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

Percentage Accurate: 98.4% → 98.4%

Time: 21.6s

Alternatives: 14

Speedup: 1.0×

• 47.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

3. Final simplification 98.7%

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

Alternative 2: 92.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+97} \lor \neg \left(t \leq 8 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -2.15e+97) (not (<= t 8e+53)))
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.15e+97) || !(t <= 8e+53)) {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-2.15d+97)) .or. (.not. (t <= 8d+53))) then
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -2.15e+97) || !(t <= 8e+53)) {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -2.15e+97) or not (t <= 8e+53):
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -2.15e+97) || !(t <= 8e+53))
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -2.15e+97) || ~((t <= 8e+53)))
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -2.15e+97], N[Not[LessEqual[t, 8e+53]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1499999999999999e97 or 7.9999999999999999e53 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.3%

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

   if -2.1499999999999999e97 < t < 7.9999999999999999e53

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 96.7%

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

      1. +-commutative 96.7%

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

      2. mul-1-neg 96.7%

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

      3. unsub-neg 96.7%

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

   5. Simplified 96.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+97} \lor \neg \left(t \leq 8 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+136} \lor \neg \left(y \leq 1.25 \cdot 10^{+104}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.3e+136) (not (<= y 1.25e+104)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (log a) (+ t -1.0)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+136) || !(y <= 1.25e+104)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2.3d+136)) .or. (.not. (y <= 1.25d+104))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp(((log(a) * (t + (-1.0d0))) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2.3e+136) || !(y <= 1.25e+104)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp(((Math.log(a) * (t + -1.0)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2.3e+136) or not (y <= 1.25e+104):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp(((math.log(a) * (t + -1.0)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2.3e+136) || !(y <= 1.25e+104))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(log(a) * Float64(t + -1.0)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2.3e+136) || ~((y <= 1.25e+104)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp(((log(a) * (t + -1.0)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2.3e+136], N[Not[LessEqual[y, 1.25e+104]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[Log[a], $MachinePrecision] * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e136 or 1.2499999999999999e104 < 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. Add Preprocessing

   3. Taylor expanded in t around 0 90.5%

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

      1. +-commutative 90.5%

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

      2. mul-1-neg 90.5%

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

      3. unsub-neg 90.5%

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

   5. Simplified 90.5%

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

   6. Taylor expanded in b around 0 88.4%

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

      1. div-exp 88.4%

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

      2. *-commutative 88.4%

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

      3. exp-to-pow 88.4%

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

      4. rem-exp-log 88.4%

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

   8. Simplified 88.4%

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

   if -2.3e136 < y < 1.2499999999999999e104

   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. Add Preprocessing

   3. Taylor expanded in y around 0 89.1%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+136} \lor \neg \left(y \leq 1.25 \cdot 10^{+104}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\log a \cdot \left(t + -1\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+29} \lor \neg \left(y \leq 7.2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1e+29) (not (<= y 7.2e+18)))
   (/ (* 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 <= -1e+29) || !(y <= 7.2e+18)) {
		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 <= (-1d+29)) .or. (.not. (y <= 7.2d+18))) 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 <= -1e+29) || !(y <= 7.2e+18)) {
		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 <= -1e+29) or not (y <= 7.2e+18):
		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 <= -1e+29) || !(y <= 7.2e+18))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64(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 <= -1e+29) || ~((y <= 7.2e+18)))
		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, -1e+29], N[Not[LessEqual[y, 7.2e+18]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999914e28 or 7.2e18 < 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. Add Preprocessing

   3. Taylor expanded in t around 0 88.8%

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

      1. +-commutative 88.8%

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

      2. mul-1-neg 88.8%

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

      3. unsub-neg 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in b around 0 80.6%

