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

Percentage Accurate: 98.5% → 98.5%

Time: 22.7s

Alternatives: 24

Speedup: 1.0×

• 47.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Final simplification 98.3%

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

Alternative 2: 92.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+26} \lor \neg \left(t \leq 5.9 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -9.5e+26) (not (<= t 5.9e+84)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e+26) || !(t <= 5.9e+84)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-9.5d+26)) .or. (.not. (t <= 5.9d+84))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -9.5e+26) || !(t <= 5.9e+84)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -9.5e+26) or not (t <= 5.9e+84):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -9.5e+26) || !(t <= 5.9e+84))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -9.5e+26) || ~((t <= 5.9e+84)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -9.5e+26], N[Not[LessEqual[t, 5.9e+84]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.50000000000000054e26 or 5.89999999999999984e84 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.9%

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

   if -9.50000000000000054e26 < t < 5.89999999999999984e84

   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 t around 0 95.2%

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

      1. +-commutative 95.2%

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

      2. mul-1-neg 95.2%

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

      3. unsub-neg 95.2%

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

   5. Simplified 95.2%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+26} \lor \neg \left(t \leq 5.9 \cdot 10^{+84}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+132} \lor \neg \left(y \leq 5.8 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.4e+132) (not (<= y 5.8e+57)))
   (/ (/ (* 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 <= -5.4e+132) || !(y <= 5.8e+57)) {
		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 <= (-5.4d+132)) .or. (.not. (y <= 5.8d+57))) 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 <= -5.4e+132) || !(y <= 5.8e+57)) {
		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 <= -5.4e+132) or not (y <= 5.8e+57):
		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 <= -5.4e+132) || !(y <= 5.8e+57))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.4e+132) || ~((y <= 5.8e+57)))
		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, -5.4e+132], N[Not[LessEqual[y, 5.8e+57]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.3999999999999999e132 or 5.8000000000000003e57 < 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 b around 0 94.2%

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

      1. exp-sum 73.0%

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

      2. *-commutative 73.0%

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

      3. exp-to-pow 73.0%

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

      4. exp-to-pow 73.0%

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

      5. sub-neg 73.0%

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

      6. metadata-eval 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in t around 0 88.4%

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

   if -5.3999999999999999e132 < y < 5.8000000000000003e57

   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 91.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+132} \lor \neg \left(y \leq 5.8 \cdot 10^{+57}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 36000\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.4) (not (<= y 36000.0)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (/ (/ (pow a t) a) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4) || !(y <= 36000.0)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * ((pow(a, t) / a) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.4d0)) .or. (.not. (y <= 36000.0d0))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * (((a ** t) / a) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.4) || !(y <= 36000.0)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * ((Math.pow(a, t) / a) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.4) or not (y <= 36000.0):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * ((math.pow(a, t) / a) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.4) || !(y <= 36000.0))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * Float64(Float64((a ^ t) / a) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.4) || ~((y <= 36000.0)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * (((a ^ t) / a) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.4], N[Not[LessEqual[y, 36000.0]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[(N[Power[a, t], $MachinePrecision] / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3999999999999999 or 36000 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in b around 0 90.0%

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

      1. exp-sum 69.1%

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

      2. *-commutative 69.1%

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

      3. exp-to-pow 69.2%

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

      4. exp-to-pow 69.2%

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

      5. sub-neg 69.2%

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

      6. metadata-eval 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in t around 0 80.3%

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

   if -1.3999999999999999 < y < 36000

   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 96.8%

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

      1. div-exp 85.0%

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

      2. exp-to-pow 85.9%

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

      3. sub-neg 85.9%

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

      4. metadata-eval 85.9%

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

   5. Simplified 85.9%

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

      1. unpow-prod-up 85.9%

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

      2. unpow-1 85.9%

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

   7. Applied egg-rr 85.9%

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

      1. associate-*r/ 85.9%

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

      2. *-rgt-identity 85.9%

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

   9. Simplified 85.9%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \lor \neg \left(y \leq 36000\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{\frac{{a}^{t}}{a}}{e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -5.5e+24)
     t_1
     (if (<= t 4.1e-162)
       (* (/ x a) (/ (pow z y) (* y (exp b))))
       (if (<= t 7.8e-105)
         (/ (/ (* x (pow z y)) a) y)
         (if (<= t 1.65e+28) (/ (/ x (* a (exp b))) y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -5.5e+24) {
		tmp = t_1;
	} else if (t <= 4.1e-162) {
		tmp = (x / a) * (pow(z, y) / (y * exp(b)));
	} else if (t <= 7.8e-105) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (t <= 1.65e+28) {
		tmp = (x / (a * exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-5.5d+24)) then
        tmp = t_1
    else if (t <= 4.1d-162) then
        tmp = (x / a) * ((z ** y) / (y * exp(b)))
    else if (t <= 7.8d-105) then
        tmp = ((x * (z ** y)) / a) / y
    else if (t <= 1.65d+28) then
        tmp = (x / (a * exp(b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -5.5e+24) {
		tmp = t_1;
	} else if (t <= 4.1e-162) {
		tmp = (x / a) * (Math.pow(z, y) / (y * Math.exp(b)));
	} else if (t <= 7.8e-105) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (t <= 1.65e+28) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -5.5e+24:
		tmp = t_1
	elif t <= 4.1e-162:
		tmp = (x / a) * (math.pow(z, y) / (y * math.exp(b)))
	elif t <= 7.8e-105:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif t <= 1.65e+28:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -5.5e+24)
		tmp = t_1;
	elseif (t <= 4.1e-162)
		tmp = Float64(Float64(x / a) * Float64((z ^ y) / Float64(y * exp(b))));
	elseif (t <= 7.8e-105)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (t <= 1.65e+28)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -5.5e+24)
		tmp = t_1;
	elseif (t <= 4.1e-162)
		tmp = (x / a) * ((z ^ y) / (y * exp(b)));
	elseif (t <= 7.8e-105)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (t <= 1.65e+28)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -5.5e+24], t$95$1, If[LessEqual[t, 4.1e-162], N[(N[(x / a), $MachinePrecision] * N[(N[Power[z, y], $MachinePrecision] / N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.8e-105], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 1.65e+28], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.5000000000000002e24 or 1.65e28 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.1%

