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

Percentage Accurate: 98.3% → 98.3%

Time: 20.1s

Alternatives: 29

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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. Final simplification 97.9%

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

Alternative 2: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+48} \lor \neg \left(y \leq 60000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -2.4e+48) (not (<= y 60000000.0)))
   (/ (* 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 <= -2.4e+48) || !(y <= 60000000.0)) {
		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 <= (-2.4d+48)) .or. (.not. (y <= 60000000.0d0))) 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 <= -2.4e+48) || !(y <= 60000000.0)) {
		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 <= -2.4e+48) or not (y <= 60000000.0):
		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 <= -2.4e+48) || !(y <= 60000000.0))
		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 <= -2.4e+48) || ~((y <= 60000000.0)))
		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, -2.4e+48], N[Not[LessEqual[y, 60000000.0]], $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 < -2.4000000000000001e48 or 6e7 < 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 95.6%

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

      1. +-commutative 95.6%

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

      2. mul-1-neg 95.6%

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

      3. unsub-neg 95.6%

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

   5. Simplified 95.6%

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

   if -2.4000000000000001e48 < y < 6e7

   1. Initial program 96.3%

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

   3. Taylor expanded in y around 0 93.9%

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

4. Final simplification 94.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+48} \lor \neg \left(y \leq 60000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+58} \lor \neg \left(y \leq 4 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.8e+58) (not (<= y 4e+38)))
   (* 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 <= -8.8e+58) || !(y <= 4e+38)) {
		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 <= (-8.8d+58)) .or. (.not. (y <= 4d+38))) 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 <= -8.8e+58) || !(y <= 4e+38)) {
		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 <= -8.8e+58) or not (y <= 4e+38):
		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 <= -8.8e+58) || !(y <= 4e+38))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.8e+58) || ~((y <= 4e+38)))
		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, -8.8e+58], N[Not[LessEqual[y, 4e+38]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000003e58 or 3.99999999999999991e38 < 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 96.3%

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

      1. +-commutative 96.3%

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

      2. mul-1-neg 96.3%

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

      3. unsub-neg 96.3%

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

   5. Simplified 96.3%

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

   6. Taylor expanded in b around 0 84.1%

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

      1. associate-/l* 84.1%

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

      2. div-exp 84.1%

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

      3. *-commutative 84.1%

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

      4. exp-to-pow 84.1%

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

      5. rem-exp-log 84.1%

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

   8. Simplified 84.1%

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

   if -8.8000000000000003e58 < y < 3.99999999999999991e38

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 93.0%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{+58} \lor \neg \left(y \leq 4 \cdot 10^{+38}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+24} \lor \neg \left(y \leq 2.3 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.25e+24) (not (<= y 2.3e+39)))
   (* x (/ (/ (pow z y) a) y))
   (* x (/ (pow a (+ t -1.0)) (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+24) || !(y <= 2.3e+39)) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = x * (pow(a, (t + -1.0)) / (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.25d+24)) .or. (.not. (y <= 2.3d+39))) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = x * ((a ** (t + (-1.0d0))) / (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.25e+24) || !(y <= 2.3e+39)) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.25e+24) or not (y <= 2.3e+39):
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.25e+24) || !(y <= 2.3e+39))
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.25e+24) || ~((y <= 2.3e+39)))
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = x * ((a ^ (t + -1.0)) / (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.25e+24], N[Not[LessEqual[y, 2.3e+39]], $MachinePrecision]], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000011e24 or 2.30000000000000012e39 < 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 93.8%

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

      1. +-commutative 93.8%

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

      2. mul-1-neg 93.8%

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

      3. unsub-neg 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in b around 0 83.2%

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

      1. associate-/l* 83.2%

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

      2. div-exp 83.2%

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

      3. *-commutative 83.2%

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

      4. exp-to-pow 83.2%

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

      5. rem-exp-log 83.2%

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

   8. Simplified 83.2%

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

   if -1.25000000000000011e24 < y < 2.30000000000000012e39

   1. Initial program 96.3%

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

      1. associate-/l* 97.0%

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

      2. associate--l+ 97.0%

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

      3. exp-sum 92.1%

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

      4. associate-/l* 92.1%

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

      5. *-commutative 92.1%

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

      6. exp-to-pow 92.1%

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

      7. exp-diff 79.7%

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

      8. *-commutative 79.7%

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

      9. exp-to-pow 80.8%

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

      10. sub-neg 80.8%

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

      11. metadata-eval 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. exp-to-pow 79.1%

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

      2. sub-neg 79.1%

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

      3. metadata-eval 79.1%

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

      4. associate-*r/ 83.2%

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

   7. Simplified 83.2%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+24} \lor \neg \left(y \leq 2.3 \cdot 10^{+39}\right):\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.3% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} \cdot -0.6666666666666666\\ t_2 := \frac{\frac{x}{e^{b}}}{y}\\ t_3 := 0.5 \cdot \frac{x}{a}\\ \mathbf{if}\;b \leq -3900:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(t\_3 - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - t\_3\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot t\_1}{t\_1}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x a) -0.6666666666666666))
        (t_2 (/ (/ x (exp b)) y))
        (t_3 (* 0.5 (/ x a))))
   (if (<= b -3900.0)
     t_2
     (if (<= b -7.5e-276)
       (* x (/ (pow a t) y))
       (if (<= b 2.7e-36)
         (/ x (* b (* a (+ y (/ y b)))))
         (if (<= b 3e-12)
           (/
            (-
             (/ x a)
             (*
              b
              (+
               (/ x a)
               (*
                b
                (+
                 (- t_3 (/ x a))
                 (*
                  b
                  (+
                   (- (/ x a) t_3)
                   (/ (* (* (/ x a) -0.3333333333333333) t_1) t_1))))))))
            y)
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) * -0.6666666666666666;
	double t_2 = (x / exp(b)) / y;
	double t_3 = 0.5 * (x / a);
	double tmp;
	if (b <= -3900.0) {
		tmp = t_2;
	} else if (b <= -7.5e-276) {
		tmp = x * (pow(a, t) / y);
	} else if (b <= 2.7e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 3e-12) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_3 - (x / a)) + (b * (((x / a) - t_3) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / 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) :: t_3
    real(8) :: tmp
    t_1 = (x / a) * (-0.6666666666666666d0)
    t_2 = (x / exp(b)) / y
    t_3 = 0.5d0 * (x / a)
    if (b <= (-3900.0d0)) then
        tmp = t_2
    else if (b <= (-7.5d-276)) then
        tmp = x * ((a ** t) / y)
    else if (b <= 2.7d-36) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (b <= 3d-12) then
        tmp = ((x / a) - (b * ((x / a) + (b * ((t_3 - (x / a)) + (b * (((x / a) - t_3) + ((((x / a) * (-0.3333333333333333d0)) * t_1) / t_1)))))))) / 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 = (x / a) * -0.6666666666666666;
	double t_2 = (x / Math.exp(b)) / y;
	double t_3 = 0.5 * (x / a);
	double tmp;
	if (b <= -3900.0) {
		tmp = t_2;
	} else if (b <= -7.5e-276) {
		tmp = x * (Math.pow(a, t) / y);
	} else if (b <= 2.7e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 3e-12) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_3 - (x / a)) + (b * (((x / a) - t_3) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) * -0.6666666666666666
	t_2 = (x / math.exp(b)) / y
	t_3 = 0.5 * (x / a)
	tmp = 0
	if b <= -3900.0:
		tmp = t_2
	elif b <= -7.5e-276:
		tmp = x * (math.pow(a, t) / y)
	elif b <= 2.7e-36:
		tmp = x / (b * (a * (y + (y / b))))
	elif b <= 3e-12:
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_3 - (x / a)) + (b * (((x / a) - t_3) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) * -0.6666666666666666)
	t_2 = Float64(Float64(x / exp(b)) / y)
	t_3 = Float64(0.5 * Float64(x / a))
	tmp = 0.0
	if (b <= -3900.0)
		tmp = t_2;
	elseif (b <= -7.5e-276)
		tmp = Float64(x * Float64((a ^ t) / y));
	elseif (b <= 2.7e-36)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (b <= 3e-12)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x / a) + Float64(b * Float64(Float64(t_3 - Float64(x / a)) + Float64(b * Float64(Float64(Float64(x / a) - t_3) + Float64(Float64(Float64(Float64(x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) * -0.6666666666666666;
	t_2 = (x / exp(b)) / y;
	t_3 = 0.5 * (x / a);
	tmp = 0.0;
	if (b <= -3900.0)
		tmp = t_2;
	elseif (b <= -7.5e-276)
		tmp = x * ((a ^ t) / y);
	elseif (b <= 2.7e-36)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (b <= 3e-12)
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_3 - (x / a)) + (b * (((x / a) - t_3) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3900.0], t$95$2, If[LessEqual[b, -7.5e-276], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.7e-36], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3e-12], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(t$95$3 - N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(N[(x / a), $MachinePrecision] - t$95$3), $MachinePrecision] + N[(N[(N[(N[(x / a), $MachinePrecision] * -0.3333333333333333), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3900 or 3.0000000000000001e-12 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in b around inf 80.0%

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

      1. neg-mul-1 80.0%

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

   8. Simplified 80.0%

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

   9. Taylor expanded in b around -inf 80.0%

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

       1. mul-1-neg 80.0%

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

       2. rec-exp 80.0%

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

       3. associate-/l* 80.0%

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

       4. *-rgt-identity 80.0%

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

   11. Simplified 80.0%

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

   if -3900 < b < -7.500000000000001e-276

   1. Initial program 96.8%

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

      1. associate-/l* 95.2%

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

      2. associate--l+ 95.2%

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

      3. exp-sum 83.5%

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

      4. associate-/l* 81.5%

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

      5. *-commutative 81.5%

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

      6. exp-to-pow 81.5%

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

      7. exp-diff 81.5%

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

      8. *-commutative 81.5%

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

      9. exp-to-pow 82.7%

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

      10. sub-neg 82.7%

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

      11. metadata-eval 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in y around 0 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 68.3%

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

      2. sub-neg 68.3%

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

      3. metadata-eval 68.3%

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

      4. associate-*r/ 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in b around 0 64.8%

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

   9. Taylor expanded in t around inf 53.0%

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

   if -7.500000000000001e-276 < b < 2.70000000000000007e-36

   1. Initial program 94.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 80.4%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 80.4%

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

      8. *-commutative 80.4%

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

      9. exp-to-pow 81.6%

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

      10. sub-neg 81.6%

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

      11. metadata-eval 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 66.9%

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

      1. exp-to-pow 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. associate-*r/ 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0 49.4%

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

   9. Taylor expanded in b around 0 49.4%

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

       1. distribute-rgt1-in 49.4%

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

   11. Simplified 49.4%

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

   12. Taylor expanded in b around inf 53.6%

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

       1. associate-/l* 59.5%

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

       2. distribute-lft-out 61.0%

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

   14. Simplified 61.0%

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

   if 2.70000000000000007e-36 < b < 3.0000000000000001e-12

   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 y around 0 36.9%

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

      1. div-exp 36.5%

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

      2. exp-to-pow 38.3%

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

      3. sub-neg 38.3%

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

      4. metadata-eval 38.3%

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

   5. Simplified 38.3%

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

   6. Taylor expanded in t around 0 29.6%

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

      1. associate-/r* 29.6%

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

   8. Simplified 29.6%

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

   9. Taylor expanded in b around 0 20.2%

      \[\leadsto \frac{\color{blue}{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \left(-0.5 \cdot \frac{x}{a} + 0.16666666666666666 \cdot \frac{x}{a}\right)\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. flip-+ 18.4%

