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

Percentage Accurate: 98.5% → 98.5%

Time: 20.1s

Alternatives: 22

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% 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 98.2%

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

2. Final simplification 98.2%

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

Alternative 2: 92.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+99} \lor \neg \left(y \leq 1.8 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.4e+99) (not (<= y 1.8e-21)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) 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 <= -3.4e+99) || !(y <= 1.8e-21)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 <= (-3.4d+99)) .or. (.not. (y <= 1.8d-21))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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 <= -3.4e+99) || !(y <= 1.8e-21)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / 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 <= -3.4e+99) or not (y <= 1.8e-21):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / 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 <= -3.4e+99) || !(y <= 1.8e-21))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / 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 <= -3.4e+99) || ~((y <= 1.8e-21)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / 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, -3.4e+99], N[Not[LessEqual[y, 1.8e-21]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(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 < -3.39999999999999984e99 or 1.79999999999999995e-21 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 92.3%

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

      1. mul-1-neg 92.3%

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

   4. Simplified 92.3%

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

   if -3.39999999999999984e99 < y < 1.79999999999999995e-21

   1. Initial program 96.7%

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

   2. Taylor expanded in y around 0 95.4%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+99} \lor \neg \left(y \leq 1.8 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 3: 81.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -3400000 \lor \neg \left(t + -1 \leq -0.9999999998\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -3400000.0) (not (<= (+ t -1.0) -0.9999999998)))
   (/ (* x (pow a (+ t -1.0))) y)
   (* x (/ (/ (pow z y) a) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -3400000.0) || !((t + -1.0) <= -0.9999999998)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = x * ((pow(z, y) / a) / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-3400000.0d0)) .or. (.not. ((t + (-1.0d0)) <= (-0.9999999998d0)))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = x * (((z ** y) / a) / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -3400000.0) || !((t + -1.0) <= -0.9999999998)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = x * ((Math.pow(z, y) / a) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -3400000.0) or not ((t + -1.0) <= -0.9999999998):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = x * ((math.pow(z, y) / a) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -3400000.0) || !(Float64(t + -1.0) <= -0.9999999998))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -3400000.0) || ~(((t + -1.0) <= -0.9999999998)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = x * (((z ^ y) / a) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -3400000.0], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.9999999998]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -3.4e6 or -0.9999999998 < (-.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 88.8%

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

   3. Taylor expanded in b around 0 81.0%

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

   if -3.4e6 < (-.f64 t 1) < -0.9999999998

   1. Initial program 96.7%

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

      1. associate-*r/ 96.1%

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

      2. sub-neg 96.1%

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

      3. exp-sum 84.8%

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

      4. associate-/l* 84.8%

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

      5. associate-/r/ 83.4%

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

      6. exp-neg 83.4%

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

      7. associate-*r/ 83.4%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in t around 0 83.2%

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

      1. associate-/r* 86.7%

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

   6. Simplified 86.7%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -3400000 \lor \neg \left(t + -1 \leq -0.9999999998\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y \cdot e^{b}}\\ \end{array} \]

Alternative 4: 82.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.24 \cdot 10^{+132} \lor \neg \left(b \leq 16000000000\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t + -1\right)}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.24e+132) (not (<= b 16000000000.0)))
   (/ x (* y (* a (exp b))))
   (/ (* x (* (pow z y) (pow a (+ t -1.0)))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.24e+132) || !(b <= 16000000000.0)) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = (x * (pow(z, y) * 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 ((b <= (-1.24d+132)) .or. (.not. (b <= 16000000000.0d0))) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = (x * ((z ** y) * (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 ((b <= -1.24e+132) || !(b <= 16000000000.0)) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = (x * (Math.pow(z, y) * Math.pow(a, (t + -1.0)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.24e+132) or not (b <= 16000000000.0):
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = (x * (math.pow(z, y) * math.pow(a, (t + -1.0)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.24e+132) || !(b <= 16000000000.0))
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(Float64(x * Float64((z ^ y) * (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 ((b <= -1.24e+132) || ~((b <= 16000000000.0)))
		tmp = x / (y * (a * exp(b)));
	else
		tmp = (x * ((z ^ y) * (a ^ (t + -1.0)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.24e+132], N[Not[LessEqual[b, 16000000000.0]], $MachinePrecision]], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.24000000000000006e132 or 1.6e10 < 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 67.4%

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

      4. associate-/l* 67.4%

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

      5. associate-/r/ 65.2%

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

      6. exp-neg 65.2%

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

      7. associate-*r/ 65.2%

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

   3. Simplified 55.4%

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

   4. Taylor expanded in t around 0 70.7%

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

      1. associate-/r* 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in y around 0 85.0%

