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

   if -1.02e9 < b < 1.25000000000000001e40

   1. Initial program 97.1%

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

   2. Taylor expanded in y around 0 71.1%

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

   3. Taylor expanded in b around 0 73.0%

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

      1. expm1-log1p-u 57.2%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)\right)}}{y} \]

      2. expm1-udef 46.8%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)} - 1}}{y} \]

      3. *-commutative 46.8%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(\color{blue}{x \cdot {a}^{\left(t - 1\right)}}\right)} - 1}{y} \]

      4. pow-sub 46.8%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1}{y} \]

      5. pow1 46.8%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)} - 1}{y} \]

   5. Applied egg-rr 46.8%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)} - 1}}{y} \]
   6. Step-by-step derivation

      1. expm1-def 57.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)\right)}}{y} \]

      2. expm1-log1p 73.1%

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

   7. Simplified 73.1%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{t}}{a}}}{y} \]
   8. Step-by-step derivation

      1. div-inv 73.1%

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

      2. *-commutative 73.1%

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

      3. associate-*l* 65.6%

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

      4. div-inv 65.6%

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

   9. Applied egg-rr 65.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x \cdot \frac{e^{b}}{y}}{a}\\ \mathbf{elif}\;b \leq -1020000000:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+40}:\\ \;\;\;\;\frac{{a}^{t}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 12: 72.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-274}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ (pow z y) a) (/ x y))) (t_2 (/ x (* a (* y (exp b))))))
   (if (<= b -2.2e+113)
     t_2
     (if (<= b -6.3e+34)
       t_1
       (if (<= b 2.9e-274)
         (/ (* x (/ (pow a t) a)) y)
         (if (<= b 4.2e+39) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (pow(z, y) / a) * (x / y);
	double t_2 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -2.2e+113) {
		tmp = t_2;
	} else if (b <= -6.3e+34) {
		tmp = t_1;
	} else if (b <= 2.9e-274) {
		tmp = (x * (pow(a, t) / a)) / y;
	} else if (b <= 4.2e+39) {
		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 = ((z ** y) / a) * (x / y)
    t_2 = x / (a * (y * exp(b)))
    if (b <= (-2.2d+113)) then
        tmp = t_2
    else if (b <= (-6.3d+34)) then
        tmp = t_1
    else if (b <= 2.9d-274) then
        tmp = (x * ((a ** t) / a)) / y
    else if (b <= 4.2d+39) 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 = (Math.pow(z, y) / a) * (x / y);
	double t_2 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -2.2e+113) {
		tmp = t_2;
	} else if (b <= -6.3e+34) {
		tmp = t_1;
	} else if (b <= 2.9e-274) {
		tmp = (x * (Math.pow(a, t) / a)) / y;
	} else if (b <= 4.2e+39) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (math.pow(z, y) / a) * (x / y)
	t_2 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -2.2e+113:
		tmp = t_2
	elif b <= -6.3e+34:
		tmp = t_1
	elif b <= 2.9e-274:
		tmp = (x * (math.pow(a, t) / a)) / y
	elif b <= 4.2e+39:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64((z ^ y) / a) * Float64(x / y))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -2.2e+113)
		tmp = t_2;
	elseif (b <= -6.3e+34)
		tmp = t_1;
	elseif (b <= 2.9e-274)
		tmp = Float64(Float64(x * Float64((a ^ t) / a)) / y);
	elseif (b <= 4.2e+39)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((z ^ y) / a) * (x / y);
	t_2 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -2.2e+113)
		tmp = t_2;
	elseif (b <= -6.3e+34)
		tmp = t_1;
	elseif (b <= 2.9e-274)
		tmp = (x * ((a ^ t) / a)) / y;
	elseif (b <= 4.2e+39)
		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[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.2e+113], t$95$2, If[LessEqual[b, -6.3e+34], t$95$1, If[LessEqual[b, 2.9e-274], N[(N[(x * N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.2e+39], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2000000000000001e113 or 4.1999999999999997e39 < b

   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 94.3%

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

      1. mul-1-neg 94.3%

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

   4. Simplified 94.3%

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

   5. Taylor expanded in y around 0 86.7%

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

      1. exp-neg 86.7%

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

      2. associate-*l/ 86.7%

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

      3. *-lft-identity 86.7%

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

      4. exp-sum 86.7%

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

      5. rem-exp-log 86.7%

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

      6. *-commutative 86.7%

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

      7. associate-/r* 80.0%

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

      8. associate-/r* 80.0%

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

      9. *-commutative 80.0%

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

      10. associate-/r* 86.7%

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

   7. Simplified 86.7%

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

   if -2.2000000000000001e113 < b < -6.3000000000000001e34 or 2.89999999999999976e-274 < b < 4.1999999999999997e39

   1. Initial program 97.8%

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

      1. associate-*r/ 96.6%

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

      2. sub-neg 96.6%

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

      3. exp-sum 74.7%

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

      4. associate-/l* 74.7%

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

      5. associate-/r/ 74.7%

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

      6. exp-neg 74.7%

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

      7. associate-*r/ 74.7%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in t around 0 56.6%

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

      1. associate-*r* 56.6%

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

      2. *-commutative 56.6%

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

      3. associate-*r* 56.6%

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

      4. times-frac 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in b around 0 72.8%

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

   if -6.3000000000000001e34 < b < 2.89999999999999976e-274

   1. Initial program 97.4%

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

   2. Taylor expanded in y around 0 80.0%

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

   3. Taylor expanded in b around 0 82.3%

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

      1. expm1-log1p-u 63.3%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)\right)}}{y} \]

      2. expm1-udef 51.2%

         \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left({a}^{\left(t - 1\right)} \cdot x\right)} - 1}}{y} \]

      3. *-commutative 51.2%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(\color{blue}{x \cdot {a}^{\left(t - 1\right)}}\right)} - 1}{y} \]

      4. pow-sub 51.2%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \color{blue}{\frac{{a}^{t}}{{a}^{1}}}\right)} - 1}{y} \]

      5. pow1 51.2%

         \[\leadsto \frac{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{\color{blue}{a}}\right)} - 1}{y} \]

   5. Applied egg-rr 51.2%

      \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)} - 1}}{y} \]
   6. Step-by-step derivation

      1. expm1-def 63.4%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \frac{{a}^{t}}{a}\right)\right)}}{y} \]

      2. expm1-log1p 82.3%

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

   7. Simplified 82.3%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -6.3 \cdot 10^{+34}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-274}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{t}}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{+39}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 13: 60.3% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

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 * exp(b)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in t around 0 82.1%