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

       2. *-commutative 18.4%

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

       3. metadata-eval 18.4%

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

       4. distribute-rgt-out 18.4%

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

       5. *-commutative 18.4%

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

       6. metadata-eval 18.4%

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

       7. distribute-rgt-out 18.4%

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

       8. pow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{{\left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)}^{2}} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. distribute-rgt-out 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{x}{a} \cdot \left(-1 + 0.5\right)\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. metadata-eval 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{x}{a} \cdot \color{blue}{-0.5}\right)}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(-0.5 \cdot \frac{x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{-0.5 \cdot x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. pow2 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - \color{blue}{{\left(0.16666666666666666 \cdot \frac{x}{a}\right)}^{2}}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\color{blue}{\left(\frac{x}{a} \cdot 0.16666666666666666\right)}}^{2}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\color{blue}{\frac{-0.5 \cdot x}{a}} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       16. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \color{blue}{\frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   11. Applied egg-rr 18.4%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]
   12. Step-by-step derivation

       1. unpow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{\frac{-0.5 \cdot x}{a} \cdot \frac{-0.5 \cdot x}{a}} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       2. unpow2 18.4%

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

       3. difference-of-squares 54.8%

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

       4. associate-*r/ 54.8%

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

       5. *-commutative 54.8%

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

       6. distribute-lft-out 54.8%

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

       7. metadata-eval 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       8. associate-*r/ 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. *-commutative 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \color{blue}{\left(\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)\right)}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. *-commutative 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   13. Simplified 54.8%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3900:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-276}:\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-12}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(0.5 \cdot \frac{x}{a} - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.9% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{a}\\ t_2 := \frac{\frac{x}{e^{b}}}{y}\\ t_3 := \frac{x}{a} \cdot -0.6666666666666666\\ \mathbf{if}\;b \leq -300:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(t\_1 - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - t\_1\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot t\_3}{t\_3}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x a)))
        (t_2 (/ (/ x (exp b)) y))
        (t_3 (* (/ x a) -0.6666666666666666)))
   (if (<= b -300.0)
     t_2
     (if (<= b -1.12e-275)
       (/
        (+
         (/ x a)
         (*
          b
          (-
           (*
            b
            (* b (- (* 0.5 (/ (/ x b) a)) (* (/ x a) 0.16666666666666666))))
           (/ x a))))
        y)
       (if (<= b 3e-36)
         (/ x (* b (* a (+ y (/ y b)))))
         (if (<= b 6.2e-13)
           (/
            (-
             (/ x a)
             (*
              b
              (+
               (/ x a)
               (*
                b
                (+
                 (- t_1 (/ x a))
                 (*
                  b
                  (+
                   (- (/ x a) t_1)
                   (/ (* (* (/ x a) -0.3333333333333333) t_3) t_3))))))))
            y)
           t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (x / a);
	double t_2 = (x / exp(b)) / y;
	double t_3 = (x / a) * -0.6666666666666666;
	double tmp;
	if (b <= -300.0) {
		tmp = t_2;
	} else if (b <= -1.12e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 3e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 6.2e-13) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_3) / t_3)))))))) / 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) :: t_3
    real(8) :: tmp
    t_1 = 0.5d0 * (x / a)
    t_2 = (x / exp(b)) / y
    t_3 = (x / a) * (-0.6666666666666666d0)
    if (b <= (-300.0d0)) then
        tmp = t_2
    else if (b <= (-1.12d-275)) then
        tmp = ((x / a) + (b * ((b * (b * ((0.5d0 * ((x / b) / a)) - ((x / a) * 0.16666666666666666d0)))) - (x / a)))) / y
    else if (b <= 3d-36) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (b <= 6.2d-13) then
        tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * (-0.3333333333333333d0)) * t_3) / t_3)))))))) / 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 = 0.5 * (x / a);
	double t_2 = (x / Math.exp(b)) / y;
	double t_3 = (x / a) * -0.6666666666666666;
	double tmp;
	if (b <= -300.0) {
		tmp = t_2;
	} else if (b <= -1.12e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 3e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 6.2e-13) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_3) / t_3)))))))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (x / a)
	t_2 = (x / math.exp(b)) / y
	t_3 = (x / a) * -0.6666666666666666
	tmp = 0
	if b <= -300.0:
		tmp = t_2
	elif b <= -1.12e-275:
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y
	elif b <= 3e-36:
		tmp = x / (b * (a * (y + (y / b))))
	elif b <= 6.2e-13:
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_3) / t_3)))))))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(x / a))
	t_2 = Float64(Float64(x / exp(b)) / y)
	t_3 = Float64(Float64(x / a) * -0.6666666666666666)
	tmp = 0.0
	if (b <= -300.0)
		tmp = t_2;
	elseif (b <= -1.12e-275)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(b * Float64(b * Float64(Float64(0.5 * Float64(Float64(x / b) / a)) - Float64(Float64(x / a) * 0.16666666666666666)))) - Float64(x / a)))) / y);
	elseif (b <= 3e-36)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (b <= 6.2e-13)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x / a) + Float64(b * Float64(Float64(t_1 - Float64(x / a)) + Float64(b * Float64(Float64(Float64(x / a) - t_1) + Float64(Float64(Float64(Float64(x / a) * -0.3333333333333333) * t_3) / t_3)))))))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (x / a);
	t_2 = (x / exp(b)) / y;
	t_3 = (x / a) * -0.6666666666666666;
	tmp = 0.0;
	if (b <= -300.0)
		tmp = t_2;
	elseif (b <= -1.12e-275)
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	elseif (b <= 3e-36)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (b <= 6.2e-13)
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_3) / t_3)))))))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / a), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]}, If[LessEqual[b, -300.0], t$95$2, If[LessEqual[b, -1.12e-275], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(b * N[(b * N[(N[(0.5 * N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3e-36], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-13], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(t$95$1 - N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(N[(x / a), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(N[(N[(x / a), $MachinePrecision] * -0.3333333333333333), $MachinePrecision] * t$95$3), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -300 or 6.1999999999999998e-13 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 90.0%

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

      1. +-commutative 90.0%

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

      2. mul-1-neg 90.0%

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

      3. unsub-neg 90.0%

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

   5. Simplified 90.0%

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

   6. Taylor expanded in b around inf 80.0%

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

      1. neg-mul-1 80.0%

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

   8. Simplified 80.0%

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

   9. Taylor expanded in b around -inf 80.0%

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

       1. mul-1-neg 80.0%

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

       2. rec-exp 80.0%

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

       3. associate-/l* 80.0%

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

       4. *-rgt-identity 80.0%

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

   11. Simplified 80.0%

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

   if -300 < b < -1.11999999999999995e-275

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 67.2%

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

      1. div-exp 67.2%

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

      2. exp-to-pow 68.3%

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

      3. sub-neg 68.3%

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

      4. metadata-eval 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 26.5%

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

      1. associate-/r* 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in b around 0 22.5%

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

   10. Taylor expanded in b around inf 33.4%

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

   12. Simplified 39.3%

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

   if -1.11999999999999995e-275 < b < 3.0000000000000002e-36

   1. Initial program 94.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 80.4%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 80.4%

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

      8. *-commutative 80.4%

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

      9. exp-to-pow 81.6%

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

      10. sub-neg 81.6%

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

      11. metadata-eval 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 66.9%

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

      1. exp-to-pow 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. associate-*r/ 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0 49.4%

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

   9. Taylor expanded in b around 0 49.4%

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

       1. distribute-rgt1-in 49.4%

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

   11. Simplified 49.4%

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

   12. Taylor expanded in b around inf 53.6%

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

       1. associate-/l* 59.5%

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

       2. distribute-lft-out 61.0%

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

   14. Simplified 61.0%

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

   if 3.0000000000000002e-36 < b < 6.1999999999999998e-13

   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 y around 0 36.9%

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

      1. div-exp 36.5%

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

      2. exp-to-pow 38.3%

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

      3. sub-neg 38.3%

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

      4. metadata-eval 38.3%

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

   5. Simplified 38.3%

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

   6. Taylor expanded in t around 0 29.6%

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

      1. associate-/r* 29.6%

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

   8. Simplified 29.6%

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

   9. Taylor expanded in b around 0 20.2%

      \[\leadsto \frac{\color{blue}{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \left(-0.5 \cdot \frac{x}{a} + 0.16666666666666666 \cdot \frac{x}{a}\right)\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. flip-+ 18.4%

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

       2. *-commutative 18.4%

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

       3. metadata-eval 18.4%

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

       4. distribute-rgt-out 18.4%

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

       5. *-commutative 18.4%

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

       6. metadata-eval 18.4%

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

       7. distribute-rgt-out 18.4%

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

       8. pow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{{\left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)}^{2}} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. distribute-rgt-out 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{x}{a} \cdot \left(-1 + 0.5\right)\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. metadata-eval 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{x}{a} \cdot \color{blue}{-0.5}\right)}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(-0.5 \cdot \frac{x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{-0.5 \cdot x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. pow2 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - \color{blue}{{\left(0.16666666666666666 \cdot \frac{x}{a}\right)}^{2}}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\color{blue}{\left(\frac{x}{a} \cdot 0.16666666666666666\right)}}^{2}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\color{blue}{\frac{-0.5 \cdot x}{a}} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       16. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \color{blue}{\frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   11. Applied egg-rr 18.4%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]
   12. Step-by-step derivation

       1. unpow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{\frac{-0.5 \cdot x}{a} \cdot \frac{-0.5 \cdot x}{a}} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       2. unpow2 18.4%

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

       3. difference-of-squares 54.8%

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

       4. associate-*r/ 54.8%

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

       5. *-commutative 54.8%

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

       6. distribute-lft-out 54.8%

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

       7. metadata-eval 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       8. associate-*r/ 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. *-commutative 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \color{blue}{\left(\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)\right)}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. *-commutative 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   13. Simplified 54.8%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -300:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \mathbf{elif}\;b \leq -1.12 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(0.5 \cdot \frac{x}{a} - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+164}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 135000:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.1e+164)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b 0.5))))) y)
   (if (<= b 135000.0) (* x (/ (/ (pow z y) a) y)) (/ x (* a (* y (exp b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+164) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= 135000.0) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.1d+164)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0))))) / y
    else if (b <= 135000.0d0) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.1e+164) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= 135000.0) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.1e+164:
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y
	elif b <= 135000.0:
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.1e+164)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5))))) / y);
	elseif (b <= 135000.0)
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.1e+164)
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	elseif (b <= 135000.0)
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.1e+164], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 135000.0], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.10000000000000003e164

   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 0 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in b around inf 100.0%

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

      1. neg-mul-1 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in b around 0 100.0%

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

   if -1.10000000000000003e164 < b < 135000

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 72.1%

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

      1. +-commutative 72.1%

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

      2. mul-1-neg 72.1%

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

      3. unsub-neg 72.1%

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

   5. Simplified 72.1%

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

   6. Taylor expanded in b around 0 68.7%

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

      1. associate-/l* 70.0%

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

      2. div-exp 70.0%

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

      3. *-commutative 70.0%

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

      4. exp-to-pow 70.0%

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

      5. rem-exp-log 70.9%

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

   8. Simplified 70.9%

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

   if 135000 < b

   1. Initial program 100.0%

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

      1. associate-/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 82.5%

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

      4. associate-/l* 82.5%

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

      5. *-commutative 82.5%

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

      6. exp-to-pow 82.5%

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

      7. exp-diff 59.6%

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

      8. *-commutative 59.6%

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

      9. exp-to-pow 59.6%

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

      10. sub-neg 59.6%

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

      11. metadata-eval 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in y around 0 68.4%

