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

Percentage Accurate: 98.5% → 98.5%

Time: 20.6s

Alternatives: 19

Speedup: 1.0×

• 21.4% 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: 98.5% 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: 98.5% 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 98.9%

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

2. Final simplification 98.9%

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

Alternative 2: 79.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t - 1 \leq 10^{+81}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- t 1.0) -1e+125)
   (/ (* x (pow a t)) (* y a))
   (if (<= (- t 1.0) 1e+81)
     (* x (/ (pow z y) (* a (* y (exp b)))))
     (/ (* x (pow a (- t 1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t - 1.0) <= -1e+125) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if ((t - 1.0) <= 1e+81) {
		tmp = x * (pow(z, y) / (a * (y * exp(b))));
	} else {
		tmp = (x * pow(a, (t - 1.0))) / 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) <= (-1d+125)) then
        tmp = (x * (a ** t)) / (y * a)
    else if ((t - 1.0d0) <= 1d+81) then
        tmp = x * ((z ** y) / (a * (y * exp(b))))
    else
        tmp = (x * (a ** (t - 1.0d0))) / 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) <= -1e+125) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if ((t - 1.0) <= 1e+81) {
		tmp = x * (Math.pow(z, y) / (a * (y * Math.exp(b))));
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t - 1.0) <= -1e+125:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif (t - 1.0) <= 1e+81:
		tmp = x * (math.pow(z, y) / (a * (y * math.exp(b))))
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t - 1.0) <= -1e+125)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (Float64(t - 1.0) <= 1e+81)
		tmp = Float64(x * Float64((z ^ y) / Float64(a * Float64(y * exp(b)))));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t - 1.0) <= -1e+125)
		tmp = (x * (a ^ t)) / (y * a);
	elseif ((t - 1.0) <= 1e+81)
		tmp = x * ((z ^ y) / (a * (y * exp(b))));
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t - 1.0), $MachinePrecision], -1e+125], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t - 1.0), $MachinePrecision], 1e+81], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -9.9999999999999992e124

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 73.3%

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

      4. associate-/l* 73.3%

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

      5. associate-/r/ 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 64.4%

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

   4. Taylor expanded in y around 0 71.1%

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

   5. Taylor expanded in b around 0 97.8%

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

   if -9.9999999999999992e124 < (-.f64 t 1) < 9.99999999999999921e80

   1. Initial program 98.3%

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

      1. associate-*r/ 97.9%

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

      2. sub-neg 97.9%

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

      3. exp-sum 81.3%

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

      4. associate-/l* 81.3%

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

      5. associate-/r/ 78.5%

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

      6. exp-neg 78.5%

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

      7. associate-*r/ 78.5%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in t around 0 79.5%

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

   if 9.99999999999999921e80 < (-.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 89.1%

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

   3. Taylor expanded in b around 0 83.6%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+125}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t - 1 \leq 10^{+81}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]

Alternative 3: 81.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t - 1 \leq 10^{+81}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot \frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (- t 1.0) -1e+127)
   (/ (* x (pow a t)) (* y a))
   (if (<= (- t 1.0) 1e+81)
     (/ (* (/ (pow z y) a) (/ x (exp b))) y)
     (/ (* x (pow a (- t 1.0))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t - 1.0) <= -1e+127) {
		tmp = (x * pow(a, t)) / (y * a);
	} else if ((t - 1.0) <= 1e+81) {
		tmp = ((pow(z, y) / a) * (x / exp(b))) / y;
	} else {
		tmp = (x * pow(a, (t - 1.0))) / 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) <= (-1d+127)) then
        tmp = (x * (a ** t)) / (y * a)
    else if ((t - 1.0d0) <= 1d+81) then
        tmp = (((z ** y) / a) * (x / exp(b))) / y
    else
        tmp = (x * (a ** (t - 1.0d0))) / 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) <= -1e+127) {
		tmp = (x * Math.pow(a, t)) / (y * a);
	} else if ((t - 1.0) <= 1e+81) {
		tmp = ((Math.pow(z, y) / a) * (x / Math.exp(b))) / y;
	} else {
		tmp = (x * Math.pow(a, (t - 1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t - 1.0) <= -1e+127:
		tmp = (x * math.pow(a, t)) / (y * a)
	elif (t - 1.0) <= 1e+81:
		tmp = ((math.pow(z, y) / a) * (x / math.exp(b))) / y
	else:
		tmp = (x * math.pow(a, (t - 1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t - 1.0) <= -1e+127)
		tmp = Float64(Float64(x * (a ^ t)) / Float64(y * a));
	elseif (Float64(t - 1.0) <= 1e+81)
		tmp = Float64(Float64(Float64((z ^ y) / a) * Float64(x / exp(b))) / y);
	else
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t - 1.0) <= -1e+127)
		tmp = (x * (a ^ t)) / (y * a);
	elseif ((t - 1.0) <= 1e+81)
		tmp = (((z ^ y) / a) * (x / exp(b))) / y;
	else
		tmp = (x * (a ^ (t - 1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t - 1.0), $MachinePrecision], -1e+127], N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t - 1.0), $MachinePrecision], 1e+81], N[(N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -9.99999999999999955e126

   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 72.7%

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

      4. associate-/l* 72.7%

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

      5. associate-/r/ 72.7%

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

      6. exp-neg 72.7%

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

      7. associate-*r/ 72.7%

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

   3. Simplified 63.6%

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

   4. Taylor expanded in y around 0 70.5%

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

   5. Taylor expanded in b around 0 97.8%

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

   if -9.99999999999999955e126 < (-.f64 t 1) < 9.99999999999999921e80

   1. Initial program 98.3%

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

      1. associate-*r/ 97.9%

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

      2. sub-neg 97.9%

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

      3. exp-sum 81.4%

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

      4. associate-/l* 81.4%

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

      5. associate-/r/ 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 76.1%

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

   4. Taylor expanded in t around 0 79.2%

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

      1. *-commutative 79.2%

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

      2. associate-*l* 79.2%

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

      3. *-commutative 79.2%

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

      4. times-frac 77.5%

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

      5. *-commutative 77.5%

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

      6. associate-/r* 77.5%

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

   6. Simplified 77.5%

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

      1. associate-*r/ 83.0%

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

   8. Applied egg-rr 83.0%

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

   if 9.99999999999999921e80 < (-.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 89.1%

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

   3. Taylor expanded in b around 0 83.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t - 1 \leq -1 \cdot 10^{+127}:\\ \;\;\;\;\frac{x \cdot {a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t - 1 \leq 10^{+81}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a} \cdot \frac{x}{e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \end{array} \]