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

   1. mul-1-neg 82.1%

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

4. Simplified 82.1%

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

5. Taylor expanded in y around 0 59.3%

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

   1. exp-neg 59.3%

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

   2. associate-*l/ 59.3%

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

   3. *-lft-identity 59.3%

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

   4. exp-sum 59.3%

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

   5. rem-exp-log 59.9%

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

   6. *-commutative 59.9%

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

   7. associate-/r* 56.7%

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

   8. associate-/r* 56.7%

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

   9. *-commutative 56.7%

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

   10. associate-/r* 59.8%

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

7. Simplified 59.8%

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

8. Final simplification 59.8%

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

Alternative 14: 42.0% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y + y \cdot b\right)}\\ t_2 := \frac{\frac{x}{a}}{y}\\ \mathbf{if}\;b \leq -6 \cdot 10^{+99}:\\ \;\;\;\;\left(t_2 - \frac{x}{a} \cdot \frac{b}{y}\right) + t_2 \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 340000000000 \lor \neg \left(b \leq 9.5 \cdot 10^{+61}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \left(b \cdot \frac{x}{a}\right) \cdot \left(a \cdot \frac{y}{x}\right)}{a \cdot \left(y \cdot \frac{y}{x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (+ y (* y b))))) (t_2 (/ (/ x a) y)))
   (if (<= b -6e+99)
     (+ (- t_2 (* (/ x a) (/ b y))) (* t_2 (* 0.5 (* b b))))
     (if (<= b -8.5e+72)
       t_1
       (if (<= b -2e-21)
         (/ (- x (* x b)) (* y a))
         (if (<= b 3.7e-54)
           (/ 1.0 (* y (/ a x)))
           (if (or (<= b 340000000000.0) (not (<= b 9.5e+61)))
             t_1
             (/
              (- y (* (* b (/ x a)) (* a (/ y x))))
              (* a (* y (/ y x)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (y * b)));
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -6e+99) {
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)));
	} else if (b <= -8.5e+72) {
		tmp = t_1;
	} else if (b <= -2e-21) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 3.7e-54) {
		tmp = 1.0 / (y * (a / x));
	} else if ((b <= 340000000000.0) || !(b <= 9.5e+61)) {
		tmp = t_1;
	} else {
		tmp = (y - ((b * (x / a)) * (a * (y / x)))) / (a * (y * (y / x)));
	}
	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 / (a * (y + (y * b)))
    t_2 = (x / a) / y
    if (b <= (-6d+99)) then
        tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5d0 * (b * b)))
    else if (b <= (-8.5d+72)) then
        tmp = t_1
    else if (b <= (-2d-21)) then
        tmp = (x - (x * b)) / (y * a)
    else if (b <= 3.7d-54) then
        tmp = 1.0d0 / (y * (a / x))
    else if ((b <= 340000000000.0d0) .or. (.not. (b <= 9.5d+61))) then
        tmp = t_1
    else
        tmp = (y - ((b * (x / a)) * (a * (y / x)))) / (a * (y * (y / x)))
    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 + (y * b)));
	double t_2 = (x / a) / y;
	double tmp;
	if (b <= -6e+99) {
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)));
	} else if (b <= -8.5e+72) {
		tmp = t_1;
	} else if (b <= -2e-21) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 3.7e-54) {
		tmp = 1.0 / (y * (a / x));
	} else if ((b <= 340000000000.0) || !(b <= 9.5e+61)) {
		tmp = t_1;
	} else {
		tmp = (y - ((b * (x / a)) * (a * (y / x)))) / (a * (y * (y / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y + (y * b)))
	t_2 = (x / a) / y
	tmp = 0
	if b <= -6e+99:
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)))
	elif b <= -8.5e+72:
		tmp = t_1
	elif b <= -2e-21:
		tmp = (x - (x * b)) / (y * a)
	elif b <= 3.7e-54:
		tmp = 1.0 / (y * (a / x))
	elif (b <= 340000000000.0) or not (b <= 9.5e+61):
		tmp = t_1
	else:
		tmp = (y - ((b * (x / a)) * (a * (y / x)))) / (a * (y * (y / x)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y + Float64(y * b))))
	t_2 = Float64(Float64(x / a) / y)
	tmp = 0.0
	if (b <= -6e+99)
		tmp = Float64(Float64(t_2 - Float64(Float64(x / a) * Float64(b / y))) + Float64(t_2 * Float64(0.5 * Float64(b * b))));
	elseif (b <= -8.5e+72)
		tmp = t_1;
	elseif (b <= -2e-21)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	elseif (b <= 3.7e-54)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	elseif ((b <= 340000000000.0) || !(b <= 9.5e+61))
		tmp = t_1;
	else
		tmp = Float64(Float64(y - Float64(Float64(b * Float64(x / a)) * Float64(a * Float64(y / x)))) / Float64(a * Float64(y * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y + (y * b)));
	t_2 = (x / a) / y;
	tmp = 0.0;
	if (b <= -6e+99)
		tmp = (t_2 - ((x / a) * (b / y))) + (t_2 * (0.5 * (b * b)));
	elseif (b <= -8.5e+72)
		tmp = t_1;
	elseif (b <= -2e-21)
		tmp = (x - (x * b)) / (y * a);
	elseif (b <= 3.7e-54)
		tmp = 1.0 / (y * (a / x));
	elseif ((b <= 340000000000.0) || ~((b <= 9.5e+61)))
		tmp = t_1;
	else
		tmp = (y - ((b * (x / a)) * (a * (y / x)))) / (a * (y * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -6e+99], N[(N[(t$95$2 - N[(N[(x / a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(0.5 * N[(b * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.5e+72], t$95$1, If[LessEqual[b, -2e-21], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-54], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 340000000000.0], N[Not[LessEqual[b, 9.5e+61]], $MachinePrecision]], t$95$1, N[(N[(y - N[(N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision] * N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.00000000000000029e99

   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 97.9%

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

      1. mul-1-neg 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in y around 0 91.4%

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

      1. exp-neg 91.4%

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

      2. associate-*l/ 91.4%

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

      3. *-lft-identity 91.4%

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

      4. exp-sum 91.4%

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

      5. rem-exp-log 91.4%

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

      6. *-commutative 91.4%

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

      7. associate-/r* 84.9%

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

      8. associate-/r* 84.9%

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

      9. *-commutative 84.9%

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

      10. associate-/r* 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in b around 0 54.6%

      \[\leadsto \color{blue}{-1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) + \left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}\right)} \]
   9. Step-by-step derivation

      1. +-commutative 54.6%

         \[\leadsto \color{blue}{\left(-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right)} \]

      2. +-commutative 54.6%

         \[\leadsto \color{blue}{\left(\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      3. mul-1-neg 54.6%

         \[\leadsto \left(\frac{x}{y \cdot a} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      4. unsub-neg 54.6%

         \[\leadsto \color{blue}{\left(\frac{x}{y \cdot a} - \frac{b \cdot x}{a \cdot y}\right)} + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      5. *-commutative 54.6%

         \[\leadsto \left(\frac{x}{\color{blue}{a \cdot y}} - \frac{b \cdot x}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      6. associate-/r* 54.6%

         \[\leadsto \left(\color{blue}{\frac{\frac{x}{a}}{y}} - \frac{b \cdot x}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      7. *-commutative 54.6%

         \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{\color{blue}{x \cdot b}}{a \cdot y}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      8. times-frac 52.5%

         \[\leadsto \left(\frac{\frac{x}{a}}{y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}}\right) + -1 \cdot \left({b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right) \]