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

   4. Taylor expanded in b around 0 86.5%

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

      1. exp-to-pow 86.5%

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

      2. sub-neg 86.5%

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

      3. metadata-eval 86.5%

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

      4. +-commutative 86.5%

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

   6. Simplified 86.5%

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

   if -5.5000000000000002e24 < t < 4.10000000000000019e-162

   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* 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* 80.9%

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

      5. *-commutative 80.9%

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

      6. exp-to-pow 80.9%

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

      7. exp-diff 79.8%

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

      8. *-commutative 79.8%

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

      9. exp-to-pow 81.0%

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

      10. sub-neg 81.0%

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

      11. metadata-eval 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in t around 0 84.2%

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

      1. times-frac 78.8%

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

   7. Simplified 78.8%

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

   if 4.10000000000000019e-162 < t < 7.8e-105

   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 b around 0 89.1%

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

      1. exp-sum 89.1%

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

      2. *-commutative 89.1%

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

      3. exp-to-pow 89.1%

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

      4. exp-to-pow 89.1%

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

      5. sub-neg 89.1%

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

      6. metadata-eval 89.1%

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

   5. Simplified 89.1%

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

   6. Taylor expanded in t around 0 89.1%

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

   if 7.8e-105 < t < 1.65e28

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. div-exp 87.4%

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

      2. exp-to-pow 88.6%

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

      3. sub-neg 88.6%

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

      4. metadata-eval 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in t around 0 90.5%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-105}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.6% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ t_2 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_3 := \frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-235}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-303}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-162}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y))
        (t_2 (/ (* x (pow a (+ t -1.0))) y))
        (t_3 (/ x (* (exp b) (* y a)))))
   (if (<= t -3.9e+24)
     t_2
     (if (<= t -2.8e-235)
       t_1
       (if (<= t 1.25e-303)
         t_3
         (if (<= t 6.5e-237)
           t_1
           (if (<= t 2.1e-162)
             t_3
             (if (<= t 3.2e-106)
               t_1
               (if (<= t 1.82e+28) (/ (/ x (* a (exp b))) y) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double t_2 = (x * pow(a, (t + -1.0))) / y;
	double t_3 = x / (exp(b) * (y * a));
	double tmp;
	if (t <= -3.9e+24) {
		tmp = t_2;
	} else if (t <= -2.8e-235) {
		tmp = t_1;
	} else if (t <= 1.25e-303) {
		tmp = t_3;
	} else if (t <= 6.5e-237) {
		tmp = t_1;
	} else if (t <= 2.1e-162) {
		tmp = t_3;
	} else if (t <= 3.2e-106) {
		tmp = t_1;
	} else if (t <= 1.82e+28) {
		tmp = (x / (a * exp(b))) / 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 * (z ** y)) / a) / y
    t_2 = (x * (a ** (t + (-1.0d0)))) / y
    t_3 = x / (exp(b) * (y * a))
    if (t <= (-3.9d+24)) then
        tmp = t_2
    else if (t <= (-2.8d-235)) then
        tmp = t_1
    else if (t <= 1.25d-303) then
        tmp = t_3
    else if (t <= 6.5d-237) then
        tmp = t_1
    else if (t <= 2.1d-162) then
        tmp = t_3
    else if (t <= 3.2d-106) then
        tmp = t_1
    else if (t <= 1.82d+28) then
        tmp = (x / (a * exp(b))) / 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 * Math.pow(z, y)) / a) / y;
	double t_2 = (x * Math.pow(a, (t + -1.0))) / y;
	double t_3 = x / (Math.exp(b) * (y * a));
	double tmp;
	if (t <= -3.9e+24) {
		tmp = t_2;
	} else if (t <= -2.8e-235) {
		tmp = t_1;
	} else if (t <= 1.25e-303) {
		tmp = t_3;
	} else if (t <= 6.5e-237) {
		tmp = t_1;
	} else if (t <= 2.1e-162) {
		tmp = t_3;
	} else if (t <= 3.2e-106) {
		tmp = t_1;
	} else if (t <= 1.82e+28) {
		tmp = (x / (a * Math.exp(b))) / y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	t_2 = (x * math.pow(a, (t + -1.0))) / y
	t_3 = x / (math.exp(b) * (y * a))
	tmp = 0
	if t <= -3.9e+24:
		tmp = t_2
	elif t <= -2.8e-235:
		tmp = t_1
	elif t <= 1.25e-303:
		tmp = t_3
	elif t <= 6.5e-237:
		tmp = t_1
	elif t <= 2.1e-162:
		tmp = t_3
	elif t <= 3.2e-106:
		tmp = t_1
	elif t <= 1.82e+28:
		tmp = (x / (a * math.exp(b))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	t_2 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_3 = Float64(x / Float64(exp(b) * Float64(y * a)))
	tmp = 0.0
	if (t <= -3.9e+24)
		tmp = t_2;
	elseif (t <= -2.8e-235)
		tmp = t_1;
	elseif (t <= 1.25e-303)
		tmp = t_3;
	elseif (t <= 6.5e-237)
		tmp = t_1;
	elseif (t <= 2.1e-162)
		tmp = t_3;
	elseif (t <= 3.2e-106)
		tmp = t_1;
	elseif (t <= 1.82e+28)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	t_2 = (x * (a ^ (t + -1.0))) / y;
	t_3 = x / (exp(b) * (y * a));
	tmp = 0.0;
	if (t <= -3.9e+24)
		tmp = t_2;
	elseif (t <= -2.8e-235)
		tmp = t_1;
	elseif (t <= 1.25e-303)
		tmp = t_3;
	elseif (t <= 6.5e-237)
		tmp = t_1;
	elseif (t <= 2.1e-162)
		tmp = t_3;
	elseif (t <= 3.2e-106)
		tmp = t_1;
	elseif (t <= 1.82e+28)
		tmp = (x / (a * exp(b))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.9e+24], t$95$2, If[LessEqual[t, -2.8e-235], t$95$1, If[LessEqual[t, 1.25e-303], t$95$3, If[LessEqual[t, 6.5e-237], t$95$1, If[LessEqual[t, 2.1e-162], t$95$3, If[LessEqual[t, 3.2e-106], t$95$1, If[LessEqual[t, 1.82e+28], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.8999999999999998e24 or 1.82000000000000001e28 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.1%