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

      1. div-exp 80.6%

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

      2. *-commutative 80.6%

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

      3. exp-to-pow 80.6%

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

      4. rem-exp-log 80.6%

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

   8. Simplified 80.6%

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

   if -9.99999999999999914e28 < y < 7.2e18

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 94.4%

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

      1. div-exp 81.5%

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

      2. exp-to-pow 82.2%

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

      3. sub-neg 82.2%

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

      4. metadata-eval 82.2%

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

      5. associate-*r/ 83.8%

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

   5. Simplified 83.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+29} \lor \neg \left(y \leq 7.2 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+81} \lor \neg \left(b \leq 2.6 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.7e+81) (not (<= b 2.6e+15)))
   (/ x (* a (* y (exp b))))
   (* (/ (pow z y) a) (/ x y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.7e+81) || !(b <= 2.6e+15)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (pow(z, y) / a) * (x / 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 <= (-6.7d+81)) .or. (.not. (b <= 2.6d+15))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = ((z ** y) / a) * (x / 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 <= -6.7e+81) || !(b <= 2.6e+15)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (Math.pow(z, y) / a) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.7e+81) or not (b <= 2.6e+15):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (math.pow(z, y) / a) * (x / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.7e+81) || !(b <= 2.6e+15))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64((z ^ y) / a) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.7e+81) || ~((b <= 2.6e+15)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = ((z ^ y) / a) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.7e+81], N[Not[LessEqual[b, 2.6e+15]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.69999999999999962e81 or 2.6e15 < 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. Add Preprocessing

   3. Taylor expanded in y around 0 86.3%

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

      1. div-exp 65.9%

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

      2. exp-to-pow 65.9%

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

      3. sub-neg 65.9%

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

      4. metadata-eval 65.9%

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

      5. associate-*r/ 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in t around 0 75.4%

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

   if -6.69999999999999962e81 < b < 2.6e15

   1. Initial program 97.7%

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

      1. add-cube-cbrt 97.7%

         \[\leadsto \frac{x \cdot \color{blue}{\left(\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}\right) \cdot \sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}\right)}}{y} \]

      2. pow3 97.7%

         \[\leadsto \frac{x \cdot \color{blue}{{\left(\sqrt[3]{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}\right)}^{3}}}{y} \]

      3. exp-diff 89.6%

         \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\color{blue}{\frac{e^{y \cdot \log z + \left(t - 1\right) \cdot \log a}}{e^{b}}}}\right)}^{3}}{y} \]

      4. exp-sum 78.1%

         \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a}}}{e^{b}}}\right)}^{3}}{y} \]

      5. *-commutative 78.1%

         \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\frac{e^{\color{blue}{\log z \cdot y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right)}^{3}}{y} \]

      6. pow-to-exp 78.1%

         \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\frac{\color{blue}{{z}^{y}} \cdot e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}\right)}^{3}}{y} \]

      7. sub-neg 78.1%

         \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\frac{{z}^{y} \cdot e^{\color{blue}{\left(t + \left(-1\right)\right)} \cdot \log a}}{e^{b}}}\right)}^{3}}{y} \]

      8. metadata-eval 78.1%

         \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\frac{{z}^{y} \cdot e^{\left(t + \color{blue}{-1}\right) \cdot \log a}}{e^{b}}}\right)}^{3}}{y} \]

      9. *-commutative 78.1%

         \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\frac{{z}^{y} \cdot e^{\color{blue}{\log a \cdot \left(t + -1\right)}}}{e^{b}}}\right)}^{3}}{y} \]

      10. pow-to-exp 78.9%

          \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\frac{{z}^{y} \cdot \color{blue}{{a}^{\left(t + -1\right)}}}{e^{b}}}\right)}^{3}}{y} \]

      11. associate-*r/ 78.9%

          \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\color{blue}{{z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}\right)}^{3}}{y} \]

   4. Applied egg-rr 78.9%

      \[\leadsto \frac{x \cdot \color{blue}{{\left(\sqrt[3]{{z}^{y} \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}\right)}^{3}}}{y} \]

   5. Taylor expanded in t around 0 72.6%

      \[\leadsto \frac{x \cdot {\left(\sqrt[3]{\color{blue}{\frac{{z}^{y}}{a \cdot e^{b}}}}\right)}^{3}}{y} \]

   6. Taylor expanded in b around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. times-frac 69.2%

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

   8. Simplified 69.2%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.7 \cdot 10^{+81} \lor \neg \left(b \leq 2.6 \cdot 10^{+15}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{z}^{y}}{a} \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.5% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+37} \lor \neg \left(y \leq 2.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3.3e+37) (not (<= y 2.2e+19)))
   (/ (* x (/ (pow z y) a)) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3.3e+37) || !(y <= 2.2e+19)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x / (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 ((y <= (-3.3d+37)) .or. (.not. (y <= 2.2d+19))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x / (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 ((y <= -3.3e+37) || !(y <= 2.2e+19)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3.3e+37) or not (y <= 2.2e+19):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3.3e+37) || !(y <= 2.2e+19))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3.3e+37) || ~((y <= 2.2e+19)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3.3e+37], N[Not[LessEqual[y, 2.2e+19]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3000000000000001e37 or 2.2e19 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in b around 0 82.3%