      9. mul-1-neg 52.5%

         \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \color{blue}{\left(-{b}^{2} \cdot \left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right)\right)} \]

      10. *-commutative 52.5%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\color{blue}{\left(0.5 \cdot \frac{x}{y \cdot a} + -1 \cdot \frac{x}{y \cdot a}\right) \cdot {b}^{2}}\right) \]

      11. distribute-rgt-out 76.4%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\color{blue}{\left(\frac{x}{y \cdot a} \cdot \left(0.5 + -1\right)\right)} \cdot {b}^{2}\right) \]

      12. metadata-eval 76.4%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\left(\frac{x}{y \cdot a} \cdot \color{blue}{-0.5}\right) \cdot {b}^{2}\right) \]

      13. *-commutative 76.4%

          \[\leadsto \left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \left(-\color{blue}{\left(-0.5 \cdot \frac{x}{y \cdot a}\right)} \cdot {b}^{2}\right) \]

   10. Simplified 78.6%

       \[\leadsto \color{blue}{\left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \frac{\frac{x}{a}}{y} \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)} \]

   if -6.00000000000000029e99 < b < -8.5000000000000004e72 or 3.7000000000000003e-54 < b < 3.4e11 or 9.49999999999999959e61 < b

   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 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 68.3%

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

      1. exp-neg 68.3%

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

      2. associate-*l/ 68.3%

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

      3. *-lft-identity 68.3%

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

      4. exp-sum 68.3%

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

      5. rem-exp-log 68.3%

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

      6. *-commutative 68.3%

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

      7. associate-/r* 62.9%

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

      8. associate-/r* 62.9%

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

      9. *-commutative 62.9%

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

      10. associate-/r* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in b around 0 44.4%

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

   if -8.5000000000000004e72 < b < -1.99999999999999982e-21

   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 64.4%

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

      1. mul-1-neg 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in y around 0 58.8%

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

      1. exp-neg 58.8%

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

      2. associate-*l/ 58.8%

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

      3. *-lft-identity 58.8%

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

      4. exp-sum 58.8%

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

      5. rem-exp-log 59.5%

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

      6. *-commutative 59.5%

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

      7. associate-/r* 53.5%

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

      8. associate-/r* 53.5%

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

      9. *-commutative 53.5%

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

      10. associate-/r* 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in b around 0 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

      5. associate-/r* 54.5%

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

      6. *-commutative 54.5%

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

      7. times-frac 54.5%

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

   10. Simplified 54.5%

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

       1. associate-/l/ 54.5%

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

       2. frac-times 65.6%

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

       3. *-commutative 65.6%

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

       4. sub-div 65.6%

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

       5. *-commutative 65.6%

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

   12. Applied egg-rr 65.6%

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

   if -1.99999999999999982e-21 < b < 3.7000000000000003e-54

   1. Initial program 97.6%

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

      1. associate-*r/ 96.1%

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

      2. sub-neg 96.1%

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

      3. exp-sum 96.1%

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

      4. associate-/l* 96.1%

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

      5. associate-/r/ 96.1%

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

      6. exp-neg 96.1%

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

      7. associate-*r/ 96.1%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in t around 0 68.1%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*r* 68.1%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in y around 0 38.9%

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

      1. associate-/r* 38.1%

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

      2. *-commutative 38.1%

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

      3. associate-/r* 38.1%

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

      4. associate-/r* 38.1%

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

      5. *-commutative 38.1%

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

      6. associate-/r* 38.1%

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

      7. exp-neg 38.1%

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

   9. Simplified 38.1%

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

   10. Taylor expanded in b around 0 38.9%

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

       1. associate-/r* 38.1%

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

   12. Simplified 38.1%

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

       1. associate-*r/ 41.8%

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

       2. div-inv 41.8%

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

       3. div-inv 41.7%

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

       4. clear-num 41.8%

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

       5. frac-times 41.8%

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

       6. metadata-eval 41.8%

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

   14. Applied egg-rr 41.8%

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

   if 3.4e11 < b < 9.49999999999999959e61

   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 90.2%

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

      1. mul-1-neg 90.2%

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

   4. Simplified 90.2%

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

   5. Taylor expanded in y around 0 50.8%

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

      1. exp-neg 50.8%

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

      2. associate-*l/ 50.8%

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

      3. *-lft-identity 50.8%

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

      4. exp-sum 50.8%

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

      5. rem-exp-log 50.8%

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

      6. *-commutative 50.8%

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

      7. associate-/r* 50.6%

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

      8. associate-/r* 50.6%

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

      9. *-commutative 50.6%

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

      10. associate-/r* 50.8%

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

   7. Simplified 50.8%

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

   8. Taylor expanded in b around 0 1.7%

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

      1. +-commutative 1.7%

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

      2. mul-1-neg 1.7%

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

      3. unsub-neg 1.7%

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

      4. *-commutative 1.7%

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

      5. associate-/r* 11.8%

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

      6. *-commutative 11.8%

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

      7. times-frac 11.7%

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

   10. Simplified 11.7%

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

       1. clear-num 11.7%

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

       2. associate-*r/ 11.7%

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

       3. frac-sub 10.9%

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

       4. *-un-lft-identity 10.9%

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

       5. clear-num 10.9%

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

       6. associate-/l/ 10.8%

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

       7. clear-num 10.8%

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

       8. *-commutative 10.8%

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

       9. *-un-lft-identity 10.8%

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

       10. times-frac 30.9%

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

       11. /-rgt-identity 30.9%

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

       12. clear-num 30.9%

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

       13. associate-/l/ 21.5%

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

       14. clear-num 21.5%

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

       15. *-commutative 21.5%

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

       16. *-un-lft-identity 21.5%

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

       17. times-frac 21.4%

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

       18. /-rgt-identity 21.4%

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

   12. Applied egg-rr 21.4%

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

       1. associate-*l* 30.8%

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

   14. Simplified 30.8%

       \[\leadsto \color{blue}{\frac{y - \left(a \cdot \frac{y}{x}\right) \cdot \left(\frac{x}{a} \cdot b\right)}{a \cdot \left(\frac{y}{x} \cdot y\right)}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+99}:\\ \;\;\;\;\left(\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}\right) + \frac{\frac{x}{a}}{y} \cdot \left(0.5 \cdot \left(b \cdot b\right)\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 340000000000 \lor \neg \left(b \leq 9.5 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \left(b \cdot \frac{x}{a}\right) \cdot \left(a \cdot \frac{y}{x}\right)}{a \cdot \left(y \cdot \frac{y}{x}\right)}\\ \end{array} \]