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

   4. Taylor expanded in b around 0 86.5%

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

      1. exp-to-pow 86.5%

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

      2. sub-neg 86.5%

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

      3. metadata-eval 86.5%

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

      4. +-commutative 86.5%

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

   6. Simplified 86.5%

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

   if -3.8999999999999998e24 < t < -2.79999999999999995e-235 or 1.25e-303 < t < 6.5000000000000001e-237 or 2.1e-162 < t < 3.2e-106

   1. Initial program 97.8%

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

   3. Taylor expanded in b around 0 80.1%

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

      1. exp-sum 77.5%

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

      2. *-commutative 77.5%

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

      3. exp-to-pow 77.5%

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

      4. exp-to-pow 78.4%

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

      5. sub-neg 78.4%

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

      6. metadata-eval 78.4%

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

   5. Simplified 78.4%

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

   6. Taylor expanded in t around 0 81.0%

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

   if -2.79999999999999995e-235 < t < 1.25e-303 or 6.5000000000000001e-237 < t < 2.1e-162

   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* 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 90.0%

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

      4. associate-/l* 90.0%

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

      5. *-commutative 90.0%

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

      6. exp-to-pow 90.0%

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

      7. exp-diff 90.0%

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

      8. *-commutative 90.0%

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

      9. exp-to-pow 91.3%

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

      10. sub-neg 91.3%

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

      11. metadata-eval 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in t around 0 91.4%

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

      1. times-frac 80.1%

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

   7. Simplified 80.1%

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

   8. Taylor expanded in y around 0 89.0%

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

      1. associate-*r* 89.0%

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

   10. Simplified 89.0%

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

   if 3.2e-106 < t < 1.82000000000000001e28

   1. Initial program 93.1%

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

   3. Taylor expanded in y around 0 87.4%

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

      1. div-exp 87.4%

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

      2. exp-to-pow 88.6%

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

      3. sub-neg 88.6%

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

      4. metadata-eval 88.6%

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

   5. Simplified 88.6%

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

   6. Taylor expanded in t around 0 90.5%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+24}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-303}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 1.82 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.9% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+25} \lor \neg \left(t \leq 3.2 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.38e+25) (not (<= t 3.2e+28)))
   (/ (* x (pow a (+ t -1.0))) y)
   (/ (/ x (* a (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.38e+25) || !(t <= 3.2e+28)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-1.38d+25)) .or. (.not. (t <= 3.2d+28))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -1.38e+25) || !(t <= 3.2e+28)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -1.38e+25) or not (t <= 3.2e+28):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -1.38e+25) || !(t <= 3.2e+28))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -1.38e+25) || ~((t <= 3.2e+28)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -1.38e+25], N[Not[LessEqual[t, 3.2e+28]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.3800000000000001e25 or 3.2e28 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.1%

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

   4. Taylor expanded in b around 0 86.5%

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

      1. exp-to-pow 86.5%

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

      2. sub-neg 86.5%

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

      3. metadata-eval 86.5%

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

      4. +-commutative 86.5%

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

   6. Simplified 86.5%

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

   if -1.3800000000000001e25 < t < 3.2e28

   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 y around 0 67.9%

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

      1. div-exp 67.1%

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

      2. exp-to-pow 68.1%

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

      3. sub-neg 68.1%

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

      4. metadata-eval 68.1%

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

   5. Simplified 68.1%

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

   6. Taylor expanded in t around 0 69.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.38 \cdot 10^{+25} \lor \neg \left(t \leq 3.2 \cdot 10^{+28}\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 53.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+218} \lor \neg \left(y \leq 4.4 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.75e+218) (not (<= y 4.4e+99)))
   (/
    (/ x (+ a (* b (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5)))))))
    y)
   (/ x (* (exp b) (* y a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.75e+218) || !(y <= 4.4e+99)) {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	} else {
		tmp = x / (exp(b) * (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 ((y <= (-1.75d+218)) .or. (.not. (y <= 4.4d+99))) then
        tmp = (x / (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 0.5d0))))))) / y
    else
        tmp = x / (exp(b) * (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 ((y <= -1.75e+218) || !(y <= 4.4e+99)) {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	} else {
		tmp = x / (Math.exp(b) * (y * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.75e+218) or not (y <= 4.4e+99):
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y
	else:
		tmp = x / (math.exp(b) * (y * a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.75e+218) || !(y <= 4.4e+99))
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))) / y);
	else
		tmp = Float64(x / Float64(exp(b) * Float64(y * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.75e+218) || ~((y <= 4.4e+99)))
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	else
		tmp = x / (exp(b) * (y * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.75e+218], N[Not[LessEqual[y, 4.4e+99]], $MachinePrecision]], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[Exp[b], $MachinePrecision] * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e218 or 4.39999999999999956e99 < 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 y around 0 59.6%