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

      1. exp-to-pow 68.4%

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

      2. sub-neg 68.4%

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

      3. metadata-eval 68.4%

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

      4. associate-*r/ 72.0%

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

   7. Simplified 72.0%

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

   8. Taylor expanded in t around 0 86.2%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+164}:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 135000:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 73.6% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+29} \lor \neg \left(t \leq 1.1 \cdot 10^{+98}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.8e+29) (not (<= t 1.1e+98)))
   (* x (/ (pow a t) y))
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.8e+29) || !(t <= 1.1e+98)) {
		tmp = x * (pow(a, t) / y);
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-5.8d+29)) .or. (.not. (t <= 1.1d+98))) then
        tmp = x * ((a ** t) / y)
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.8e+29) || !(t <= 1.1e+98)) {
		tmp = x * (Math.pow(a, t) / y);
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.8e+29) or not (t <= 1.1e+98):
		tmp = x * (math.pow(a, t) / y)
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.8e+29) || !(t <= 1.1e+98))
		tmp = Float64(x * Float64((a ^ t) / y));
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.8e+29) || ~((t <= 1.1e+98)))
		tmp = x * ((a ^ t) / y);
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.8e+29], N[Not[LessEqual[t, 1.1e+98]], $MachinePrecision]], N[(x * N[(N[Power[a, t], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.7999999999999999e29 or 1.10000000000000004e98 < t

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 73.8%

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

      4. associate-/l* 73.8%

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

      5. *-commutative 73.8%

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

      6. exp-to-pow 73.8%

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

      7. exp-diff 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 67.1%

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

      1. exp-to-pow 67.1%

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

      2. sub-neg 67.1%

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

      3. metadata-eval 67.1%

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

      4. associate-*r/ 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in b around 0 79.9%

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

   9. Taylor expanded in t around inf 79.9%

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

   if -5.7999999999999999e29 < t < 1.10000000000000004e98

   1. Initial program 96.5%

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

      1. associate-/l* 97.1%

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

      2. associate--l+ 97.1%

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

      3. exp-sum 80.1%

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

      4. associate-/l* 78.2%

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

      5. *-commutative 78.2%

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

      6. exp-to-pow 78.2%

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

      7. exp-diff 73.6%

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

      8. *-commutative 73.6%

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

      9. exp-to-pow 74.6%

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

      10. sub-neg 74.6%

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

      11. metadata-eval 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in y around 0 59.8%

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

      1. exp-to-pow 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/ 64.7%

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

   7. Simplified 64.7%

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

   8. Taylor expanded in t around 0 65.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+29} \lor \neg \left(t \leq 1.1 \cdot 10^{+98}\right):\\ \;\;\;\;x \cdot \frac{{a}^{t}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x}{a}\\ t_2 := \frac{x}{a} \cdot -0.6666666666666666\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(t\_1 - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - t\_1\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot t\_2}{t\_2}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ x a))) (t_2 (* (/ x a) -0.6666666666666666)))
   (if (<= b -2.4e+96)
     (/
      (- x (* b (- x (* b (+ (* -0.16666666666666666 (* x b)) (* x 0.5))))))
      y)
     (if (<= b -3.5e+16)
       (* x (/ (exp b) y))
       (if (<= b -1.4e-275)
         (/
          (+
           (/ x a)
           (*
            b
            (-
             (*
              b
              (* b (- (* 0.5 (/ (/ x b) a)) (* (/ x a) 0.16666666666666666))))
             (/ x a))))
          y)
         (if (<= b 3.7e-36)
           (/ x (* b (* a (+ y (/ y b)))))
           (if (<= b 2.1e-14)
             (/
              (-
               (/ x a)
               (*
                b
                (+
                 (/ x a)
                 (*
                  b
                  (+
                   (- t_1 (/ x a))
                   (*
                    b
                    (+
                     (- (/ x a) t_1)
                     (/ (* (* (/ x a) -0.3333333333333333) t_2) t_2))))))))
              y)
             (/
              x
              (*
               a
               (*
                y
                (-
                 1.0
                 (*
                  b
                  (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 0.5 * (x / a);
	double t_2 = (x / a) * -0.6666666666666666;
	double tmp;
	if (b <= -2.4e+96) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= -3.5e+16) {
		tmp = x * (exp(b) / y);
	} else if (b <= -1.4e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 3.7e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 2.1e-14) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_2) / t_2)))))))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.5d0 * (x / a)
    t_2 = (x / a) * (-0.6666666666666666d0)
    if (b <= (-2.4d+96)) then
        tmp = (x - (b * (x - (b * (((-0.16666666666666666d0) * (x * b)) + (x * 0.5d0)))))) / y
    else if (b <= (-3.5d+16)) then
        tmp = x * (exp(b) / y)
    else if (b <= (-1.4d-275)) then
        tmp = ((x / a) + (b * ((b * (b * ((0.5d0 * ((x / b) / a)) - ((x / a) * 0.16666666666666666d0)))) - (x / a)))) / y
    else if (b <= 3.7d-36) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (b <= 2.1d-14) then
        tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * (-0.3333333333333333d0)) * t_2) / t_2)))))))) / y
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (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 t_1 = 0.5 * (x / a);
	double t_2 = (x / a) * -0.6666666666666666;
	double tmp;
	if (b <= -2.4e+96) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= -3.5e+16) {
		tmp = x * (Math.exp(b) / y);
	} else if (b <= -1.4e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 3.7e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 2.1e-14) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_2) / t_2)))))))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 0.5 * (x / a)
	t_2 = (x / a) * -0.6666666666666666
	tmp = 0
	if b <= -2.4e+96:
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y
	elif b <= -3.5e+16:
		tmp = x * (math.exp(b) / y)
	elif b <= -1.4e-275:
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y
	elif b <= 3.7e-36:
		tmp = x / (b * (a * (y + (y / b))))
	elif b <= 2.1e-14:
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_2) / t_2)))))))) / y
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.5 * Float64(x / a))
	t_2 = Float64(Float64(x / a) * -0.6666666666666666)
	tmp = 0.0
	if (b <= -2.4e+96)
		tmp = Float64(Float64(x - Float64(b * Float64(x - Float64(b * Float64(Float64(-0.16666666666666666 * Float64(x * b)) + Float64(x * 0.5)))))) / y);
	elseif (b <= -3.5e+16)
		tmp = Float64(x * Float64(exp(b) / y));
	elseif (b <= -1.4e-275)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(b * Float64(b * Float64(Float64(0.5 * Float64(Float64(x / b) / a)) - Float64(Float64(x / a) * 0.16666666666666666)))) - Float64(x / a)))) / y);
	elseif (b <= 3.7e-36)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (b <= 2.1e-14)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x / a) + Float64(b * Float64(Float64(t_1 - Float64(x / a)) + Float64(b * Float64(Float64(Float64(x / a) - t_1) + Float64(Float64(Float64(Float64(x / a) * -0.3333333333333333) * t_2) / t_2)))))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 0.5 * (x / a);
	t_2 = (x / a) * -0.6666666666666666;
	tmp = 0.0;
	if (b <= -2.4e+96)
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	elseif (b <= -3.5e+16)
		tmp = x * (exp(b) / y);
	elseif (b <= -1.4e-275)
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	elseif (b <= 3.7e-36)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (b <= 2.1e-14)
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_1 - (x / a)) + (b * (((x / a) - t_1) + ((((x / a) * -0.3333333333333333) * t_2) / t_2)))))))) / y;
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / a), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]}, If[LessEqual[b, -2.4e+96], N[(N[(x - N[(b * N[(x - N[(b * N[(N[(-0.16666666666666666 * N[(x * b), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -3.5e+16], N[(x * N[(N[Exp[b], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.4e-275], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(b * N[(b * N[(N[(0.5 * N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.7e-36], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-14], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(t$95$1 - N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(N[(x / a), $MachinePrecision] - t$95$1), $MachinePrecision] + N[(N[(N[(N[(x / a), $MachinePrecision] * -0.3333333333333333), $MachinePrecision] * t$95$2), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.39999999999999993e96

   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 93.7%

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

      1. +-commutative 93.7%

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

      2. mul-1-neg 93.7%

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

      3. unsub-neg 93.7%

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

   5. Simplified 93.7%

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

   6. Taylor expanded in b around inf 89.5%

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

      1. neg-mul-1 89.5%

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

   8. Simplified 89.5%

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

   9. Taylor expanded in b around 0 87.6%

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

   if -2.39999999999999993e96 < b < -3.5e16

   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 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. unsub-neg 76.8%

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

   5. Simplified 76.8%

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

   6. Taylor expanded in b around inf 47.9%

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

      1. neg-mul-1 47.9%

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

   8. Simplified 47.9%

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

      1. associate-/l* 47.9%

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

      2. add-sqr-sqrt 47.9%

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

      3. sqrt-unprod 47.9%

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

      4. sqr-neg 47.9%

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

      5. sqrt-unprod 0.0%

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

      6. add-sqr-sqrt 53.7%

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

   10. Applied egg-rr 53.7%

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

   if -3.5e16 < b < -1.39999999999999997e-275

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0 66.5%

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

      1. div-exp 66.5%

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

      2. exp-to-pow 67.6%

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

      3. sub-neg 67.6%

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

      4. metadata-eval 67.6%

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

   5. Simplified 67.6%

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

   6. Taylor expanded in t around 0 29.3%

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

      1. associate-/r* 27.4%

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

   8. Simplified 27.4%

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

   9. Taylor expanded in b around 0 21.8%

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

   10. Taylor expanded in b around inf 32.2%

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

   12. Simplified 37.9%

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

   if -1.39999999999999997e-275 < b < 3.70000000000000002e-36

   1. Initial program 94.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 80.4%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 80.4%

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

      8. *-commutative 80.4%

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

      9. exp-to-pow 81.6%

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

      10. sub-neg 81.6%

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

      11. metadata-eval 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 66.9%

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

      1. exp-to-pow 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. associate-*r/ 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0 49.4%

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

   9. Taylor expanded in b around 0 49.4%

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

       1. distribute-rgt1-in 49.4%

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

   11. Simplified 49.4%

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

   12. Taylor expanded in b around inf 53.6%

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

       1. associate-/l* 59.5%

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

       2. distribute-lft-out 61.0%

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

   14. Simplified 61.0%

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

   if 3.70000000000000002e-36 < b < 2.0999999999999999e-14

   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 y around 0 36.9%

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

      1. div-exp 36.5%

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

      2. exp-to-pow 38.3%

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

      3. sub-neg 38.3%

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

      4. metadata-eval 38.3%

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

   5. Simplified 38.3%

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

   6. Taylor expanded in t around 0 29.6%

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

      1. associate-/r* 29.6%

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

   8. Simplified 29.6%

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

   9. Taylor expanded in b around 0 20.2%

      \[\leadsto \frac{\color{blue}{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \left(-0.5 \cdot \frac{x}{a} + 0.16666666666666666 \cdot \frac{x}{a}\right)\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. flip-+ 18.4%

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

       2. *-commutative 18.4%

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

       3. metadata-eval 18.4%

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

       4. distribute-rgt-out 18.4%

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

       5. *-commutative 18.4%

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

       6. metadata-eval 18.4%

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

       7. distribute-rgt-out 18.4%

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

       8. pow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{{\left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)}^{2}} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. distribute-rgt-out 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{x}{a} \cdot \left(-1 + 0.5\right)\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. metadata-eval 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{x}{a} \cdot \color{blue}{-0.5}\right)}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(-0.5 \cdot \frac{x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{-0.5 \cdot x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. pow2 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - \color{blue}{{\left(0.16666666666666666 \cdot \frac{x}{a}\right)}^{2}}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\color{blue}{\left(\frac{x}{a} \cdot 0.16666666666666666\right)}}^{2}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\color{blue}{\frac{-0.5 \cdot x}{a}} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       16. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \color{blue}{\frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   11. Applied egg-rr 18.4%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]
   12. Step-by-step derivation

       1. unpow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{\frac{-0.5 \cdot x}{a} \cdot \frac{-0.5 \cdot x}{a}} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       2. unpow2 18.4%

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

       3. difference-of-squares 54.8%

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

       4. associate-*r/ 54.8%

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

       5. *-commutative 54.8%

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

       6. distribute-lft-out 54.8%

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

       7. metadata-eval 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       8. associate-*r/ 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. *-commutative 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \color{blue}{\left(\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)\right)}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. *-commutative 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   13. Simplified 54.8%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   if 2.0999999999999999e-14 < b