Alternative 4: 89.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+103} \lor \neg \left(y \leq 3.3 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.65e+103) (not (<= y 3.3e+131)))
   (/ (/ (* x (pow z y)) a) 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 <= -1.65e+103) || !(y <= 3.3e+131)) {
		tmp = ((x * pow(z, y)) / a) / 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 <= (-1.65d+103)) .or. (.not. (y <= 3.3d+131))) then
        tmp = ((x * (z ** y)) / a) / 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 <= -1.65e+103) || !(y <= 3.3e+131)) {
		tmp = ((x * Math.pow(z, y)) / a) / 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 <= -1.65e+103) or not (y <= 3.3e+131):
		tmp = ((x * math.pow(z, y)) / a) / 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 <= -1.65e+103) || !(y <= 3.3e+131))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / 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 <= -1.65e+103) || ~((y <= 3.3e+131)))
		tmp = ((x * (z ^ y)) / a) / 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, -1.65e+103], N[Not[LessEqual[y, 3.3e+131]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $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 < -1.65000000000000004e103 or 3.2999999999999998e131 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 74.4%

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

      4. associate-/l* 74.4%

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

      5. associate-/r/ 74.4%

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

      6. exp-neg 74.4%

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

      7. associate-*r/ 74.4%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in t around 0 65.4%

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

      1. *-commutative 65.4%

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

      2. associate-*l* 65.4%

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

      3. *-commutative 65.4%

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

      4. times-frac 65.4%

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

      5. *-commutative 65.4%

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

      6. associate-/r* 65.4%

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

   6. Simplified 65.4%

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

      1. associate-*r/ 74.4%

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

   8. Applied egg-rr 74.4%

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

   9. Taylor expanded in b around 0 91.2%

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

   if -1.65000000000000004e103 < y < 3.2999999999999998e131

   1. Initial program 98.4%

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

   2. Taylor expanded in y around 0 92.1%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+103} \lor \neg \left(y \leq 3.3 \cdot 10^{+131}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t - 1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 74.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_2 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ t_3 := \frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-26}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b)))))
        (t_2 (/ (/ (* x (pow z y)) a) y))
        (t_3 (/ (* x (pow a (- t 1.0))) y)))
   (if (<= y -4.2e+21)
     t_2
     (if (<= y -1.3e-292)
       t_1
       (if (<= y 9.5e-290)
         t_3
         (if (<= y 3.4e-191) t_1 (if (<= y 5.2e-26) t_3 t_2)))))))

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(z, y)) / a) / y;
	double t_3 = (x * pow(a, (t - 1.0))) / y;
	double tmp;
	if (y <= -4.2e+21) {
		tmp = t_2;
	} else if (y <= -1.3e-292) {
		tmp = t_1;
	} else if (y <= 9.5e-290) {
		tmp = t_3;
	} else if (y <= 3.4e-191) {
		tmp = t_1;
	} else if (y <= 5.2e-26) {
		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 * (y * exp(b)))
    t_2 = ((x * (z ** y)) / a) / y
    t_3 = (x * (a ** (t - 1.0d0))) / y
    if (y <= (-4.2d+21)) then
        tmp = t_2
    else if (y <= (-1.3d-292)) then
        tmp = t_1
    else if (y <= 9.5d-290) then
        tmp = t_3
    else if (y <= 3.4d-191) then
        tmp = t_1
    else if (y <= 5.2d-26) 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 / (a * (y * Math.exp(b)));
	double t_2 = ((x * Math.pow(z, y)) / a) / y;
	double t_3 = (x * Math.pow(a, (t - 1.0))) / y;
	double tmp;
	if (y <= -4.2e+21) {
		tmp = t_2;
	} else if (y <= -1.3e-292) {
		tmp = t_1;
	} else if (y <= 9.5e-290) {
		tmp = t_3;
	} else if (y <= 3.4e-191) {
		tmp = t_1;
	} else if (y <= 5.2e-26) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * math.exp(b)))
	t_2 = ((x * math.pow(z, y)) / a) / y
	t_3 = (x * math.pow(a, (t - 1.0))) / y
	tmp = 0
	if y <= -4.2e+21:
		tmp = t_2
	elif y <= -1.3e-292:
		tmp = t_1
	elif y <= 9.5e-290:
		tmp = t_3
	elif y <= 3.4e-191:
		tmp = t_1
	elif y <= 5.2e-26:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_2 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	t_3 = Float64(Float64(x * (a ^ Float64(t - 1.0))) / y)
	tmp = 0.0
	if (y <= -4.2e+21)
		tmp = t_2;
	elseif (y <= -1.3e-292)
		tmp = t_1;
	elseif (y <= 9.5e-290)
		tmp = t_3;
	elseif (y <= 3.4e-191)
		tmp = t_1;
	elseif (y <= 5.2e-26)
		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 * (y * exp(b)));
	t_2 = ((x * (z ^ y)) / a) / y;
	t_3 = (x * (a ^ (t - 1.0))) / y;
	tmp = 0.0;
	if (y <= -4.2e+21)
		tmp = t_2;
	elseif (y <= -1.3e-292)
		tmp = t_1;
	elseif (y <= 9.5e-290)
		tmp = t_3;
	elseif (y <= 3.4e-191)
		tmp = t_1;
	elseif (y <= 5.2e-26)
		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[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -4.2e+21], t$95$2, If[LessEqual[y, -1.3e-292], t$95$1, If[LessEqual[y, 9.5e-290], t$95$3, If[LessEqual[y, 3.4e-191], t$95$1, If[LessEqual[y, 5.2e-26], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.2e21 or 5.2000000000000002e-26 < y

   1. Initial program 99.9%

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

      1. associate-*r/ 99.9%

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

      2. sub-neg 99.9%

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

      3. exp-sum 71.9%

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

      4. associate-/l* 71.9%

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

      5. associate-/r/ 71.9%

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

      6. exp-neg 71.9%

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

      7. associate-*r/ 71.9%

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

   3. Simplified 57.6%

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

   4. Taylor expanded in t around 0 60.9%

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

      1. *-commutative 60.9%

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

      2. associate-*l* 60.9%

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

      3. *-commutative 60.9%

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

      4. times-frac 60.1%

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

      5. *-commutative 60.1%

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

      6. associate-/r* 60.1%

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

   6. Simplified 60.1%

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

      1. associate-*r/ 66.5%

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

   8. Applied egg-rr 66.5%

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

   9. Taylor expanded in b around 0 83.5%

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

   if -4.2e21 < y < -1.30000000000000007e-292 or 9.50000000000000023e-290 < y < 3.39999999999999994e-191

   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. Step-by-step derivation

      1. associate-*r/ 97.4%

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

      2. sub-neg 97.4%

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

      3. exp-sum 86.2%

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

      4. associate-/l* 86.2%

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

      5. associate-/r/ 79.9%

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

      6. exp-neg 79.9%

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

      7. associate-*r/ 79.9%

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

   3. Simplified 81.2%

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

   4. Taylor expanded in y around 0 88.9%

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

      1. associate-/r* 82.8%

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

      2. associate-*r/ 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in t around 0 86.8%