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

   if -1.24000000000000006e132 < b < 1.6e10

   1. Initial program 97.2%

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

   2. Taylor expanded in b around 0 93.9%

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

      1. log-pow 89.7%

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

      2. exp-sum 84.8%

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

      3. rem-exp-log 84.8%

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

      4. sub-neg 84.8%

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

      5. metadata-eval 84.8%

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

      6. *-commutative 84.8%

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

      7. exp-to-pow 85.7%

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

   4. Simplified 85.7%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.24 \cdot 10^{+132} \lor \neg \left(b \leq 16000000000\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t + -1\right)}\right)}{y}\\ \end{array} \]

Alternative 5: 88.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+99} \lor \neg \left(y \leq 2.75 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -4.5e+99) (not (<= y 2.75e+63)))
   (* 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 <= -4.5e+99) || !(y <= 2.75e+63)) {
		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 <= (-4.5d+99)) .or. (.not. (y <= 2.75d+63))) 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 <= -4.5e+99) || !(y <= 2.75e+63)) {
		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 <= -4.5e+99) or not (y <= 2.75e+63):
		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 <= -4.5e+99) || !(y <= 2.75e+63))
		tmp = Float64(x * Float64(Float64((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 <= -4.5e+99) || ~((y <= 2.75e+63)))
		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, -4.5e+99], N[Not[LessEqual[y, 2.75e+63]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $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 < -4.5e99 or 2.75000000000000002e63 < 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 77.0%

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

      4. associate-/l* 77.0%

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

      5. associate-/r/ 77.0%

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

      6. exp-neg 77.0%

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

      7. associate-*r/ 77.0%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in t around 0 69.1%

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

      1. associate-/r* 73.1%

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

   6. Simplified 73.1%

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

   7. Taylor expanded in b around 0 88.2%

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

   if -4.5e99 < y < 2.75000000000000002e63

   1. Initial program 97.0%

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

   2. Taylor expanded in y around 0 92.7%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+99} \lor \neg \left(y \leq 2.75 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 6: 82.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -400000000000 \lor \neg \left(y \leq 7 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -400000000000.0) (not (<= y 7e+63)))
   (* x (/ (/ (pow z y) a) y))
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -400000000000.0) || !(y <= 7e+63)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-400000000000.0d0)) .or. (.not. (y <= 7d+63))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -400000000000.0) || !(y <= 7e+63)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -400000000000.0) or not (y <= 7e+63):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -400000000000.0) || !(y <= 7e+63))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -400000000000.0) || ~((y <= 7e+63)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -400000000000.0], N[Not[LessEqual[y, 7e+63]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e11 or 7.00000000000000059e63 < 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 75.6%

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

      4. associate-/l* 75.6%

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

      5. associate-/r/ 75.6%

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

      6. exp-neg 75.6%

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

      7. associate-*r/ 75.6%

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

   3. Simplified 58.8%

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

   4. Taylor expanded in t around 0 67.3%

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

      1. associate-/r* 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in b around 0 86.8%

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

   if -4e11 < y < 7.00000000000000059e63

   1. Initial program 96.6%

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

   2. Taylor expanded in y around 0 93.1%

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

      1. exp-diff 81.3%

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

      2. sub-neg 81.3%

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

      3. metadata-eval 81.3%

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

      4. *-commutative 81.3%

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

      5. exp-to-pow 82.6%

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

   4. Simplified 82.6%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -400000000000 \lor \neg \left(y \leq 7 \cdot 10^{+63}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 7: 75.2% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{if}\;y \leq -460000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))))
   (if (<= y -460000000000.0)
     t_1
     (if (<= y 4.5e-285)
       (/ (/ x (* a (exp b))) y)
       (if (<= y 3e-6) (/ (* 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 * ((pow(z, y) / a) / y);
	double tmp;
	if (y <= -460000000000.0) {
		tmp = t_1;
	} else if (y <= 4.5e-285) {
		tmp = (x / (a * exp(b))) / y;
	} else if (y <= 3e-6) {
		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 * (((z ** y) / a) / y)
    if (y <= (-460000000000.0d0)) then
        tmp = t_1
    else if (y <= 4.5d-285) then
        tmp = (x / (a * exp(b))) / y
    else if (y <= 3d-6) 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 * ((Math.pow(z, y) / a) / y);
	double tmp;
	if (y <= -460000000000.0) {
		tmp = t_1;
	} else if (y <= 4.5e-285) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else if (y <= 3e-6) {
		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 * ((math.pow(z, y) / a) / y)
	tmp = 0
	if y <= -460000000000.0:
		tmp = t_1
	elif y <= 4.5e-285:
		tmp = (x / (a * math.exp(b))) / y
	elif y <= 3e-6:
		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(Float64((z ^ y) / a) / y))
	tmp = 0.0
	if (y <= -460000000000.0)
		tmp = t_1;
	elseif (y <= 4.5e-285)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	elseif (y <= 3e-6)
		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 * (((z ^ y) / a) / y);
	tmp = 0.0;
	if (y <= -460000000000.0)
		tmp = t_1;
	elseif (y <= 4.5e-285)
		tmp = (x / (a * exp(b))) / y;
	elseif (y <= 3e-6)
		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[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -460000000000.0], t$95$1, If[LessEqual[y, 4.5e-285], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[y, 3e-6], 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 y < -4.6e11 or 3.0000000000000001e-6 < 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 76.7%