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

      1. div-exp 82.3%

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

      2. *-commutative 82.3%

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

      3. exp-to-pow 82.3%

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

      4. rem-exp-log 82.3%

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

   8. Simplified 82.3%

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

   if -3.3000000000000001e37 < y < 2.2e19

   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. Add Preprocessing

   3. Taylor expanded in y around 0 94.5%

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

      1. div-exp 79.0%

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

      2. exp-to-pow 79.7%

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

      3. sub-neg 79.7%

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

      4. metadata-eval 79.7%

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

      5. associate-*r/ 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in t around 0 71.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+37} \lor \neg \left(y \leq 2.2 \cdot 10^{+19}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3800000000000 \lor \neg \left(t \leq 7.2 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -3800000000000.0) (not (<= t 7.2e+53)))
   (/ (* x (pow a (+ t -1.0))) y)
   (/ (* x (/ (pow z y) a)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3800000000000.0) || !(t <= 7.2e+53)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x * (pow(z, y) / a)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-3800000000000.0d0)) .or. (.not. (t <= 7.2d+53))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = (x * ((z ** y) / a)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -3800000000000.0) || !(t <= 7.2e+53)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -3800000000000.0) or not (t <= 7.2e+53):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = (x * (math.pow(z, y) / a)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -3800000000000.0) || !(t <= 7.2e+53))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -3800000000000.0) || ~((t <= 7.2e+53)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = (x * ((z ^ y) / a)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -3800000000000.0], N[Not[LessEqual[t, 7.2e+53]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.8e12 or 7.2e53 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 89.5%

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

      1. div-exp 63.2%

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

      2. exp-to-pow 63.2%

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

      3. sub-neg 63.2%

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

      4. metadata-eval 63.2%

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

      5. associate-*r/ 63.2%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in b around 0 85.7%

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

   8. Simplified 85.7%

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

   if -3.8e12 < t < 7.2e53

   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. Add Preprocessing

   3. Taylor expanded in t around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. mul-1-neg 97.6%

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

      3. unsub-neg 97.6%

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

   5. Simplified 97.6%

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

   6. Taylor expanded in b around 0 73.3%

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

      1. div-exp 73.3%

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

      2. *-commutative 73.3%

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

      3. exp-to-pow 73.3%

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

      4. rem-exp-log 74.1%

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

   8. Simplified 74.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3800000000000 \lor \neg \left(t \leq 7.2 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{x}{a} - x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.5e-246)
   (/ x (* a (* y (exp b))))
   (if (<= b 1.7e-29)
     (/ (* y (- (* a (/ x a)) (* x b))) (* a (* y y)))
     (* x (/ (/ (exp (- b)) a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5e-246) {
		tmp = x / (a * (y * exp(b)));
	} else if (b <= 1.7e-29) {
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	} else {
		tmp = x * ((exp(-b) / a) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.5d-246)) then
        tmp = x / (a * (y * exp(b)))
    else if (b <= 1.7d-29) then
        tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y))
    else
        tmp = x * ((exp(-b) / a) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.5e-246) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (b <= 1.7e-29) {
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	} else {
		tmp = x * ((Math.exp(-b) / a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.5e-246:
		tmp = x / (a * (y * math.exp(b)))
	elif b <= 1.7e-29:
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y))
	else:
		tmp = x * ((math.exp(-b) / a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.5e-246)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (b <= 1.7e-29)
		tmp = Float64(Float64(y * Float64(Float64(a * Float64(x / a)) - Float64(x * b))) / Float64(a * Float64(y * y)));
	else
		tmp = Float64(x * Float64(Float64(exp(Float64(-b)) / a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.5e-246)
		tmp = x / (a * (y * exp(b)));
	elseif (b <= 1.7e-29)
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	else
		tmp = x * ((exp(-b) / a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.5e-246], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-29], N[(N[(y * N[(N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[Exp[(-b)], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.5e-246