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

      1. div-exp 50.7%

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

      2. exp-to-pow 50.7%

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

      3. sub-neg 50.7%

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

      4. metadata-eval 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in t around 0 48.1%

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

   7. Taylor expanded in b around 0 49.9%

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

   if -1.7500000000000001e218 < y < 4.39999999999999956e99

   1. Initial program 97.7%

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

      1. associate-/l* 97.3%

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

      2. associate--l+ 97.3%

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

      3. exp-sum 85.6%

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

      4. associate-/l* 85.6%

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

      5. *-commutative 85.6%

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

      6. exp-to-pow 85.6%

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

      7. exp-diff 74.4%

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

      8. *-commutative 74.4%

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

      9. exp-to-pow 75.1%

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

      10. sub-neg 75.1%

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

      11. metadata-eval 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in t around 0 65.7%

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

      1. times-frac 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in y around 0 60.3%

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

      1. associate-*r* 57.7%

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

   10. Simplified 57.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+218} \lor \neg \left(y \leq 4.4 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{b} \cdot \left(y \cdot a\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{+232}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y 4.4e+232)
   (/ (/ x (* a (exp b))) y)
   (/ 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 (y <= 4.4e+232) {
		tmp = (x / (a * exp(b))) / y;
	} 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 (y <= 4.4d+232) then
        tmp = (x / (a * exp(b))) / y
    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 (y <= 4.4e+232) {
		tmp = (x / (a * Math.exp(b))) / y;
	} 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 y <= 4.4e+232:
		tmp = (x / (a * math.exp(b))) / y
	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 (y <= 4.4e+232)
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	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 (y <= 4.4e+232)
		tmp = (x / (a * exp(b))) / y;
	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[y, 4.4e+232], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $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 2 regimes

2. if y < 4.4e232

   1. Initial program 98.2%

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

   3. Taylor expanded in y around 0 82.1%

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

      1. div-exp 70.5%

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

      2. exp-to-pow 71.0%

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

      3. sub-neg 71.0%

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

      4. metadata-eval 71.0%

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

   5. Simplified 71.0%

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

   6. Taylor expanded in t around 0 59.4%

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

   if 4.4e232 < 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 y around 0 36.7%

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

      1. div-exp 22.4%

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

      2. exp-to-pow 22.4%

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

      3. sub-neg 22.4%

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

      4. metadata-eval 22.4%

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

   5. Simplified 22.4%

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

   6. Taylor expanded in t around 0 22.9%

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

   7. Taylor expanded in b around 0 51.1%

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

   8. Taylor expanded in a around 0 57.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot \left(1 + b \cdot \left(1 + 0.5 \cdot b\right)\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{+232}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 46.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x - x \cdot \left(b \cdot 0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -1.92 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-246}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-278}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-278}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+191)
   (/ (- (/ x a) (* b (/ (- x (* x (* b 0.5))) a))) y)
   (if (<= b -1.92e+130)
     (/ x (* a (* y (- 1.0 (* b (- -1.0 (* b 0.5)))))))
     (if (<= b -3.5e-206)
       (/ 1.0 (* a (/ y x)))
       (if (<= b -8.8e-246)
         (* (/ b y) (/ x (- a)))
         (if (<= b -1.7e-278)
           (/ (* b (/ x a)) (- y))
           (if (<= b 5.3e-278)
             (* b (- (/ x (* a (* y b))) (/ x (* y a))))
             (/
              (/
               x
               (+
                a
                (*
                 b
                 (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5)))))))
              y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+191) {
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y;
	} else if (b <= -1.92e+130) {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	} else if (b <= -3.5e-206) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -8.8e-246) {
		tmp = (b / y) * (x / -a);
	} else if (b <= -1.7e-278) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= 5.3e-278) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 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 <= (-1.25d+191)) then
        tmp = ((x / a) - (b * ((x - (x * (b * 0.5d0))) / a))) / y
    else if (b <= (-1.92d+130)) then
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * 0.5d0))))))
    else if (b <= (-3.5d-206)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-8.8d-246)) then
        tmp = (b / y) * (x / -a)
    else if (b <= (-1.7d-278)) then
        tmp = (b * (x / a)) / -y
    else if (b <= 5.3d-278) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else
        tmp = (x / (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 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 <= -1.25e+191) {
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y;
	} else if (b <= -1.92e+130) {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	} else if (b <= -3.5e-206) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -8.8e-246) {
		tmp = (b / y) * (x / -a);
	} else if (b <= -1.7e-278) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= 5.3e-278) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+191:
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y
	elif b <= -1.92e+130:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))))
	elif b <= -3.5e-206:
		tmp = 1.0 / (a * (y / x))
	elif b <= -8.8e-246:
		tmp = (b / y) * (x / -a)
	elif b <= -1.7e-278:
		tmp = (b * (x / a)) / -y
	elif b <= 5.3e-278:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	else:
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x - Float64(x * Float64(b * 0.5))) / a))) / y);
	elseif (b <= -1.92e+130)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 0.5)))))));
	elseif (b <= -3.5e-206)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -8.8e-246)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	elseif (b <= -1.7e-278)
		tmp = Float64(Float64(b * Float64(x / a)) / Float64(-y));
	elseif (b <= 5.3e-278)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y;
	elseif (b <= -1.92e+130)
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	elseif (b <= -3.5e-206)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -8.8e-246)
		tmp = (b / y) * (x / -a);
	elseif (b <= -1.7e-278)
		tmp = (b * (x / a)) / -y;
	elseif (b <= 5.3e-278)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	else
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+191], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x - N[(x * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.92e+130], 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], If[LessEqual[b, -3.5e-206], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8.8e-246], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e-278], N[(N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, 5.3e-278], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -1.25000000000000005e191