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

      4. associate-/l* 76.7%

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

      5. associate-/r/ 76.7%

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

      6. exp-neg 76.7%

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

      7. associate-*r/ 76.7%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in t around 0 66.3%

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

      1. associate-/r* 70.0%

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

   6. Simplified 70.0%

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

   7. Taylor expanded in b around 0 83.7%

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

   if -4.6e11 < y < 4.5000000000000002e-285

   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. Taylor expanded in t around 0 76.9%

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

      1. mul-1-neg 76.9%

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

   4. Simplified 76.9%

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

   5. Taylor expanded in y around 0 76.9%

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

      1. exp-neg 76.9%

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

      2. associate-*l/ 76.9%

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

      3. *-lft-identity 76.9%

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

      4. +-commutative 76.9%

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

      5. exp-sum 76.9%

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

      6. rem-exp-log 78.4%

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

   7. Simplified 78.4%

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

   if 4.5000000000000002e-285 < y < 3.0000000000000001e-6

   1. Initial program 95.7%

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

   2. Taylor expanded in y around 0 95.7%

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

   3. Taylor expanded in b around 0 76.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -460000000000:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-6}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \end{array} \]

Alternative 8: 75.3% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -240000000000 \lor \neg \left(y \leq 2.1\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -240000000000.0) (not (<= y 2.1)))
   (* x (/ (/ (pow z y) a) y))
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -240000000000.0) || !(y <= 2.1)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-240000000000.0d0)) .or. (.not. (y <= 2.1d0))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -240000000000.0) || !(y <= 2.1)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -240000000000.0) or not (y <= 2.1):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -240000000000.0) || !(y <= 2.1))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -240000000000.0) || ~((y <= 2.1)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -240000000000.0], N[Not[LessEqual[y, 2.1]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e11 or 2.10000000000000009 < 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 77.3%

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

      4. associate-/l* 77.3%

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

      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 59.1%

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

   4. Taylor expanded in t around 0 66.0%

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

      1. associate-/r* 69.8%

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

   6. Simplified 69.8%

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

   7. Taylor expanded in b around 0 84.3%

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

   if -2.4e11 < y < 2.10000000000000009

   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. Taylor expanded in t around 0 70.4%

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

      1. mul-1-neg 70.4%

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

   4. Simplified 70.4%

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

   5. Taylor expanded in y around 0 70.4%

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

      1. exp-neg 70.4%

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

      2. associate-*l/ 70.4%

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

      3. *-lft-identity 70.4%

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

      4. +-commutative 70.4%

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

      5. exp-sum 70.3%

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

      6. rem-exp-log 71.8%

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

   7. Simplified 71.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -240000000000 \lor \neg \left(y \leq 2.1\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]

Alternative 9: 59.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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/ 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 79.9%