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 71.2%

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

      1. div-exp 59.4%

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

      2. exp-to-pow 59.8%

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

      3. sub-neg 59.8%

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

      4. metadata-eval 59.8%

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

      5. associate-*r/ 61.6%

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

   5. Simplified 61.6%

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

   6. Taylor expanded in t around 0 55.9%

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

   if -1.5e-246 < b < 1.69999999999999986e-29

   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. Add Preprocessing

   3. Taylor expanded in y around 0 71.2%

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

      1. div-exp 71.2%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

      5. associate-*r/ 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 33.6%

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

   7. Taylor expanded in b around 0 24.5%

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

      1. +-commutative 24.5%

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

      2. associate-/r* 24.4%

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

      3. associate-*r/ 24.4%

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

      4. frac-add 25.3%

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

      5. div-inv 25.3%

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

      6. div-inv 25.3%

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

      7. *-commutative 25.3%

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

      8. neg-mul-1 25.3%

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

      9. *-commutative 25.3%

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

      10. distribute-rgt-neg-in 25.3%

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

      11. *-commutative 25.3%

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

   9. Applied egg-rr 25.3%

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

       1. +-commutative 25.3%

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

       2. *-commutative 25.3%

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

       3. associate-*l* 37.5%

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

       4. distribute-lft-out 37.5%

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

       5. associate-*r* 46.2%

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

   11. Simplified 46.2%

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

   if 1.69999999999999986e-29 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 87.5%

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

      1. div-exp 65.0%

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

      2. exp-to-pow 65.1%

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

      3. sub-neg 65.1%

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

      4. metadata-eval 65.1%

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

      5. associate-*r/ 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in t around 0 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-/r* 71.7%

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

      3. exp-neg 71.7%

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

   8. Simplified 71.7%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-29}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{x}{a} - x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{e^{-b}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.46 \cdot 10^{-249} \lor \neg \left(b \leq 7.2 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{x}{a} - x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.46e-249) (not (<= b 7.2e-29)))
   (/ x (* a (* y (exp b))))
   (/ (* y (- (* a (/ x a)) (* x b))) (* a (* y y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.46e-249) || !(b <= 7.2e-29)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * 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 <= (-1.46d-249)) .or. (.not. (b <= 7.2d-29))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * 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 <= -1.46e-249) || !(b <= 7.2e-29)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.46e-249) or not (b <= 7.2e-29):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.46e-249) || !(b <= 7.2e-29))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(y * Float64(Float64(a * Float64(x / a)) - Float64(x * b))) / Float64(a * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.46e-249) || ~((b <= 7.2e-29)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.46e-249], N[Not[LessEqual[b, 7.2e-29]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.46e-249 or 7.19999999999999948e-29 < b

   1. Initial program 98.9%

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

   3. Taylor expanded in y around 0 78.1%

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

      1. div-exp 61.8%

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

      2. exp-to-pow 62.1%

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

      3. sub-neg 62.1%

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

      4. metadata-eval 62.1%

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

      5. associate-*r/ 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in t around 0 62.5%

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

   if -1.46e-249 < b < 7.19999999999999948e-29

   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. Add Preprocessing

   3. Taylor expanded in y around 0 71.2%

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

      1. div-exp 71.2%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

      5. associate-*r/ 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in t around 0 33.6%