   1. Initial program 100.0%

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

      1. associate-/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 82.3%

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

      4. associate-/l* 82.3%

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

      5. *-commutative 82.3%

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

      6. exp-to-pow 82.3%

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

      7. exp-diff 61.3%

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

      8. *-commutative 61.3%

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

      9. exp-to-pow 61.3%

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

      10. sub-neg 61.3%

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

      11. metadata-eval 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around 0 67.8%

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

      1. exp-to-pow 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. associate-*r/ 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around 0 81.0%

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

   9. Taylor expanded in b around 0 68.5%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 68.5%

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

   11. Simplified 68.5%

       \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+16}:\\ \;\;\;\;x \cdot \frac{e^{b}}{y}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(0.5 \cdot \frac{x}{a} - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 54.6% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a} \cdot -0.6666666666666666\\ t_2 := 0.5 \cdot \frac{x}{a}\\ \mathbf{if}\;b \leq -16500:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(t\_2 - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - t\_2\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot t\_1}{t\_1}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ x a) -0.6666666666666666)) (t_2 (* 0.5 (/ x a))))
   (if (<= b -16500.0)
     (/
      (- x (* b (- x (* b (+ (* -0.16666666666666666 (* x b)) (* x 0.5))))))
      y)
     (if (<= b -1.75e-275)
       (/
        (+
         (/ x a)
         (*
          b
          (-
           (*
            b
            (* b (- (* 0.5 (/ (/ x b) a)) (* (/ x a) 0.16666666666666666))))
           (/ x a))))
        y)
       (if (<= b 2.1e-36)
         (/ x (* b (* a (+ y (/ y b)))))
         (if (<= b 2.1e-14)
           (/
            (-
             (/ x a)
             (*
              b
              (+
               (/ x a)
               (*
                b
                (+
                 (- t_2 (/ x a))
                 (*
                  b
                  (+
                   (- (/ x a) t_2)
                   (/ (* (* (/ x a) -0.3333333333333333) t_1) t_1))))))))
            y)
           (/
            x
            (*
             a
             (*
              y
              (-
               1.0
               (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) * -0.6666666666666666;
	double t_2 = 0.5 * (x / a);
	double tmp;
	if (b <= -16500.0) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= -1.75e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 2.1e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 2.1e-14) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_2 - (x / a)) + (b * (((x / a) - t_2) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / a) * (-0.6666666666666666d0)
    t_2 = 0.5d0 * (x / a)
    if (b <= (-16500.0d0)) then
        tmp = (x - (b * (x - (b * (((-0.16666666666666666d0) * (x * b)) + (x * 0.5d0)))))) / y
    else if (b <= (-1.75d-275)) then
        tmp = ((x / a) + (b * ((b * (b * ((0.5d0 * ((x / b) / a)) - ((x / a) * 0.16666666666666666d0)))) - (x / a)))) / y
    else if (b <= 2.1d-36) then
        tmp = x / (b * (a * (y + (y / b))))
    else if (b <= 2.1d-14) then
        tmp = ((x / a) - (b * ((x / a) + (b * ((t_2 - (x / a)) + (b * (((x / a) - t_2) + ((((x / a) * (-0.3333333333333333d0)) * t_1) / t_1)))))))) / y
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (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 t_1 = (x / a) * -0.6666666666666666;
	double t_2 = 0.5 * (x / a);
	double tmp;
	if (b <= -16500.0) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= -1.75e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 2.1e-36) {
		tmp = x / (b * (a * (y + (y / b))));
	} else if (b <= 2.1e-14) {
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_2 - (x / a)) + (b * (((x / a) - t_2) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y;
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) * -0.6666666666666666
	t_2 = 0.5 * (x / a)
	tmp = 0
	if b <= -16500.0:
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y
	elif b <= -1.75e-275:
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y
	elif b <= 2.1e-36:
		tmp = x / (b * (a * (y + (y / b))))
	elif b <= 2.1e-14:
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_2 - (x / a)) + (b * (((x / a) - t_2) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) * -0.6666666666666666)
	t_2 = Float64(0.5 * Float64(x / a))
	tmp = 0.0
	if (b <= -16500.0)
		tmp = Float64(Float64(x - Float64(b * Float64(x - Float64(b * Float64(Float64(-0.16666666666666666 * Float64(x * b)) + Float64(x * 0.5)))))) / y);
	elseif (b <= -1.75e-275)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(b * Float64(b * Float64(Float64(0.5 * Float64(Float64(x / b) / a)) - Float64(Float64(x / a) * 0.16666666666666666)))) - Float64(x / a)))) / y);
	elseif (b <= 2.1e-36)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	elseif (b <= 2.1e-14)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x / a) + Float64(b * Float64(Float64(t_2 - Float64(x / a)) + Float64(b * Float64(Float64(Float64(x / a) - t_2) + Float64(Float64(Float64(Float64(x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * Float64(0.5 + Float64(b * 0.16666666666666666)))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) * -0.6666666666666666;
	t_2 = 0.5 * (x / a);
	tmp = 0.0;
	if (b <= -16500.0)
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	elseif (b <= -1.75e-275)
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	elseif (b <= 2.1e-36)
		tmp = x / (b * (a * (y + (y / b))));
	elseif (b <= 2.1e-14)
		tmp = ((x / a) - (b * ((x / a) + (b * ((t_2 - (x / a)) + (b * (((x / a) - t_2) + ((((x / a) * -0.3333333333333333) * t_1) / t_1)))))))) / y;
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] * -0.6666666666666666), $MachinePrecision]}, Block[{t$95$2 = N[(0.5 * N[(x / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -16500.0], N[(N[(x - N[(b * N[(x - N[(b * N[(N[(-0.16666666666666666 * N[(x * b), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.75e-275], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(b * N[(b * N[(N[(0.5 * N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.1e-36], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e-14], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(t$95$2 - N[(x / a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(N[(x / a), $MachinePrecision] - t$95$2), $MachinePrecision] + N[(N[(N[(N[(x / a), $MachinePrecision] * -0.3333333333333333), $MachinePrecision] * t$95$1), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -16500

   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 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0 67.6%

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

   if -16500 < b < -1.74999999999999984e-275

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 67.2%

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

      1. div-exp 67.2%

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

      2. exp-to-pow 68.3%

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

      3. sub-neg 68.3%

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

      4. metadata-eval 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 26.5%

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

      1. associate-/r* 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in b around 0 22.5%

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

   10. Taylor expanded in b around inf 33.4%

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

   12. Simplified 39.3%

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

   if -1.74999999999999984e-275 < b < 2.09999999999999991e-36

   1. Initial program 94.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   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 80.4%

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

      4. associate-/l* 80.4%

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

      5. *-commutative 80.4%

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

      6. exp-to-pow 80.4%

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

      7. exp-diff 80.4%

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

      8. *-commutative 80.4%

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

      9. exp-to-pow 81.6%

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

      10. sub-neg 81.6%

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

      11. metadata-eval 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 66.9%

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

      1. exp-to-pow 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. associate-*r/ 70.6%

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

   7. Simplified 70.6%

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

   8. Taylor expanded in t around 0 49.4%

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

   9. Taylor expanded in b around 0 49.4%

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

       1. distribute-rgt1-in 49.4%

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

   11. Simplified 49.4%

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

   12. Taylor expanded in b around inf 53.6%

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

       1. associate-/l* 59.5%

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

       2. distribute-lft-out 61.0%

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

   14. Simplified 61.0%

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

   if 2.09999999999999991e-36 < b < 2.0999999999999999e-14

   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 y around 0 36.9%

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

      1. div-exp 36.5%

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

      2. exp-to-pow 38.3%

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

      3. sub-neg 38.3%

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

      4. metadata-eval 38.3%

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

   5. Simplified 38.3%

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

   6. Taylor expanded in t around 0 29.6%

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

      1. associate-/r* 29.6%

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

   8. Simplified 29.6%

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

   9. Taylor expanded in b around 0 20.2%

      \[\leadsto \frac{\color{blue}{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \left(-0.5 \cdot \frac{x}{a} + 0.16666666666666666 \cdot \frac{x}{a}\right)\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. flip-+ 18.4%

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

       2. *-commutative 18.4%

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

       3. metadata-eval 18.4%

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

       4. distribute-rgt-out 18.4%

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

       5. *-commutative 18.4%

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

       6. metadata-eval 18.4%

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

       7. distribute-rgt-out 18.4%

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

       8. pow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{{\left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)}^{2}} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. distribute-rgt-out 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{x}{a} \cdot \left(-1 + 0.5\right)\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. metadata-eval 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{x}{a} \cdot \color{blue}{-0.5}\right)}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(-0.5 \cdot \frac{x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\color{blue}{\left(\frac{-0.5 \cdot x}{a}\right)}}^{2} - \left(0.16666666666666666 \cdot \frac{x}{a}\right) \cdot \left(0.16666666666666666 \cdot \frac{x}{a}\right)}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. pow2 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - \color{blue}{{\left(0.16666666666666666 \cdot \frac{x}{a}\right)}^{2}}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\color{blue}{\left(\frac{x}{a} \cdot 0.16666666666666666\right)}}^{2}}{-0.5 \cdot \frac{x}{a} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. associate-*r/ 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\color{blue}{\frac{-0.5 \cdot x}{a}} - 0.16666666666666666 \cdot \frac{x}{a}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       16. *-commutative 18.4%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \color{blue}{\frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   11. Applied egg-rr 18.4%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{{\left(\frac{-0.5 \cdot x}{a}\right)}^{2} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]
   12. Step-by-step derivation

       1. unpow2 18.4%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\color{blue}{\frac{-0.5 \cdot x}{a} \cdot \frac{-0.5 \cdot x}{a}} - {\left(\frac{x}{a} \cdot 0.16666666666666666\right)}^{2}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       2. unpow2 18.4%

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

       3. difference-of-squares 54.8%

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

       4. associate-*r/ 54.8%

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

       5. *-commutative 54.8%

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

       6. distribute-lft-out 54.8%

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

       7. metadata-eval 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       8. associate-*r/ 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       9. *-commutative 54.8%

          \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       10. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \color{blue}{\left(\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)\right)}}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       11. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}\right)}{\frac{-0.5 \cdot x}{a} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       12. associate-*r/ 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{-0.5 \cdot \frac{x}{a}} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       13. *-commutative 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot -0.5} - \frac{x}{a} \cdot 0.16666666666666666}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       14. distribute-lft-out-- 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\color{blue}{\frac{x}{a} \cdot \left(-0.5 - 0.16666666666666666\right)}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