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

   4. associate-/l* 79.9%

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

   5. associate-/r/ 79.1%

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

   6. exp-neg 79.1%

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

   7. associate-*r/ 79.1%

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

3. Simplified 70.4%

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

4. Taylor expanded in t around 0 68.4%

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

   1. associate-/r* 70.4%

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

6. Simplified 70.4%

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

7. Taylor expanded in y around 0 56.4%

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

8. Final simplification 56.4%

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

Alternative 10: 44.2% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -14000:\\ \;\;\;\;\left(\frac{x}{y \cdot a} - \frac{b}{y} \cdot \frac{x}{a}\right) + \frac{\frac{x \cdot \left(b \cdot b\right)}{y}}{a}\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -14000.0)
   (+ (- (/ x (* y a)) (* (/ b y) (/ x a))) (/ (/ (* x (* b b)) y) a))
   (if (<= b -4.1e-279)
     (/ (/ x (* a (+ 1.0 b))) y)
     (if (<= b 1.15e-31) (* x (/ (/ 1.0 a) y)) (/ (/ x (* a b)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -14000.0) {
		tmp = ((x / (y * a)) - ((b / y) * (x / a))) + (((x * (b * b)) / y) / a);
	} else if (b <= -4.1e-279) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 1.15e-31) {
		tmp = x * ((1.0 / a) / y);
	} else {
		tmp = (x / (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 (b <= (-14000.0d0)) then
        tmp = ((x / (y * a)) - ((b / y) * (x / a))) + (((x * (b * b)) / y) / a)
    else if (b <= (-4.1d-279)) then
        tmp = (x / (a * (1.0d0 + b))) / y
    else if (b <= 1.15d-31) then
        tmp = x * ((1.0d0 / a) / y)
    else
        tmp = (x / (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 (b <= -14000.0) {
		tmp = ((x / (y * a)) - ((b / y) * (x / a))) + (((x * (b * b)) / y) / a);
	} else if (b <= -4.1e-279) {
		tmp = (x / (a * (1.0 + b))) / y;
	} else if (b <= 1.15e-31) {
		tmp = x * ((1.0 / a) / y);
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -14000.0:
		tmp = ((x / (y * a)) - ((b / y) * (x / a))) + (((x * (b * b)) / y) / a)
	elif b <= -4.1e-279:
		tmp = (x / (a * (1.0 + b))) / y
	elif b <= 1.15e-31:
		tmp = x * ((1.0 / a) / y)
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -14000.0)
		tmp = Float64(Float64(Float64(x / Float64(y * a)) - Float64(Float64(b / y) * Float64(x / a))) + Float64(Float64(Float64(x * Float64(b * b)) / y) / a));
	elseif (b <= -4.1e-279)
		tmp = Float64(Float64(x / Float64(a * Float64(1.0 + b))) / y);
	elseif (b <= 1.15e-31)
		tmp = Float64(x * Float64(Float64(1.0 / a) / y));
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -14000.0)
		tmp = ((x / (y * a)) - ((b / y) * (x / a))) + (((x * (b * b)) / y) / a);
	elseif (b <= -4.1e-279)
		tmp = (x / (a * (1.0 + b))) / y;
	elseif (b <= 1.15e-31)
		tmp = x * ((1.0 / a) / y);
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -14000.0], N[(N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(N[(b / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * N[(b * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.1e-279], N[(N[(x / N[(a * N[(1.0 + b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.15e-31], N[(x * N[(N[(1.0 / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -14000

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 89.1%

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

      1. mul-1-neg 89.1%

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

   4. Simplified 89.1%

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

   5. Taylor expanded in y around 0 79.7%

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

      1. exp-neg 79.7%

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

      2. associate-*l/ 79.7%

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

      3. *-lft-identity 79.7%

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

      4. +-commutative 79.7%

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

      5. exp-sum 79.7%

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

      6. rem-exp-log 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in b around 0 10.8%

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

   9. Taylor expanded in b around 0 56.7%

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

       1. +-commutative 56.7%

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

       2. mul-1-neg 56.7%

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

       3. times-frac 61.1%

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

       4. *-commutative 61.1%

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

       5. associate-/r* 68.9%

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

       6. *-commutative 68.9%

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

       7. unpow2 68.9%

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

   11. Simplified 68.9%

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

   if -14000 < b < -4.10000000000000017e-279

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 80.2%

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

      1. mul-1-neg 80.2%

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

   4. Simplified 80.2%

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

   5. Taylor expanded in y around 0 36.8%

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

      1. exp-neg 36.8%

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

      2. associate-*l/ 36.8%

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

      3. *-lft-identity 36.8%

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

      4. +-commutative 36.8%

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

      5. exp-sum 36.6%

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

      6. rem-exp-log 38.0%

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

   7. Simplified 38.0%

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

   8. Taylor expanded in b around 0 38.0%

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

      1. *-commutative 38.0%

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

      2. distribute-lft1-in 38.0%

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

   10. Applied egg-rr 38.0%

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

   if -4.10000000000000017e-279 < b < 1.1499999999999999e-31

   1. Initial program 94.4%

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

      1. associate-*r/ 96.8%

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

      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 96.8%

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

      4. associate-/l* 96.8%

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

      5. associate-/r/ 96.8%

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

      6. exp-neg 96.8%

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

      7. associate-*r/ 96.8%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in t around 0 73.0%

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

      1. associate-/r* 77.4%

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

   6. Simplified 77.4%

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

   7. Taylor expanded in b around 0 77.4%

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

   8. Taylor expanded in y around 0 44.1%

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

      1. associate-/l/ 44.1%

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

   10. Simplified 44.1%

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

   if 1.1499999999999999e-31 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 83.8%

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

      1. mul-1-neg 83.8%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in y around 0 69.0%

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

      1. exp-neg 69.0%

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

      2. associate-*l/ 69.0%

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

      3. *-lft-identity 69.0%

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

      4. +-commutative 69.0%

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

      5. exp-sum 69.0%

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

      6. rem-exp-log 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in b around 0 42.4%

