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

Percentage Accurate: 98.2% → 98.2%

Time: 23.0s

Alternatives: 22

Speedup: 1.0×

• 47.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% 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: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

3. Final simplification 98.4%

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

Alternative 2: 92.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+52} \lor \neg \left(y \leq 1.85 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2e+52) (not (<= y 1.85e+48)))
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2e+52) || !(y <= 1.85e+48)) {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-2d+52)) .or. (.not. (y <= 1.85d+48))) then
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -2e+52) || !(y <= 1.85e+48)) {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -2e+52) or not (y <= 1.85e+48):
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -2e+52) || !(y <= 1.85e+48))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -2e+52) || ~((y <= 1.85e+48)))
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -2e+52], N[Not[LessEqual[y, 1.85e+48]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e52 or 1.85e48 < 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 90.9%

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

      1. +-commutative 90.9%

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

      2. mul-1-neg 90.9%

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

      3. unsub-neg 90.9%

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

   5. Simplified 90.9%

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

   if -2e52 < y < 1.85e48

   1. Initial program 97.5%

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

   3. Taylor expanded in y around 0 96.3%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+52} \lor \neg \left(y \leq 1.85 \cdot 10^{+48}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+165} \lor \neg \left(y \leq 5.1 \cdot 10^{+126}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.9e+165) (not (<= y 5.1e+126)))
   (/ (* x (/ (pow z y) a)) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+165) || !(y <= 5.1e+126)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.9d+165)) .or. (.not. (y <= 5.1d+126))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.9e+165) || !(y <= 5.1e+126)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.9e+165) or not (y <= 5.1e+126):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.9e+165) || !(y <= 5.1e+126))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.9e+165) || ~((y <= 5.1e+126)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.9e+165], N[Not[LessEqual[y, 5.1e+126]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999995e165 or 5.1000000000000001e126 < 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 92.4%

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

      1. +-commutative 92.4%

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

      2. mul-1-neg 92.4%

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

      3. unsub-neg 92.4%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in b around 0 92.4%

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

      1. div-exp 92.4%

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

      2. *-commutative 92.4%

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

      3. exp-to-pow 92.4%

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

      4. rem-exp-log 92.4%

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

   8. Simplified 92.4%

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

   if -1.89999999999999995e165 < y < 5.1000000000000001e126

   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 91.9%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+165} \lor \neg \left(y \leq 5.1 \cdot 10^{+126}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -27000000000000 \lor \neg \left(y \leq 7.6 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{y}}{e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -27000000000000.0) (not (<= y 7.6e+64)))
   (/ (* x (/ (pow z y) a)) y)
   (* x (/ (/ (/ (pow a t) a) y) (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -27000000000000.0) || !(y <= 7.6e+64)) {
		tmp = (x * (pow(z, y) / a)) / y;
	} else {
		tmp = x * (((pow(a, t) / 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 <= (-27000000000000.0d0)) .or. (.not. (y <= 7.6d+64))) then
        tmp = (x * ((z ** y) / a)) / y
    else
        tmp = x * ((((a ** t) / 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 <= -27000000000000.0) || !(y <= 7.6e+64)) {
		tmp = (x * (Math.pow(z, y) / a)) / y;
	} else {
		tmp = x * (((Math.pow(a, t) / a) / y) / Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -27000000000000.0) or not (y <= 7.6e+64):
		tmp = (x * (math.pow(z, y) / a)) / y
	else:
		tmp = x * (((math.pow(a, t) / a) / y) / math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -27000000000000.0) || !(y <= 7.6e+64))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(x * Float64(Float64(Float64((a ^ t) / a) / y) / exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -27000000000000.0) || ~((y <= 7.6e+64)))
		tmp = (x * ((z ^ y) / a)) / y;
	else
		tmp = x * ((((a ^ t) / a) / y) / exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -27000000000000.0], N[Not[LessEqual[y, 7.6e+64]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e13 or 7.6000000000000002e64 < 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 90.3%

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

      1. +-commutative 90.3%

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

      2. mul-1-neg 90.3%

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

      3. unsub-neg 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in b around 0 83.6%

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

      1. div-exp 83.6%

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

      2. *-commutative 83.6%

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

      3. exp-to-pow 83.6%

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

      4. rem-exp-log 83.6%

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

   8. Simplified 83.6%

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

   if -2.7e13 < y < 7.6000000000000002e64

   1. Initial program 97.4%

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

      1. associate-/l* 97.8%

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

      2. associate--l+ 97.8%

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

      3. exp-sum 94.6%

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

      4. associate-/l* 94.6%

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

      5. *-commutative 94.6%

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

      6. exp-to-pow 94.6%

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

      7. exp-diff 83.5%

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

      8. *-commutative 83.5%

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

      9. exp-to-pow 84.3%

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

      10. sub-neg 84.3%

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

      11. metadata-eval 84.3%

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

   3. Simplified 84.3%

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

   5. Taylor expanded in y around 0 81.2%

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

      1. exp-to-pow 81.9%

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

      2. sub-neg 81.9%

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

      3. metadata-eval 81.9%

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

      4. associate-*r/ 86.9%

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

      5. associate-/r* 81.7%

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

   7. Simplified 81.7%

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

      1. unpow-prod-up 81.8%

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

      2. unpow-1 81.8%

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

   9. Applied egg-rr 81.8%

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

       1. associate-*r/ 81.8%

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

       2. *-rgt-identity 81.8%

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

   11. Simplified 81.8%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -27000000000000 \lor \neg \left(y \leq 7.6 \cdot 10^{+64}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{{a}^{t}}{a}}{y}}{e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+16} \lor \neg \left(y \leq 2.5 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.3e+16) (not (<= y 2.5e+66)))
   (/ (* 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 <= -1.3e+16) || !(y <= 2.5e+66)) {
		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 <= (-1.3d+16)) .or. (.not. (y <= 2.5d+66))) 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 <= -1.3e+16) || !(y <= 2.5e+66)) {
		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 <= -1.3e+16) or not (y <= 2.5e+66):
		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 <= -1.3e+16) || !(y <= 2.5e+66))
		tmp = Float64(Float64(x * Float64((z ^ y) / a)) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.3e+16) || ~((y <= 2.5e+66)))
		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, -1.3e+16], N[Not[LessEqual[y, 2.5e+66]], $MachinePrecision]], N[(N[(x * N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e16 or 2.49999999999999996e66 < 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 90.3%

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

      1. +-commutative 90.3%

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

      2. mul-1-neg 90.3%

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

      3. unsub-neg 90.3%

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

   5. Simplified 90.3%

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

   6. Taylor expanded in b around 0 83.6%

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

      1. div-exp 83.6%

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

      2. *-commutative 83.6%

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

      3. exp-to-pow 83.6%

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

      4. rem-exp-log 83.6%

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

   8. Simplified 83.6%

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

   if -1.3e16 < y < 2.49999999999999996e66

   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 96.8%

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

      1. div-exp 85.7%

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

      2. exp-to-pow 86.4%

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

      3. sub-neg 86.4%

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

      4. metadata-eval 86.4%

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

   5. Simplified 86.4%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+16} \lor \neg \left(y \leq 2.5 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{x \cdot \frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.1% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq -0.5:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -1e+78)
   (* x (/ (pow a t) (* y a)))
   (if (<= (+ t -1.0) -0.5)
     (/ x (* a (* y (exp b))))
     (* x (/ (pow a (+ t -1.0)) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -1e+78) {
		tmp = x * (pow(a, t) / (y * a));
	} else if ((t + -1.0) <= -0.5) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-1d+78)) then
        tmp = x * ((a ** t) / (y * a))
    else if ((t + (-1.0d0)) <= (-0.5d0)) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -1e+78) {
		tmp = x * (Math.pow(a, t) / (y * a));
	} else if ((t + -1.0) <= -0.5) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -1e+78:
		tmp = x * (math.pow(a, t) / (y * a))
	elif (t + -1.0) <= -0.5:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -1e+78)
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	elseif (Float64(t + -1.0) <= -0.5)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -1e+78)
		tmp = x * ((a ^ t) / (y * a));
	elseif ((t + -1.0) <= -0.5)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -1e+78], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], -0.5], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.00000000000000001e78