   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 93.0%

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

      1. div-exp 75.1%

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

      2. exp-to-pow 75.1%

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

      3. sub-neg 75.1%

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

      4. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 93.0%

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

   7. Taylor expanded in b around 0 71.7%

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

   8. Taylor expanded in b around 0 71.7%

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

   10. Simplified 89.6%

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

   if -1.25000000000000005e191 < b < -1.9199999999999999e130

   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 54.1%

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

      1. div-exp 40.7%

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

      2. exp-to-pow 40.7%

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

      3. sub-neg 40.7%

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

      4. metadata-eval 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in t around 0 40.9%

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

   7. Taylor expanded in b around 0 60.8%

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

   8. Taylor expanded in a around 0 67.3%

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

   if -1.9199999999999999e130 < b < -3.49999999999999989e-206

   1. Initial program 99.1%

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

      1. associate-/l* 96.6%

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

      2. associate--l+ 96.6%

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

      3. exp-sum 82.8%

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

      4. associate-/l* 82.8%

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

      5. *-commutative 82.8%

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

      6. exp-to-pow 82.8%

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

      7. exp-diff 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 69.3%

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

      10. sub-neg 69.3%

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

      11. metadata-eval 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in t around 0 58.9%

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

      1. times-frac 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in y around 0 47.3%

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

      1. associate-*r* 44.2%

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

   10. Simplified 44.2%

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

   11. Taylor expanded in b around 0 35.4%

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

       1. clear-num 35.6%

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

       2. inv-pow 35.6%

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

   13. Applied egg-rr 35.6%

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

       1. unpow-1 35.6%

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

       2. associate-/l* 40.1%

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

   15. Simplified 40.1%

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

   if -3.49999999999999989e-206 < b < -8.79999999999999992e-246

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 26.6%

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

      1. div-exp 26.6%

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

      2. exp-to-pow 27.8%

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

      3. sub-neg 27.8%

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

      4. metadata-eval 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in t around 0 28.3%

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

   7. Taylor expanded in b around 0 28.3%

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

      1. +-commutative 28.3%

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

      2. mul-1-neg 28.3%

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

      3. unsub-neg 28.3%

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

      4. associate-/l* 28.3%

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

   9. Simplified 28.3%

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

   10. Taylor expanded in b around inf 58.3%

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

       1. mul-1-neg 58.3%

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

       2. *-commutative 58.3%

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

       3. times-frac 76.1%

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

       4. distribute-rgt-neg-in 76.1%

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

   12. Simplified 76.1%

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

   if -8.79999999999999992e-246 < b < -1.7e-278

   1. Initial program 76.7%

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

   3. Taylor expanded in y around 0 76.7%

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

      1. div-exp 76.7%

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

      2. exp-to-pow 76.7%

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

      3. sub-neg 76.7%

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

      4. metadata-eval 76.7%

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

   5. Simplified 76.7%

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

   6. Taylor expanded in t around 0 28.0%

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

   7. Taylor expanded in b around 0 28.0%

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

      1. +-commutative 28.0%

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

      2. mul-1-neg 28.0%

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

      3. unsub-neg 28.0%

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

      4. associate-/l* 28.0%

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

   9. Simplified 28.0%

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

   10. Taylor expanded in b around inf 27.7%

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

       1. associate-/l* 52.1%

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

       2. associate-*r* 52.1%

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

       3. neg-mul-1 52.1%

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

       4. *-commutative 52.1%

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

   12. Simplified 52.1%

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

   if -1.7e-278 < b < 5.3e-278

   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 69.7%

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

      1. div-exp 69.7%

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

      2. exp-to-pow 70.0%

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

      3. sub-neg 70.0%

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

      4. metadata-eval 70.0%

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

   5. Simplified 70.0%

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

   6. Taylor expanded in t around 0 50.7%

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

   7. Taylor expanded in b around 0 50.7%

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

      1. +-commutative 50.7%

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

      2. mul-1-neg 50.7%

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

      3. unsub-neg 50.7%

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

      4. associate-/l* 35.2%

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

   9. Simplified 35.2%

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

   10. Taylor expanded in b around inf 62.7%

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

       1. mul-1-neg 62.7%

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

       2. +-commutative 62.7%

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

       3. unsub-neg 62.7%

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

       4. *-commutative 62.7%

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

   12. Simplified 62.7%

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

   if 5.3e-278 < b

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 83.5%

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

      1. div-exp 72.1%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 59.5%

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

   7. Taylor expanded in b around 0 50.9%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}}}{y} \]
3. Recombined 7 regimes into one program.