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

   9. Taylor expanded in b around inf 42.5%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -14000:\\ \;\;\;\;\left(\frac{x}{y \cdot a} - \frac{b}{y} \cdot \frac{x}{a}\right) + \frac{\frac{x \cdot \left(b \cdot b\right)}{y}}{a}\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{x}{a \cdot \left(1 + b\right)}}{y}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-31}:\\ \;\;\;\;x \cdot \frac{\frac{1}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 11: 42.7% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{-167}:\\ \;\;\;\;\frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + \frac{b \cdot b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.6e-167)
   (/ (+ (- (/ x a) (/ b (/ a x))) (/ (* b b) (/ a x))) y)
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.6e-167) {
		tmp = (((x / a) - (b / (a / x))) + ((b * b) / (a / x))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.6d-167)) then
        tmp = (((x / a) - (b / (a / x))) + ((b * b) / (a / x))) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.6e-167) {
		tmp = (((x / a) - (b / (a / x))) + ((b * b) / (a / x))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.6e-167:
		tmp = (((x / a) - (b / (a / x))) + ((b * b) / (a / x))) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.6e-167)
		tmp = Float64(Float64(Float64(Float64(x / a) - Float64(b / Float64(a / x))) + Float64(Float64(b * b) / Float64(a / x))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.6e-167)
		tmp = (((x / a) - (b / (a / x))) + ((b * b) / (a / x))) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.6e-167], N[(N[(N[(N[(x / a), $MachinePrecision] - N[(b / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(b * b), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.59999999999999972e-167

   1. Initial program 99.3%

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

   2. Taylor expanded in t around 0 88.2%

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

      1. mul-1-neg 88.2%

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

   4. Simplified 88.2%

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

   5. Taylor expanded in y around 0 67.1%

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

      1. exp-neg 67.2%

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

      2. associate-*l/ 67.2%

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

      3. *-lft-identity 67.2%

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

      4. +-commutative 67.2%

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

      5. exp-sum 67.1%

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

      6. rem-exp-log 67.8%

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

   7. Simplified 67.8%

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

   8. Taylor expanded in b around 0 23.1%

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

   9. Taylor expanded in b around 0 57.9%

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

       1. +-commutative 57.9%

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

       2. +-commutative 57.9%

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

       3. mul-1-neg 57.9%

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

       4. unsub-neg 57.9%

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

       5. associate-/l* 57.9%

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

       6. associate-/l* 49.9%

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

       7. unpow2 49.9%

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

   11. Simplified 49.9%

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

   if -9.59999999999999972e-167 < b

   1. Initial program 97.5%

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

      1. associate-*r/ 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 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/ 82.8%

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

      6. exp-neg 82.8%

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

      7. associate-*r/ 82.8%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in t around 0 66.0%

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

      1. associate-/r* 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in y around 0 51.2%

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

   8. Taylor expanded in b around 0 39.3%

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

4. Final simplification 43.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.6 \cdot 10^{-167}:\\ \;\;\;\;\frac{\left(\frac{x}{a} - \frac{b}{\frac{a}{x}}\right) + \frac{b \cdot b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 12: 38.6% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{-274}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} - \frac{b}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.6e-274)
   (- (/ (/ x a) y) (* (/ b y) (/ x a)))
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.6e-274) {
		tmp = ((x / a) / y) - ((b / y) * (x / a));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.6d-274)) then
        tmp = ((x / a) / y) - ((b / y) * (x / a))
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.6e-274) {
		tmp = ((x / a) / y) - ((b / y) * (x / a));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.6e-274:
		tmp = ((x / a) / y) - ((b / y) * (x / a))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.6e-274)
		tmp = Float64(Float64(Float64(x / a) / y) - Float64(Float64(b / y) * Float64(x / a)));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.6e-274)
		tmp = ((x / a) / y) - ((b / y) * (x / a));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.6e-274], N[(N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision] - N[(N[(b / y), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.59999999999999992e-274

   1. Initial program 99.4%

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

      1. associate-*r/ 97.2%

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

      2. sub-neg 97.2%

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

      3. exp-sum 78.2%

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

      4. associate-/l* 78.2%

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

      5. associate-/r/ 78.2%

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

      6. exp-neg 78.2%

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

      7. associate-*r/ 78.2%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. associate-/r* 72.3%

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

   6. Simplified 72.3%

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

   7. Taylor expanded in y around 0 56.6%

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

   8. Taylor expanded in b around 0 29.7%

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

      1. *-commutative 29.7%

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

      2. mul-1-neg 29.7%

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

      3. unsub-neg 29.7%

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

      4. associate-/l/ 30.5%

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

      5. *-commutative 30.5%

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

      6. *-commutative 30.5%

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

      7. times-frac 36.8%

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

   10. Simplified 36.8%

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

   if -4.59999999999999992e-274 < b

   1. Initial program 97.1%

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

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 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/ 79.8%

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

      6. exp-neg 79.8%

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

      7. associate-*r/ 79.8%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in t around 0 66.4%

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

      1. associate-/r* 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in y around 0 56.2%

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

   8. Taylor expanded in b around 0 42.2%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.6 \cdot 10^{-274}:\\ \;\;\;\;\frac{\frac{x}{a}}{y} - \frac{b}{y} \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 13: 39.1% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-276}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.9e-276)
   (/ (- (/ x a) (/ b (/ a x))) y)
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e-276) {
		tmp = ((x / a) - (b / (a / x))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.9d-276)) then
        tmp = ((x / a) - (b / (a / x))) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.9e-276) {
		tmp = ((x / a) - (b / (a / x))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.9e-276:
		tmp = ((x / a) - (b / (a / x))) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.9e-276)
		tmp = Float64(Float64(Float64(x / a) - Float64(b / Float64(a / x))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.9e-276)
		tmp = ((x / a) - (b / (a / x))) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.9e-276], N[(N[(N[(x / a), $MachinePrecision] - N[(b / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.89999999999999987e-276