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 70.0%

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

      4. associate-/l* 70.0%

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

      5. *-commutative 70.0%

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

      6. exp-to-pow 70.0%

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

      7. exp-diff 54.0%

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

      8. *-commutative 54.0%

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

      9. exp-to-pow 54.0%

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

      10. sub-neg 54.0%

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

      11. metadata-eval 54.0%

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

   3. Simplified 54.0%

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

   5. Taylor expanded in y around 0 70.2%

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

      1. exp-to-pow 70.2%

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

      2. sub-neg 70.2%

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

      3. metadata-eval 70.2%

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

      4. associate-*r/ 70.2%

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

      5. associate-/r* 70.2%

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

   7. Simplified 70.2%

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

      1. unpow-prod-up 70.2%

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

      2. unpow-1 70.2%

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

   9. Applied egg-rr 70.2%

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

       1. associate-*r/ 70.2%

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

       2. *-rgt-identity 70.2%

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

   11. Simplified 70.2%

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

   12. Taylor expanded in b around 0 80.3%

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

   if -1.00000000000000001e78 < (-.f64 t #s(literal 1 binary64)) < -0.5

   1. Initial program 97.2%

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

      1. associate-/l* 97.7%

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

      2. associate--l+ 97.7%

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

      3. exp-sum 86.8%

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

      4. associate-/l* 86.8%

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

      5. *-commutative 86.8%

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

      6. exp-to-pow 86.8%

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

      7. exp-diff 82.6%

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

      8. *-commutative 82.6%

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

      9. exp-to-pow 83.4%

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

      10. sub-neg 83.4%

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

      11. metadata-eval 83.4%

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

   3. Simplified 83.4%

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

   5. Taylor expanded in y around 0 64.9%

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

      1. exp-to-pow 65.7%

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

      2. sub-neg 65.7%

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

      3. metadata-eval 65.7%

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

      4. associate-*r/ 73.0%

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

      5. associate-/r* 66.1%

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

   7. Simplified 66.1%

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

   8. Taylor expanded in t around 0 77.2%

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

   if -0.5 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 80.0%

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

      4. associate-/l* 80.0%

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

      5. *-commutative 80.0%

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

      6. exp-to-pow 80.0%

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

      7. exp-diff 65.0%

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

      8. *-commutative 65.0%

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

      9. exp-to-pow 65.0%

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

      10. sub-neg 65.0%

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

      11. metadata-eval 65.0%

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

   3. Simplified 65.0%

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

   5. Taylor expanded in y around 0 70.2%

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

      1. exp-to-pow 70.2%

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

      2. sub-neg 70.2%

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

      3. metadata-eval 70.2%

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

      4. associate-*r/ 70.2%

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

      5. associate-/r* 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in b around 0 83.6%

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

   10. Simplified 83.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \mathbf{elif}\;t + -1 \leq -0.5:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -55 \lor \neg \left(b \leq 1.9 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -55.0) (not (<= b 1.9e-72)))
   (/ x (* a (* y (exp b))))
   (* x (/ (pow a t) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -55.0) || !(b <= 1.9e-72)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = x * (pow(a, t) / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-55.0d0)) .or. (.not. (b <= 1.9d-72))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = x * ((a ** t) / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -55.0) || !(b <= 1.9e-72)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = x * (Math.pow(a, t) / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -55.0) or not (b <= 1.9e-72):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = x * (math.pow(a, t) / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -55.0) || !(b <= 1.9e-72))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(x * Float64((a ^ t) / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -55.0) || ~((b <= 1.9e-72)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = x * ((a ^ t) / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -55.0], N[Not[LessEqual[b, 1.9e-72]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, t], $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -55 or 1.90000000000000001e-72 < b

   1. Initial program 99.4%

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

      1. associate-/l* 99.2%

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

      2. associate--l+ 99.2%

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

      3. exp-sum 79.8%

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

      4. associate-/l* 79.8%

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

      5. *-commutative 79.8%

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

      6. exp-to-pow 79.8%

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

      7. exp-diff 63.2%

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

      8. *-commutative 63.2%

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

      9. exp-to-pow 63.3%

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

      10. sub-neg 63.3%

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

      11. metadata-eval 63.3%

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

   3. Simplified 63.3%

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

   5. Taylor expanded in y around 0 60.7%

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

      1. exp-to-pow 60.8%

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

      2. sub-neg 60.8%

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

      3. metadata-eval 60.8%

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

      4. associate-*r/ 67.8%

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

      5. associate-/r* 60.6%

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

   7. Simplified 60.6%

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

   8. Taylor expanded in t around 0 79.5%

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

   if -55 < b < 1.90000000000000001e-72

   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. Step-by-step derivation

      1. associate-/l* 98.1%

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

      2. associate--l+ 98.1%

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

      3. exp-sum 84.4%

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

      4. associate-/l* 84.4%

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

      5. *-commutative 84.4%

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

      6. exp-to-pow 84.4%

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

      7. exp-diff 84.4%

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

      8. *-commutative 84.4%

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

      9. exp-to-pow 85.3%

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

      10. sub-neg 85.3%

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

      11. metadata-eval 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in y around 0 74.9%

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

      1. exp-to-pow 75.7%

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

      2. sub-neg 75.7%

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

      3. metadata-eval 75.7%

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

      4. associate-*r/ 76.5%

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

      5. associate-/r* 76.5%

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

   7. Simplified 76.5%

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

      1. unpow-prod-up 76.7%

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

      2. unpow-1 76.7%

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

   9. Applied egg-rr 76.7%

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

       1. associate-*r/ 76.7%

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

       2. *-rgt-identity 76.7%

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

   11. Simplified 76.7%

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

   12. Taylor expanded in b around 0 70.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -55 \lor \neg \left(b \leq 1.9 \cdot 10^{-72}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.3% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.4%

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

   1. associate-/l* 98.7%

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

   2. associate--l+ 98.7%

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

   3. exp-sum 81.9%

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

   4. associate-/l* 81.9%

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

   5. *-commutative 81.9%

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

   6. exp-to-pow 81.9%

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

   7. exp-diff 72.9%

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

   8. *-commutative 72.9%

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

   9. exp-to-pow 73.3%

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

   10. sub-neg 73.3%

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

   11. metadata-eval 73.3%

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

3. Simplified 73.3%

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

5. Taylor expanded in y around 0 67.2%

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

   1. exp-to-pow 67.6%

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

   2. sub-neg 67.6%

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

   3. metadata-eval 67.6%

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

   4. associate-*r/ 71.8%

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

   5. associate-/r* 67.9%

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

7. Simplified 67.9%

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

8. Taylor expanded in t around 0 61.5%

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

9. Final simplification 61.5%

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

Alternative 9: 46.0% accurate, 4.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := t\_1 \cdot 0.5\\ \mathbf{if}\;b \leq -6 \cdot 10^{+219}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(\left(t\_1 - t\_2\right) + b \cdot \left(\left(t\_2 - t\_1\right) - \left(-0.5 \cdot t\_1 + t\_1 \cdot 0.16666666666666666\right)\right)\right) - t\_1\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (* t_1 0.5)))
   (if (<= b -6e+219)
     (+
      t_1
      (*
       b
       (-
        (*
         b
         (+
          (- t_1 t_2)
          (* b (- (- t_2 t_1) (+ (* -0.5 t_1) (* t_1 0.16666666666666666))))))
        t_1)))
     (if (<= b -2e-289)
       (/ (- (/ x a) (/ (* x b) a)) y)
       (/
        x
        (*
         y
         (+
          a
          (*
           b
           (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = t_1 * 0.5;
	double tmp;
	if (b <= -6e+219) {
		tmp = t_1 + (b * ((b * ((t_1 - t_2) + (b * ((t_2 - t_1) - ((-0.5 * t_1) + (t_1 * 0.16666666666666666)))))) - t_1));
	} else if (b <= -2e-289) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = t_1 * 0.5d0
    if (b <= (-6d+219)) then
        tmp = t_1 + (b * ((b * ((t_1 - t_2) + (b * ((t_2 - t_1) - (((-0.5d0) * t_1) + (t_1 * 0.16666666666666666d0)))))) - t_1))
    else if (b <= (-2d-289)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = t_1 * 0.5;
	double tmp;
	if (b <= -6e+219) {
		tmp = t_1 + (b * ((b * ((t_1 - t_2) + (b * ((t_2 - t_1) - ((-0.5 * t_1) + (t_1 * 0.16666666666666666)))))) - t_1));
	} else if (b <= -2e-289) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = t_1 * 0.5
	tmp = 0
	if b <= -6e+219:
		tmp = t_1 + (b * ((b * ((t_1 - t_2) + (b * ((t_2 - t_1) - ((-0.5 * t_1) + (t_1 * 0.16666666666666666)))))) - t_1))
	elif b <= -2e-289:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(t_1 * 0.5)
	tmp = 0.0
	if (b <= -6e+219)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(b * Float64(Float64(t_1 - t_2) + Float64(b * Float64(Float64(t_2 - t_1) - Float64(Float64(-0.5 * t_1) + Float64(t_1 * 0.16666666666666666)))))) - t_1)));
	elseif (b <= -2e-289)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	t_2 = t_1 * 0.5;
	tmp = 0.0;
	if (b <= -6e+219)
		tmp = t_1 + (b * ((b * ((t_1 - t_2) + (b * ((t_2 - t_1) - ((-0.5 * t_1) + (t_1 * 0.16666666666666666)))))) - t_1));
	elseif (b <= -2e-289)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 * 0.5), $MachinePrecision]}, If[LessEqual[b, -6e+219], N[(t$95$1 + N[(b * N[(N[(b * N[(N[(t$95$1 - t$95$2), $MachinePrecision] + N[(b * N[(N[(t$95$2 - t$95$1), $MachinePrecision] - N[(N[(-0.5 * t$95$1), $MachinePrecision] + N[(t$95$1 * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2e-289], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.9999999999999995e219