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x - x \cdot \left(b \cdot 0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -1.92 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-206}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -8.8 \cdot 10^{-246}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-278}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-278}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.3% accurate, 6.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a} - \frac{b \cdot \left(x - b \cdot \left(x - x \cdot 0.5\right)\right)}{a}}{y}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-204}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-266}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (/ x a) (/ (* b (- x (* b (- x (* x 0.5))))) a)) y)))
   (if (<= b -1.25e+191)
     t_1
     (if (<= b -2.6e+130)
       (/ x (* a (* y (- 1.0 (* b (- -1.0 (* b 0.5)))))))
       (if (<= b -3.5e+103)
         t_1
         (if (<= b -1.6e-204)
           (/ 1.0 (* a (/ y x)))
           (if (<= b -8e-266)
             (* (/ b y) (/ x (- a)))
             (/
              (/
               x
               (+
                a
                (*
                 b
                 (+ a (* b (+ (* 0.16666666666666666 (* a b)) (* a 0.5)))))))
              y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x / a) - ((b * (x - (b * (x - (x * 0.5))))) / a)) / y;
	double tmp;
	if (b <= -1.25e+191) {
		tmp = t_1;
	} else if (b <= -2.6e+130) {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	} else if (b <= -3.5e+103) {
		tmp = t_1;
	} else if (b <= -1.6e-204) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -8e-266) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 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) :: t_1
    real(8) :: tmp
    t_1 = ((x / a) - ((b * (x - (b * (x - (x * 0.5d0))))) / a)) / y
    if (b <= (-1.25d+191)) then
        tmp = t_1
    else if (b <= (-2.6d+130)) then
        tmp = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * 0.5d0))))))
    else if (b <= (-3.5d+103)) then
        tmp = t_1
    else if (b <= (-1.6d-204)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-8d-266)) then
        tmp = (b / y) * (x / -a)
    else
        tmp = (x / (a + (b * (a + (b * ((0.16666666666666666d0 * (a * b)) + (a * 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 t_1 = ((x / a) - ((b * (x - (b * (x - (x * 0.5))))) / a)) / y;
	double tmp;
	if (b <= -1.25e+191) {
		tmp = t_1;
	} else if (b <= -2.6e+130) {
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	} else if (b <= -3.5e+103) {
		tmp = t_1;
	} else if (b <= -1.6e-204) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -8e-266) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x / a) - ((b * (x - (b * (x - (x * 0.5))))) / a)) / y
	tmp = 0
	if b <= -1.25e+191:
		tmp = t_1
	elif b <= -2.6e+130:
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))))
	elif b <= -3.5e+103:
		tmp = t_1
	elif b <= -1.6e-204:
		tmp = 1.0 / (a * (y / x))
	elif b <= -8e-266:
		tmp = (b / y) * (x / -a)
	else:
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x / a) - Float64(Float64(b * Float64(x - Float64(b * Float64(x - Float64(x * 0.5))))) / a)) / y)
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = t_1;
	elseif (b <= -2.6e+130)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 0.5)))))));
	elseif (b <= -3.5e+103)
		tmp = t_1;
	elseif (b <= -1.6e-204)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -8e-266)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * b)) + Float64(a * 0.5))))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x / a) - ((b * (x - (b * (x - (x * 0.5))))) / a)) / y;
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = t_1;
	elseif (b <= -2.6e+130)
		tmp = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	elseif (b <= -3.5e+103)
		tmp = t_1;
	elseif (b <= -1.6e-204)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -8e-266)
		tmp = (b / y) * (x / -a);
	else
		tmp = (x / (a + (b * (a + (b * ((0.16666666666666666 * (a * b)) + (a * 0.5))))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x / a), $MachinePrecision] - N[(N[(b * N[(x - N[(b * N[(x - N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.25e+191], t$95$1, If[LessEqual[b, -2.6e+130], 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], If[LessEqual[b, -3.5e+103], t$95$1, If[LessEqual[b, -1.6e-204], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -8e-266], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(b * N[(N[(0.16666666666666666 * N[(a * b), $MachinePrecision]), $MachinePrecision] + N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.25000000000000005e191 or -2.5999999999999998e130 < b < -3.5e103

   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 94.2%

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

      1. div-exp 79.5%

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

      2. exp-to-pow 79.5%

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

      3. sub-neg 79.5%

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

      4. metadata-eval 79.5%

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

   5. Simplified 79.5%

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

   6. Taylor expanded in t around 0 94.2%

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

   7. Taylor expanded in b around 0 68.0%

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

   8. Taylor expanded in a around 0 91.3%

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

   if -1.25000000000000005e191 < b < -2.5999999999999998e130

   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 54.1%

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

      1. div-exp 40.7%

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

      2. exp-to-pow 40.7%

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

      3. sub-neg 40.7%

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

      4. metadata-eval 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in t around 0 40.9%

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

   7. Taylor expanded in b around 0 60.8%

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

   8. Taylor expanded in a around 0 67.3%

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

   if -3.5e103 < b < -1.6e-204

   1. Initial program 99.0%

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

      1. associate-/l* 96.3%

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

      2. associate--l+ 96.3%

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

      3. exp-sum 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 82.8%

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

      7. exp-diff 67.5%

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

      8. *-commutative 67.5%

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

      9. exp-to-pow 67.9%

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

      10. sub-neg 67.9%

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

      11. metadata-eval 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in t around 0 56.5%

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

      1. times-frac 54.9%

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

   7. Simplified 54.9%

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

   8. Taylor expanded in y around 0 42.0%

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

      1. associate-*r* 40.3%

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

   10. Simplified 40.3%

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

   11. Taylor expanded in b around 0 35.5%

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

       1. clear-num 35.7%

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

       2. inv-pow 35.7%

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

   13. Applied egg-rr 35.7%

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

       1. unpow-1 35.7%

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

       2. associate-/l* 42.1%

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

   15. Simplified 42.1%

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

   if -1.6e-204 < b < -7.9999999999999999e-266

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 41.3%

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

      1. div-exp 41.3%

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

      2. exp-to-pow 42.3%

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

      3. sub-neg 42.3%

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

      4. metadata-eval 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in t around 0 23.2%