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

   if -1.30000000000000007e-292 < y < 9.50000000000000023e-290 or 3.39999999999999994e-191 < y < 5.2000000000000002e-26

   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 y around 0 98.8%

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

   3. Taylor expanded in b around 0 82.0%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-191}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-26}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 6: 72.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -4.1 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (exp b))))))
   (if (<= b -4.1e+34)
     t_1
     (if (<= b 4.8e-113)
       (* x (/ (pow z y) (* y a)))
       (if (<= b 9.5e+24) (/ (* x (pow a (- t 1.0))) 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 <= -4.1e+34) {
		tmp = t_1;
	} else if (b <= 4.8e-113) {
		tmp = x * (pow(z, y) / (y * a));
	} else if (b <= 9.5e+24) {
		tmp = (x * pow(a, (t - 1.0))) / 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 <= (-4.1d+34)) then
        tmp = t_1
    else if (b <= 4.8d-113) then
        tmp = x * ((z ** y) / (y * a))
    else if (b <= 9.5d+24) then
        tmp = (x * (a ** (t - 1.0d0))) / 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 <= -4.1e+34) {
		tmp = t_1;
	} else if (b <= 4.8e-113) {
		tmp = x * (Math.pow(z, y) / (y * a));
	} else if (b <= 9.5e+24) {
		tmp = (x * Math.pow(a, (t - 1.0))) / 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 <= -4.1e+34:
		tmp = t_1
	elif b <= 4.8e-113:
		tmp = x * (math.pow(z, y) / (y * a))
	elif b <= 9.5e+24:
		tmp = (x * math.pow(a, (t - 1.0))) / 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 <= -4.1e+34)
		tmp = t_1;
	elseif (b <= 4.8e-113)
		tmp = Float64(x * Float64((z ^ y) / Float64(y * a)));
	elseif (b <= 9.5e+24)
		tmp = Float64(Float64(x * (a ^ Float64(t - 1.0))) / 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 <= -4.1e+34)
		tmp = t_1;
	elseif (b <= 4.8e-113)
		tmp = x * ((z ^ y) / (y * a));
	elseif (b <= 9.5e+24)
		tmp = (x * (a ^ (t - 1.0))) / 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, -4.1e+34], t$95$1, If[LessEqual[b, 4.8e-113], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+24], N[(N[(x * N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.0999999999999998e34 or 9.5000000000000001e24 < 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. 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 65.8%

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

      4. associate-/l* 65.8%

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

      5. associate-/r/ 61.5%

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

      6. exp-neg 61.5%

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

      7. associate-*r/ 61.5%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in y around 0 72.8%

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

      1. associate-/r* 67.6%

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

      2. associate-*r/ 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in t around 0 81.5%

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

   if -4.0999999999999998e34 < b < 4.80000000000000024e-113

   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/ 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 93.9%

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

      4. associate-/l* 93.9%

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

      5. associate-/r/ 93.9%

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

      6. exp-neg 93.9%

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

      7. associate-*r/ 93.9%

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

   3. Simplified 85.4%

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

   4. Taylor expanded in t around 0 71.5%

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

   5. Taylor expanded in b around 0 73.7%

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

   if 4.80000000000000024e-113 < b < 9.5000000000000001e24

   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 y around 0 82.4%

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

   3. Taylor expanded in b around 0 81.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t - 1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 7: 71.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+34} \lor \neg \left(b \leq 1.05 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -7.5e+34) (not (<= b 1.05e+25)))
   (/ x (* a (* y (exp b))))
   (* x (/ (pow z y) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -7.5e+34) || !(b <= 1.05e+25)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * (pow(z, y) / (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 <= (-7.5d+34)) .or. (.not. (b <= 1.05d+25))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * ((z ** y) / (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 <= -7.5e+34) || !(b <= 1.05e+25)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * (Math.pow(z, y) / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -7.5e+34) or not (b <= 1.05e+25):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * (math.pow(z, y) / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -7.5e+34) || !(b <= 1.05e+25))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64((z ^ y) / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -7.5e+34) || ~((b <= 1.05e+25)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * ((z ^ y) / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -7.5e+34], N[Not[LessEqual[b, 1.05e+25]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -7.49999999999999976e34 or 1.05e25 < 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. 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 65.8%

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

      4. associate-/l* 65.8%

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

      5. associate-/r/ 61.5%

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

      6. exp-neg 61.5%

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

      7. associate-*r/ 61.5%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in y around 0 72.8%

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

      1. associate-/r* 67.6%

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

      2. associate-*r/ 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in t around 0 81.5%

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

   if -7.49999999999999976e34 < b < 1.05e25

   1. Initial program 97.9%

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

      1. associate-*r/ 97.3%

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

      2. sub-neg 97.3%

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

      3. exp-sum 90.9%

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

      4. associate-/l* 90.9%

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

      5. associate-/r/ 90.9%

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

      6. exp-neg 90.9%

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

      7. associate-*r/ 90.9%

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

   3. Simplified 83.4%

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

   4. Taylor expanded in t around 0 69.0%

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

   5. Taylor expanded in b around 0 71.9%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+34} \lor \neg \left(b \leq 1.05 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{y \cdot a}\\ \end{array} \]