       15. metadata-eval 54.8%

           \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot \color{blue}{-0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   13. Simplified 54.8%

       \[\leadsto \frac{b \cdot \left(b \cdot \left(-1 \cdot \left(b \cdot \left(-1 \cdot \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right) + \color{blue}{\frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}}\right)\right) - \left(-1 \cdot \frac{x}{a} + 0.5 \cdot \frac{x}{a}\right)\right) - \frac{x}{a}\right) + \frac{x}{a}}{y} \]

   if 2.0999999999999999e-14 < b

   1. Initial program 100.0%

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

      1. associate-/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 82.3%

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

      4. associate-/l* 82.3%

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

      5. *-commutative 82.3%

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

      6. exp-to-pow 82.3%

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

      7. exp-diff 61.3%

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

      8. *-commutative 61.3%

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

      9. exp-to-pow 61.3%

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

      10. sub-neg 61.3%

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

      11. metadata-eval 61.3%

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

   3. Simplified 61.3%

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

   5. Taylor expanded in y around 0 67.8%

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

      1. exp-to-pow 67.8%

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

      2. sub-neg 67.8%

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

      3. metadata-eval 67.8%

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

      4. associate-*r/ 71.1%

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

   7. Simplified 71.1%

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

   8. Taylor expanded in t around 0 81.0%

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

   9. Taylor expanded in b around 0 68.5%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 68.5%

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

   11. Simplified 68.5%

       \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -16500:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -1.75 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \left(\frac{x}{a} + b \cdot \left(\left(0.5 \cdot \frac{x}{a} - \frac{x}{a}\right) + b \cdot \left(\left(\frac{x}{a} - 0.5 \cdot \frac{x}{a}\right) + \frac{\left(\frac{x}{a} \cdot -0.3333333333333333\right) \cdot \left(\frac{x}{a} \cdot -0.6666666666666666\right)}{\frac{x}{a} \cdot -0.6666666666666666}\right)\right)\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.7% accurate, 8.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1550:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1550.0)
   (/ (- x (* b (- x (* b (+ (* -0.16666666666666666 (* x b)) (* x 0.5)))))) y)
   (if (<= b -2.85e-275)
     (/
      (+
       (/ x a)
       (*
        b
        (-
         (* b (* b (- (* 0.5 (/ (/ x b) a)) (* (/ x a) 0.16666666666666666))))
         (/ x a))))
      y)
     (if (<= b 5.7e+29)
       (/ x (* b (* a (+ y (/ y b)))))
       (/
        x
        (*
         a
         (*
          y
          (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1550.0) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= -2.85e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 5.7e+29) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (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 <= (-1550.0d0)) then
        tmp = (x - (b * (x - (b * (((-0.16666666666666666d0) * (x * b)) + (x * 0.5d0)))))) / y
    else if (b <= (-2.85d-275)) then
        tmp = ((x / a) + (b * ((b * (b * ((0.5d0 * ((x / b) / a)) - ((x / a) * 0.16666666666666666d0)))) - (x / a)))) / y
    else if (b <= 5.7d+29) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (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 <= -1550.0) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= -2.85e-275) {
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	} else if (b <= 5.7e+29) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1550.0:
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y
	elif b <= -2.85e-275:
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y
	elif b <= 5.7e+29:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1550.0)
		tmp = Float64(Float64(x - Float64(b * Float64(x - Float64(b * Float64(Float64(-0.16666666666666666 * Float64(x * b)) + Float64(x * 0.5)))))) / y);
	elseif (b <= -2.85e-275)
		tmp = Float64(Float64(Float64(x / a) + Float64(b * Float64(Float64(b * Float64(b * Float64(Float64(0.5 * Float64(Float64(x / b) / a)) - Float64(Float64(x / a) * 0.16666666666666666)))) - Float64(x / a)))) / y);
	elseif (b <= 5.7e+29)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 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 <= -1550.0)
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	elseif (b <= -2.85e-275)
		tmp = ((x / a) + (b * ((b * (b * ((0.5 * ((x / b) / a)) - ((x / a) * 0.16666666666666666)))) - (x / a)))) / y;
	elseif (b <= 5.7e+29)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1550.0], N[(N[(x - N[(b * N[(x - N[(b * N[(N[(-0.16666666666666666 * N[(x * b), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -2.85e-275], N[(N[(N[(x / a), $MachinePrecision] + N[(b * N[(N[(b * N[(b * N[(N[(0.5 * N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(N[(x / a), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.7e+29], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * 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 < -1550

   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 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0 67.6%

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

   if -1550 < b < -2.84999999999999995e-275

   1. Initial program 96.8%

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

   3. Taylor expanded in y around 0 67.2%

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

      1. div-exp 67.2%

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

      2. exp-to-pow 68.3%

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

      3. sub-neg 68.3%

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

      4. metadata-eval 68.3%

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

   5. Simplified 68.3%

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

   6. Taylor expanded in t around 0 26.5%

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

      1. associate-/r* 26.5%

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

   8. Simplified 26.5%

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

   9. Taylor expanded in b around 0 22.5%

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

   10. Taylor expanded in b around inf 33.4%

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

   12. Simplified 39.3%

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

   if -2.84999999999999995e-275 < b < 5.6999999999999999e29

   1. Initial program 95.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 79.3%

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

      4. associate-/l* 77.0%

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

      5. *-commutative 77.0%

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

      6. exp-to-pow 77.0%

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

      7. exp-diff 75.9%

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

      8. *-commutative 75.9%

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

      9. exp-to-pow 76.9%

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

      10. sub-neg 76.9%

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

      11. metadata-eval 76.9%

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

   3. Simplified 76.9%

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

   5. Taylor expanded in y around 0 62.3%

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

      1. exp-to-pow 63.3%

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

      2. sub-neg 63.3%

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

      3. metadata-eval 63.3%

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

      4. associate-*r/ 64.3%

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

   7. Simplified 64.3%

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

   8. Taylor expanded in t around 0 43.8%

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

   9. Taylor expanded in b around 0 41.6%

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

       1. distribute-rgt1-in 41.6%

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

   11. Simplified 41.6%

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

   12. Taylor expanded in b around inf 44.8%

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

       1. associate-/l* 49.3%

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

       2. distribute-lft-out 50.4%

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

   14. Simplified 50.4%

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

   if 5.6999999999999999e29 < b

   1. Initial program 100.0%

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

      1. associate-/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 82.7%

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

      4. associate-/l* 82.7%

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

      5. *-commutative 82.7%

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

      6. exp-to-pow 82.7%

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

      7. exp-diff 59.6%

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

      8. *-commutative 59.6%

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

      9. exp-to-pow 59.6%

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

      10. sub-neg 59.6%

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

      11. metadata-eval 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. exp-to-pow 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-*r/ 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 88.6%

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

   9. Taylor expanded in b around 0 77.5%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 77.5%

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

   11. Simplified 77.5%

       \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1550:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq -2.85 \cdot 10^{-275}:\\ \;\;\;\;\frac{\frac{x}{a} + b \cdot \left(b \cdot \left(b \cdot \left(0.5 \cdot \frac{\frac{x}{b}}{a} - \frac{x}{a} \cdot 0.16666666666666666\right)\right) - \frac{x}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 55.0% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05)
   (/ (- x (* b (- x (* b (+ (* -0.16666666666666666 (* x b)) (* x 0.5)))))) y)
   (if (<= b 7.5e+30)
     (/ x (* b (* a (+ y (/ y b)))))
     (/
      x
      (*
       a
       (*
        y
        (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= 7.5e+30) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (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 <= (-1.05d0)) then
        tmp = (x - (b * (x - (b * (((-0.16666666666666666d0) * (x * b)) + (x * 0.5d0)))))) / y
    else if (b <= 7.5d+30) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (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 <= -1.05) {
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	} else if (b <= 7.5e+30) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05:
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y
	elif b <= 7.5e+30:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05)
		tmp = Float64(Float64(x - Float64(b * Float64(x - Float64(b * Float64(Float64(-0.16666666666666666 * Float64(x * b)) + Float64(x * 0.5)))))) / y);
	elseif (b <= 7.5e+30)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 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 <= -1.05)
		tmp = (x - (b * (x - (b * ((-0.16666666666666666 * (x * b)) + (x * 0.5)))))) / y;
	elseif (b <= 7.5e+30)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05], N[(N[(x - N[(b * N[(x - N[(b * N[(N[(-0.16666666666666666 * N[(x * b), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 7.5e+30], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.05000000000000004

   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 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0 67.6%

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

   if -1.05000000000000004 < b < 7.49999999999999973e30

   1. Initial program 96.1%

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

      1. associate-/l* 96.8%

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

      2. associate--l+ 96.8%

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

      3. exp-sum 80.9%

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

      4. associate-/l* 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 78.0%

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

      8. *-commutative 78.0%

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

      9. exp-to-pow 79.1%

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

      10. sub-neg 79.1%

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

      11. metadata-eval 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in y around 0 64.1%

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

      1. exp-to-pow 65.1%

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

      2. sub-neg 65.1%

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

      3. metadata-eval 65.1%

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

      4. associate-*r/ 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 34.7%

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

       1. distribute-rgt1-in 34.7%

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

   11. Simplified 34.7%

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

   12. Taylor expanded in b around inf 37.2%

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

       1. associate-/l* 40.8%

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

       2. distribute-lft-out 41.6%

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

   14. Simplified 41.6%

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

   if 7.49999999999999973e30 < b

   1. Initial program 100.0%

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

      1. associate-/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 82.7%

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

      4. associate-/l* 82.7%

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

      5. *-commutative 82.7%

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

      6. exp-to-pow 82.7%

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

      7. exp-diff 59.6%

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

      8. *-commutative 59.6%

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

      9. exp-to-pow 59.6%

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

      10. sub-neg 59.6%

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

      11. metadata-eval 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. exp-to-pow 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-*r/ 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 88.6%

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

   9. Taylor expanded in b around 0 77.5%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 77.5%

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

   11. Simplified 77.5%

       \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05:\\ \;\;\;\;\frac{x - b \cdot \left(x - b \cdot \left(-0.16666666666666666 \cdot \left(x \cdot b\right) + x \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 55.8% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.00085:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.00085)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666))))))) y)
   (if (<= b 5.5e+29)
     (/ x (* b (* a (+ y (/ y b)))))
     (/
      x
      (*
       a
       (*
        y
        (- 1.0 (* b (- -1.0 (* b (+ 0.5 (* b 0.16666666666666666))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.00085) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else if (b <= 5.5e+29) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (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 <= (-0.00085d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0)))))))) / y
    else if (b <= 5.5d+29) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * (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 <= -0.00085) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else if (b <= 5.5e+29) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.00085:
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y
	elif b <= 5.5e+29:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.00085)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))))) / y);
	elseif (b <= 5.5e+29)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 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 <= -0.00085)
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	elseif (b <= 5.5e+29)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * (0.5 + (b * 0.16666666666666666))))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.00085], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5.5e+29], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * N[(0.5 + N[(b * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.49999999999999953e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0 67.6%

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

   if -8.49999999999999953e-4 < b < 5.5e29

   1. Initial program 96.1%

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

      1. associate-/l* 96.8%

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

      2. associate--l+ 96.8%

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

      3. exp-sum 80.9%

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

      4. associate-/l* 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 78.0%

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

      8. *-commutative 78.0%

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

      9. exp-to-pow 79.1%

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

      10. sub-neg 79.1%

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

      11. metadata-eval 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in y around 0 64.1%

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

      1. exp-to-pow 65.1%

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

      2. sub-neg 65.1%

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

      3. metadata-eval 65.1%

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

      4. associate-*r/ 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 34.7%

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

       1. distribute-rgt1-in 34.7%

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

   11. Simplified 34.7%

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

   12. Taylor expanded in b around inf 37.2%

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

       1. associate-/l* 40.8%

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

       2. distribute-lft-out 41.6%

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

   14. Simplified 41.6%

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

   if 5.5e29 < b

   1. Initial program 100.0%

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

      1. associate-/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 82.7%

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

      4. associate-/l* 82.7%

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

      5. *-commutative 82.7%

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

      6. exp-to-pow 82.7%

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

      7. exp-diff 59.6%

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

      8. *-commutative 59.6%

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

      9. exp-to-pow 59.6%

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

      10. sub-neg 59.6%

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

      11. metadata-eval 59.6%

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

   3. Simplified 59.6%

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

   5. Taylor expanded in y around 0 69.2%

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

      1. exp-to-pow 69.2%

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

      2. sub-neg 69.2%

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

      3. metadata-eval 69.2%

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

      4. associate-*r/ 73.1%

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

   7. Simplified 73.1%

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

   8. Taylor expanded in t around 0 88.6%

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

   9. Taylor expanded in b around 0 77.5%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + 0.16666666666666666 \cdot b\right)\right)\right)}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 77.5%