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 84.8%

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

      1. mul-1-neg 84.8%

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

   4. Simplified 84.8%

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

   5. Taylor expanded in y around 0 59.1%

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

      1. exp-neg 59.1%

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

      2. associate-*l/ 59.1%

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

      3. *-lft-identity 59.1%

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

      4. +-commutative 59.1%

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

      5. exp-sum 59.0%

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

      6. rem-exp-log 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in b around 0 23.8%

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

   9. Taylor expanded in b around 0 33.6%

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

       1. +-commutative 33.6%

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

       2. mul-1-neg 33.6%

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

       3. unsub-neg 33.6%

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

       4. associate-/l* 32.0%

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

   11. Simplified 32.0%

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

   if -2.89999999999999987e-276 < b

   1. Initial program 97.1%

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

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 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/ 79.8%

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

      6. exp-neg 79.8%

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

      7. associate-*r/ 79.8%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in t around 0 66.4%

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

      1. associate-/r* 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in y around 0 56.2%

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

   8. Taylor expanded in b around 0 42.2%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{-276}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 14: 39.8% accurate, 24.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x}{\frac{a}{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.5e-279)
   (/ (- (/ x a) (/ x (/ a b))) y)
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e-279) {
		tmp = ((x / a) - (x / (a / b))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.5d-279)) then
        tmp = ((x / a) - (x / (a / b))) / y
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.5e-279) {
		tmp = ((x / a) - (x / (a / b))) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.5e-279:
		tmp = ((x / a) - (x / (a / b))) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.5e-279)
		tmp = Float64(Float64(Float64(x / a) - Float64(x / Float64(a / b))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.5e-279)
		tmp = ((x / a) - (x / (a / b))) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.5e-279], N[(N[(N[(x / a), $MachinePrecision] - N[(x / N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.49999999999999984e-279

   1. Initial program 99.4%

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

   2. Taylor expanded in t around 0 84.8%

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

      1. mul-1-neg 84.8%

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

   4. Simplified 84.8%

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

   5. Taylor expanded in y around 0 59.1%

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

      1. exp-neg 59.1%

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

      2. associate-*l/ 59.1%

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

      3. *-lft-identity 59.1%

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

      4. +-commutative 59.1%

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

      5. exp-sum 59.0%

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

      6. rem-exp-log 59.7%

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

   7. Simplified 59.7%

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

   8. Taylor expanded in b around 0 33.6%

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

      1. +-commutative 33.6%

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

      2. mul-1-neg 33.6%

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

      3. unsub-neg 33.6%

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

      4. *-commutative 33.6%

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

      5. associate-/l* 35.1%

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

   10. Simplified 35.1%

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

   if -2.49999999999999984e-279 < b

   1. Initial program 97.1%

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

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 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/ 79.8%

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

      6. exp-neg 79.8%

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

      7. associate-*r/ 79.8%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in t around 0 66.4%

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

      1. associate-/r* 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in y around 0 56.2%

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

   8. Taylor expanded in b around 0 42.2%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-279}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x}{\frac{a}{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 15: 35.7% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.16e-275) (/ (/ x y) a) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.16e-275) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.16d-275)) then
        tmp = (x / y) / a
    else
        tmp = x / (y * (a + (a * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.16e-275) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.16e-275:
		tmp = (x / y) / a
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.16e-275)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.16e-275)
		tmp = (x / y) / a;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.16e-275], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.15999999999999995e-275

   1. Initial program 99.4%

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

      1. associate-*r/ 97.2%

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

      2. sub-neg 97.2%

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

      3. exp-sum 78.2%

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

      4. associate-/l* 78.2%

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

      5. associate-/r/ 78.2%

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

      6. exp-neg 78.2%

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

      7. associate-*r/ 78.2%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in t around 0 70.6%

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

      1. associate-/r* 72.3%

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

   6. Simplified 72.3%

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

   7. Taylor expanded in b around 0 63.6%

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

   8. Taylor expanded in y around 0 24.5%

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

      1. div-inv 23.7%

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

      2. associate-/r* 28.6%

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

   10. Applied egg-rr 28.6%

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

   if -1.15999999999999995e-275 < b

   1. Initial program 97.1%

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

      1. associate-*r/ 98.4%

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

      2. sub-neg 98.4%

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

      3. exp-sum 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/ 79.8%

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

      6. exp-neg 79.8%

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

      7. associate-*r/ 79.8%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in t around 0 66.4%