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

   7. Taylor expanded in b around 0 24.5%

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

      1. +-commutative 24.5%

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

      2. associate-/r* 24.4%

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

      3. associate-*r/ 24.4%

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

      4. frac-add 25.3%

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

      5. div-inv 25.3%

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

      6. div-inv 25.3%

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

      7. *-commutative 25.3%

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

      8. neg-mul-1 25.3%

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

      9. *-commutative 25.3%

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

      10. distribute-rgt-neg-in 25.3%

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

      11. *-commutative 25.3%

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

   9. Applied egg-rr 25.3%

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

       1. +-commutative 25.3%

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

       2. *-commutative 25.3%

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

       3. associate-*l* 37.5%

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

       4. distribute-lft-out 37.5%

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

       5. associate-*r* 46.2%

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

   11. Simplified 46.2%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.46 \cdot 10^{-249} \lor \neg \left(b \leq 7.2 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{x}{a} - x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 31.8% accurate, 11.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.05 \cdot 10^{-101}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{x}{a} - x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.05e-101)
   (/ 1.0 (/ a (/ x y)))
   (if (<= x 7.3e+89)
     (/ (* y (- (* a (/ x a)) (* x b))) (* a (* y y)))
     (* (/ x (* y a)) (- 1.0 b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.05e-101) {
		tmp = 1.0 / (a / (x / y));
	} else if (x <= 7.3e+89) {
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	} else {
		tmp = (x / (y * a)) * (1.0 - b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.05d-101) then
        tmp = 1.0d0 / (a / (x / y))
    else if (x <= 7.3d+89) then
        tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y))
    else
        tmp = (x / (y * a)) * (1.0d0 - b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.05e-101) {
		tmp = 1.0 / (a / (x / y));
	} else if (x <= 7.3e+89) {
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	} else {
		tmp = (x / (y * a)) * (1.0 - b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.05e-101:
		tmp = 1.0 / (a / (x / y))
	elif x <= 7.3e+89:
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y))
	else:
		tmp = (x / (y * a)) * (1.0 - b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.05e-101)
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	elseif (x <= 7.3e+89)
		tmp = Float64(Float64(y * Float64(Float64(a * Float64(x / a)) - Float64(x * b))) / Float64(a * Float64(y * y)));
	else
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(1.0 - b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= 1.05e-101)
		tmp = 1.0 / (a / (x / y));
	elseif (x <= 7.3e+89)
		tmp = (y * ((a * (x / a)) - (x * b))) / (a * (y * y));
	else
		tmp = (x / (y * a)) * (1.0 - b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.05e-101], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.3e+89], N[(N[(y * N[(N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.05000000000000008e-101

   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-/l* 99.5%

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

      2. associate--l+ 99.5%

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

      3. exp-sum 75.2%

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

      4. associate-/l* 73.0%

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

      5. *-commutative 73.0%

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

      6. exp-to-pow 73.0%

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

      7. exp-diff 64.2%

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

      8. *-commutative 64.2%

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

      9. exp-to-pow 64.6%

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

      10. sub-neg 64.6%

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

      11. metadata-eval 64.6%

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

   3. Simplified 64.6%

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

   5. Taylor expanded in b around 0 66.7%

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

      1. associate-/l* 66.7%

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

      2. exp-to-pow 67.1%

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

      3. sub-neg 67.1%

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

      4. metadata-eval 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in y around 0 61.2%

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

   9. Taylor expanded in t around 0 35.7%

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

       1. associate-/r* 35.1%

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

   11. Simplified 35.1%

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

       1. associate-/l/ 35.7%

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

       2. div-inv 35.7%

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

       3. associate-/r* 37.7%

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

       4. clear-num 37.7%

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

   13. Applied egg-rr 37.7%

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

   if 1.05000000000000008e-101 < x < 7.29999999999999972e89

   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. Add Preprocessing

   3. Taylor expanded in y around 0 74.4%

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

      1. div-exp 58.8%

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

      2. exp-to-pow 59.8%

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

      3. sub-neg 59.8%

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

      4. metadata-eval 59.8%

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

      5. associate-*r/ 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in t around 0 48.4%

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

   7. Taylor expanded in b around 0 27.2%

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

      1. +-commutative 27.2%

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

      2. associate-/r* 26.8%

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

      3. associate-*r/ 26.8%

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

      4. frac-add 28.8%

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

      5. div-inv 28.8%

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

      6. div-inv 28.8%

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

      7. *-commutative 28.8%

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

      8. neg-mul-1 28.8%

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

      9. *-commutative 28.8%

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

      10. distribute-rgt-neg-in 28.8%

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

      11. *-commutative 28.8%

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

   9. Applied egg-rr 28.8%

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

       1. +-commutative 28.8%

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

       2. *-commutative 28.8%

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

       3. associate-*l* 38.3%

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

       4. distribute-lft-out 38.3%

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

       5. associate-*r* 47.4%

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

   11. Simplified 47.4%

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

   if 7.29999999999999972e89 < x

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 74.4%

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

      1. div-exp 65.1%

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

      2. exp-to-pow 65.5%

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

      3. sub-neg 65.5%

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

      4. metadata-eval 65.5%

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

      5. associate-*r/ 65.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in t around 0 59.2%