Alternative 15: 38.5% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+73} \lor \neg \left(b \leq 4.5 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.4e+99)
   (* (/ x a) (/ (- b) y))
   (if (or (<= b -1.05e+73) (not (<= b 4.5e-54)))
     (/ x (* a (+ y (* y b))))
     (/ 1.0 (* y (/ a x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.4e+99) {
		tmp = (x / a) * (-b / y);
	} else if ((b <= -1.05e+73) || !(b <= 4.5e-54)) {
		tmp = x / (a * (y + (y * b)));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	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 <= (-7.4d+99)) then
        tmp = (x / a) * (-b / y)
    else if ((b <= (-1.05d+73)) .or. (.not. (b <= 4.5d-54))) then
        tmp = x / (a * (y + (y * b)))
    else
        tmp = 1.0d0 / (y * (a / x))
    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 <= -7.4e+99) {
		tmp = (x / a) * (-b / y);
	} else if ((b <= -1.05e+73) || !(b <= 4.5e-54)) {
		tmp = x / (a * (y + (y * b)));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.4e+99:
		tmp = (x / a) * (-b / y)
	elif (b <= -1.05e+73) or not (b <= 4.5e-54):
		tmp = x / (a * (y + (y * b)))
	else:
		tmp = 1.0 / (y * (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.4e+99)
		tmp = Float64(Float64(x / a) * Float64(Float64(-b) / y));
	elseif ((b <= -1.05e+73) || !(b <= 4.5e-54))
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	else
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.4e+99)
		tmp = (x / a) * (-b / y);
	elseif ((b <= -1.05e+73) || ~((b <= 4.5e-54)))
		tmp = x / (a * (y + (y * b)));
	else
		tmp = 1.0 / (y * (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.4e+99], N[(N[(x / a), $MachinePrecision] * N[((-b) / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.05e+73], N[Not[LessEqual[b, 4.5e-54]], $MachinePrecision]], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4000000000000002e99

   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 97.9%

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

      1. mul-1-neg 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in y around 0 91.4%

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

      1. exp-neg 91.4%

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

      2. associate-*l/ 91.4%

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

      3. *-lft-identity 91.4%

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

      4. exp-sum 91.4%

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

      5. rem-exp-log 91.4%

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

      6. *-commutative 91.4%

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

      7. associate-/r* 84.9%

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

      8. associate-/r* 84.9%

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

      9. *-commutative 84.9%

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

      10. associate-/r* 91.4%

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

   7. Simplified 91.4%

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

   8. Taylor expanded in b around 0 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

      5. associate-/r* 51.9%

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

      6. *-commutative 51.9%

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

      7. times-frac 54.0%

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

   10. Simplified 54.0%

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

   11. Taylor expanded in b around inf 49.9%

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

       1. associate-*r/ 49.9%

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

       2. *-commutative 49.9%

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

       3. neg-mul-1 49.9%

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

       4. distribute-frac-neg 49.9%

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

       5. times-frac 54.0%

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

       6. distribute-rgt-neg-out 54.0%

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

       7. distribute-neg-frac 54.0%

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

   13. Simplified 54.0%

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

   if -7.4000000000000002e99 < b < -1.0500000000000001e73 or 4.4999999999999998e-54 < b

   1. Initial program 98.9%

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

   2. Taylor expanded in t around 0 86.0%

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

      1. mul-1-neg 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in y around 0 66.2%

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

      1. exp-neg 66.2%

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

      2. associate-*l/ 66.2%

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

      3. *-lft-identity 66.2%

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

      4. exp-sum 66.2%

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

      5. rem-exp-log 66.2%

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

      6. *-commutative 66.2%

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

      7. associate-/r* 61.4%

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

      8. associate-/r* 61.4%

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

      9. *-commutative 61.4%

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

      10. associate-/r* 69.5%

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

   7. Simplified 69.5%

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

   8. Taylor expanded in b around 0 40.7%

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

   if -1.0500000000000001e73 < b < 4.4999999999999998e-54

   1. Initial program 97.8%

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

      1. associate-*r/ 96.5%

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

      2. sub-neg 96.5%

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

      3. exp-sum 92.6%

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

      4. associate-/l* 92.6%

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

      5. associate-/r/ 92.6%

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

      6. exp-neg 92.6%

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

      7. associate-*r/ 92.6%

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

   3. Simplified 77.1%

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

   4. Taylor expanded in t around 0 65.3%

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

      1. associate-*r* 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* 65.3%

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

   6. Simplified 65.3%

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

   7. Taylor expanded in y around 0 41.7%

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

      1. associate-/r* 41.0%

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

      2. *-commutative 41.0%

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

      3. associate-/r* 41.0%

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

      4. associate-/r* 41.0%

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

      5. *-commutative 41.0%

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

      6. associate-/r* 41.0%

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

      7. exp-neg 41.0%

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

   9. Simplified 41.0%

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

   10. Taylor expanded in b around 0 41.0%

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

       1. associate-/r* 40.2%

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

   12. Simplified 40.2%

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

       1. associate-*r/ 42.6%

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

       2. div-inv 42.6%

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

       3. div-inv 42.6%

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

       4. clear-num 42.6%

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

       5. frac-times 42.7%

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

       6. metadata-eval 42.7%

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

   14. Applied egg-rr 42.7%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{x} \cdot y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+73} \lor \neg \left(b \leq 4.5 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \]

Alternative 16: 40.1% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-147}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-54}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+99)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b -1.4e-147)
     (/ (- x (* x b)) (* y a))
     (if (<= b 1.9e-54) (/ 1.0 (* y (/ a x))) (/ x (* a (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+99) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -1.4e-147) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 1.9e-54) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x / (a * (y + (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 <= (-9.5d+99)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= (-1.4d-147)) then
        tmp = (x - (x * b)) / (y * a)
    else if (b <= 1.9d-54) then
        tmp = 1.0d0 / (y * (a / x))
    else
        tmp = x / (a * (y + (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 <= -9.5e+99) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -1.4e-147) {
		tmp = (x - (x * b)) / (y * a);
	} else if (b <= 1.9e-54) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+99:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= -1.4e-147:
		tmp = (x - (x * b)) / (y * a)
	elif b <= 1.9e-54:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+99)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= -1.4e-147)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	elseif (b <= 1.9e-54)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+99)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= -1.4e-147)
		tmp = (x - (x * b)) / (y * a);
	elseif (b <= 1.9e-54)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+99], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.4e-147], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-54], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.49999999999999908e99

   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 97.8%

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

      1. mul-1-neg 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in y around 0 91.3%

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

      1. exp-neg 91.3%

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

      2. associate-*l/ 91.3%

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

      3. *-lft-identity 91.3%

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

      4. exp-sum 91.3%

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

      5. rem-exp-log 91.3%

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

      6. *-commutative 91.3%

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

      7. associate-/r* 84.5%

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

      8. associate-/r* 84.5%

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

      9. *-commutative 84.5%

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

      10. associate-/r* 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in b around 0 48.8%