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 87.5%

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

      5. *-commutative 87.5%

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

      6. exp-to-pow 87.5%

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

      7. exp-diff 56.3%

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

      8. *-commutative 56.3%

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

      9. exp-to-pow 56.3%

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

      10. sub-neg 56.3%

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

      11. metadata-eval 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in y around 0 50.0%

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

      1. exp-to-pow 50.0%

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

      2. sub-neg 50.0%

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

      3. metadata-eval 50.0%

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

      4. associate-*r/ 56.3%

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

      5. associate-/r* 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in t around 0 93.8%

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

   9. Taylor expanded in b around 0 81.3%

      \[\leadsto \color{blue}{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right) + \left(-0.5 \cdot \frac{x}{a \cdot y} + 0.16666666666666666 \cdot \frac{x}{a \cdot y}\right)\right)\right) - \left(-1 \cdot \frac{x}{a \cdot y} + 0.5 \cdot \frac{x}{a \cdot y}\right)\right) - \frac{x}{a \cdot y}\right) + \frac{x}{a \cdot y}} \]

   if -5.9999999999999995e219 < b < -2e-289

   1. Initial program 99.0%

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

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 76.7%

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

      4. associate-/l* 76.7%

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

      5. *-commutative 76.7%

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

      6. exp-to-pow 76.7%

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

      7. exp-diff 67.1%

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

      8. *-commutative 67.1%

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

      9. exp-to-pow 67.4%

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

      10. sub-neg 67.4%

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

      11. metadata-eval 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around 0 61.8%

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

      1. exp-to-pow 62.3%

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

      2. sub-neg 62.3%

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

      3. metadata-eval 62.3%

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

      4. associate-*r/ 66.3%

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

      5. associate-/r* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 52.1%

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

   9. Taylor expanded in b around 0 31.8%

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

   10. Taylor expanded in y around 0 37.2%

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

       1. +-commutative 37.2%

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

       2. mul-1-neg 37.2%

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

       3. unsub-neg 37.2%

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

   12. Simplified 37.2%

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

   if -2e-289 < b

   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. Step-by-step derivation

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 85.9%

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

      4. associate-/l* 85.9%

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

      5. *-commutative 85.9%

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

      6. exp-to-pow 85.9%

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

      7. exp-diff 80.3%

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

      8. *-commutative 80.3%

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

      9. exp-to-pow 80.9%

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

      10. sub-neg 80.9%

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

      11. metadata-eval 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around 0 74.2%

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

      1. exp-to-pow 74.7%

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

      2. sub-neg 74.7%

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

      3. metadata-eval 74.7%

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

      4. associate-*r/ 78.7%

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

      5. associate-/r* 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in t around 0 65.9%

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

   9. Taylor expanded in b around 0 54.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + b \cdot \left(a \cdot y + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(b \cdot y\right)\right) + 0.5 \cdot \left(a \cdot y\right)\right)\right)}} \]

   10. Taylor expanded in y around 0 56.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+219}:\\ \;\;\;\;\frac{x}{y \cdot a} + b \cdot \left(b \cdot \left(\left(\frac{x}{y \cdot a} - \frac{x}{y \cdot a} \cdot 0.5\right) + b \cdot \left(\left(\frac{x}{y \cdot a} \cdot 0.5 - \frac{x}{y \cdot a}\right) - \left(-0.5 \cdot \frac{x}{y \cdot a} + \frac{x}{y \cdot a} \cdot 0.16666666666666666\right)\right)\right) - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 43.6% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{a}}{y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.2e+197)
   (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
   (if (<= b -3.4e-290)
     (/ (/ x a) (- y (* b (* y (- -1.0 (* b 0.5))))))
     (if (<= b 6.2e-307)
       (* b (- (/ x (* a (* y b))) (/ x (* y a))))
       (/
        x
        (*
         y
         (+
          a
          (*
           b
           (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+197) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -3.4e-290) {
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))));
	} else if (b <= 6.2e-307) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.2d+197)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-3.4d-290)) then
        tmp = (x / a) / (y - (b * (y * ((-1.0d0) - (b * 0.5d0)))))
    else if (b <= 6.2d-307) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else
        tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+197) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -3.4e-290) {
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))));
	} else if (b <= 6.2e-307) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.2e+197:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -3.4e-290:
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))))
	elif b <= 6.2e-307:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	else:
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.2e+197)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -3.4e-290)
		tmp = Float64(Float64(x / a) / Float64(y - Float64(b * Float64(y * Float64(-1.0 - Float64(b * 0.5))))));
	elseif (b <= 6.2e-307)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.2e+197)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -3.4e-290)
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))));
	elseif (b <= 6.2e-307)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	else
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.2e+197], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.4e-290], N[(N[(x / a), $MachinePrecision] / N[(y - N[(b * N[(y * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-307], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.2000000000000002e197

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. exp-diff 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in y around 0 50.1%

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

      1. exp-to-pow 50.1%

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

      2. sub-neg 50.1%

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

      3. metadata-eval 50.1%

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

      4. associate-*r/ 62.6%

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

      5. associate-/r* 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in t around 0 91.8%

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

   9. Taylor expanded in b around 0 35.9%

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

   10. Taylor expanded in x around 0 52.0%

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

       1. +-commutative 52.0%

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

       2. mul-1-neg 52.0%

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

       3. unsub-neg 52.0%

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

   12. Simplified 52.0%

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

   if -9.2000000000000002e197 < b < -3.39999999999999984e-290

   1. Initial program 99.0%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 78.7%

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

      4. associate-/l* 78.7%

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

      5. *-commutative 78.7%

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

      6. exp-to-pow 78.7%

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

      7. exp-diff 69.3%

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

      8. *-commutative 69.3%

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

      9. exp-to-pow 69.7%

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

      10. sub-neg 69.7%

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

      11. metadata-eval 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in y around 0 62.7%

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

      1. exp-to-pow 63.2%

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

      2. sub-neg 63.2%

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

      3. metadata-eval 63.2%

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

      4. associate-*r/ 65.6%

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

      5. associate-/r* 63.7%

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

   7. Simplified 63.7%

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

      1. unpow-prod-up 63.8%

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

      2. unpow-1 63.8%

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

   9. Applied egg-rr 63.8%

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

       1. associate-*r/ 63.8%

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

       2. *-rgt-identity 63.8%

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

   11. Simplified 63.8%

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

   12. Taylor expanded in t around 0 49.4%

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

       1. associate-/r* 46.0%

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

   14. Simplified 46.0%

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

   15. Taylor expanded in b around 0 37.1%

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

       1. associate-*r* 33.0%

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

       2. distribute-rgt1-in 33.0%

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

   17. Simplified 37.1%

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

   if -3.39999999999999984e-290 < b < 6.1999999999999996e-307

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 83.3%

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

      4. associate-/l* 83.3%

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

      5. *-commutative 83.3%

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

      6. exp-to-pow 83.3%

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

      7. exp-diff 83.3%

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

      8. *-commutative 83.3%

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

      9. exp-to-pow 83.3%

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

      10. sub-neg 83.3%

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

      11. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 67.6%

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

      1. exp-to-pow 67.6%

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

      2. sub-neg 67.6%

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

      3. metadata-eval 67.6%

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

      4. associate-*r/ 67.6%

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

      5. associate-/r* 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in t around 0 18.8%