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

   7. Taylor expanded in b around 0 42.8%

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

   8. Taylor expanded in x around 0 45.6%

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

      1. +-commutative 45.6%

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

      2. *-commutative 45.6%

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

      3. mul-1-neg 45.6%

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

      4. *-commutative 45.6%

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

      5. unsub-neg 45.6%

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

      6. distribute-lft-out-- 45.5%

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

      7. associate-*r/ 45.5%

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

      8. associate-*l/ 45.5%

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

      9. associate-*r/ 42.8%

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

      10. associate-*l/ 43.2%

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

      11. distribute-lft-out-- 48.0%

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

   10. Simplified 48.0%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.05 \cdot 10^{-101}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{+89}:\\ \;\;\;\;\frac{y \cdot \left(a \cdot \frac{x}{a} - x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -5.8e-131) (/ 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 <= -5.8e-131) {
		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 <= (-5.8d-131)) 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 <= -5.8e-131) {
		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 <= -5.8e-131:
		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 <= -5.8e-131)
		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 <= -5.8e-131)
		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, -5.8e-131], 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 < -5.8000000000000004e-131

   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-/l* 99.4%

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

      2. associate--l+ 99.4%

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

      3. exp-sum 68.9%

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

      4. associate-/l* 67.6%

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

      5. *-commutative 67.6%

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

      6. exp-to-pow 67.6%

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

      7. exp-diff 53.0%

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

      8. *-commutative 53.0%

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

      9. exp-to-pow 53.6%

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

      10. sub-neg 53.6%

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

      11. metadata-eval 53.6%

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

   3. Simplified 53.6%

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

   5. Taylor expanded in b around 0 64.3%

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

      1. associate-/l* 64.3%

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

      2. exp-to-pow 64.8%

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

      3. sub-neg 64.8%

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

      4. metadata-eval 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around 0 70.5%

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

   9. Taylor expanded in t around 0 41.5%

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

       1. associate-/r* 41.5%

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

   11. Simplified 41.5%

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

       1. associate-/l/ 41.5%

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

       2. div-inv 41.5%

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

       3. clear-num 41.5%

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

       4. associate-/l* 42.7%

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

   13. Applied egg-rr 42.7%

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

   if -5.8000000000000004e-131 < t

   1. Initial program 98.4%

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

      1. associate-/l* 99.3%

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

      2. associate--l+ 99.3%

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

      3. exp-sum 80.4%

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

      4. associate-/l* 78.1%

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

      5. *-commutative 78.1%

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

      6. exp-to-pow 78.1%

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

      7. exp-diff 71.2%

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

      8. *-commutative 71.2%

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

      9. exp-to-pow 71.8%

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

      10. sub-neg 71.8%

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

      11. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in b around 0 70.9%

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

      1. associate-/l* 70.9%

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

      2. exp-to-pow 71.5%

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

      3. sub-neg 71.5%

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

      4. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around 0 55.6%

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

   9. Taylor expanded in t around 0 33.1%

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

       1. associate-/r* 32.5%

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

   11. Simplified 32.5%

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

       1. associate-/l/ 33.1%

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

       2. div-inv 33.1%

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

       3. associate-/r* 37.7%

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

   13. Applied egg-rr 37.7%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{-131}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 31.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.5e-130) (/ 1.0 (* y (/ a x))) (/ 1.0 (/ a (/ x y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e-130) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = 1.0 / (a / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-1.5d-130)) then
        tmp = 1.0d0 / (y * (a / x))
    else
        tmp = 1.0d0 / (a / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.5e-130) {
		tmp = 1.0 / (y * (a / x));
	} else {
		tmp = 1.0 / (a / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.5e-130:
		tmp = 1.0 / (y * (a / x))
	else:
		tmp = 1.0 / (a / (x / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.5e-130)
		tmp = Float64(1.0 / Float64(y * Float64(a / x)));
	else
		tmp = Float64(1.0 / Float64(a / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.5e-130)
		tmp = 1.0 / (y * (a / x));
	else
		tmp = 1.0 / (a / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.5e-130], N[(1.0 / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999993e-130

   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-/l* 99.4%

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

      2. associate--l+ 99.4%

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

      3. exp-sum 68.9%

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

      4. associate-/l* 67.6%

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

      5. *-commutative 67.6%

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

      6. exp-to-pow 67.6%

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

      7. exp-diff 53.0%

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

      8. *-commutative 53.0%

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

      9. exp-to-pow 53.6%

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

      10. sub-neg 53.6%

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

      11. metadata-eval 53.6%

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

   3. Simplified 53.6%

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

   5. Taylor expanded in b around 0 64.3%

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

      1. associate-/l* 64.3%

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

      2. exp-to-pow 64.8%

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

      3. sub-neg 64.8%

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

      4. metadata-eval 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in y around 0 70.5%