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

      1. +-commutative 48.8%

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

      2. mul-1-neg 48.8%

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

      3. unsub-neg 48.8%

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

      4. *-commutative 48.8%

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

      5. associate-/r* 50.8%

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

      6. *-commutative 50.8%

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

      7. times-frac 53.0%

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

   10. Simplified 53.0%

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

   11. Taylor expanded in y around 0 63.5%

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

   if -9.49999999999999908e99 < b < -1.4e-147

   1. Initial program 97.7%

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

   2. Taylor expanded in t around 0 71.9%

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

      1. mul-1-neg 71.9%

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

   4. Simplified 71.9%

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

   5. Taylor expanded in y around 0 42.4%

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

      1. exp-neg 42.4%

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

      2. associate-*l/ 42.4%

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

      3. *-lft-identity 42.4%

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

      4. exp-sum 42.5%

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

      5. rem-exp-log 42.9%

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

      6. *-commutative 42.9%

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

      7. associate-/r* 41.0%

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

      8. associate-/r* 41.0%

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

      9. *-commutative 41.0%

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

      10. associate-/r* 44.7%

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

   7. Simplified 44.7%

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

   8. Taylor expanded in b around 0 48.7%

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

      1. +-commutative 48.7%

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

      2. mul-1-neg 48.7%

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

      3. unsub-neg 48.7%

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

      4. *-commutative 48.7%

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

      5. associate-/r* 43.5%

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

      6. *-commutative 43.5%

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

      7. times-frac 41.8%

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

   10. Simplified 41.8%

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

       1. associate-/l/ 45.3%

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

       2. frac-times 48.7%

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

       3. *-commutative 48.7%

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

       4. sub-div 50.6%

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

       5. *-commutative 50.6%

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

   12. Applied egg-rr 50.6%

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

   if -1.4e-147 < b < 1.9000000000000001e-54

   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/ 95.0%

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

      2. sub-neg 95.0%

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

      3. exp-sum 95.0%

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

      4. associate-/l* 95.0%

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

      5. associate-/r/ 95.0%

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

      6. exp-neg 95.0%

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

      7. associate-*r/ 95.0%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in t around 0 68.0%

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

      1. associate-*r* 68.0%

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

      2. *-commutative 68.0%

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

      3. associate-*r* 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in y around 0 38.3%

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

      1. associate-/r* 37.1%

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

      2. *-commutative 37.1%

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

      3. associate-/r* 37.1%

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

      4. associate-/r* 37.1%

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

      5. *-commutative 37.1%

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

      6. associate-/r* 37.1%

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

      7. exp-neg 37.1%

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

   9. Simplified 37.1%

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

   10. Taylor expanded in b around 0 38.3%

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

       1. associate-/r* 37.1%

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

   12. Simplified 37.1%

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

       1. associate-*r/ 43.2%

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

       2. div-inv 43.2%

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

       3. div-inv 43.1%

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

       4. clear-num 43.2%

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

       5. frac-times 43.3%

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

       6. metadata-eval 43.3%

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

   14. Applied egg-rr 43.3%

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

   if 1.9000000000000001e-54 < b

   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 86.0%

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

      1. mul-1-neg 86.0%

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

   4. Simplified 86.0%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 70.8%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 70.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 70.8%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 70.8%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 70.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 70.8%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 70.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 65.6%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

      8. associate-/r* 65.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      9. *-commutative 65.6%

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      10. associate-/r* 74.4%

          \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Simplified 74.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 36.6%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b + y\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-147}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-54}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 17: 40.5% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00043:\\ \;\;\;\;x \cdot \left(\frac{\frac{1}{a}}{y} - \frac{\frac{b}{a}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.00043)
   (* x (- (/ (/ 1.0 a) y) (/ (/ b a) y)))
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.00043) {
		tmp = x * (((1.0 / a) / y) - ((b / a) / y));
	} else {
		tmp = x / (a * (y + (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 <= (-0.00043d0)) then
        tmp = x * (((1.0d0 / a) / y) - ((b / a) / y))
    else
        tmp = x / (a * (y + (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 <= -0.00043) {
		tmp = x * (((1.0 / a) / y) - ((b / a) / y));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.00043:
		tmp = x * (((1.0 / a) / y) - ((b / a) / y))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.00043)
		tmp = Float64(x * Float64(Float64(Float64(1.0 / a) / y) - Float64(Float64(b / a) / y)));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.00043)
		tmp = x * (((1.0 / a) / y) - ((b / a) / y));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.00043], N[(x * N[(N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision] - N[(N[(b / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.29999999999999989e-4

   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 57.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a} \cdot e^{-b}}}{y} \]

      4. associate-/l* 57.4%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{\frac{y}{e^{-b}}}} \]

      5. associate-/r/ 57.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot e^{-b}\right)} \]

      6. exp-neg 57.4%

         \[\leadsto x \cdot \left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot \color{blue}{\frac{1}{e^{b}}}\right) \]

      7. associate-*r/ 57.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot 1}{e^{b}}} \]

   3. Simplified 45.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{\frac{y}{{z}^{y}}}}{e^{b}}} \]

   4. Taylor expanded in t around 0 61.9%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r* 58.9%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 58.9%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

      3. associate-*r* 61.9%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   6. Simplified 61.9%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}} \]

   7. Taylor expanded in y around 0 76.9%

      \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot \left(a \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-/r* 76.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{y}}{a \cdot e^{b}}} \]

      2. *-commutative 76.9%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{e^{b} \cdot a}} \]

      3. associate-/r* 76.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{\frac{1}{y}}{e^{b}}}{a}} \]

      4. associate-/r* 76.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{y \cdot e^{b}}}}{a} \]

      5. *-commutative 76.9%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot y}}}{a} \]

      6. associate-/r* 76.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{y}}}{a} \]

      7. exp-neg 76.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{e^{-b}}}{y}}{a} \]

   9. Simplified 76.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{y}}{a}} \]

   10. Taylor expanded in b around 0 57.6%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y \cdot a} + -1 \cdot \frac{b}{a \cdot y}\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 57.6%

          \[\leadsto x \cdot \left(\frac{1}{y \cdot a} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       2. unsub-neg 57.6%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{y \cdot a} - \frac{b}{a \cdot y}\right)} \]

       3. *-commutative 57.6%

          \[\leadsto x \cdot \left(\frac{1}{\color{blue}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

       4. associate-/r* 57.6%

          \[\leadsto x \cdot \left(\color{blue}{\frac{\frac{1}{a}}{y}} - \frac{b}{a \cdot y}\right) \]

       5. associate-/r* 64.5%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} - \color{blue}{\frac{\frac{b}{a}}{y}}\right) \]

   12. Simplified 64.5%

       \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{\frac{b}{a}}{y}\right)} \]

   if -4.29999999999999989e-4 < b

   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. Taylor expanded in t around 0 79.3%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 79.3%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 79.3%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 52.9%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 52.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 52.9%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 52.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 52.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 53.8%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 53.8%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 51.6%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

      8. associate-/r* 51.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      9. *-commutative 51.6%

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      10. associate-/r* 53.6%

          \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Simplified 53.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 38.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b + y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00043:\\ \;\;\;\;x \cdot \left(\frac{\frac{1}{a}}{y} - \frac{\frac{b}{a}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]