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

   11. Simplified 77.5%

       \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.00085:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot \left(0.5 + b \cdot 0.16666666666666666\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 52.7% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -62:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -62.0)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b (+ 0.5 (* b -0.16666666666666666))))))) y)
   (if (<= b 4.1e-18)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ (/ (/ x a) (+ 1.0 (* b (+ 1.0 (* b 0.5))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -62.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else if (b <= 4.1e-18) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-62.0d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * (0.5d0 + (b * (-0.16666666666666666d0)))))))) / y
    else if (b <= 4.1d-18) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = ((x / a) / (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -62.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	} else if (b <= 4.1e-18) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -62.0:
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y
	elif b <= 4.1e-18:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -62.0)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(0.5 + Float64(b * -0.16666666666666666))))))) / y);
	elseif (b <= 4.1e-18)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(Float64(x / a) / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -62.0)
		tmp = (x * (1.0 + (b * (-1.0 + (b * (0.5 + (b * -0.16666666666666666))))))) / y;
	elseif (b <= 4.1e-18)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -62.0], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(0.5 + N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.1e-18], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] / N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -62

   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 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0 67.6%

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

   if -62 < b < 4.0999999999999998e-18

   1. Initial program 95.7%

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

      1. associate-/l* 97.2%

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

      2. associate--l+ 97.2%

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

      3. exp-sum 81.8%

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

      4. associate-/l* 80.2%

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

      5. *-commutative 80.2%

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

      6. exp-to-pow 80.2%

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

      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 81.4%

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

      10. sub-neg 81.4%

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

      11. metadata-eval 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. exp-to-pow 66.7%

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

      2. sub-neg 66.7%

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

      3. metadata-eval 66.7%

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

      4. associate-*r/ 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around 0 36.6%

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

   9. Taylor expanded in b around 0 36.6%

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

       1. distribute-rgt1-in 36.6%

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

   11. Simplified 36.6%

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

   12. Taylor expanded in b around inf 39.4%

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

       1. associate-/l* 43.5%

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

       2. distribute-lft-out 44.3%

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

   14. Simplified 44.3%

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

   if 4.0999999999999998e-18 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 89.6%

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

      1. div-exp 68.3%

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

      2. exp-to-pow 68.4%

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

      3. sub-neg 68.4%

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

      4. metadata-eval 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in t around 0 79.3%

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

      1. associate-/r* 73.2%

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

   8. Simplified 73.2%

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

   9. Taylor expanded in b around 0 59.9%

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

       1. *-commutative 59.9%

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

   11. Simplified 59.9%

       \[\leadsto \frac{\frac{\frac{x}{a}}{\color{blue}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -62:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(0.5 + b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.7% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -0.0012:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -0.0012)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b (* b -0.16666666666666666)))))) y)
   (if (<= b 3.4e-16)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ (/ (/ x a) (+ 1.0 (* b (+ 1.0 (* b 0.5))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0012) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y;
	} else if (b <= 3.4e-16) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-0.0012d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * (b * (-0.16666666666666666d0))))))) / y
    else if (b <= 3.4d-16) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = ((x / a) / (1.0d0 + (b * (1.0d0 + (b * 0.5d0))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -0.0012) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y;
	} else if (b <= 3.4e-16) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -0.0012:
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y
	elif b <= 3.4e-16:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -0.0012)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(b * -0.16666666666666666)))))) / y);
	elseif (b <= 3.4e-16)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(Float64(x / a) / Float64(1.0 + Float64(b * Float64(1.0 + Float64(b * 0.5))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -0.0012)
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y;
	elseif (b <= 3.4e-16)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = ((x / a) / (1.0 + (b * (1.0 + (b * 0.5))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -0.0012], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.4e-16], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] / N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -0.00119999999999999989

   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 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0 67.6%

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

   10. Taylor expanded in b around inf 67.6%

       \[\leadsto \frac{x \cdot \left(1 + b \cdot \left(b \cdot \color{blue}{\left(-0.16666666666666666 \cdot b\right)} - 1\right)\right)}{y} \]
   11. Step-by-step derivation

       1. *-commutative 67.6%

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

   12. Simplified 67.6%

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

   if -0.00119999999999999989 < b < 3.4e-16

   1. Initial program 95.7%

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

      1. associate-/l* 97.2%

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

      2. associate--l+ 97.2%

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

      3. exp-sum 81.8%

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

      4. associate-/l* 80.2%

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

      5. *-commutative 80.2%

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

      6. exp-to-pow 80.2%

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

      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 81.4%

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

      10. sub-neg 81.4%

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

      11. metadata-eval 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in y around 0 65.6%

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

      1. exp-to-pow 66.7%

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

      2. sub-neg 66.7%

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

      3. metadata-eval 66.7%

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

      4. associate-*r/ 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around 0 36.6%

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

   9. Taylor expanded in b around 0 36.6%

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

       1. distribute-rgt1-in 36.6%

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

   11. Simplified 36.6%

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

   12. Taylor expanded in b around inf 39.4%

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

       1. associate-/l* 43.5%

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

       2. distribute-lft-out 44.3%

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

   14. Simplified 44.3%

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

   if 3.4e-16 < b

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 89.6%

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

      1. div-exp 68.3%

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

      2. exp-to-pow 68.4%

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

      3. sub-neg 68.4%

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

      4. metadata-eval 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in t around 0 79.3%

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

      1. associate-/r* 73.2%

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

   8. Simplified 73.2%

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

   9. Taylor expanded in b around 0 59.9%

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

       1. *-commutative 59.9%

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

   11. Simplified 59.9%

       \[\leadsto \frac{\frac{\frac{x}{a}}{\color{blue}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -0.0012:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{1 + b \cdot \left(1 + b \cdot 0.5\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 54.1% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.2:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.2)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b (* b -0.16666666666666666)))))) y)
   (if (<= b 3.6e+30)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.2) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y;
	} else if (b <= 3.6e+30) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 + (b * (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 <= (-7.2d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * (b * (-0.16666666666666666d0))))))) / y
    else if (b <= 3.6d+30) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (a * (y * (1.0d0 + (b * (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 <= -7.2) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y;
	} else if (b <= 3.6e+30) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.2:
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y
	elif b <= 3.6e+30:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.2)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * Float64(b * -0.16666666666666666)))))) / y);
	elseif (b <= 3.6e+30)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * 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 <= -7.2)
		tmp = (x * (1.0 + (b * (-1.0 + (b * (b * -0.16666666666666666)))))) / y;
	elseif (b <= 3.6e+30)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.2], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * N[(b * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.6e+30], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.20000000000000018

   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 89.6%

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

      1. +-commutative 89.6%

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

      2. mul-1-neg 89.6%

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

      3. unsub-neg 89.6%

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

   5. Simplified 89.6%

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

   6. Taylor expanded in b around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   8. Simplified 79.1%

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

   9. Taylor expanded in b around 0 67.6%

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

   10. Taylor expanded in b around inf 67.6%

       \[\leadsto \frac{x \cdot \left(1 + b \cdot \left(b \cdot \color{blue}{\left(-0.16666666666666666 \cdot b\right)} - 1\right)\right)}{y} \]
   11. Step-by-step derivation

       1. *-commutative 67.6%

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

   12. Simplified 67.6%

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

   if -7.20000000000000018 < b < 3.6000000000000002e30

   1. Initial program 96.1%

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

      1. associate-/l* 96.8%

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

      2. associate--l+ 96.8%

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

      3. exp-sum 80.9%

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

      4. associate-/l* 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 78.0%

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

      8. *-commutative 78.0%

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

      9. exp-to-pow 79.1%

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

      10. sub-neg 79.1%

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

      11. metadata-eval 79.1%

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

   3. Simplified 79.1%

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

   5. Taylor expanded in y around 0 64.1%

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

      1. exp-to-pow 65.1%

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

      2. sub-neg 65.1%

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

      3. metadata-eval 65.1%

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

      4. associate-*r/ 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in t around 0 36.1%

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

   9. Taylor expanded in b around 0 34.7%

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

       1. distribute-rgt1-in 34.7%

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

   11. Simplified 34.7%

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

   12. Taylor expanded in b around inf 37.2%

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

       1. associate-/l* 40.8%

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

       2. distribute-lft-out 41.6%

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

   14. Simplified 41.6%

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

   if 3.6000000000000002e30 < b

   1. Initial program 100.0%

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

      1. associate-/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 82.7%

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

      4. associate-/l* 82.7%

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

      5. *-commutative 82.7%

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

      6. exp-to-pow 82.7%

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

      7. exp-diff 59.6%

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

      8. *-commutative 59.6%

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

      9. exp-to-pow 59.6%

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

      10. sub-neg 59.6%

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

      11. metadata-eval 59.6%

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

   3. Simplified 59.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 69.2%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 69.2%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 69.2%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 73.1%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 73.1%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 88.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 69.4%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 67.7%

          \[\leadsto \frac{\frac{\frac{x}{a}}{1 + b \cdot \left(1 + \color{blue}{b \cdot 0.5}\right)}}{y} \]

   11. Simplified 69.4%

       \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot \left(b \cdot -0.16666666666666666\right)\right)\right)}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.5% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -30:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -30.0)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b 0.5))))) y)
   (if (<= b 1.95e+30)
     (/ x (* b (* a (+ y (/ y b)))))
     (/ x (* a (* y (+ 1.0 (* b (+ 1.0 (* b 0.5))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -30.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= 1.95e+30) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 + (b * (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 <= (-30.0d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0))))) / y
    else if (b <= 1.95d+30) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = x / (a * (y * (1.0d0 + (b * (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 <= -30.0) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= 1.95e+30) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -30.0:
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y
	elif b <= 1.95e+30:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -30.0)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5))))) / y);
	elseif (b <= 1.95e+30)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 + Float64(b * 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 <= -30.0)
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	elseif (b <= 1.95e+30)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = x / (a * (y * (1.0 + (b * (1.0 + (b * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -30.0], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.95e+30], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * N[(1.0 + N[(b * N[(1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -30

   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 89.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 89.6%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 89.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 89.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around inf 79.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. neg-mul-1 79.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 79.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   9. Taylor expanded in b around 0 64.9%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(0.5 \cdot b - 1\right)\right)}}{y} \]

   if -30 < b < 1.95000000000000005e30

   1. Initial program 96.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.8%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.8%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 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 78.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 78.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 79.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 79.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 79.1%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 79.1%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 64.1%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 65.1%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 65.1%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 65.1%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 64.5%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 64.5%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 36.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.7%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 34.7%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 34.7%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 37.2%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 40.8%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 41.6%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 41.6%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 1.95000000000000005e30 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/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 82.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 59.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 59.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 59.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 59.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 59.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 59.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 69.2%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 69.2%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 69.2%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 73.1%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 73.1%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 88.6%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 69.4%

      \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 67.7%

          \[\leadsto \frac{\frac{\frac{x}{a}}{1 + b \cdot \left(1 + \color{blue}{b \cdot 0.5}\right)}}{y} \]

   11. Simplified 69.4%

       \[\leadsto \frac{x}{a \cdot \left(y \cdot \color{blue}{\left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -30:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 47.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.8:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.8)
   (/ (* x (+ 1.0 (* b (+ -1.0 (* b 0.5))))) y)
   (if (<= b 2.9e-38) (/ x (* b (* a (+ y (/ y b))))) (/ (/ (/ x b) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= 2.9e-38) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.8d0)) then
        tmp = (x * (1.0d0 + (b * ((-1.0d0) + (b * 0.5d0))))) / y
    else if (b <= 2.9d-38) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = ((x / b) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.8) {
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	} else if (b <= 2.9e-38) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.8:
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y
	elif b <= 2.9e-38:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = ((x / b) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.8)
		tmp = Float64(Float64(x * Float64(1.0 + Float64(b * Float64(-1.0 + Float64(b * 0.5))))) / y);
	elseif (b <= 2.9e-38)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(Float64(x / b) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.8)
		tmp = (x * (1.0 + (b * (-1.0 + (b * 0.5))))) / y;
	elseif (b <= 2.9e-38)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = ((x / b) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.8], N[(N[(x * N[(1.0 + N[(b * N[(-1.0 + N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.9e-38], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.79999999999999982