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

   9. Taylor expanded in b around 0 18.8%

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

   10. Taylor expanded in b around inf 51.2%

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

       1. mul-1-neg 51.2%

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

       2. +-commutative 51.2%

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

       3. unsub-neg 51.2%

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

       4. *-commutative 51.2%

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

   12. Simplified 51.2%

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

   if 6.1999999999999996e-307 < b

   1. Initial program 97.6%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 86.0%

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

      4. associate-/l* 86.0%

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

      5. *-commutative 86.0%

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

      6. exp-to-pow 86.0%

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

      7. exp-diff 80.2%

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

      8. *-commutative 80.2%

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

      9. exp-to-pow 80.7%

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

      10. sub-neg 80.7%

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

      11. metadata-eval 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. exp-to-pow 75.0%

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

      2. sub-neg 75.0%

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

      3. metadata-eval 75.0%

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

      4. associate-*r/ 79.3%

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

      5. associate-/r* 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in t around 0 68.2%

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

   9. Taylor expanded in b around 0 57.1%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + b \cdot \left(a \cdot y + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(b \cdot y\right)\right) + 0.5 \cdot \left(a \cdot y\right)\right)\right)}} \]

   10. Taylor expanded in y around 0 58.0%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{a}}{y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.5% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a}}{y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.2e+197)
   (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
   (if (<= b -1.15e-289)
     (/ (/ x a) (- y (* b (* y (- -1.0 (* b 0.5))))))
     (if (<= b 6.1e-304)
       (* b (- (/ x (* a (* y b))) (/ x (* y a))))
       (/
        x
        (*
         a
         (+ y (* b (+ y (* b (* y (+ 0.5 (* b 0.16666666666666666)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+197) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.15e-289) {
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))));
	} else if (b <= 6.1e-304) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.2d+197)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-1.15d-289)) then
        tmp = (x / a) / (y - (b * (y * ((-1.0d0) - (b * 0.5d0)))))
    else if (b <= 6.1d-304) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else
        tmp = x / (a * (y + (b * (y + (b * (y * (0.5d0 + (b * 0.16666666666666666d0))))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.2e+197) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.15e-289) {
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))));
	} else if (b <= 6.1e-304) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.2e+197:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -1.15e-289:
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))))
	elif b <= 6.1e-304:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	else:
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.2e+197)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -1.15e-289)
		tmp = Float64(Float64(x / a) / Float64(y - Float64(b * Float64(y * Float64(-1.0 - Float64(b * 0.5))))));
	elseif (b <= 6.1e-304)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(y * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.2e+197)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -1.15e-289)
		tmp = (x / a) / (y - (b * (y * (-1.0 - (b * 0.5)))));
	elseif (b <= 6.1e-304)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	else
		tmp = x / (a * (y + (b * (y + (b * (y * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.2e+197], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e-289], N[(N[(x / a), $MachinePrecision] / N[(y - N[(b * N[(y * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.1e-304], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(y * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.2000000000000002e197

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/l* 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. exp-diff 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in y around 0 50.1%

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

      1. exp-to-pow 50.1%

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

      2. sub-neg 50.1%

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

      3. metadata-eval 50.1%

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

      4. associate-*r/ 62.6%

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

      5. associate-/r* 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in t around 0 91.8%

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

   9. Taylor expanded in b around 0 35.9%

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

   10. Taylor expanded in x around 0 52.0%

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

       1. +-commutative 52.0%

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

       2. mul-1-neg 52.0%

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

       3. unsub-neg 52.0%

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

   12. Simplified 52.0%

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

   if -9.2000000000000002e197 < b < -1.1500000000000001e-289

   1. Initial program 99.0%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 78.7%

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

      4. associate-/l* 78.7%

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

      5. *-commutative 78.7%

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

      6. exp-to-pow 78.7%

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

      7. exp-diff 69.3%

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

      8. *-commutative 69.3%

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

      9. exp-to-pow 69.7%

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

      10. sub-neg 69.7%

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

      11. metadata-eval 69.7%

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

   3. Simplified 69.7%

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

   5. Taylor expanded in y around 0 62.7%

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

      1. exp-to-pow 63.2%

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

      2. sub-neg 63.2%

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

      3. metadata-eval 63.2%

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

      4. associate-*r/ 65.6%

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

      5. associate-/r* 63.7%

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

   7. Simplified 63.7%

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

      1. unpow-prod-up 63.8%

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

      2. unpow-1 63.8%

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

   9. Applied egg-rr 63.8%

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

       1. associate-*r/ 63.8%

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

       2. *-rgt-identity 63.8%

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

   11. Simplified 63.8%

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

   12. Taylor expanded in t around 0 49.4%

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

       1. associate-/r* 46.0%

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

   14. Simplified 46.0%

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

   15. Taylor expanded in b around 0 37.1%

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

       1. associate-*r* 33.0%

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

       2. distribute-rgt1-in 33.0%

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

   17. Simplified 37.1%

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

   if -1.1500000000000001e-289 < b < 6.1000000000000004e-304

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 83.3%

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

      4. associate-/l* 83.3%

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

      5. *-commutative 83.3%

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

      6. exp-to-pow 83.3%

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

      7. exp-diff 83.3%

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

      8. *-commutative 83.3%

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

      9. exp-to-pow 83.3%

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

      10. sub-neg 83.3%

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

      11. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 67.6%

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

      1. exp-to-pow 67.6%

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

      2. sub-neg 67.6%

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

      3. metadata-eval 67.6%

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

      4. associate-*r/ 67.6%

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

      5. associate-/r* 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in t around 0 18.8%

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

   9. Taylor expanded in b around 0 18.8%

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

   10. Taylor expanded in b around inf 51.2%

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

       1. mul-1-neg 51.2%

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

       2. +-commutative 51.2%

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

       3. unsub-neg 51.2%

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

       4. *-commutative 51.2%

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

   12. Simplified 51.2%

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

   if 6.1000000000000004e-304 < b

   1. Initial program 97.6%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 86.0%

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

      4. associate-/l* 86.0%

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

      5. *-commutative 86.0%

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

      6. exp-to-pow 86.0%

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

      7. exp-diff 80.2%

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

      8. *-commutative 80.2%

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

      9. exp-to-pow 80.7%

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

      10. sub-neg 80.7%

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

      11. metadata-eval 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. exp-to-pow 75.0%

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

      2. sub-neg 75.0%

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

      3. metadata-eval 75.0%

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

      4. associate-*r/ 79.3%

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

      5. associate-/r* 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in t around 0 68.2%

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

   9. Taylor expanded in b around 0 57.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(b \cdot y\right) + 0.5 \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 57.1%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(\color{blue}{\left(0.16666666666666666 \cdot b\right) \cdot y} + 0.5 \cdot y\right)\right)\right)} \]

       2. distribute-rgt-out 57.1%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \color{blue}{\left(y \cdot \left(0.16666666666666666 \cdot b + 0.5\right)\right)}\right)\right)} \]

   11. Simplified 57.1%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.16666666666666666 \cdot b + 0.5\right)\right)\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a}}{y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{-304}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(y \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 45.6% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{+221}:\\ \;\;\;\;t\_1 + b \cdot \left(b \cdot \left(t\_1 - t\_1 \cdot 0.5\right) - t\_1\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -5.2e+221)
     (+ t_1 (* b (- (* b (- t_1 (* t_1 0.5))) t_1)))
     (if (<= b -7.2e-290)
       (/ (- (/ x a) (/ (* x b) a)) y)
       (/
        x
        (*
         y
         (+
          a
          (*
           b
           (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -5.2e+221) {
		tmp = t_1 + (b * ((b * (t_1 - (t_1 * 0.5))) - t_1));
	} else if (b <= -7.2e-290) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (b <= (-5.2d+221)) then
        tmp = t_1 + (b * ((b * (t_1 - (t_1 * 0.5d0))) - t_1))
    else if (b <= (-7.2d-290)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else
        tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -5.2e+221) {
		tmp = t_1 + (b * ((b * (t_1 - (t_1 * 0.5))) - t_1));
	} else if (b <= -7.2e-290) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -5.2e+221:
		tmp = t_1 + (b * ((b * (t_1 - (t_1 * 0.5))) - t_1))
	elif b <= -7.2e-290:
		tmp = ((x / a) - ((x * b) / a)) / y
	else:
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -5.2e+221)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(b * Float64(t_1 - Float64(t_1 * 0.5))) - t_1)));
	elseif (b <= -7.2e-290)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -5.2e+221)
		tmp = t_1 + (b * ((b * (t_1 - (t_1 * 0.5))) - t_1));
	elseif (b <= -7.2e-290)
		tmp = ((x / a) - ((x * b) / a)) / y;
	else
		tmp = x / (y * (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e+221], N[(t$95$1 + N[(b * N[(N[(b * N[(t$95$1 - N[(t$95$1 * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.2e-290], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.20000000000000008e221