Alternative 18: 34.8% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.4e+99) (* (/ x a) (/ (- b) y)) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.4e+99) {
		tmp = (x / a) * (-b / y);
	} else {
		tmp = x / (y * 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 (b <= (-6.4d+99)) then
        tmp = (x / a) * (-b / y)
    else
        tmp = x / (y * 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 (b <= -6.4e+99) {
		tmp = (x / a) * (-b / y);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.4e+99:
		tmp = (x / a) * (-b / y)
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.4e+99)
		tmp = Float64(Float64(x / a) * Float64(Float64(-b) / y));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.4e+99)
		tmp = (x / a) * (-b / y);
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.4e+99], N[(N[(x / a), $MachinePrecision] * N[((-b) / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.39999999999999999e99

   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 97.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 97.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 97.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 91.4%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 91.4%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 91.4%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 91.4%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 91.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 91.4%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 91.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 84.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

      8. associate-/r* 84.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      9. *-commutative 84.9%

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      10. associate-/r* 91.4%

          \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Simplified 91.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 49.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. +-commutative 49.9%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 49.9%

         \[\leadsto \frac{x}{y \cdot a} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 49.9%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{b \cdot x}{a \cdot y}} \]

      4. *-commutative 49.9%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} - \frac{b \cdot x}{a \cdot y} \]

      5. associate-/r* 51.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} - \frac{b \cdot x}{a \cdot y} \]

      6. *-commutative 51.9%

         \[\leadsto \frac{\frac{x}{a}}{y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      7. times-frac 54.0%

         \[\leadsto \frac{\frac{x}{a}}{y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   10. Simplified 54.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   11. Taylor expanded in b around inf 49.9%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. associate-*r/ 49.9%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. *-commutative 49.9%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(x \cdot b\right)}}{a \cdot y} \]

       3. neg-mul-1 49.9%

          \[\leadsto \frac{\color{blue}{-x \cdot b}}{a \cdot y} \]

       4. distribute-frac-neg 49.9%

          \[\leadsto \color{blue}{-\frac{x \cdot b}{a \cdot y}} \]

       5. times-frac 54.0%

          \[\leadsto -\color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

       6. distribute-rgt-neg-out 54.0%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

       7. distribute-neg-frac 54.0%

          \[\leadsto \frac{x}{a} \cdot \color{blue}{\frac{-b}{y}} \]

   13. Simplified 54.0%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{-b}{y}} \]

   if -6.39999999999999999e99 < b

   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 t around 0 78.6%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 78.6%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 78.6%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in b around 0 63.9%

      \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 63.9%

         \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]

      2. exp-diff 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      3. *-commutative 63.9%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      4. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      5. rem-exp-log 64.5%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

      6. associate-*r/ 64.5%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

      7. associate-/l* 64.5%

         \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   7. Simplified 64.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   8. Taylor expanded in y around 0 36.6%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.4 \cdot 10^{+99}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 19: 34.3% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -16.5:\\ \;\;\;\;b \cdot \left(-\frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -16.5) (* b (- (/ x (* y a)))) (/ 1.0 (* y (/ a x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -16.5) {
		tmp = b * -(x / (y * a));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	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 <= (-16.5d0)) then
        tmp = b * -(x / (y * a))
    else
        tmp = 1.0d0 / (y * (a / x))
    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 <= -16.5) {
		tmp = b * -(x / (y * a));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -16.5:
		tmp = b * -(x / (y * a))
	else:
		tmp = 1.0 / (y * (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -16.5)
		tmp = Float64(b * Float64(-Float64(x / Float64(y * a))));
	else
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -16.5)
		tmp = b * -(x / (y * a));
	else
		tmp = 1.0 / (y * (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -16.5], N[(b * (-N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision])), $MachinePrecision], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -16.5

   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 89.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 89.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 89.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 76.9%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 76.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 76.9%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 76.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 76.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 76.9%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 76.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 70.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

      8. associate-/r* 70.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      9. *-commutative 70.9%

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      10. associate-/r* 76.9%

          \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 53.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 53.4%

         \[\leadsto \frac{x}{y \cdot a} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 53.4%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{b \cdot x}{a \cdot y}} \]

      4. *-commutative 53.4%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} - \frac{b \cdot x}{a \cdot y} \]

      5. associate-/r* 50.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} - \frac{b \cdot x}{a \cdot y} \]

      6. *-commutative 50.6%

         \[\leadsto \frac{\frac{x}{a}}{y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      7. times-frac 50.7%

         \[\leadsto \frac{\frac{x}{a}}{y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   10. Simplified 50.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   11. Taylor expanded in b around inf 53.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. associate-*r/ 53.4%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a \cdot y}} \]

       2. *-commutative 53.4%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(x \cdot b\right)}}{a \cdot y} \]

       3. neg-mul-1 53.4%

          \[\leadsto \frac{\color{blue}{-x \cdot b}}{a \cdot y} \]

       4. distribute-frac-neg 53.4%

          \[\leadsto \color{blue}{-\frac{x \cdot b}{a \cdot y}} \]

       5. associate-/r* 57.6%

          \[\leadsto -\color{blue}{\frac{\frac{x \cdot b}{a}}{y}} \]

       6. associate-*l/ 53.4%

          \[\leadsto -\frac{\color{blue}{\frac{x}{a} \cdot b}}{y} \]

       7. associate-*l/ 49.1%

          \[\leadsto -\color{blue}{\frac{\frac{x}{a}}{y} \cdot b} \]

       8. associate-/r* 53.4%

          \[\leadsto -\color{blue}{\frac{x}{a \cdot y}} \cdot b \]

       9. distribute-rgt-neg-in 53.4%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} \cdot \left(-b\right)} \]

   13. Simplified 53.4%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y} \cdot \left(-b\right)} \]

   if -16.5 < b

   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/ 97.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. sub-neg 97.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) + \left(-b\right)}}}{y} \]

      3. exp-sum 82.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a} \cdot e^{-b}}}{y} \]

      4. associate-/l* 82.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{\frac{y}{e^{-b}}}} \]

      5. associate-/r/ 81.1%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot e^{-b}\right)} \]

      6. exp-neg 81.1%

         \[\leadsto x \cdot \left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot \color{blue}{\frac{1}{e^{b}}}\right) \]

      7. associate-*r/ 81.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot 1}{e^{b}}} \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{\frac{y}{{z}^{y}}}}{e^{b}}} \]

   4. Taylor expanded in t around 0 66.7%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r* 65.1%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 65.1%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

      3. associate-*r* 66.7%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   6. Simplified 66.7%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}} \]

   7. Taylor expanded in y around 0 53.6%

      \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot \left(a \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-/r* 53.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{y}}{a \cdot e^{b}}} \]

      2. *-commutative 53.1%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{e^{b} \cdot a}} \]

      3. associate-/r* 53.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{\frac{1}{y}}{e^{b}}}{a}} \]

      4. associate-/r* 53.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{y \cdot e^{b}}}}{a} \]

      5. *-commutative 53.1%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot y}}}{a} \]

      6. associate-/r* 53.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{y}}}{a} \]

      7. exp-neg 53.1%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{e^{-b}}}{y}}{a} \]

   9. Simplified 53.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{y}}{a}} \]

   10. Taylor expanded in b around 0 34.3%

       \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-/r* 33.8%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{y}} \]