Alternative 8: 59.1% 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 98.9%

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

   1. associate-*r/ 98.5%

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

   2. sub-neg 98.5%

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

   3. exp-sum 79.4%

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

   4. associate-/l* 79.4%

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

   5. associate-/r/ 77.5%

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

   6. exp-neg 77.5%

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

   7. associate-*r/ 77.5%

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

3. Simplified 71.1%

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

4. Taylor expanded in y around 0 67.4%

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

   1. associate-/r* 65.5%

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

   2. associate-*r/ 60.8%

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

6. Simplified 60.8%

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

7. Taylor expanded in t around 0 59.5%

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

8. Final simplification 59.5%

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

Alternative 9: 33.4% accurate, 11.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-192}:\\ \;\;\;\;\left(\frac{x}{y \cdot a} - \frac{x \cdot \frac{b}{a}}{y}\right) + \frac{b \cdot b}{y} \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (+ y (* y b))))))
   (if (<= y -1e+197)
     t_1
     (if (<= y -5.2e-192)
       (+ (- (/ x (* y a)) (/ (* x (/ b a)) y)) (* (/ (* b b) y) (/ x a)))
       (if (<= y 1.7e+19)
         (/ (/ x a) y)
         (if (<= y 7.8e+192) t_1 (/ (- (/ x a) (/ (* x b) a)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (y * b)));
	double tmp;
	if (y <= -1e+197) {
		tmp = t_1;
	} else if (y <= -5.2e-192) {
		tmp = ((x / (y * a)) - ((x * (b / a)) / y)) + (((b * b) / y) * (x / a));
	} else if (y <= 1.7e+19) {
		tmp = (x / a) / y;
	} else if (y <= 7.8e+192) {
		tmp = t_1;
	} else {
		tmp = ((x / a) - ((x * b) / 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) :: t_1
    real(8) :: tmp
    t_1 = x / (a * (y + (y * b)))
    if (y <= (-1d+197)) then
        tmp = t_1
    else if (y <= (-5.2d-192)) then
        tmp = ((x / (y * a)) - ((x * (b / a)) / y)) + (((b * b) / y) * (x / a))
    else if (y <= 1.7d+19) then
        tmp = (x / a) / y
    else if (y <= 7.8d+192) then
        tmp = t_1
    else
        tmp = ((x / a) - ((x * b) / 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 t_1 = x / (a * (y + (y * b)));
	double tmp;
	if (y <= -1e+197) {
		tmp = t_1;
	} else if (y <= -5.2e-192) {
		tmp = ((x / (y * a)) - ((x * (b / a)) / y)) + (((b * b) / y) * (x / a));
	} else if (y <= 1.7e+19) {
		tmp = (x / a) / y;
	} else if (y <= 7.8e+192) {
		tmp = t_1;
	} else {
		tmp = ((x / a) - ((x * b) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y + (y * b)))
	tmp = 0
	if y <= -1e+197:
		tmp = t_1
	elif y <= -5.2e-192:
		tmp = ((x / (y * a)) - ((x * (b / a)) / y)) + (((b * b) / y) * (x / a))
	elif y <= 1.7e+19:
		tmp = (x / a) / y
	elif y <= 7.8e+192:
		tmp = t_1
	else:
		tmp = ((x / a) - ((x * b) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y + Float64(y * b))))
	tmp = 0.0
	if (y <= -1e+197)
		tmp = t_1;
	elseif (y <= -5.2e-192)
		tmp = Float64(Float64(Float64(x / Float64(y * a)) - Float64(Float64(x * Float64(b / a)) / y)) + Float64(Float64(Float64(b * b) / y) * Float64(x / a)));
	elseif (y <= 1.7e+19)
		tmp = Float64(Float64(x / a) / y);
	elseif (y <= 7.8e+192)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y + (y * b)));
	tmp = 0.0;
	if (y <= -1e+197)
		tmp = t_1;
	elseif (y <= -5.2e-192)
		tmp = ((x / (y * a)) - ((x * (b / a)) / y)) + (((b * b) / y) * (x / a));
	elseif (y <= 1.7e+19)
		tmp = (x / a) / y;
	elseif (y <= 7.8e+192)
		tmp = t_1;
	else
		tmp = ((x / a) - ((x * b) / a)) / y;
	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]}, If[LessEqual[y, -1e+197], t$95$1, If[LessEqual[y, -5.2e-192], N[(N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(b * b), $MachinePrecision] / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e+19], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 7.8e+192], t$95$1, N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -9.9999999999999995e196 or 1.7e19 < y < 7.7999999999999996e192

   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 59.0%

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

      4. associate-/l* 59.0%

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

      5. associate-/r/ 59.0%

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

      6. exp-neg 59.0%

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

      7. associate-*r/ 59.0%

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

   3. Simplified 45.9%

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

   4. Taylor expanded in y around 0 40.2%

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

      1. associate-/r* 41.7%

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

      2. associate-*r/ 36.8%

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

   6. Simplified 36.8%

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

   7. Taylor expanded in t around 0 35.9%

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

   8. Taylor expanded in b around 0 34.5%

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

   if -9.9999999999999995e196 < y < -5.2000000000000003e-192

   1. Initial program 98.2%

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

      1. associate-*r/ 99.4%

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

      2. sub-neg 99.4%

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

      3. exp-sum 84.1%

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

      4. associate-/l* 84.1%

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

      5. associate-/r/ 81.3%

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

      6. exp-neg 81.3%

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

      7. associate-*r/ 81.3%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in y around 0 71.4%

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

      1. associate-/r* 70.1%

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

      2. associate-*r/ 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in t around 0 64.9%

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

   8. Taylor expanded in b around 0 21.6%

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

   9. Taylor expanded in b around 0 33.5%

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

       1. +-commutative 33.5%

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

       2. *-commutative 33.5%

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

       3. associate-*r/ 33.5%

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

       4. *-commutative 33.5%

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

       5. associate-*r/ 33.5%

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

       6. mul-1-neg 33.5%

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

       7. times-frac 32.0%

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

       8. distribute-lft-neg-out 32.0%

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

       9. cancel-sign-sub-inv 32.0%

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

       10. *-commutative 32.0%

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

       11. associate-*l/ 33.4%

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

       12. *-commutative 33.4%

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

       13. times-frac 38.9%

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

       14. unpow2 38.9%

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

   11. Simplified 38.9%

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

   if -5.2000000000000003e-192 < y < 1.7e19

   1. Initial program 98.4%

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

      1. associate-*r/ 96.7%

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

      2. sub-neg 96.7%

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

      3. exp-sum 87.8%

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

      4. associate-/l* 87.8%

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

      5. associate-/r/ 84.8%

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

      6. exp-neg 84.8%

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

      7. associate-*r/ 84.8%

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

   3. Simplified 86.0%

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

   4. Taylor expanded in y around 0 87.5%

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

      1. associate-/r* 82.6%

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

      2. associate-*r/ 78.6%

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

   6. Simplified 78.6%

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

   7. Taylor expanded in t around 0 73.3%

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

   8. Taylor expanded in b around 0 44.1%

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

      1. associate-/r* 47.9%

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

   10. Simplified 47.9%

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

   if 7.7999999999999996e192 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 82.6%

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

      4. associate-/l* 82.6%

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

      5. associate-/r/ 82.6%

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

      6. exp-neg 82.6%

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

      7. associate-*r/ 82.6%

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

   3. Simplified 60.9%

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

   4. Taylor expanded in y around 0 39.9%

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

      1. associate-/r* 40.5%

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

      2. associate-*r/ 36.1%

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

   6. Simplified 36.1%

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

   7. Taylor expanded in t around 0 44.9%

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

   8. Taylor expanded in b around 0 19.1%

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

   9. Taylor expanded in y around 0 44.8%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+197}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-192}:\\ \;\;\;\;\left(\frac{x}{y \cdot a} - \frac{x \cdot \frac{b}{a}}{y}\right) + \frac{b \cdot b}{y} \cdot \frac{x}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+192}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \end{array} \]