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 87.5%

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

      5. *-commutative 87.5%

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

      6. exp-to-pow 87.5%

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

      7. exp-diff 56.3%

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

      8. *-commutative 56.3%

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

      9. exp-to-pow 56.3%

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

      10. sub-neg 56.3%

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

      11. metadata-eval 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in y around 0 50.0%

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

      1. exp-to-pow 50.0%

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

      2. sub-neg 50.0%

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

      3. metadata-eval 50.0%

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

      4. associate-*r/ 56.3%

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

      5. associate-/r* 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in t around 0 93.8%

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

   9. Taylor expanded in b around 0 63.9%

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

   if -5.20000000000000008e221 < b < -7.19999999999999959e-290

   1. Initial program 99.0%

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

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 76.7%

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

      4. associate-/l* 76.7%

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

      5. *-commutative 76.7%

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

      6. exp-to-pow 76.7%

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

      7. exp-diff 67.1%

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

      8. *-commutative 67.1%

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

      9. exp-to-pow 67.4%

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

      10. sub-neg 67.4%

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

      11. metadata-eval 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around 0 61.8%

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

      1. exp-to-pow 62.3%

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

      2. sub-neg 62.3%

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

      3. metadata-eval 62.3%

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

      4. associate-*r/ 66.3%

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

      5. associate-/r* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 52.1%

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

   9. Taylor expanded in b around 0 31.8%

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

   10. Taylor expanded in y around 0 37.2%

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

       1. +-commutative 37.2%

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

       2. mul-1-neg 37.2%

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

       3. unsub-neg 37.2%

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

   12. Simplified 37.2%

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

   if -7.19999999999999959e-290 < b

   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. Step-by-step derivation

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 85.9%

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

      4. associate-/l* 85.9%

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

      5. *-commutative 85.9%

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

      6. exp-to-pow 85.9%

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

      7. exp-diff 80.3%

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

      8. *-commutative 80.3%

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

      9. exp-to-pow 80.9%

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

      10. sub-neg 80.9%

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

      11. metadata-eval 80.9%

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

   3. Simplified 80.9%

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

   5. Taylor expanded in y around 0 74.2%

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

      1. exp-to-pow 74.7%

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

      2. sub-neg 74.7%

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

      3. metadata-eval 74.7%

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

      4. associate-*r/ 78.7%

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

      5. associate-/r* 72.4%

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

   7. Simplified 72.4%

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

   8. Taylor expanded in t around 0 65.9%

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

   9. Taylor expanded in b around 0 54.5%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + b \cdot \left(a \cdot y + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(b \cdot y\right)\right) + 0.5 \cdot \left(a \cdot y\right)\right)\right)}} \]

   10. Taylor expanded in y around 0 56.1%

       \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{+221}:\\ \;\;\;\;\frac{x}{y \cdot a} + b \cdot \left(b \cdot \left(\frac{x}{y \cdot a} - \frac{x}{y \cdot a} \cdot 0.5\right) - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.2% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-306}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5e+220)
   (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
   (if (<= b -2.6e-289)
     (/ (- (/ x a) (/ (* x b) a)) y)
     (if (<= b 1.36e-306)
       (* b (- (/ x (* a (* y b))) (/ x (* y a))))
       (/ x (* a (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+220) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -2.6e-289) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.36e-306) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5d+220)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-2.6d-289)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 1.36d-306) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5e+220) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -2.6e-289) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.36e-306) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5e+220:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -2.6e-289:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 1.36e-306:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5e+220)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -2.6e-289)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 1.36e-306)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5e+220)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -2.6e-289)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 1.36e-306)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5e+220], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-289], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.36e-306], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -5.0000000000000002e220

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 87.5%

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

      5. *-commutative 87.5%

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

      6. exp-to-pow 87.5%

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

      7. exp-diff 56.3%

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

      8. *-commutative 56.3%

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

      9. exp-to-pow 56.3%

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

      10. sub-neg 56.3%

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

      11. metadata-eval 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in y around 0 50.0%

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

      1. exp-to-pow 50.0%

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

      2. sub-neg 50.0%

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

      3. metadata-eval 50.0%

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

      4. associate-*r/ 56.3%

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

      5. associate-/r* 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in t around 0 93.8%

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

   9. Taylor expanded in b around 0 28.4%

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

   10. Taylor expanded in x around 0 57.9%

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

       1. +-commutative 57.9%

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

       2. mul-1-neg 57.9%

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

       3. unsub-neg 57.9%

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

   12. Simplified 57.9%

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

   if -5.0000000000000002e220 < b < -2.5999999999999999e-289

   1. Initial program 99.0%

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

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 76.7%

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

      4. associate-/l* 76.7%

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

      5. *-commutative 76.7%

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

      6. exp-to-pow 76.7%

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

      7. exp-diff 67.1%

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

      8. *-commutative 67.1%

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

      9. exp-to-pow 67.4%

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

      10. sub-neg 67.4%

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

      11. metadata-eval 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around 0 61.8%

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

      1. exp-to-pow 62.3%

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

      2. sub-neg 62.3%

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

      3. metadata-eval 62.3%

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

      4. associate-*r/ 66.3%

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

      5. associate-/r* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 52.1%

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

   9. Taylor expanded in b around 0 31.8%

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

   10. Taylor expanded in y around 0 37.2%

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

       1. +-commutative 37.2%

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

       2. mul-1-neg 37.2%

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

       3. unsub-neg 37.2%

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

   12. Simplified 37.2%

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

   if -2.5999999999999999e-289 < b < 1.35999999999999996e-306

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 83.3%

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

      4. associate-/l* 83.3%

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

      5. *-commutative 83.3%

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

      6. exp-to-pow 83.3%

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

      7. exp-diff 83.3%

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

      8. *-commutative 83.3%

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

      9. exp-to-pow 83.3%

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

      10. sub-neg 83.3%

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

      11. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 67.6%

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

      1. exp-to-pow 67.6%

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

      2. sub-neg 67.6%

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

      3. metadata-eval 67.6%

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

      4. associate-*r/ 67.6%

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

      5. associate-/r* 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in t around 0 18.8%

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

   9. Taylor expanded in b around 0 18.8%

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

   10. Taylor expanded in b around inf 51.2%

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

       1. mul-1-neg 51.2%

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

       2. +-commutative 51.2%

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

       3. unsub-neg 51.2%

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

       4. *-commutative 51.2%

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

   12. Simplified 51.2%

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

   if 1.35999999999999996e-306 < b

   1. Initial program 97.6%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 86.0%

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

      4. associate-/l* 86.0%

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

      5. *-commutative 86.0%

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

      6. exp-to-pow 86.0%

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

      7. exp-diff 80.2%

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

      8. *-commutative 80.2%

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

      9. exp-to-pow 80.7%

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

      10. sub-neg 80.7%

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

      11. metadata-eval 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. exp-to-pow 75.0%

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

      2. sub-neg 75.0%

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

      3. metadata-eval 75.0%

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

      4. associate-*r/ 79.3%

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

      5. associate-/r* 72.6%

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

   7. Simplified 72.6%

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

   8. Taylor expanded in t around 0 68.2%

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

   9. Taylor expanded in b around 0 45.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{+220}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-306}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.3% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.5e+219)
   (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
   (if (<= b -5.2e-290)
     (/ (- (/ x a) (/ (* x b) a)) y)
     (if (<= b 2e-305)
       (* b (- (/ x (* a (* y b))) (/ x (* y a))))
       (/ x (* a (- y (* b (* y (- -1.0 (* b 0.5)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+219) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -5.2e-290) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2e-305) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y - (b * (y * (-1.0 - (b * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-9.5d+219)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-5.2d-290)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 2d-305) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else
        tmp = x / (a * (y - (b * (y * ((-1.0d0) - (b * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.5e+219) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -5.2e-290) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2e-305) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * (y - (b * (y * (-1.0 - (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.5e+219:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -5.2e-290:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 2e-305:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	else:
		tmp = x / (a * (y - (b * (y * (-1.0 - (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.5e+219)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -5.2e-290)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 2e-305)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * Float64(y - Float64(b * Float64(y * Float64(-1.0 - Float64(b * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.5e+219)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -5.2e-290)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 2e-305)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	else
		tmp = x / (a * (y - (b * (y * (-1.0 - (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.5e+219], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e-290], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2e-305], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y - N[(b * N[(y * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.49999999999999959e219