   12. Simplified 33.8%

       \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ 34.8%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{a}}{y}} \]

       2. div-inv 34.8%

          \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

       3. div-inv 34.8%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{1}{y}} \]

       4. clear-num 34.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}}} \cdot \frac{1}{y} \]

       5. frac-times 34.8%

          \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{a}{x} \cdot y}} \]

       6. metadata-eval 34.8%

          \[\leadsto \frac{\color{blue}{1}}{\frac{a}{x} \cdot y} \]

   14. Applied egg-rr 34.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{x} \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -16.5:\\ \;\;\;\;b \cdot \left(-\frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \]

Alternative 20: 35.2% accurate, 31.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00061:\\ \;\;\;\;-\frac{x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.00061) (- (/ (* x b) (* y a))) (/ 1.0 (* y (/ a x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.00061) {
		tmp = -((x * b) / (y * a));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	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 <= (-0.00061d0)) then
        tmp = -((x * b) / (y * a))
    else
        tmp = 1.0d0 / (y * (a / x))
    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 <= -0.00061) {
		tmp = -((x * b) / (y * a));
	} else {
		tmp = 1.0 / (y * (a / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.00061:
		tmp = -((x * b) / (y * a))
	else:
		tmp = 1.0 / (y * (a / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.00061)
		tmp = Float64(-Float64(Float64(x * b) / Float64(y * a)));
	else
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.00061)
		tmp = -((x * b) / (y * a));
	else
		tmp = 1.0 / (y * (a / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.00061], (-N[(N[(x * b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.09999999999999974e-4

   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 89.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 89.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 89.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in y around 0 76.9%

      \[\leadsto \color{blue}{\frac{e^{-\left(b + \log a\right)} \cdot x}{y}} \]
   6. Step-by-step derivation

      1. exp-neg 76.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{e^{b + \log a}}} \cdot x}{y} \]

      2. associate-*l/ 76.9%

         \[\leadsto \frac{\color{blue}{\frac{1 \cdot x}{e^{b + \log a}}}}{y} \]

      3. *-lft-identity 76.9%

         \[\leadsto \frac{\frac{\color{blue}{x}}{e^{b + \log a}}}{y} \]

      4. exp-sum 76.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{b} \cdot e^{\log a}}}}{y} \]

      5. rem-exp-log 76.9%

         \[\leadsto \frac{\frac{x}{e^{b} \cdot \color{blue}{a}}}{y} \]

      6. *-commutative 76.9%

         \[\leadsto \frac{\frac{x}{\color{blue}{a \cdot e^{b}}}}{y} \]

      7. associate-/r* 70.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

      8. associate-/r* 70.9%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{e^{b} \cdot y}} \]

      9. *-commutative 70.9%

         \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y \cdot e^{b}}} \]

      10. associate-/r* 76.9%

          \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   7. Simplified 76.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   8. Taylor expanded in b around 0 53.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

      2. mul-1-neg 53.4%

         \[\leadsto \frac{x}{y \cdot a} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

      3. unsub-neg 53.4%

         \[\leadsto \color{blue}{\frac{x}{y \cdot a} - \frac{b \cdot x}{a \cdot y}} \]

      4. *-commutative 53.4%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} - \frac{b \cdot x}{a \cdot y} \]

      5. associate-/r* 50.6%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} - \frac{b \cdot x}{a \cdot y} \]

      6. *-commutative 50.6%

         \[\leadsto \frac{\frac{x}{a}}{y} - \frac{\color{blue}{x \cdot b}}{a \cdot y} \]

      7. times-frac 50.7%

         \[\leadsto \frac{\frac{x}{a}}{y} - \color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

   10. Simplified 50.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y} - \frac{x}{a} \cdot \frac{b}{y}} \]

   11. Taylor expanded in b around -inf 53.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y \cdot a}} \]

   if -6.09999999999999974e-4 < b

   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/ 97.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. sub-neg 97.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) + \left(-b\right)}}}{y} \]

      3. exp-sum 82.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a} \cdot e^{-b}}}{y} \]

      4. associate-/l* 82.7%

         \[\leadsto x \cdot \color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{\frac{y}{e^{-b}}}} \]

      5. associate-/r/ 81.1%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot e^{-b}\right)} \]

      6. exp-neg 81.1%

         \[\leadsto x \cdot \left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot \color{blue}{\frac{1}{e^{b}}}\right) \]

      7. associate-*r/ 81.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot 1}{e^{b}}} \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{\frac{y}{{z}^{y}}}}{e^{b}}} \]

   4. Taylor expanded in t around 0 66.7%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r* 65.1%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 65.1%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

      3. associate-*r* 66.7%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   6. Simplified 66.7%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}} \]

   7. Taylor expanded in y around 0 53.6%

      \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot \left(a \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-/r* 53.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{y}}{a \cdot e^{b}}} \]

      2. *-commutative 53.1%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{e^{b} \cdot a}} \]

      3. associate-/r* 53.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{\frac{1}{y}}{e^{b}}}{a}} \]

      4. associate-/r* 53.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{y \cdot e^{b}}}}{a} \]

      5. *-commutative 53.1%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot y}}}{a} \]

      6. associate-/r* 53.1%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{y}}}{a} \]

      7. exp-neg 53.1%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{e^{-b}}}{y}}{a} \]

   9. Simplified 53.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{y}}{a}} \]

   10. Taylor expanded in b around 0 34.3%

       \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-/r* 33.8%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{y}} \]

   12. Simplified 33.8%

       \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ 34.8%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{a}}{y}} \]

       2. div-inv 34.8%

          \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

       3. div-inv 34.8%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{1}{y}} \]

       4. clear-num 34.8%

          \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}}} \cdot \frac{1}{y} \]

       5. frac-times 34.8%

          \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{a}{x} \cdot y}} \]

       6. metadata-eval 34.8%

          \[\leadsto \frac{\color{blue}{1}}{\frac{a}{x} \cdot y} \]

   14. Applied egg-rr 34.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{x} \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00061:\\ \;\;\;\;-\frac{x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \end{array} \]

Alternative 21: 32.3% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2e-54) (* (/ x a) (/ 1.0 y)) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2e-54) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * 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 <= 2d-54) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y * 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 <= 2e-54) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2e-54:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2e-54)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2e-54)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2e-54], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.0000000000000001e-54

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 82.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in b around 0 68.7%

      \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]

      2. exp-diff 68.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      3. *-commutative 68.7%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      4. exp-to-pow 68.7%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      5. rem-exp-log 69.0%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

      6. associate-*r/ 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

      7. associate-/l* 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   7. Simplified 69.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   8. Taylor expanded in y around 0 30.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. associate-/l/ 38.2%

         \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y}} \]

      2. div-inv 38.2%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{1}{y}} \]

   10. Applied egg-rr 38.2%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{1}{y}} \]

   if 2.0000000000000001e-54 < a

   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. Taylor expanded in t around 0 81.8%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 81.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 81.8%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in b around 0 58.5%

      \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 58.5%

         \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]