   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 89.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 89.6%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 89.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 89.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around inf 79.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. neg-mul-1 79.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 79.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   9. Taylor expanded in b around 0 64.9%

      \[\leadsto \frac{x \cdot \color{blue}{\left(1 + b \cdot \left(0.5 \cdot b - 1\right)\right)}}{y} \]

   if -4.79999999999999982 < b < 2.89999999999999994e-38

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 67.8%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 67.8%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 67.8%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 67.8%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 67.8%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 37.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 37.3%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 37.3%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 40.3%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 44.6%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 45.5%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 45.5%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 2.89999999999999994e-38 < b

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 81.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      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 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.4%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 71.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 31.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 31.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 29.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 33.6%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. associate-/r* 38.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot b}}{y}} \]

       3. *-commutative 38.7%

          \[\leadsto \frac{\frac{x}{\color{blue}{b \cdot a}}}{y} \]

       4. associate-/r* 41.7%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{b}}{a}}}{y} \]

   14. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{b}}{a}}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8:\\ \;\;\;\;\frac{x \cdot \left(1 + b \cdot \left(-1 + b \cdot 0.5\right)\right)}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -25000:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -25000.0)
   (/ (- (/ x a) (* b (/ x a))) y)
   (if (<= b 3.1e-38) (/ x (* b (* a (+ y (/ y b))))) (/ (/ (/ x b) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -25000.0) {
		tmp = ((x / a) - (b * (x / a))) / y;
	} else if (b <= 3.1e-38) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-25000.0d0)) then
        tmp = ((x / a) - (b * (x / a))) / y
    else if (b <= 3.1d-38) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = ((x / b) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -25000.0) {
		tmp = ((x / a) - (b * (x / a))) / y;
	} else if (b <= 3.1e-38) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -25000.0:
		tmp = ((x / a) - (b * (x / a))) / y
	elif b <= 3.1e-38:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = ((x / b) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -25000.0)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(x / a))) / y);
	elseif (b <= 3.1e-38)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(Float64(x / b) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -25000.0)
		tmp = ((x / a) - (b * (x / a))) / y;
	elseif (b <= 3.1e-38)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = ((x / b) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -25000.0], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.1e-38], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -25000

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 84.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 63.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 63.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 63.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 63.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 63.2%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 78.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   7. Step-by-step derivation

      1. associate-/r* 64.9%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   8. Simplified 64.9%

      \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 42.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   10. Step-by-step derivation

       1. +-commutative 42.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

       2. mul-1-neg 42.0%

          \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

       3. unsub-neg 42.0%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

       4. associate-/l* 40.4%

          \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   11. Simplified 40.4%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   if -25000 < b < 3.09999999999999983e-38

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.9%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 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 80.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 67.2%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 67.2%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 67.2%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 67.2%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 67.2%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 37.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 37.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 37.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 39.9%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 44.2%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 45.1%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 45.1%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 3.09999999999999983e-38 < b

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 81.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      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 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.4%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 71.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 31.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 31.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 29.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 33.6%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. associate-/r* 38.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot b}}{y}} \]

       3. *-commutative 38.7%

          \[\leadsto \frac{\frac{x}{\color{blue}{b \cdot a}}}{y} \]

       4. associate-/r* 41.7%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{b}}{a}}}{y} \]

   14. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{b}}{a}}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 20: 41.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -30:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -30.0)
   (/ (* x (- 1.0 b)) y)
   (if (<= b 2.9e-38) (/ x (* b (* a (+ y (/ y b))))) (/ (/ (/ x b) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -30.0) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 2.9e-38) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-30.0d0)) then
        tmp = (x * (1.0d0 - b)) / y
    else if (b <= 2.9d-38) then
        tmp = x / (b * (a * (y + (y / b))))
    else
        tmp = ((x / b) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -30.0) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 2.9e-38) {
		tmp = x / (b * (a * (y + (y / b))));
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -30.0:
		tmp = (x * (1.0 - b)) / y
	elif b <= 2.9e-38:
		tmp = x / (b * (a * (y + (y / b))))
	else:
		tmp = ((x / b) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -30.0)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	elseif (b <= 2.9e-38)
		tmp = Float64(x / Float64(b * Float64(a * Float64(y + Float64(y / b)))));
	else
		tmp = Float64(Float64(Float64(x / b) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -30.0)
		tmp = (x * (1.0 - b)) / y;
	elseif (b <= 2.9e-38)
		tmp = x / (b * (a * (y + (y / b))));
	else
		tmp = ((x / b) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -30.0], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.9e-38], N[(x / N[(b * N[(a * N[(y + N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -30

   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 89.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 89.6%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 89.6%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 89.6%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around inf 79.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. neg-mul-1 79.1%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 79.1%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   9. Taylor expanded in b around 0 35.7%

      \[\leadsto \frac{\color{blue}{x + -1 \cdot \left(b \cdot x\right)}}{y} \]
   10. Step-by-step derivation

       1. *-lft-identity 35.7%

          \[\leadsto \frac{\color{blue}{1 \cdot x} + -1 \cdot \left(b \cdot x\right)}{y} \]

       2. associate-*r* 35.7%

          \[\leadsto \frac{1 \cdot x + \color{blue}{\left(-1 \cdot b\right) \cdot x}}{y} \]

       3. distribute-rgt-out 35.7%

          \[\leadsto \frac{\color{blue}{x \cdot \left(1 + -1 \cdot b\right)}}{y} \]

       4. mul-1-neg 35.7%

          \[\leadsto \frac{x \cdot \left(1 + \color{blue}{\left(-b\right)}\right)}{y} \]

       5. unsub-neg 35.7%

          \[\leadsto \frac{x \cdot \color{blue}{\left(1 - b\right)}}{y} \]

   11. Simplified 35.7%

       \[\leadsto \frac{\color{blue}{x \cdot \left(1 - b\right)}}{y} \]

   if -30 < b < 2.89999999999999994e-38

   1. Initial program 95.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 80.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 80.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 80.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 80.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 80.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.7%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 67.8%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 67.8%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 67.8%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 67.8%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 67.8%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 37.3%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 37.3%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 37.3%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 37.3%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 40.3%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot y + \frac{a \cdot y}{b}\right)}} \]
   13. Step-by-step derivation

       1. associate-/l* 44.6%

          \[\leadsto \frac{x}{b \cdot \left(a \cdot y + \color{blue}{a \cdot \frac{y}{b}}\right)} \]

       2. distribute-lft-out 45.5%

          \[\leadsto \frac{x}{b \cdot \color{blue}{\left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   14. Simplified 45.5%

       \[\leadsto \frac{x}{\color{blue}{b \cdot \left(a \cdot \left(y + \frac{y}{b}\right)\right)}} \]

   if 2.89999999999999994e-38 < b

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 81.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      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 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.4%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 71.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 31.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 31.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 29.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 33.6%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. associate-/r* 38.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot b}}{y}} \]

       3. *-commutative 38.7%

          \[\leadsto \frac{\frac{x}{\color{blue}{b \cdot a}}}{y} \]

       4. associate-/r* 41.7%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{b}}{a}}}{y} \]

   14. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{b}}{a}}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 21: 38.6% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-14}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e+87)
   (/ (* x (- 1.0 b)) y)
   (if (<= b 2e-14) (/ (/ x a) y) (/ (/ (/ x b) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+87) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 2e-14) {
		tmp = (x / a) / y;
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.6d+87)) then
        tmp = (x * (1.0d0 - b)) / y
    else if (b <= 2d-14) then
        tmp = (x / a) / y
    else
        tmp = ((x / b) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e+87) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 2e-14) {
		tmp = (x / a) / y;
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.6e+87:
		tmp = (x * (1.0 - b)) / y
	elif b <= 2e-14:
		tmp = (x / a) / y
	else:
		tmp = ((x / b) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e+87)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	elseif (b <= 2e-14)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(Float64(Float64(x / b) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.6e+87)
		tmp = (x * (1.0 - b)) / y;
	elseif (b <= 2e-14)
		tmp = (x / a) / y;
	else
		tmp = ((x / b) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e+87], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2e-14], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.6e87

   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 91.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 91.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 91.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 91.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 91.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around inf 87.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. neg-mul-1 87.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 87.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   9. Taylor expanded in b around 0 43.8%

      \[\leadsto \frac{\color{blue}{x + -1 \cdot \left(b \cdot x\right)}}{y} \]
   10. Step-by-step derivation

       1. *-lft-identity 43.8%

          \[\leadsto \frac{\color{blue}{1 \cdot x} + -1 \cdot \left(b \cdot x\right)}{y} \]

       2. associate-*r* 43.8%

          \[\leadsto \frac{1 \cdot x + \color{blue}{\left(-1 \cdot b\right) \cdot x}}{y} \]

       3. distribute-rgt-out 43.8%

          \[\leadsto \frac{\color{blue}{x \cdot \left(1 + -1 \cdot b\right)}}{y} \]

       4. mul-1-neg 43.8%

          \[\leadsto \frac{x \cdot \left(1 + \color{blue}{\left(-b\right)}\right)}{y} \]

       5. unsub-neg 43.8%

          \[\leadsto \frac{x \cdot \color{blue}{\left(1 - b\right)}}{y} \]

   11. Simplified 43.8%

       \[\leadsto \frac{\color{blue}{x \cdot \left(1 - b\right)}}{y} \]

   if -1.6e87 < b < 2e-14

   1. Initial program 96.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.5%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 62.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 63.4%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 63.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 63.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 63.4%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 39.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   7. Step-by-step derivation

      1. associate-/r* 37.5%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   8. Simplified 37.5%

      \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 34.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 2e-14 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/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 82.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 60.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 66.8%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 66.8%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 66.8%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 66.8%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 70.0%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 70.0%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 79.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 32.6%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 32.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 32.6%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 32.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 37.0%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. associate-/r* 41.5%

          \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot b}}{y}} \]

       3. *-commutative 41.5%

          \[\leadsto \frac{\frac{x}{\color{blue}{b \cdot a}}}{y} \]

       4. associate-/r* 43.6%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{b}}{a}}}{y} \]

   14. Simplified 43.6%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{b}}{a}}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 22: 38.1% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot \left(1 - b\right)}{y}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.6e+93)
   (/ (* x (- 1.0 b)) y)
   (if (<= b 4.6e+27) (/ (/ x a) y) (/ x (* a (* y b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+93) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 4.6e+27) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.6d+93)) then
        tmp = (x * (1.0d0 - b)) / y
    else if (b <= 4.6d+27) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.6e+93) {
		tmp = (x * (1.0 - b)) / y;
	} else if (b <= 4.6e+27) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.6e+93:
		tmp = (x * (1.0 - b)) / y
	elif b <= 4.6e+27:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.6e+93)
		tmp = Float64(Float64(x * Float64(1.0 - b)) / y);
	elseif (b <= 4.6e+27)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.6e+93)
		tmp = (x * (1.0 - b)) / y;
	elseif (b <= 4.6e+27)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.6e+93], N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.6e+27], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.5999999999999999e93

   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 91.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 91.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 91.8%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 91.8%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 91.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around inf 87.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
   7. Step-by-step derivation

      1. neg-mul-1 87.7%

         \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   8. Simplified 87.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

   9. Taylor expanded in b around 0 43.8%

      \[\leadsto \frac{\color{blue}{x + -1 \cdot \left(b \cdot x\right)}}{y} \]
   10. Step-by-step derivation

       1. *-lft-identity 43.8%

          \[\leadsto \frac{\color{blue}{1 \cdot x} + -1 \cdot \left(b \cdot x\right)}{y} \]