Alternative 10: 37.5% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.1:\\ \;\;\;\;\frac{b}{a} \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-220}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.1)
   (* (/ b a) (- (/ x y)))
   (if (<= b -1.15e-118)
     (* (/ x a) (/ 1.0 y))
     (if (<= b 4.8e-220) (* (/ x (* y a)) (- 1.0 b)) (/ x (* y (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.1) {
		tmp = (b / a) * -(x / y);
	} else if (b <= -1.15e-118) {
		tmp = (x / a) * (1.0 / y);
	} else if (b <= 4.8e-220) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.1d0)) then
        tmp = (b / a) * -(x / y)
    else if (b <= (-1.15d-118)) then
        tmp = (x / a) * (1.0d0 / y)
    else if (b <= 4.8d-220) then
        tmp = (x / (y * a)) * (1.0d0 - b)
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.1) {
		tmp = (b / a) * -(x / y);
	} else if (b <= -1.15e-118) {
		tmp = (x / a) * (1.0 / y);
	} else if (b <= 4.8e-220) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.1:
		tmp = (b / a) * -(x / y)
	elif b <= -1.15e-118:
		tmp = (x / a) * (1.0 / y)
	elif b <= 4.8e-220:
		tmp = (x / (y * a)) * (1.0 - b)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.1)
		tmp = Float64(Float64(b / a) * Float64(-Float64(x / y)));
	elseif (b <= -1.15e-118)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	elseif (b <= 4.8e-220)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(1.0 - b));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.1)
		tmp = (b / a) * -(x / y);
	elseif (b <= -1.15e-118)
		tmp = (x / a) * (1.0 / y);
	elseif (b <= 4.8e-220)
		tmp = (x / (y * a)) * (1.0 - b);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.1], N[(N[(b / a), $MachinePrecision] * (-N[(x / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, -1.15e-118], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.8e-220], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -0.10000000000000001

   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 62.9%

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

      4. associate-/l* 62.9%

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

      5. associate-/r/ 62.9%

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

      6. exp-neg 62.9%

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

      7. associate-*r/ 62.9%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in y around 0 67.3%

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

      1. associate-/r* 65.9%

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

      2. associate-*r/ 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in t around 0 74.7%

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

   8. Taylor expanded in b around 0 32.2%

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

   9. Taylor expanded in b around inf 32.2%

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

       1. mul-1-neg 32.2%

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

       2. times-frac 34.8%

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

       3. distribute-lft-neg-out 34.8%

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

       4. *-commutative 34.8%

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

       5. distribute-neg-frac 34.8%

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

   11. Simplified 34.8%

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

   if -0.10000000000000001 < b < -1.1500000000000001e-118

   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/ 94.7%

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

      2. sub-neg 94.7%

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

      3. exp-sum 94.8%

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

      4. associate-/l* 94.8%

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

      5. associate-/r/ 94.8%

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

      6. exp-neg 94.8%

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

      7. associate-*r/ 94.8%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in y around 0 71.8%

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

      1. associate-/r* 71.7%

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

      2. associate-*r/ 64.6%

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

   6. Simplified 64.6%

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

   7. Taylor expanded in t around 0 47.7%

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

   8. Taylor expanded in b around 0 45.3%

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

      1. *-commutative 45.3%

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

   10. Simplified 45.3%

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

       1. *-rgt-identity 45.3%

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

       2. *-commutative 45.3%

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

       3. times-frac 55.5%

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

   12. Applied egg-rr 55.5%

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

   if -1.1500000000000001e-118 < b < 4.8000000000000003e-220

   1. Initial program 96.3%

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

      1. associate-*r/ 98.0%

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

      2. sub-neg 98.0%

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

      3. exp-sum 98.0%

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

      4. associate-/l* 98.0%

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

      5. associate-/r/ 98.0%

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

      6. exp-neg 98.0%

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

      7. associate-*r/ 98.0%

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

   3. Simplified 86.2%

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

   4. Taylor expanded in y around 0 68.5%

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

      1. associate-/r* 65.1%

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

      2. associate-*r/ 55.3%

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

   6. Simplified 55.3%

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

   7. Taylor expanded in t around 0 44.1%

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

   8. Taylor expanded in b around 0 44.1%

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

   9. Taylor expanded in b around 0 40.2%

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

       1. *-commutative 40.2%

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

       2. metadata-eval 40.2%

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

       3. associate-*r/ 42.2%

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

       4. cancel-sign-sub-inv 42.2%

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

       5. *-lft-identity 42.2%

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

       6. *-lft-identity 42.2%

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

       7. distribute-rgt-out-- 44.1%

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

   11. Simplified 44.1%

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

   if 4.8000000000000003e-220 < b

   1. Initial program 99.6%

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

      1. associate-*r/ 98.8%

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

      2. sub-neg 98.8%

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

      3. exp-sum 77.4%

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

      4. associate-/l* 77.4%

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

      5. associate-/r/ 72.7%

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

      6. exp-neg 72.7%

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

      7. associate-*r/ 72.7%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate-/r* 63.9%

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

      2. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in t around 0 59.9%

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

   8. Taylor expanded in b around 0 31.3%

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

   9. Taylor expanded in b around inf 31.4%

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

       1. associate-*r* 29.5%

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

       2. *-commutative 29.5%

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

       3. associate-*r* 34.8%

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

   11. Simplified 34.8%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.1:\\ \;\;\;\;\frac{b}{a} \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-118}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{elif}\;b \leq 4.8 \cdot 10^{-220}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 11: 32.4% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{if}\;y \leq -7500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y b)))))
   (if (<= y -7500000.0)
     t_1
     (if (<= y -7e-217) (/ x (* y a)) (if (<= y 3.2e+19) (/ (/ x a) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * b));
	double tmp;
	if (y <= -7500000.0) {
		tmp = t_1;
	} else if (y <= -7e-217) {
		tmp = x / (y * a);
	} else if (y <= 3.2e+19) {
		tmp = (x / a) / 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 * b))
    if (y <= (-7500000.0d0)) then
        tmp = t_1
    else if (y <= (-7d-217)) then
        tmp = x / (y * a)
    else if (y <= 3.2d+19) then
        tmp = (x / a) / 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 * b));
	double tmp;
	if (y <= -7500000.0) {
		tmp = t_1;
	} else if (y <= -7e-217) {
		tmp = x / (y * a);
	} else if (y <= 3.2e+19) {
		tmp = (x / a) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * b))
	tmp = 0
	if y <= -7500000.0:
		tmp = t_1
	elif y <= -7e-217:
		tmp = x / (y * a)
	elif y <= 3.2e+19:
		tmp = (x / a) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * b)))
	tmp = 0.0
	if (y <= -7500000.0)
		tmp = t_1;
	elseif (y <= -7e-217)
		tmp = Float64(x / Float64(y * a));
	elseif (y <= 3.2e+19)
		tmp = Float64(Float64(x / a) / 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 * b));
	tmp = 0.0;
	if (y <= -7500000.0)
		tmp = t_1;
	elseif (y <= -7e-217)
		tmp = x / (y * a);
	elseif (y <= 3.2e+19)
		tmp = (x / a) / 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 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7500000.0], t$95$1, If[LessEqual[y, -7e-217], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+19], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.5e6 or 3.2e19 < y