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

   9. Taylor expanded in t around 0 41.5%

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

       1. associate-/r* 41.5%

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

   11. Simplified 41.5%

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

       1. associate-/l/ 41.5%

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

       2. div-inv 41.5%

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

       3. clear-num 41.5%

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

       4. associate-/l* 42.7%

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

   13. Applied egg-rr 42.7%

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

   if -1.49999999999999993e-130 < t

   1. Initial program 98.4%

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

      1. associate-/l* 99.3%

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

      2. associate--l+ 99.3%

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

      3. exp-sum 80.4%

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

      4. associate-/l* 78.1%

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

      5. *-commutative 78.1%

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

      6. exp-to-pow 78.1%

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

      7. exp-diff 71.2%

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

      8. *-commutative 71.2%

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

      9. exp-to-pow 71.8%

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

      10. sub-neg 71.8%

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

      11. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in b around 0 70.9%

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

      1. associate-/l* 70.9%

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

      2. exp-to-pow 71.5%

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

      3. sub-neg 71.5%

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

      4. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around 0 55.6%

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

   9. Taylor expanded in t around 0 33.1%

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

       1. associate-/r* 32.5%

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

   11. Simplified 32.5%

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

       1. associate-/l/ 33.1%

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

       2. div-inv 33.1%

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

       3. associate-/r* 37.7%

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

       4. clear-num 37.8%

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

   13. Applied egg-rr 37.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{a}{\frac{x}{y}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-130}:\\ \;\;\;\;\frac{1}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{a}{\frac{x}{y}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 31.0% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -6.2e-132) (/ x (* y a)) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -6.2e-132) {
		tmp = x / (y * a);
	} 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 <= (-6.2d-132)) then
        tmp = x / (y * a)
    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 <= -6.2e-132) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -6.2e-132:
		tmp = x / (y * a)
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -6.2e-132)
		tmp = Float64(x / Float64(y * a));
	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 <= -6.2e-132)
		tmp = x / (y * a);
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -6.2e-132], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.20000000000000016e-132

   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. Add Preprocessing

   3. Taylor expanded in y around 0 81.9%

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

      1. div-exp 63.5%

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

      2. exp-to-pow 63.9%

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

      3. sub-neg 63.9%

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

      4. metadata-eval 63.9%

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

      5. associate-*r/ 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in t around 0 55.2%

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

   7. Taylor expanded in b around 0 41.5%

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

      1. *-commutative 41.5%

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

   9. Simplified 41.5%

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

   if -6.20000000000000016e-132 < t

   1. Initial program 98.4%

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

      1. associate-/l* 99.3%

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

      2. associate--l+ 99.3%

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

      3. exp-sum 80.4%

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

      4. associate-/l* 78.1%

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

      5. *-commutative 78.1%

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

      6. exp-to-pow 78.1%

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

      7. exp-diff 71.2%

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

      8. *-commutative 71.2%

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

      9. exp-to-pow 71.8%

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

      10. sub-neg 71.8%

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

      11. metadata-eval 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in b around 0 70.9%

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

      1. associate-/l* 70.9%

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

      2. exp-to-pow 71.5%

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

      3. sub-neg 71.5%

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

      4. metadata-eval 71.5%

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

   7. Simplified 71.5%

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

   8. Taylor expanded in y around 0 55.6%

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

   9. Taylor expanded in t around 0 33.1%

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

       1. associate-/r* 32.5%

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

   11. Simplified 32.5%

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

       1. associate-/l/ 33.1%

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

       2. div-inv 33.1%

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

       3. associate-/r* 37.7%

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

   13. Applied egg-rr 37.7%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-132}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 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 98.7%

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

3. Taylor expanded in y around 0 76.3%

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

   1. div-exp 64.2%

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

   2. exp-to-pow 64.5%

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

   3. sub-neg 64.5%

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

   4. metadata-eval 64.5%

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

   5. associate-*r/ 65.7%

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

5. Simplified 65.7%

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

6. Taylor expanded in t around 0 55.1%

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

7. Taylor expanded in b around 0 35.8%

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

   1. *-commutative 35.8%

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

9. Simplified 35.8%

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

10. Final simplification 35.8%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 70.8% 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 2024050 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (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))