       2. associate-*r* 43.8%

          \[\leadsto \frac{1 \cdot x + \color{blue}{\left(-1 \cdot b\right) \cdot x}}{y} \]

       3. distribute-rgt-out 43.8%

          \[\leadsto \frac{\color{blue}{x \cdot \left(1 + -1 \cdot b\right)}}{y} \]

       4. mul-1-neg 43.8%

          \[\leadsto \frac{x \cdot \left(1 + \color{blue}{\left(-b\right)}\right)}{y} \]

       5. unsub-neg 43.8%

          \[\leadsto \frac{x \cdot \color{blue}{\left(1 - b\right)}}{y} \]

   11. Simplified 43.8%

       \[\leadsto \frac{\color{blue}{x \cdot \left(1 - b\right)}}{y} \]

   if -3.5999999999999999e93 < b < 4.6000000000000001e27

   1. Initial program 96.6%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.3%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 62.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 63.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 63.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 63.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 63.2%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 39.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   7. Step-by-step derivation

      1. associate-/r* 37.7%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   8. Simplified 37.7%

      \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 34.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 4.6000000000000001e27 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/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 83.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 58.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 58.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 58.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 58.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 58.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 67.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 67.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 67.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 71.7%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 71.7%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 87.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.6%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 34.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 34.6%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 34.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 34.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 34.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 23: 38.6% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.1e-38) (* (/ x (* y a)) (- 1.0 b)) (/ (/ (/ x b) a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.1e-38) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.1d-38) then
        tmp = (x / (y * a)) * (1.0d0 - b)
    else
        tmp = ((x / b) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.1e-38) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = ((x / b) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.1e-38:
		tmp = (x / (y * a)) * (1.0 - b)
	else:
		tmp = ((x / b) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.1e-38)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(1.0 - b));
	else
		tmp = Float64(Float64(Float64(x / b) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.1e-38)
		tmp = (x / (y * a)) * (1.0 - b);
	else
		tmp = ((x / b) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.1e-38], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / b), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.09999999999999983e-38

   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* 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 76.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 75.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 75.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 75.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 69.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 69.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 69.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 69.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 69.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 62.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.0%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.0%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.0%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.8%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 65.8%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 52.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 25.9%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 25.9%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 25.9%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around 0 33.3%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 33.3%

          \[\leadsto \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} + \frac{x}{a \cdot y} \]

       2. remove-double-neg 33.3%

          \[\leadsto \left(-\frac{b \cdot x}{a \cdot y}\right) + \color{blue}{\left(-\left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. distribute-neg-out 33.3%

          \[\leadsto \color{blue}{-\left(\frac{b \cdot x}{a \cdot y} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       4. associate-/l* 30.1%

          \[\leadsto -\left(\color{blue}{b \cdot \frac{x}{a \cdot y}} + \left(-\frac{x}{a \cdot y}\right)\right) \]

       5. mul-1-neg 30.1%

          \[\leadsto -\left(b \cdot \frac{x}{a \cdot y} + \color{blue}{-1 \cdot \frac{x}{a \cdot y}}\right) \]

       6. distribute-rgt-out 35.6%

          \[\leadsto -\color{blue}{\frac{x}{a \cdot y} \cdot \left(b + -1\right)} \]

   14. Simplified 35.6%

       \[\leadsto \color{blue}{-\frac{x}{a \cdot y} \cdot \left(b + -1\right)} \]

   if 3.09999999999999983e-38 < b

   1. Initial program 99.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 81.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      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 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 63.6%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 63.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 65.4%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 65.4%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 71.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.0%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 31.0%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 31.0%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 29.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. associate-*r* 33.6%

          \[\leadsto \frac{x}{\color{blue}{\left(a \cdot b\right) \cdot y}} \]

       2. associate-/r* 38.7%

          \[\leadsto \color{blue}{\frac{\frac{x}{a \cdot b}}{y}} \]

       3. *-commutative 38.7%

          \[\leadsto \frac{\frac{x}{\color{blue}{b \cdot a}}}{y} \]

       4. associate-/r* 41.7%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{b}}{a}}}{y} \]

   14. Simplified 41.7%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{b}}{a}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{b}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 35.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.2 \cdot 10^{+26}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.2e+26) (/ (/ x a) y) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.2e+26) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.2d+26) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.2e+26) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.2e+26:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.2e+26)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.2e+26)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.2e+26], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.20000000000000002e26

   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 70.8%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 63.8%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 64.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 64.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 64.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 64.5%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 51.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   7. Step-by-step derivation

      1. associate-/r* 46.1%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   8. Simplified 46.1%

      \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 32.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 1.20000000000000002e26 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/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 83.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 58.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 58.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 58.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 58.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 58.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 58.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.9%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 67.9%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 67.9%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 67.9%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 71.7%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 71.7%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 87.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.6%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
   10. Step-by-step derivation

       1. distribute-rgt1-in 34.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   11. Simplified 34.6%

       \[\leadsto \frac{x}{a \cdot \color{blue}{\left(\left(b + 1\right) \cdot y\right)}} \]

   12. Taylor expanded in b around inf 34.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(b \cdot y\right)}} \]
   13. Step-by-step derivation

       1. *-commutative 34.6%

          \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} \]

   14. Simplified 34.6%

       \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 25: 32.5% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 4.1 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 4.1e-69) (/ (/ x a) y) (* x (/ 1.0 (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4.1e-69) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 4.1d-69) then
        tmp = (x / a) / y
    else
        tmp = x * (1.0d0 / (y * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 4.1e-69) {
		tmp = (x / a) / y;
	} else {
		tmp = x * (1.0 / (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 4.1e-69:
		tmp = (x / a) / y
	else:
		tmp = x * (1.0 / (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 4.1e-69)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 4.1e-69)
		tmp = (x / a) / y;
	else
		tmp = x * (1.0 / (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 4.1e-69], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 4.0999999999999999e-69

   1. Initial program 99.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 63.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 63.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 63.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 63.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 63.9%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 66.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   7. Step-by-step derivation

      1. associate-/r* 62.4%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   8. Simplified 62.4%

      \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 34.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 4.0999999999999999e-69 < a

   1. Initial program 96.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 76.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. +-commutative 76.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

      2. mul-1-neg 76.9%

         \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

      3. unsub-neg 76.9%

         \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

   5. Simplified 76.9%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

   6. Taylor expanded in b around 0 53.2%

      \[\leadsto \color{blue}{\frac{x \cdot e^{y \cdot \log z - \log a}}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 55.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{y \cdot \log z - \log a}}{y}} \]

      2. div-exp 55.6%

         \[\leadsto x \cdot \frac{\color{blue}{\frac{e^{y \cdot \log z}}{e^{\log a}}}}{y} \]

      3. *-commutative 55.6%

         \[\leadsto x \cdot \frac{\frac{e^{\color{blue}{\log z \cdot y}}}{e^{\log a}}}{y} \]

      4. exp-to-pow 55.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{z}^{y}}}{e^{\log a}}}{y} \]

      5. rem-exp-log 56.5%

         \[\leadsto x \cdot \frac{\frac{{z}^{y}}{\color{blue}{a}}}{y} \]

   8. Simplified 56.5%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{{z}^{y}}{a}}{y}} \]

   9. Taylor expanded in y around 0 30.8%

      \[\leadsto x \cdot \color{blue}{\frac{1}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 4.1 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 32.3% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 6.2e+123) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 6.2e+123) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 6.2d+123) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 6.2e+123) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 6.2e+123:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 6.2e+123)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 6.2e+123)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 6.2e+123], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 6.20000000000000013e123

   1. Initial program 99.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.0%

      \[\leadsto \frac{\color{blue}{x \cdot e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 65.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 65.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 65.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 65.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 65.6%

      \[\leadsto \frac{\color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 57.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]
   7. Step-by-step derivation

      1. associate-/r* 53.4%

         \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   8. Simplified 53.4%

      \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   9. Taylor expanded in b around 0 29.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a}}}{y} \]

   if 6.20000000000000013e123 < a

   1. Initial program 93.5%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 73.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 72.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 72.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 72.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 63.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 63.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 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 63.4%

      \[\leadsto \color{blue}{\frac{x \cdot e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. exp-to-pow 64.3%

         \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

      2. sub-neg 64.3%

         \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

      3. metadata-eval 64.3%

         \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

      4. associate-*r/ 72.5%

         \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   7. Simplified 72.5%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

   8. Taylor expanded in t around 0 67.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 39.3%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 6.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 30.8% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 97.9%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.3%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.3%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 77.6%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 76.4%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 76.4%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 76.4%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 66.6%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 66.6%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 67.2%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 67.2%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 67.2%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 67.2%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
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 63.3%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y \cdot e^{b}} \]

   2. sub-neg 63.3%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y \cdot e^{b}} \]

   3. metadata-eval 63.3%

      \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y \cdot e^{b}} \]

   4. associate-*r/ 65.7%

      \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

7. Simplified 65.7%

   \[\leadsto \color{blue}{x \cdot \frac{{a}^{\left(t + -1\right)}}{y \cdot e^{b}}} \]

8. Taylor expanded in t around 0 57.9%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 28.7%

   \[\leadsto \frac{x}{\color{blue}{a \cdot y}} \]

10. Final simplification 28.7%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Alternative 28: 16.2% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{x}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (/ y x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (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 / (y / x)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / x);
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (y / x)

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(y / x))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / (y / x);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

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 t around 0 80.4%

   \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
4. Step-by-step derivation

   1. +-commutative 80.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

   2. mul-1-neg 80.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   3. unsub-neg 80.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

5. Simplified 80.4%

   \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

6. Taylor expanded in b around inf 45.7%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
7. Step-by-step derivation

   1. neg-mul-1 45.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

8. Simplified 45.7%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

9. Taylor expanded in b around 0 13.6%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
10. Step-by-step derivation

    1. clear-num 14.3%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

    2. inv-pow 14.3%

       \[\leadsto \color{blue}{{\left(\frac{y}{x}\right)}^{-1}} \]

11. Applied egg-rr 14.3%

    \[\leadsto \color{blue}{{\left(\frac{y}{x}\right)}^{-1}} \]
12. Step-by-step derivation

    1. unpow-1 14.3%

       \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]

13. Simplified 14.3%

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \]
14. Add Preprocessing

Alternative 29: 16.0% accurate, 105.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x y))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / 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 / y
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / y;
}

Python

def code(x, y, z, t, a, b):
	return x / y

Julia

function code(x, y, z, t, a, b)
	return Float64(x / y)
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / y;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / y), $MachinePrecision]

Derivation

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 t around 0 80.4%

   \[\leadsto \frac{\color{blue}{x \cdot e^{\left(-1 \cdot \log a + y \cdot \log z\right) - b}}}{y} \]
4. Step-by-step derivation

   1. +-commutative 80.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z + -1 \cdot \log a\right)} - b}}{y} \]

   2. mul-1-neg 80.4%

      \[\leadsto \frac{x \cdot e^{\left(y \cdot \log z + \color{blue}{\left(-\log a\right)}\right) - b}}{y} \]

   3. unsub-neg 80.4%

      \[\leadsto \frac{x \cdot e^{\color{blue}{\left(y \cdot \log z - \log a\right)} - b}}{y} \]

5. Simplified 80.4%

   \[\leadsto \frac{\color{blue}{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}}{y} \]

6. Taylor expanded in b around inf 45.7%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-1 \cdot b}}}{y} \]
7. Step-by-step derivation

   1. neg-mul-1 45.7%

      \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

8. Simplified 45.7%

   \[\leadsto \frac{x \cdot e^{\color{blue}{-b}}}{y} \]

9. Taylor expanded in b around 0 13.6%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
10. Add Preprocessing

Developer Target 1: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024185 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -8845848504127471/10000000000000000) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))) (if (< t 8520312288374073/10000000000) (/ (* (/ x y) (pow a (- t 1))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1)) y)) (- (+ b 1) (* y (log z)))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))