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 87.5%

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

      4. associate-/l* 87.5%

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

      5. *-commutative 87.5%

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

      6. exp-to-pow 87.5%

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

      7. exp-diff 56.3%

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

      8. *-commutative 56.3%

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

      9. exp-to-pow 56.3%

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

      10. sub-neg 56.3%

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

      11. metadata-eval 56.3%

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

   3. Simplified 56.3%

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

   5. Taylor expanded in y around 0 50.0%

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

      1. exp-to-pow 50.0%

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

      2. sub-neg 50.0%

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

      3. metadata-eval 50.0%

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

      4. associate-*r/ 56.3%

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

      5. associate-/r* 56.3%

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

   7. Simplified 56.3%

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

   8. Taylor expanded in t around 0 93.8%

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

   9. Taylor expanded in b around 0 28.4%

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

   10. Taylor expanded in x around 0 57.9%

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

       1. +-commutative 57.9%

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

       2. mul-1-neg 57.9%

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

       3. unsub-neg 57.9%

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

   12. Simplified 57.9%

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

   if -9.49999999999999959e219 < b < -5.20000000000000002e-290

   1. Initial program 99.0%

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

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 76.7%

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

      4. associate-/l* 76.7%

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

      5. *-commutative 76.7%

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

      6. exp-to-pow 76.7%

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

      7. exp-diff 67.1%

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

      8. *-commutative 67.1%

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

      9. exp-to-pow 67.4%

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

      10. sub-neg 67.4%

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

      11. metadata-eval 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in y around 0 61.8%

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

      1. exp-to-pow 62.3%

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

      2. sub-neg 62.3%

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

      3. metadata-eval 62.3%

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

      4. associate-*r/ 66.3%

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

      5. associate-/r* 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 52.1%

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

   9. Taylor expanded in b around 0 31.8%

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

   10. Taylor expanded in y around 0 37.2%

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

       1. +-commutative 37.2%

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

       2. mul-1-neg 37.2%

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

       3. unsub-neg 37.2%

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

   12. Simplified 37.2%

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

   if -5.20000000000000002e-290 < b < 1.99999999999999999e-305

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 83.3%

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

      4. associate-/l* 83.3%

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

      5. *-commutative 83.3%

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

      6. exp-to-pow 83.3%

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

      7. exp-diff 83.3%

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

      8. *-commutative 83.3%

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

      9. exp-to-pow 83.3%

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

      10. sub-neg 83.3%

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

      11. metadata-eval 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in y around 0 67.6%

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

      1. exp-to-pow 67.6%

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

      2. sub-neg 67.6%

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

      3. metadata-eval 67.6%

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

      4. associate-*r/ 67.6%

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

      5. associate-/r* 67.6%

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

   7. Simplified 67.6%

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

   8. Taylor expanded in t around 0 18.8%

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

   9. Taylor expanded in b around 0 18.8%

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

   10. Taylor expanded in b around inf 51.2%

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

       1. mul-1-neg 51.2%

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

       2. +-commutative 51.2%

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

       3. unsub-neg 51.2%

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

       4. *-commutative 51.2%

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

   12. Simplified 51.2%

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

   if 1.99999999999999999e-305 < b

   1. Initial program 97.6%

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

      1. associate-/l* 98.5%

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

      2. associate--l+ 98.5%

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

      3. exp-sum 86.0%

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

      4. associate-/l* 86.0%

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

      5. *-commutative 86.0%

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

      6. exp-to-pow 86.0%

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

      7. exp-diff 80.2%

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

      8. *-commutative 80.2%

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

      9. exp-to-pow 80.7%

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

      10. sub-neg 80.7%

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

      11. metadata-eval 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around 0 74.5%

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

      1. exp-to-pow 75.0%

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

      2. sub-neg 75.0%

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

      3. metadata-eval 75.0%

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

      4. associate-*r/ 79.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 72.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 68.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 51.9%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(b \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 51.9%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + \color{blue}{\left(0.5 \cdot b\right) \cdot y}\right)\right)} \]

       2. distribute-rgt1-in 51.9%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \color{blue}{\left(\left(0.5 \cdot b + 1\right) \cdot y\right)}\right)} \]

   11. Simplified 51.9%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(\left(0.5 \cdot b + 1\right) \cdot y\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+219}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-290}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-305}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 41.2% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)\\ \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-288}:\\ \;\;\;\;\frac{\frac{x}{a}}{t\_1}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- y (* b (* y (- -1.0 (* b 0.5)))))))
   (if (<= b -9.2e+197)
     (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
     (if (<= b -1.8e-288)
       (/ (/ x a) t_1)
       (if (<= b 6e-307)
         (* b (- (/ x (* a (* y b))) (/ x (* y a))))
         (/ x (* a t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (b * (y * (-1.0 - (b * 0.5))));
	double tmp;
	if (b <= -9.2e+197) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.8e-288) {
		tmp = (x / a) / t_1;
	} else if (b <= 6e-307) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (b * (y * ((-1.0d0) - (b * 0.5d0))))
    if (b <= (-9.2d+197)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-1.8d-288)) then
        tmp = (x / a) / t_1
    else if (b <= 6d-307) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else
        tmp = x / (a * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y - (b * (y * (-1.0 - (b * 0.5))));
	double tmp;
	if (b <= -9.2e+197) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.8e-288) {
		tmp = (x / a) / t_1;
	} else if (b <= 6e-307) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = x / (a * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y - (b * (y * (-1.0 - (b * 0.5))))
	tmp = 0
	if b <= -9.2e+197:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -1.8e-288:
		tmp = (x / a) / t_1
	elif b <= 6e-307:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	else:
		tmp = x / (a * t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y - Float64(b * Float64(y * Float64(-1.0 - Float64(b * 0.5)))))
	tmp = 0.0
	if (b <= -9.2e+197)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -1.8e-288)
		tmp = Float64(Float64(x / a) / t_1);
	elseif (b <= 6e-307)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(x / Float64(a * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y - (b * (y * (-1.0 - (b * 0.5))));
	tmp = 0.0;
	if (b <= -9.2e+197)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -1.8e-288)
		tmp = (x / a) / t_1;
	elseif (b <= 6e-307)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	else
		tmp = x / (a * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y - N[(b * N[(y * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.2e+197], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.8e-288], N[(N[(x / a), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[b, 6e-307], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.2000000000000002e197

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 75.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 75.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 75.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 75.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 50.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 50.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 50.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 50.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 50.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 50.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 50.1%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 50.1%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 50.1%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 62.6%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 62.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 62.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 91.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 35.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in x around 0 52.0%

       \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 52.0%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       2. mul-1-neg 52.0%

          \[\leadsto x \cdot \left(\frac{1}{a \cdot y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       3. unsub-neg 52.0%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Simplified 52.0%

       \[\leadsto \color{blue}{x \cdot \left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   if -9.2000000000000002e197 < b < -1.8000000000000001e-288

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 78.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 69.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 69.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 69.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 69.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 69.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 69.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.2%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.2%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.2%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.6%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 63.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 63.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]
   8. Step-by-step derivation

      1. unpow-prod-up 63.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot {a}^{-1}}}{y}}{e^{b}} \]

      2. unpow-1 63.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{t} \cdot \color{blue}{\frac{1}{a}}}{y}}{e^{b}} \]

   9. Applied egg-rr 63.8%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{t} \cdot \frac{1}{a}}}{y}}{e^{b}} \]
   10. Step-by-step derivation

       1. associate-*r/ 63.8%

          \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t} \cdot 1}{a}}}{y}}{e^{b}} \]

       2. *-rgt-identity 63.8%

          \[\leadsto x \cdot \frac{\frac{\frac{\color{blue}{{a}^{t}}}{a}}{y}}{e^{b}} \]

   11. Simplified 63.8%

       \[\leadsto x \cdot \frac{\frac{\color{blue}{\frac{{a}^{t}}{a}}}{y}}{e^{b}} \]