   1. Initial program 100.0%

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

      1. associate-*r/ 100.0%

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

      2. sub-neg 100.0%

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

      3. exp-sum 70.8%

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

      4. associate-/l* 70.8%

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

      5. associate-/r/ 70.8%

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

      6. exp-neg 70.8%

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

      7. associate-*r/ 70.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in y around 0 45.1%

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

      1. associate-/r* 46.0%

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

      2. associate-*r/ 41.0%

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

   6. Simplified 41.0%

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

   7. Taylor expanded in t around 0 41.5%

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

   8. Taylor expanded in b around 0 26.1%

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

   9. Taylor expanded in b around inf 26.5%

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

   if -7.5e6 < y < -7e-217

   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. Step-by-step derivation

      1. associate-*r/ 98.6%

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

      2. sub-neg 98.6%

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

      3. exp-sum 86.4%

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

      4. associate-/l* 86.4%

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

      5. associate-/r/ 81.5%

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

      6. exp-neg 81.5%

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

      7. associate-*r/ 81.5%

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

   3. Simplified 82.9%

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

   4. Taylor expanded in y around 0 87.8%

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

      1. associate-/r* 83.2%

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

      2. associate-*r/ 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in t around 0 83.5%

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

   8. Taylor expanded in b around 0 45.8%

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

      1. *-commutative 45.8%

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

   10. Simplified 45.8%

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

   if -7e-217 < y < 3.2e19

   1. Initial program 98.5%

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

      1. associate-*r/ 96.7%

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

      2. sub-neg 96.7%

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

      3. exp-sum 87.2%

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

      4. associate-/l* 87.2%

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

      5. associate-/r/ 84.1%

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

      6. exp-neg 84.1%

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

      7. associate-*r/ 84.1%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. associate-/r* 82.6%

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

      2. associate-*r/ 78.4%

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

   6. Simplified 78.4%

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

   7. Taylor expanded in t around 0 71.9%

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

   8. Taylor expanded in b around 0 42.2%

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

      1. associate-/r* 47.1%

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

   10. Simplified 47.1%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7500000:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+19}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 12: 38.2% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.4e-218) (/ (- (/ x a) (* x (/ b a))) y) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.4e-218) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.4d-218) then
        tmp = ((x / a) - (x * (b / a))) / y
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.4e-218) {
		tmp = ((x / a) - (x * (b / a))) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.4e-218:
		tmp = ((x / a) - (x * (b / a))) / y
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.4e-218)
		tmp = Float64(Float64(Float64(x / a) - Float64(x * Float64(b / a))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.4e-218)
		tmp = ((x / a) - (x * (b / a))) / y;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.4e-218], N[(N[(N[(x / a), $MachinePrecision] - N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.4000000000000001e-218

   1. Initial program 98.3%

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

      1. associate-*r/ 98.3%

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

      2. sub-neg 98.3%

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

      3. exp-sum 80.9%

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

      4. associate-/l* 80.9%

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

      5. associate-/r/ 80.9%

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

      6. exp-neg 80.9%

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

      7. associate-*r/ 80.9%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in y around 0 68.5%

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

      1. associate-/r* 66.7%

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

      2. associate-*r/ 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in t around 0 59.2%

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

   8. Taylor expanded in b around 0 37.5%

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

   9. Taylor expanded in y around 0 43.4%

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

       1. +-commutative 43.4%

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

       2. mul-1-neg 43.4%

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

       3. *-commutative 43.4%

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

       4. unsub-neg 43.4%

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

       5. associate-*r/ 42.7%

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

   11. Simplified 42.7%

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

   if 2.4000000000000001e-218 < b

   1. Initial program 99.6%

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

      1. associate-*r/ 98.8%

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

      2. sub-neg 98.8%

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

      3. exp-sum 77.4%

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

      4. associate-/l* 77.4%

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

      5. associate-/r/ 72.7%

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

      6. exp-neg 72.7%

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

      7. associate-*r/ 72.7%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate-/r* 63.9%

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

      2. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in t around 0 59.9%

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

   8. Taylor expanded in b around 0 31.3%

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

   9. Taylor expanded in b around inf 31.4%

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

       1. associate-*r* 29.5%

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

       2. *-commutative 29.5%

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

       3. associate-*r* 34.8%

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

   11. Simplified 34.8%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.4 \cdot 10^{-218}:\\ \;\;\;\;\frac{\frac{x}{a} - x \cdot \frac{b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 13: 38.1% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.7e-217) (/ (- (/ x a) (/ (* x b) a)) y) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.7e-217) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.7d-217) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.7e-217) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.7e-217:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.7e-217)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.7e-217)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.7e-217], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.70000000000000008e-217

   1. Initial program 98.3%

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

      1. associate-*r/ 98.3%

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

      2. sub-neg 98.3%

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

      3. exp-sum 80.9%

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

      4. associate-/l* 80.9%

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

      5. associate-/r/ 80.9%

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

      6. exp-neg 80.9%

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

      7. associate-*r/ 80.9%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in y around 0 68.5%

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

      1. associate-/r* 66.7%

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

      2. associate-*r/ 61.3%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in t around 0 59.2%

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

   8. Taylor expanded in b around 0 37.5%

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

   9. Taylor expanded in y around 0 43.4%

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

   if 1.70000000000000008e-217 < b

   1. Initial program 99.6%

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

      1. associate-*r/ 98.8%

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

      2. sub-neg 98.8%

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

      3. exp-sum 77.4%

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

      4. associate-/l* 77.4%

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

      5. associate-/r/ 72.7%

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

      6. exp-neg 72.7%

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

      7. associate-*r/ 72.7%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate-/r* 63.9%

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

      2. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in t around 0 59.9%

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

   8. Taylor expanded in b around 0 31.3%

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

   9. Taylor expanded in b around inf 31.4%

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

       1. associate-*r* 29.5%

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

       2. *-commutative 29.5%

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

       3. associate-*r* 34.8%

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

   11. Simplified 34.8%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{-217}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 14: 36.7% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{b}{-y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8e+154)
   (* (/ x a) (/ b (- y)))
   (if (<= b 1.95e-218) (* (/ x a) (/ 1.0 y)) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+154) {
		tmp = (x / a) * (b / -y);
	} else if (b <= 1.95e-218) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d+154)) then
        tmp = (x / a) * (b / -y)
    else if (b <= 1.95d-218) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8e+154) {
		tmp = (x / a) * (b / -y);
	} else if (b <= 1.95e-218) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8e+154:
		tmp = (x / a) * (b / -y)
	elif b <= 1.95e-218:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8e+154)
		tmp = Float64(Float64(x / a) * Float64(b / Float64(-y)));
	elseif (b <= 1.95e-218)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8e+154)
		tmp = (x / a) * (b / -y);
	elseif (b <= 1.95e-218)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8e+154], N[(N[(x / a), $MachinePrecision] * N[(b / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.95e-218], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.8000000000000003e154