      2. exp-diff 58.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      3. *-commutative 58.5%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      4. exp-to-pow 58.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      5. rem-exp-log 59.3%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

      6. associate-*r/ 59.3%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

      7. associate-/l* 59.3%

         \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   7. Simplified 59.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   8. Taylor expanded in y around 0 39.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 22: 32.2% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 5e-8) (/ 1.0 (* y (/ a x))) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 5e-8) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x / (y * 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 <= 5d-8) then
        tmp = 1.0d0 / (y * (a / x))
    else
        tmp = x / (y * 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 <= 5e-8) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 5e-8:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 5e-8)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 5e-8)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 5e-8], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.9999999999999998e-8

   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/ 97.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. sub-neg 97.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) + \left(-b\right)}}}{y} \]

      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/ 73.3%

         \[\leadsto x \cdot \color{blue}{\left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot e^{-b}\right)} \]

      6. exp-neg 73.3%

         \[\leadsto x \cdot \left(\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot \color{blue}{\frac{1}{e^{b}}}\right) \]

      7. associate-*r/ 73.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{y} \cdot 1}{e^{b}}} \]

   3. Simplified 63.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{\frac{y}{{z}^{y}}}}{e^{b}}} \]

   4. Taylor expanded in t around 0 69.5%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   5. Step-by-step derivation

      1. associate-*r* 67.2%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

      2. *-commutative 67.2%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{\left(y \cdot a\right)} \cdot e^{b}} \]

      3. associate-*r* 69.5%

         \[\leadsto x \cdot \frac{{z}^{y}}{\color{blue}{y \cdot \left(a \cdot e^{b}\right)}} \]

   6. Simplified 69.5%

      \[\leadsto x \cdot \color{blue}{\frac{{z}^{y}}{y \cdot \left(a \cdot e^{b}\right)}} \]

   7. Taylor expanded in y around 0 57.9%

      \[\leadsto x \cdot \color{blue}{\frac{1}{y \cdot \left(a \cdot e^{b}\right)}} \]
   8. Step-by-step derivation

      1. associate-/r* 57.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{y}}{a \cdot e^{b}}} \]

      2. *-commutative 57.9%

         \[\leadsto x \cdot \frac{\frac{1}{y}}{\color{blue}{e^{b} \cdot a}} \]

      3. associate-/r* 57.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{\frac{1}{y}}{e^{b}}}{a}} \]

      4. associate-/r* 57.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{y \cdot e^{b}}}}{a} \]

      5. *-commutative 57.9%

         \[\leadsto x \cdot \frac{\frac{1}{\color{blue}{e^{b} \cdot y}}}{a} \]

      6. associate-/r* 57.9%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{\frac{1}{e^{b}}}{y}}}{a} \]

      7. exp-neg 57.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{e^{-b}}}{y}}{a} \]

   9. Simplified 57.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{-b}}{y}}{a}} \]

   10. Taylor expanded in b around 0 32.3%

       \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
   11. Step-by-step derivation

       1. associate-/r* 32.3%

          \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{y}} \]

   12. Simplified 32.3%

       \[\leadsto x \cdot \color{blue}{\frac{\frac{1}{a}}{y}} \]
   13. Step-by-step derivation

       1. associate-*r/ 39.0%

          \[\leadsto \color{blue}{\frac{x \cdot \frac{1}{a}}{y}} \]

       2. div-inv 39.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

       3. div-inv 38.9%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{1}{y}} \]

       4. clear-num 39.0%

          \[\leadsto \color{blue}{\frac{1}{\frac{a}{x}}} \cdot \frac{1}{y} \]

       5. frac-times 39.0%

          \[\leadsto \color{blue}{\frac{1 \cdot 1}{\frac{a}{x} \cdot y}} \]

       6. metadata-eval 39.0%

          \[\leadsto \frac{\color{blue}{1}}{\frac{a}{x} \cdot y} \]

   14. Applied egg-rr 39.0%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{x} \cdot y}} \]

   if 4.9999999999999998e-8 < a

   1. Initial program 97.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 81.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 81.7%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 81.7%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in b around 0 58.2%

      \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 58.2%

         \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]

      2. exp-diff 58.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      3. *-commutative 58.2%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      4. exp-to-pow 58.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      5. rem-exp-log 59.0%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

      6. associate-*r/ 59.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

      7. associate-/l* 59.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   7. Simplified 59.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   8. Taylor expanded in y around 0 38.9%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 23: 32.3% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 2.2e-57) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 2.2e-57) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * 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 <= 2.2d-57) then
        tmp = (x / a) / y
    else
        tmp = x / (y * 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 <= 2.2e-57) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 2.2e-57:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 2.2e-57)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 2.2e-57)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 2.2e-57], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 2.19999999999999999e-57

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

   2. Taylor expanded in t around 0 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 82.4%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 82.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in b around 0 68.7%

      \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]

      2. exp-diff 68.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      3. *-commutative 68.7%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      4. exp-to-pow 68.7%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      5. rem-exp-log 69.0%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

      6. associate-*r/ 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

      7. associate-/l* 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   7. Simplified 69.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   8. Taylor expanded in y around 0 30.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
   9. Step-by-step derivation

      1. *-commutative 30.2%

         \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

      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 2.19999999999999999e-57 < a

   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. Taylor expanded in t around 0 81.8%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
   3. Step-by-step derivation

      1. mul-1-neg 81.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   4. Simplified 81.8%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   5. Taylor expanded in b around 0 58.5%

      \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]
   6. Step-by-step derivation

      1. *-commutative 58.5%

         \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]

      2. exp-diff 58.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      3. *-commutative 58.5%

         \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      4. exp-to-pow 58.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      5. rem-exp-log 59.3%

         \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

      6. associate-*r/ 59.3%

         \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

      7. associate-/l* 59.3%

         \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   7. Simplified 59.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

   8. Taylor expanded in y around 0 39.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 2.2 \cdot 10^{-57}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]

Alternative 24: 31.1% 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 98.5%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in t around 0 82.1%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{-1 \cdot \log a}\right) - b}}{y} \]
3. Step-by-step derivation

   1. mul-1-neg 82.1%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

4. Simplified 82.1%

   \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

5. Taylor expanded in b around 0 62.8%

   \[\leadsto \frac{\color{blue}{e^{y \cdot \log z - \log a} \cdot x}}{y} \]
6. Step-by-step derivation

   1. *-commutative 62.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{y \cdot \log z - \log a}}}{y} \]

   2. exp-diff 62.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

   3. *-commutative 62.8%

      \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

   4. exp-to-pow 62.8%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

   5. rem-exp-log 63.3%

      \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   6. associate-*r/ 63.3%

      \[\leadsto \frac{\color{blue}{\frac{x \cdot {z}^{y}}{a}}}{y} \]

   7. associate-/l* 63.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

7. Simplified 63.3%

   \[\leadsto \frac{\color{blue}{\frac{x}{\frac{a}{{z}^{y}}}}}{y} \]

8. Taylor expanded in y around 0 35.6%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

9. Final simplification 35.6%

   \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 71.3% 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 2023238 
(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))