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

   7. Taylor expanded in b around 0 23.2%

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

      1. +-commutative 23.2%

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

      2. mul-1-neg 23.2%

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

      3. unsub-neg 23.2%

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

      4. associate-/l* 23.2%

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

   9. Simplified 23.2%

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

   10. Taylor expanded in b around inf 56.8%

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

       1. mul-1-neg 56.8%

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

       2. *-commutative 56.8%

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

       3. times-frac 61.6%

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

       4. distribute-rgt-neg-in 61.6%

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

   12. Simplified 61.6%

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

   if -7.9999999999999999e-266 < b

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 81.7%

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

      1. div-exp 71.6%

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

      2. exp-to-pow 72.2%

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

      3. sub-neg 72.2%

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

      4. metadata-eval 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0 58.6%

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

   7. Taylor expanded in b around 0 50.9%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b \cdot \left(x - b \cdot \left(x - x \cdot 0.5\right)\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{b \cdot \left(x - b \cdot \left(x - x \cdot 0.5\right)\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-204}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-266}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 43.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{+129}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.66 \cdot 10^{+75}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-238}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (* y (- 1.0 (* b (- -1.0 (* b 0.5)))))))))
   (if (<= b -1.25e+191)
     (/ (* x (/ b (- a))) y)
     (if (<= b -5.4e+129)
       t_1
       (if (<= b -1.66e+75)
         (/ (* b (/ x a)) (- y))
         (if (<= b -2.2e-213)
           (/ 1.0 (* a (/ y x)))
           (if (<= b -1.15e-238)
             (* (/ b y) (/ x (- a)))
             (if (<= b 4.5e+20) (/ (/ x (+ a (* a b))) y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -5.4e+129) {
		tmp = t_1;
	} else if (b <= -1.66e+75) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -2.2e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.15e-238) {
		tmp = (b / y) * (x / -a);
	} else if (b <= 4.5e+20) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a * (y * (1.0d0 - (b * ((-1.0d0) - (b * 0.5d0))))))
    if (b <= (-1.25d+191)) then
        tmp = (x * (b / -a)) / y
    else if (b <= (-5.4d+129)) then
        tmp = t_1
    else if (b <= (-1.66d+75)) then
        tmp = (b * (x / a)) / -y
    else if (b <= (-2.2d-213)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-1.15d-238)) then
        tmp = (b / y) * (x / -a)
    else if (b <= 4.5d+20) then
        tmp = (x / (a + (a * b))) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -5.4e+129) {
		tmp = t_1;
	} else if (b <= -1.66e+75) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -2.2e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.15e-238) {
		tmp = (b / y) * (x / -a);
	} else if (b <= 4.5e+20) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))))
	tmp = 0
	if b <= -1.25e+191:
		tmp = (x * (b / -a)) / y
	elif b <= -5.4e+129:
		tmp = t_1
	elif b <= -1.66e+75:
		tmp = (b * (x / a)) / -y
	elif b <= -2.2e-213:
		tmp = 1.0 / (a * (y / x))
	elif b <= -1.15e-238:
		tmp = (b / y) * (x / -a)
	elif b <= 4.5e+20:
		tmp = (x / (a + (a * b))) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y * Float64(1.0 - Float64(b * Float64(-1.0 - Float64(b * 0.5)))))))
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= -5.4e+129)
		tmp = t_1;
	elseif (b <= -1.66e+75)
		tmp = Float64(Float64(b * Float64(x / a)) / Float64(-y));
	elseif (b <= -2.2e-213)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -1.15e-238)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	elseif (b <= 4.5e+20)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y * (1.0 - (b * (-1.0 - (b * 0.5))))));
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = (x * (b / -a)) / y;
	elseif (b <= -5.4e+129)
		tmp = t_1;
	elseif (b <= -1.66e+75)
		tmp = (b * (x / a)) / -y;
	elseif (b <= -2.2e-213)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -1.15e-238)
		tmp = (b / y) * (x / -a);
	elseif (b <= 4.5e+20)
		tmp = (x / (a + (a * b))) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y * N[(1.0 - N[(b * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+191], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -5.4e+129], t$95$1, If[LessEqual[b, -1.66e+75], N[(N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, -2.2e-213], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e-238], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+20], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.25000000000000005e191