   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 62.9%

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

      4. associate-/l* 62.9%

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

      5. associate-/r/ 62.9%

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

      6. exp-neg 62.9%

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

      7. associate-*r/ 62.9%

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

   3. Simplified 62.9%

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

   4. Taylor expanded in y around 0 74.4%

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

      1. associate-/r* 71.5%

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

      2. associate-*r/ 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in t around 0 83.1%

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

   8. Taylor expanded in b around 0 36.3%

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

   9. Taylor expanded in b around inf 36.3%

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

       1. associate-*r/ 36.3%

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

       2. *-commutative 36.3%

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

       3. associate-*r/ 36.3%

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

       4. mul-1-neg 36.3%

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

       5. associate-*r/ 33.7%

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

       6. *-lft-identity 33.7%

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

       7. metadata-eval 33.7%

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

       8. *-commutative 33.7%

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

       9. associate-/r* 33.9%

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

       10. times-frac 33.9%

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

       11. associate-*r/ 33.9%

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

       12. neg-mul-1 33.9%

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

       13. neg-mul-1 33.9%

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

       14. associate-/r* 33.7%

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

       15. associate-*r/ 36.3%

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

       16. distribute-rgt-neg-out 36.3%

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

       17. *-commutative 36.3%

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

       18. distribute-neg-frac 36.3%

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

       19. associate-/l* 41.8%

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

       20. distribute-neg-frac 41.8%

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

       21. distribute-frac-neg 41.8%

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

   11. Simplified 36.6%

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

   if -4.8000000000000003e154 < b < 1.95e-218

   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/ 97.8%

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

      2. sub-neg 97.8%

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

      3. exp-sum 86.4%

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

      4. associate-/l* 86.4%

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

      5. associate-/r/ 86.4%

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

      6. exp-neg 86.4%

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

      7. associate-*r/ 86.4%

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

   3. Simplified 78.9%

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

   4. Taylor expanded in y around 0 66.7%

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

      1. associate-/r* 65.2%

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

      2. associate-*r/ 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in t around 0 51.8%

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

   8. Taylor expanded in b around 0 39.4%

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

      1. *-commutative 39.4%

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

   10. Simplified 39.4%

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

       1. *-rgt-identity 39.4%

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

       2. *-commutative 39.4%

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

       3. times-frac 41.1%

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

   12. Applied egg-rr 41.1%

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

   if 1.95e-218 < b

   1. Initial program 99.6%

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

      1. associate-*r/ 98.8%

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

      2. sub-neg 98.8%

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

      3. exp-sum 77.4%

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

      4. associate-/l* 77.4%

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

      5. associate-/r/ 72.7%

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

      6. exp-neg 72.7%

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

      7. associate-*r/ 72.7%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate-/r* 63.9%

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

      2. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in t around 0 59.9%

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

   8. Taylor expanded in b around 0 31.3%

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

   9. Taylor expanded in b around inf 31.4%

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

       1. associate-*r* 29.5%

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

       2. *-commutative 29.5%

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

       3. associate-*r* 34.8%

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

   11. Simplified 34.8%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{b}{-y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 15: 37.6% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.216:\\ \;\;\;\;\frac{b}{a} \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.216)
   (* (/ b a) (- (/ x y)))
   (if (<= b 1.9e-217) (* (/ x a) (/ 1.0 y)) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.216) {
		tmp = (b / a) * -(x / y);
	} else if (b <= 1.9e-217) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.216d0)) then
        tmp = (b / a) * -(x / y)
    else if (b <= 1.9d-217) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.216) {
		tmp = (b / a) * -(x / y);
	} else if (b <= 1.9e-217) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.216:
		tmp = (b / a) * -(x / y)
	elif b <= 1.9e-217:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.216)
		tmp = Float64(Float64(b / a) * Float64(-Float64(x / y)));
	elseif (b <= 1.9e-217)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.216)
		tmp = (b / a) * -(x / y);
	elseif (b <= 1.9e-217)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.216], N[(N[(b / a), $MachinePrecision] * (-N[(x / y), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 1.9e-217], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.215999999999999998

   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 62.9%

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

      4. associate-/l* 62.9%

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

      5. associate-/r/ 62.9%

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

      6. exp-neg 62.9%

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

      7. associate-*r/ 62.9%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in y around 0 67.3%

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

      1. associate-/r* 65.9%

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

      2. associate-*r/ 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in t around 0 74.7%

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

   8. Taylor expanded in b around 0 32.2%

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

   9. Taylor expanded in b around inf 32.2%

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

       1. mul-1-neg 32.2%

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

       2. times-frac 34.8%

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

       3. distribute-lft-neg-out 34.8%

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

       4. *-commutative 34.8%

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

       5. distribute-neg-frac 34.8%

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

   11. Simplified 34.8%

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

   if -0.215999999999999998 < b < 1.89999999999999993e-217

   1. Initial program 96.8%

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

      1. associate-*r/ 96.8%

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

      2. sub-neg 96.8%

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

      3. exp-sum 96.9%

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

      4. associate-/l* 96.9%

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

      5. associate-/r/ 96.9%

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

      6. exp-neg 96.9%

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

      7. associate-*r/ 96.9%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in y around 0 69.6%

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

      1. associate-/r* 67.4%

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

      2. associate-*r/ 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in t around 0 45.4%

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

   8. Taylor expanded in b around 0 44.5%

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

      1. *-commutative 44.5%

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

   10. Simplified 44.5%

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

       1. *-rgt-identity 44.5%

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

       2. *-commutative 44.5%

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

       3. times-frac 46.9%

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

   12. Applied egg-rr 46.9%

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

   if 1.89999999999999993e-217 < b

   1. Initial program 99.6%

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

      1. associate-*r/ 98.8%

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

      2. sub-neg 98.8%

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

      3. exp-sum 77.4%

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

      4. associate-/l* 77.4%

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

      5. associate-/r/ 72.7%

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

      6. exp-neg 72.7%

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

      7. associate-*r/ 72.7%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate-/r* 63.9%