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

      1. associate-/r* 68.7%

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

   6. Simplified 68.7%

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

   7. Taylor expanded in y around 0 56.2%

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

   8. Taylor expanded in b around 0 42.2%

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

4. Final simplification 35.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 16: 31.6% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 9.6 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 9.6e-287) (* (/ x a) (/ 1.0 y)) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 9.6e-287) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 9.6d-287) then
        tmp = (x / a) * (1.0d0 / y)
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 9.6e-287) {
		tmp = (x / a) * (1.0 / y);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 9.6e-287:
		tmp = (x / a) * (1.0 / y)
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 9.6e-287)
		tmp = Float64(Float64(x / a) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 9.6e-287)
		tmp = (x / a) * (1.0 / y);
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 9.6e-287], N[(N[(x / a), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.59999999999999997e-287

   1. Initial program 97.9%

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

      1. associate-*r/ 98.5%

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

      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 80.2%

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

      4. associate-/l* 80.2%

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

      5. associate-/r/ 79.5%

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

      6. exp-neg 79.5%

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

      7. associate-*r/ 79.5%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around 0 68.4%

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

      1. times-frac 66.9%

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

      2. *-commutative 66.9%

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

      3. associate-/r* 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in b around 0 53.1%

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

   8. Taylor expanded in y around 0 31.4%

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

   if 9.59999999999999997e-287 < t

   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/ 97.1%

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

      2. sub-neg 97.1%

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

      3. exp-sum 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/ 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 67.3%

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

   4. Taylor expanded in t around 0 68.5%

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

      1. associate-/r* 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in b around 0 63.7%

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

   8. Taylor expanded in y around 0 25.8%

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

      1. div-inv 25.7%

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

      2. associate-/r* 30.5%

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

   10. Applied egg-rr 30.5%

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

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 9.6 \cdot 10^{-287}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]

Alternative 17: 31.6% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.3 \cdot 10^{-267}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 6.3e-267) (/ 1.0 (* y (/ a x))) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 6.3e-267) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 6.3d-267) then
        tmp = 1.0d0 / (y * (a / x))
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 6.3e-267) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 6.3e-267:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 6.3e-267)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 6.3e-267)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 6.3e-267], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.30000000000000042e-267

   1. Initial program 97.9%

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

      1. associate-*r/ 98.5%

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

      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 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/ 80.2%

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

      6. exp-neg 80.2%

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

      7. associate-*r/ 80.2%

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

   3. Simplified 74.0%

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

   4. Taylor expanded in t around 0 68.8%

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

      1. associate-/r* 72.3%

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

   6. Simplified 72.3%

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

   7. Taylor expanded in b around 0 60.3%

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

   8. Taylor expanded in y around 0 30.5%

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

      1. associate-/r* 30.5%

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

      2. associate-*r/ 28.5%

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

      3. associate-*l/ 32.4%

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

      4. clear-num 33.7%

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

      5. frac-times 33.1%

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

      6. metadata-eval 33.1%

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

   10. Applied egg-rr 33.1%

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

   if 6.30000000000000042e-267 < t

   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/ 97.0%

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

      2. sub-neg 97.0%

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

      3. exp-sum 78.6%

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

      4. associate-/l* 78.6%

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

      5. associate-/r/ 77.7%

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

      6. exp-neg 77.7%

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

      7. associate-*r/ 77.7%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in t around 0 68.0%

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

      1. associate-/r* 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in b around 0 62.1%

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

   8. Taylor expanded in y around 0 24.2%

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

      1. div-inv 24.2%

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

      2. associate-/r* 29.2%

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

   10. Applied egg-rr 29.2%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.3 \cdot 10^{-267}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]

Alternative 18: 35.1% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.7e+53) (/ (/ x y) a) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.7e+53) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.7d+53) then
        tmp = (x / y) / a
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.7e+53) {
		tmp = (x / y) / a;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.7e+53:
		tmp = (x / y) / a
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.7e+53)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.7e+53)
		tmp = (x / y) / a;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.7e+53], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.69999999999999999e53

   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/ 97.4%

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

      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 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/ 82.1%

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

      6. exp-neg 82.1%

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

      7. associate-*r/ 82.1%

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

   3. Simplified 73.9%

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

   4. Taylor expanded in t around 0 68.2%

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

      1. associate-/r* 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in b around 0 67.5%

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

   8. Taylor expanded in y around 0 30.4%

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

      1. div-inv 29.9%

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

      2. associate-/r* 31.7%

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

   10. Applied egg-rr 31.7%

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

   if 1.69999999999999999e53 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 91.4%

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

      1. mul-1-neg 91.4%

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

   4. Simplified 91.4%

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

   5. Taylor expanded in y around 0 85.0%

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

      1. exp-neg 85.0%

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

      2. associate-*l/ 85.0%

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

      3. *-lft-identity 85.0%

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

      4. +-commutative 85.0%

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

      5. exp-sum 85.0%

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

      6. rem-exp-log 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in b around 0 48.9%