   12. Taylor expanded in t around 0 49.4%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/r* 46.0%

          \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y \cdot e^{b}}} \]

   14. Simplified 46.0%

       \[\leadsto \color{blue}{\frac{\frac{x}{a}}{y \cdot e^{b}}} \]

   15. Taylor expanded in b around 0 37.1%

       \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y + b \cdot \left(y + 0.5 \cdot \left(b \cdot y\right)\right)}} \]
   16. Step-by-step derivation

       1. associate-*r* 33.0%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + \color{blue}{\left(0.5 \cdot b\right) \cdot y}\right)\right)} \]

       2. distribute-rgt1-in 33.0%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \color{blue}{\left(\left(0.5 \cdot b + 1\right) \cdot y\right)}\right)} \]

   17. Simplified 37.1%

       \[\leadsto \frac{\frac{x}{a}}{\color{blue}{y + b \cdot \left(\left(0.5 \cdot b + 1\right) \cdot y\right)}} \]

   if -1.8000000000000001e-288 < b < 5.9999999999999999e-307

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 83.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 83.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 83.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 83.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 83.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 67.6%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 67.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 67.6%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 67.6%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 67.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 67.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 18.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 18.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 51.2%

       \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + \frac{x}{a \cdot \left(b \cdot y\right)}\right)} \]
   11. Step-by-step derivation

       1. mul-1-neg 51.2%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{x}{a \cdot y}\right)} + \frac{x}{a \cdot \left(b \cdot y\right)}\right) \]

       2. +-commutative 51.2%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{a \cdot \left(b \cdot y\right)} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. unsub-neg 51.2%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{a \cdot \left(b \cdot y\right)} - \frac{x}{a \cdot y}\right)} \]

       4. *-commutative 51.2%

          \[\leadsto b \cdot \left(\frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} - \frac{x}{a \cdot y}\right) \]

   12. Simplified 51.2%

       \[\leadsto \color{blue}{b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{a \cdot y}\right)} \]

   if 5.9999999999999999e-307 < b

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 86.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 86.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 86.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 80.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 80.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 80.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 75.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 75.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 75.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 79.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 72.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 68.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 51.9%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(y + 0.5 \cdot \left(b \cdot y\right)\right)\right)}} \]
   10. Step-by-step derivation

       1. associate-*r* 51.9%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \left(y + \color{blue}{\left(0.5 \cdot b\right) \cdot y}\right)\right)} \]

       2. distribute-rgt1-in 51.9%

          \[\leadsto \frac{x}{a \cdot \left(y + b \cdot \color{blue}{\left(\left(0.5 \cdot b + 1\right) \cdot y\right)}\right)} \]

   11. Simplified 51.9%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot \left(\left(0.5 \cdot b + 1\right) \cdot y\right)\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.2 \cdot 10^{+197}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{-288}:\\ \;\;\;\;\frac{\frac{x}{a}}{y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-307}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y - b \cdot \left(y \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 39.1% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+218}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.78 \cdot 10^{-296}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-307}:\\ \;\;\;\;\frac{x}{-y} \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.05e+218)
   (* x (- (/ 1.0 (* y a)) (/ b (* y a))))
   (if (<= b -1.78e-296)
     (/ (- (/ x a) (/ (* x b) a)) y)
     (if (<= b 6e-307) (* (/ x (- y)) (/ b a)) (/ x (* a (+ y (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.05e+218) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.78e-296) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 6e-307) {
		tmp = (x / -y) * (b / a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2.05d+218)) then
        tmp = x * ((1.0d0 / (y * a)) - (b / (y * a)))
    else if (b <= (-1.78d-296)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 6d-307) then
        tmp = (x / -y) * (b / a)
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.05e+218) {
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	} else if (b <= -1.78e-296) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 6e-307) {
		tmp = (x / -y) * (b / a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.05e+218:
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)))
	elif b <= -1.78e-296:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 6e-307:
		tmp = (x / -y) * (b / a)
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.05e+218)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) - Float64(b / Float64(y * a))));
	elseif (b <= -1.78e-296)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 6e-307)
		tmp = Float64(Float64(x / Float64(-y)) * Float64(b / a));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.05e+218)
		tmp = x * ((1.0 / (y * a)) - (b / (y * a)));
	elseif (b <= -1.78e-296)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 6e-307)
		tmp = (x / -y) * (b / a);
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.05e+218], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] - N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.78e-296], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6e-307], N[(N[(x / (-y)), $MachinePrecision] * N[(b / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.04999999999999983e218

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 87.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 87.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 87.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 87.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 56.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 56.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 56.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 56.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 56.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 50.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 50.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 50.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 50.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 56.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 56.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 56.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 93.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 28.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in x around 0 57.9%

       \[\leadsto \color{blue}{x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   11. Step-by-step derivation

       1. +-commutative 57.9%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       2. mul-1-neg 57.9%

          \[\leadsto x \cdot \left(\frac{1}{a \cdot y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       3. unsub-neg 57.9%

          \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Simplified 57.9%

       \[\leadsto \color{blue}{x \cdot \left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   if -2.04999999999999983e218 < b < -1.78000000000000003e-296

   1. Initial program 99.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.7%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 76.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 76.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 76.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 76.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 66.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 66.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 67.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 67.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 67.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 67.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 61.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 62.1%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 62.1%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 62.1%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 66.0%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 64.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 51.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in y around 0 36.6%

       \[\leadsto \color{blue}{\frac{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}{y}} \]
   11. Step-by-step derivation

       1. +-commutative 36.6%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 36.6%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 36.6%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

   12. Simplified 36.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{a} - \frac{b \cdot x}{a}}{y}} \]

   if -1.78000000000000003e-296 < b < 5.9999999999999999e-307

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 100.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 100.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 100.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 100.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 100.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 100.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 100.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 100.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 100.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 76.0%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 76.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 76.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 76.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 76.0%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 76.0%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 76.0%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 27.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 27.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 51.6%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 51.6%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. times-frac 75.4%

          \[\leadsto -\color{blue}{\frac{b}{a} \cdot \frac{x}{y}} \]

       3. *-commutative 75.4%

          \[\leadsto -\color{blue}{\frac{x}{y} \cdot \frac{b}{a}} \]

       4. distribute-lft-neg-in 75.4%

          \[\leadsto \color{blue}{\left(-\frac{x}{y}\right) \cdot \frac{b}{a}} \]

       5. distribute-neg-frac2 75.4%

          \[\leadsto \color{blue}{\frac{x}{-y}} \cdot \frac{b}{a} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{\frac{x}{-y} \cdot \frac{b}{a}} \]

   if 5.9999999999999999e-307 < b

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 86.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 86.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 86.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 80.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 80.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 80.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 75.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 75.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 75.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 79.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 72.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 68.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 45.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.05 \cdot 10^{+218}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} - \frac{b}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.78 \cdot 10^{-296}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-307}:\\ \;\;\;\;\frac{x}{-y} \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.5% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(b + -1\right)}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e-288)
   (/ (* (/ x a) (+ b -1.0)) (- y))
   (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-288) {
		tmp = ((x / a) * (b + -1.0)) / -y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1d-288)) then
        tmp = ((x / a) * (b + (-1.0d0))) / -y
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-288) {
		tmp = ((x / a) * (b + -1.0)) / -y;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e-288:
		tmp = ((x / a) * (b + -1.0)) / -y
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e-288)
		tmp = Float64(Float64(Float64(x / a) * Float64(b + -1.0)) / Float64(-y));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1e-288)
		tmp = ((x / a) * (b + -1.0)) / -y;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e-288], N[(N[(N[(x / a), $MachinePrecision] * N[(b + -1.0), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.00000000000000006e-288

   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. Step-by-step derivation

      1. associate-/l* 98.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.8%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 78.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 65.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 65.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 66.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 66.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 66.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 66.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 60.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 60.8%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 60.8%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 60.8%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.0%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 63.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 63.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 57.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in y around -inf 36.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{a} + \frac{b \cdot x}{a}}{y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 36.1%

          \[\leadsto \color{blue}{-\frac{-1 \cdot \frac{x}{a} + \frac{b \cdot x}{a}}{y}} \]

       2. distribute-neg-frac2 36.1%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{a} + \frac{b \cdot x}{a}}{-y}} \]

       3. +-commutative 36.1%

          \[\leadsto \frac{\color{blue}{\frac{b \cdot x}{a} + -1 \cdot \frac{x}{a}}}{-y} \]