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

      2. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in t around 0 59.9%

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

   8. Taylor expanded in b around 0 31.3%

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

   9. Taylor expanded in b around inf 31.4%

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

       1. associate-*r* 29.5%

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

       2. *-commutative 29.5%

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

       3. associate-*r* 34.8%

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

   11. Simplified 34.8%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.216:\\ \;\;\;\;\frac{b}{a} \cdot \left(-\frac{x}{y}\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 16: 30.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-217}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.95e-217) (/ 1.0 (/ (* y a) x)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.95e-217) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = (x / 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 (y <= (-2.95d-217)) then
        tmp = 1.0d0 / ((y * a) / x)
    else
        tmp = (x / 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 (y <= -2.95e-217) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.95e-217:
		tmp = 1.0 / ((y * a) / x)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.95e-217)
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.95e-217)
		tmp = 1.0 / ((y * a) / x);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.95e-217], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9499999999999999e-217

   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. Step-by-step derivation

      1. associate-*r/ 99.4%

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

      2. sub-neg 99.4%

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

      3. exp-sum 79.3%

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

      4. associate-/l* 79.3%

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

      5. associate-/r/ 77.3%

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

      6. exp-neg 77.3%

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

      7. associate-*r/ 77.3%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in t around 0 72.3%

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

   5. Taylor expanded in b around 0 61.3%

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

   6. Taylor expanded in y around 0 24.4%

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

      1. div-inv 24.4%

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

      2. clear-num 24.6%

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

   8. Applied egg-rr 24.6%

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

   if -2.9499999999999999e-217 < y

   1. Initial program 99.0%

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

      1. associate-*r/ 97.9%

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

      2. sub-neg 97.9%

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

      3. exp-sum 79.5%

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

      4. associate-/l* 79.5%

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

      5. associate-/r/ 77.5%

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

      6. exp-neg 77.5%

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

      7. associate-*r/ 77.5%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in y around 0 70.4%

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

      1. associate-/r* 67.8%

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

      2. associate-*r/ 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in t around 0 61.2%

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

   8. Taylor expanded in b around 0 32.5%

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

      1. associate-/r* 36.9%

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

   10. Simplified 36.9%

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

4. Final simplification 31.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{-217}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 17: 33.8% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.5e-217) (/ 1.0 (/ (* y a) x)) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.5e-217) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.5d-217) then
        tmp = 1.0d0 / ((y * a) / x)
    else
        tmp = x / (y * (a * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.5e-217) {
		tmp = 1.0 / ((y * a) / x);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.5e-217:
		tmp = 1.0 / ((y * a) / x)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.5e-217)
		tmp = Float64(1.0 / Float64(Float64(y * a) / x));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.5e-217)
		tmp = 1.0 / ((y * a) / x);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.5e-217], N[(1.0 / N[(N[(y * a), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.5000000000000001e-217

   1. Initial program 98.3%

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

      1. associate-*r/ 98.3%

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

      2. sub-neg 98.3%

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

      3. exp-sum 80.9%

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

      4. associate-/l* 80.9%

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

      5. associate-/r/ 80.9%

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

      6. exp-neg 80.9%

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

      7. associate-*r/ 80.9%

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

   3. Simplified 75.1%

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

   4. Taylor expanded in t around 0 70.9%

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

   5. Taylor expanded in b around 0 62.8%

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

   6. Taylor expanded in y around 0 34.6%

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

      1. div-inv 34.7%

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

      2. clear-num 34.8%

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

   8. Applied egg-rr 34.8%

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

   if 2.5000000000000001e-217 < b

   1. Initial program 99.6%

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

      1. associate-*r/ 98.8%

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

      2. sub-neg 98.8%

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

      3. exp-sum 77.4%

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

      4. associate-/l* 77.4%

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

      5. associate-/r/ 72.7%

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

      6. exp-neg 72.7%

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

      7. associate-*r/ 72.7%

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

   3. Simplified 65.5%

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

   4. Taylor expanded in y around 0 65.9%

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

      1. associate-/r* 63.9%

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

      2. associate-*r/ 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in t around 0 59.9%

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

   8. Taylor expanded in b around 0 31.3%

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

   9. Taylor expanded in b around inf 31.4%

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

       1. associate-*r* 29.5%

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

       2. *-commutative 29.5%

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

       3. associate-*r* 34.8%

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

   11. Simplified 34.8%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{1}{\frac{y \cdot a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 18: 30.7% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-225}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -6.5e-225) (/ x (* y a)) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -6.5e-225) {
		tmp = x / (y * a);
	} else {
		tmp = (x / 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 (y <= (-6.5d-225)) then
        tmp = x / (y * a)
    else
        tmp = (x / 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 (y <= -6.5e-225) {
		tmp = x / (y * a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -6.5e-225:
		tmp = x / (y * a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -6.5e-225)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -6.5e-225)
		tmp = x / (y * a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -6.5e-225], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000005e-225

   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. Step-by-step derivation

      1. associate-*r/ 99.4%

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

      2. sub-neg 99.4%

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

      3. exp-sum 79.3%

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

      4. associate-/l* 79.3%

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

      5. associate-/r/ 77.3%

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

      6. exp-neg 77.3%

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

      7. associate-*r/ 77.3%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in y around 0 63.2%

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

      1. associate-/r* 62.2%

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

      2. associate-*r/ 55.5%

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

   6. Simplified 55.5%

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

   7. Taylor expanded in t around 0 57.0%

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

   8. Taylor expanded in b around 0 24.4%

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

      1. *-commutative 24.4%

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

   10. Simplified 24.4%

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

   if -6.5000000000000005e-225 < y

   1. Initial program 99.0%

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

      1. associate-*r/ 97.9%

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

      2. sub-neg 97.9%

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

      3. exp-sum 79.5%

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

      4. associate-/l* 79.5%

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

      5. associate-/r/ 77.5%

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

      6. exp-neg 77.5%

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

      7. associate-*r/ 77.5%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in y around 0 70.4%

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

      1. associate-/r* 67.8%

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

      2. associate-*r/ 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in t around 0 61.2%

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

   8. Taylor expanded in b around 0 32.5%

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

      1. associate-/r* 36.9%

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

   10. Simplified 36.9%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-225}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 19: 30.8% 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 98.9%

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

   1. associate-*r/ 98.5%

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

   2. sub-neg 98.5%

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

   3. exp-sum 79.4%

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

   4. associate-/l* 79.4%

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

   5. associate-/r/ 77.5%

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

   6. exp-neg 77.5%

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

   7. associate-*r/ 77.5%

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

3. Simplified 71.1%

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

4. Taylor expanded in y around 0 67.4%

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

   1. associate-/r* 65.5%

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

   2. associate-*r/ 60.8%

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

6. Simplified 60.8%

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

7. Taylor expanded in t around 0 59.5%

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

8. Taylor expanded in b around 0 29.2%

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

   1. *-commutative 29.2%

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

10. Simplified 29.2%

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

11. Final simplification 29.2%

    \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023195 
(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))