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

   9. Taylor expanded in b around inf 39.8%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{+53}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 19: 34.6% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.9e-69) (/ (/ x y) a) (/ (/ x (* a b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.9e-69) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (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 (b <= 3.9d-69) then
        tmp = (x / y) / a
    else
        tmp = (x / (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 (b <= 3.9e-69) {
		tmp = (x / y) / a;
	} else {
		tmp = (x / (a * b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.9e-69:
		tmp = (x / y) / a
	else:
		tmp = (x / (a * b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.9e-69)
		tmp = Float64(Float64(x / y) / a);
	else
		tmp = Float64(Float64(x / Float64(a * b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.9e-69)
		tmp = (x / y) / a;
	else
		tmp = (x / (a * b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.9e-69], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.89999999999999981e-69

   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/ 96.9%

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

      2. sub-neg 96.9%

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

      3. exp-sum 84.2%

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

      4. associate-/l* 84.2%

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

      5. associate-/r/ 84.2%

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

      6. exp-neg 84.2%

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

      7. associate-*r/ 84.2%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in t around 0 71.2%

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

      1. associate-/r* 74.0%

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

   6. Simplified 74.0%

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

   7. Taylor expanded in b around 0 68.1%

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

   8. Taylor expanded in y around 0 31.4%

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

      1. div-inv 30.9%

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

      2. associate-/r* 32.9%

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

   10. Applied egg-rr 32.9%

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

   if 3.89999999999999981e-69 < b

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 81.9%

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

      1. mul-1-neg 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in y around 0 63.7%

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

      1. exp-neg 63.7%

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

      2. associate-*l/ 63.7%

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

      3. *-lft-identity 63.7%

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

      4. +-commutative 63.7%

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

      5. exp-sum 63.7%

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

      6. rem-exp-log 63.7%

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

   7. Simplified 63.7%

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

   8. Taylor expanded in b around 0 40.4%

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

   9. Taylor expanded in b around inf 41.6%

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

4. Final simplification 35.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.9 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot b}}{y}\\ \end{array} \]

Alternative 20: 31.6% accurate, 44.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-286}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t 1e-286) (/ (/ x a) y) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e-286) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= 1d-286) then
        tmp = (x / a) / y
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= 1e-286) {
		tmp = (x / a) / y;
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= 1e-286:
		tmp = (x / a) / y
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= 1e-286)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= 1e-286)
		tmp = (x / a) / y;
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, 1e-286], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000005e-286

   1. Initial program 97.9%

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

      1. associate-*r/ 98.5%

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

      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 80.2%

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

      4. associate-/l* 80.2%

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

      5. associate-/r/ 79.5%

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

      6. exp-neg 79.5%

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

      7. associate-*r/ 79.5%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in t around 0 68.4%

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

      1. associate-/r* 71.3%

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

   6. Simplified 71.3%

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

   7. Taylor expanded in b around 0 58.9%

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

   8. Taylor expanded in y around 0 28.7%

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

      1. associate-/l/ 31.4%

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

   10. Simplified 31.4%

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

   if 1.00000000000000005e-286 < t

   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/ 97.1%

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

      2. sub-neg 97.1%

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

      3. exp-sum 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/ 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 67.3%

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

   4. Taylor expanded in t around 0 68.5%

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

      1. associate-/r* 69.4%

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

   6. Simplified 69.4%

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

   7. Taylor expanded in b around 0 63.7%

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

   8. Taylor expanded in y around 0 25.8%

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

      1. div-inv 25.7%

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

      2. associate-/r* 30.5%

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

   10. Applied egg-rr 30.5%

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

4. Final simplification 31.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-286}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]

Alternative 21: 30.3% 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 98.2%

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

   1. associate-*r/ 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 79.9%

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

   4. associate-/l* 79.9%

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

   5. associate-/r/ 79.1%

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

   6. exp-neg 79.1%

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

   7. associate-*r/ 79.1%

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

3. Simplified 70.4%

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

4. Taylor expanded in t around 0 68.4%

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

   1. associate-/r* 70.4%

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

6. Simplified 70.4%

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

7. Taylor expanded in b around 0 61.1%

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

8. Taylor expanded in y around 0 27.3%

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

9. Final simplification 27.3%

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

Alternative 22: 30.7% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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/ 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 79.9%

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

   4. associate-/l* 79.9%

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

   5. associate-/r/ 79.1%

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

   6. exp-neg 79.1%

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

   7. associate-*r/ 79.1%

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

3. Simplified 70.4%

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

4. Taylor expanded in t around 0 68.4%

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

   1. associate-/r* 70.4%

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

6. Simplified 70.4%

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

7. Taylor expanded in b around 0 61.1%

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

8. Taylor expanded in y around 0 27.3%

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

   1. associate-/l/ 28.0%

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

10. Simplified 28.0%

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

11. Final simplification 28.0%

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

Developer target: 71.6% 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 2023185 
(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))