       4. associate-/l* 34.7%

          \[\leadsto \frac{\color{blue}{b \cdot \frac{x}{a}} + -1 \cdot \frac{x}{a}}{-y} \]

       5. distribute-rgt-out 34.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} \cdot \left(b + -1\right)}}{-y} \]

   12. Simplified 34.7%

       \[\leadsto \color{blue}{\frac{\frac{x}{a} \cdot \left(b + -1\right)}{-y}} \]

   if -1.00000000000000006e-288 < b

   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. Step-by-step derivation

      1. associate-/l* 98.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 85.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 80.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 80.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 80.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 74.7%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 74.7%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 74.7%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 78.7%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 72.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 65.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 44.1%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-288}:\\ \;\;\;\;\frac{\frac{x}{a} \cdot \left(b + -1\right)}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.6% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{-294}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot \left(b + -1\right)}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 5e-294) (/ (* (/ x y) (+ b -1.0)) (- a)) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5e-294) {
		tmp = ((x / y) * (b + -1.0)) / -a;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 5d-294) then
        tmp = ((x / y) * (b + (-1.0d0))) / -a
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 5e-294) {
		tmp = ((x / y) * (b + -1.0)) / -a;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 5e-294:
		tmp = ((x / y) * (b + -1.0)) / -a
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 5e-294)
		tmp = Float64(Float64(Float64(x / y) * Float64(b + -1.0)) / Float64(-a));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 5e-294)
		tmp = ((x / y) * (b + -1.0)) / -a;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 5e-294], N[(N[(N[(x / y), $MachinePrecision] * N[(b + -1.0), $MachinePrecision]), $MachinePrecision] / (-a)), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.0000000000000003e-294

   1. Initial program 98.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.8%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 78.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 66.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 66.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 67.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 67.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 67.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 67.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 60.3%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 60.7%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 60.7%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 60.7%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.4%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 63.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 63.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 55.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in a around -inf 34.5%

       \[\leadsto \color{blue}{-1 \cdot \frac{-1 \cdot \frac{x}{y} + \frac{b \cdot x}{y}}{a}} \]
   11. Step-by-step derivation

       1. mul-1-neg 34.5%

          \[\leadsto \color{blue}{-\frac{-1 \cdot \frac{x}{y} + \frac{b \cdot x}{y}}{a}} \]

       2. distribute-neg-frac2 34.5%

          \[\leadsto \color{blue}{\frac{-1 \cdot \frac{x}{y} + \frac{b \cdot x}{y}}{-a}} \]

       3. +-commutative 34.5%

          \[\leadsto \frac{\color{blue}{\frac{b \cdot x}{y} + -1 \cdot \frac{x}{y}}}{-a} \]

       4. associate-/l* 36.6%

          \[\leadsto \frac{\color{blue}{b \cdot \frac{x}{y}} + -1 \cdot \frac{x}{y}}{-a} \]

       5. distribute-rgt-out 36.6%

          \[\leadsto \frac{\color{blue}{\frac{x}{y} \cdot \left(b + -1\right)}}{-a} \]

   12. Simplified 36.6%

       \[\leadsto \color{blue}{\frac{\frac{x}{y} \cdot \left(b + -1\right)}{-a}} \]

   if 5.0000000000000003e-294 < b

   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* 98.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 86.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 86.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 86.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 80.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 80.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 80.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 75.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 75.6%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 75.6%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 75.6%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 79.1%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 72.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.4%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 68.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 44.9%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 5 \cdot 10^{-294}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot \left(b + -1\right)}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 36.0% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{-y} \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6e-299) (* (/ x (- y)) (/ b a)) (/ x (* a (+ y (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-299) {
		tmp = (x / -y) * (b / a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 6d-299) then
        tmp = (x / -y) * (b / a)
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-299) {
		tmp = (x / -y) * (b / a);
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6e-299:
		tmp = (x / -y) * (b / a)
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6e-299)
		tmp = Float64(Float64(x / Float64(-y)) * Float64(b / a));
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 6e-299)
		tmp = (x / -y) * (b / a);
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6e-299], N[(N[(x / (-y)), $MachinePrecision] * N[(b / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 5.99999999999999969e-299

   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. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 78.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 66.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 66.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 66.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 66.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 66.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 60.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 61.1%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 61.1%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 61.1%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.2%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 63.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 63.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 55.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 30.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]

   10. Taylor expanded in b around inf 28.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 28.4%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. times-frac 33.9%

          \[\leadsto -\color{blue}{\frac{b}{a} \cdot \frac{x}{y}} \]

       3. *-commutative 33.9%

          \[\leadsto -\color{blue}{\frac{x}{y} \cdot \frac{b}{a}} \]

       4. distribute-lft-neg-in 33.9%

          \[\leadsto \color{blue}{\left(-\frac{x}{y}\right) \cdot \frac{b}{a}} \]

       5. distribute-neg-frac2 33.9%

          \[\leadsto \color{blue}{\frac{x}{-y}} \cdot \frac{b}{a} \]

   12. Simplified 33.9%

       \[\leadsto \color{blue}{\frac{x}{-y} \cdot \frac{b}{a}} \]

   if 5.99999999999999969e-299 < b

   1. Initial program 97.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 86.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 86.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 86.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 80.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 80.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 80.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 80.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.5%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 75.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 75.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 75.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 79.3%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

      5. associate-/r* 72.6%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   7. Simplified 72.6%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 68.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 45.4%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-299}:\\ \;\;\;\;\frac{x}{-y} \cdot \frac{b}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.2% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{a \cdot \frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (* a (/ y x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (a * (y / x));
}

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 = 1.0d0 / (a * (y / x))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (a * (y / x));
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (a * (y / x))

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(a * Float64(y / x)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / (a * (y / x));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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* 98.7%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.7%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 81.9%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 81.9%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 81.9%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 81.9%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 72.9%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 72.9%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 73.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 73.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 73.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 73.3%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 67.2%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. exp-to-pow 67.6%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

   2. sub-neg 67.6%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

   3. metadata-eval 67.6%

      \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   4. associate-*r/ 71.8%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   5. associate-/r* 67.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

7. Simplified 67.9%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

8. Taylor expanded in t around 0 61.5%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 32.6%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
10. Step-by-step derivation

    1. clear-num 32.7%

       \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

    2. inv-pow 32.7%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

11. Applied egg-rr 32.7%

    \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
12. Step-by-step derivation

    1. unpow-1 32.7%

       \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

    2. associate-/l* 35.6%

       \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

13. Simplified 35.6%

    \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

14. Final simplification 35.6%

    \[\leadsto \frac{1}{a \cdot \frac{y}{x}} \]
15. Add Preprocessing

Alternative 21: 31.1% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.7%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.7%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 81.9%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 81.9%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 81.9%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 81.9%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 72.9%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 72.9%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 73.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 73.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 73.3%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 73.3%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 67.2%

   \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. exp-to-pow 67.6%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

   2. sub-neg 67.6%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

   3. metadata-eval 67.6%

      \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   4. associate-*r/ 71.8%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   5. associate-/r* 67.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

7. Simplified 67.9%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

8. Taylor expanded in t around 0 61.5%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 32.6%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 32.6%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Alternative 22: 31.0% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ (/ x a) y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (x / a) / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x / a) / y;
}

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x / a) / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x / a) / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]

Derivation

1. Initial program 98.4%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in t around 0 78.9%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
4. Step-by-step derivation

   1. +-commutative 78.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

   2. mul-1-neg 78.9%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   3. unsub-neg 78.9%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

5. Simplified 78.9%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

6. Taylor expanded in b around 0 55.1%

   \[\leadsto \frac{x \cdot \color{blue}{e^{y \cdot \log z - \log a}}}{y} \]
7. Step-by-step derivation

   1. div-exp 55.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

   2. *-commutative 55.1%

      \[\leadsto \frac{x \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

   3. exp-to-pow 55.1%

      \[\leadsto \frac{x \cdot \frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

   4. rem-exp-log 55.5%

      \[\leadsto \frac{x \cdot \frac{{z}^{y}}{\color{blue}{a}}}{y} \]

8. Simplified 55.5%

   \[\leadsto \frac{x \cdot \color{blue}{\frac{{z}^{y}}{a}}}{y} \]

9. Taylor expanded in y around 0 33.9%

   \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

10. Final simplification 33.9%

    \[\leadsto \frac{\frac{x}{a}}{y} \]
11. Add Preprocessing

Developer target: 71.7% 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 2024066 
(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))