   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 93.0%

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

      1. div-exp 75.1%

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

      2. exp-to-pow 75.1%

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

      3. sub-neg 75.1%

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

      4. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 93.0%

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

   7. Taylor expanded in b around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. associate-/l* 62.2%

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

   9. Simplified 62.2%

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

   10. Taylor expanded in b around inf 69.0%

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

       1. associate-*r/ 69.0%

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

       2. associate-*r* 69.0%

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

       3. neg-mul-1 69.0%

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

       4. associate-*l/ 69.0%

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

       5. neg-mul-1 69.0%

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

       6. associate-*r/ 69.0%

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

       7. *-commutative 69.0%

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

       8. associate-*l* 69.0%

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

       9. mul-1-neg 69.0%

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

   12. Simplified 69.0%

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

   if -1.25000000000000005e191 < b < -5.4000000000000002e129 or 4.5e20 < b

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.3%

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

      1. div-exp 62.9%

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

      2. exp-to-pow 62.9%

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

      3. sub-neg 62.9%

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

      4. metadata-eval 62.9%

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

   5. Simplified 62.9%

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

   6. Taylor expanded in t around 0 69.8%

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

   7. Taylor expanded in b around 0 53.3%

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

   8. Taylor expanded in a around 0 60.9%

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

   if -5.4000000000000002e129 < b < -1.66e75

   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 88.4%

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

      1. div-exp 58.9%

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

      2. exp-to-pow 58.9%

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

      3. sub-neg 58.9%

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

      4. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around 0 59.5%

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

   7. Taylor expanded in b around 0 32.1%

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

      1. +-commutative 32.1%

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

      2. mul-1-neg 32.1%

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

      3. unsub-neg 32.1%

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

      4. associate-/l* 43.3%

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

   9. Simplified 43.3%

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

   10. Taylor expanded in b around inf 32.1%

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

       1. associate-/l* 43.3%

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

       2. associate-*r* 43.3%

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

       3. neg-mul-1 43.3%

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

       4. *-commutative 43.3%

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

   12. Simplified 43.3%

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

   if -1.66e75 < b < -2.2000000000000001e-213

   1. Initial program 98.8%

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

      1. associate-/l* 95.4%

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

      2. associate--l+ 95.4%

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

      3. exp-sum 85.0%

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

      4. associate-/l* 85.0%

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

      5. *-commutative 85.0%

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

      6. exp-to-pow 85.1%

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

      7. exp-diff 76.7%

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

      8. *-commutative 76.7%

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

      9. exp-to-pow 77.2%

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

      10. sub-neg 77.2%

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

      11. metadata-eval 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in t around 0 63.0%

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

      1. times-frac 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in y around 0 43.1%

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

      1. associate-*r* 43.1%

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

   10. Simplified 43.1%

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

   11. Taylor expanded in b around 0 34.8%

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

       1. clear-num 35.1%

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

       2. inv-pow 35.1%

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

   13. Applied egg-rr 35.1%

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

       1. unpow-1 35.1%

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

       2. associate-/l* 43.0%

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

   15. Simplified 43.0%

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

   if -2.2000000000000001e-213 < b < -1.15000000000000002e-238

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 29.7%

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

      1. div-exp 29.7%

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

      2. exp-to-pow 31.1%

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

      3. sub-neg 31.1%

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

      4. metadata-eval 31.1%

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

   5. Simplified 31.1%

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

   6. Taylor expanded in t around 0 31.7%

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

   7. Taylor expanded in b around 0 31.7%

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

      1. +-commutative 31.7%

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

      2. mul-1-neg 31.7%

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

      3. unsub-neg 31.7%

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

      4. associate-/l* 31.7%

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

   9. Simplified 31.7%

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

   10. Taylor expanded in b around inf 52.4%

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

       1. mul-1-neg 52.4%

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

       2. *-commutative 52.4%

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

       3. times-frac 72.6%

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

       4. distribute-rgt-neg-in 72.6%

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

   12. Simplified 72.6%

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

   if -1.15000000000000002e-238 < b < 4.5e20

   1. Initial program 95.4%

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

   3. Taylor expanded in y around 0 73.8%

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

      1. div-exp 73.8%

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

      2. exp-to-pow 74.8%

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

      3. sub-neg 74.8%

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

      4. metadata-eval 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around 0 42.9%

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

   7. Taylor expanded in b around 0 40.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -5.4 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.66 \cdot 10^{+75}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-238}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.9% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-1 - b \cdot 0.5\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - t\_1\right)\right)}\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-200}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a - a \cdot t\_1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- -1.0 (* b 0.5)))))
   (if (<= b -1.25e+191)
     (/ (* x (/ b (- a))) y)
     (if (<= b -2.4e+130)
       (/ x (* a (* y (- 1.0 t_1))))
       (if (<= b -1.25e+76)
         (/ (* b (/ x a)) (- y))
         (if (<= b -8.5e-200)
           (/ 1.0 (* a (/ y x)))
           (if (<= b -2.75e-266)
             (* (/ b y) (/ x (- a)))
             (/ (/ x (- a (* a t_1))) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (-1.0 - (b * 0.5));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -2.4e+130) {
		tmp = x / (a * (y * (1.0 - t_1)));
	} else if (b <= -1.25e+76) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -8.5e-200) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -2.75e-266) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a - (a * t_1))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((-1.0d0) - (b * 0.5d0))
    if (b <= (-1.25d+191)) then
        tmp = (x * (b / -a)) / y
    else if (b <= (-2.4d+130)) then
        tmp = x / (a * (y * (1.0d0 - t_1)))
    else if (b <= (-1.25d+76)) then
        tmp = (b * (x / a)) / -y
    else if (b <= (-8.5d-200)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-2.75d-266)) then
        tmp = (b / y) * (x / -a)
    else
        tmp = (x / (a - (a * t_1))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (-1.0 - (b * 0.5));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -2.4e+130) {
		tmp = x / (a * (y * (1.0 - t_1)));
	} else if (b <= -1.25e+76) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -8.5e-200) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -2.75e-266) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a - (a * t_1))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (-1.0 - (b * 0.5))
	tmp = 0
	if b <= -1.25e+191:
		tmp = (x * (b / -a)) / y
	elif b <= -2.4e+130:
		tmp = x / (a * (y * (1.0 - t_1)))
	elif b <= -1.25e+76:
		tmp = (b * (x / a)) / -y
	elif b <= -8.5e-200:
		tmp = 1.0 / (a * (y / x))
	elif b <= -2.75e-266:
		tmp = (b / y) * (x / -a)
	else:
		tmp = (x / (a - (a * t_1))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(-1.0 - Float64(b * 0.5)))
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= -2.4e+130)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - t_1))));
	elseif (b <= -1.25e+76)
		tmp = Float64(Float64(b * Float64(x / a)) / Float64(-y));
	elseif (b <= -8.5e-200)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -2.75e-266)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	else
		tmp = Float64(Float64(x / Float64(a - Float64(a * t_1))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (-1.0 - (b * 0.5));
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = (x * (b / -a)) / y;
	elseif (b <= -2.4e+130)
		tmp = x / (a * (y * (1.0 - t_1)));
	elseif (b <= -1.25e+76)
		tmp = (b * (x / a)) / -y;
	elseif (b <= -8.5e-200)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -2.75e-266)
		tmp = (b / y) * (x / -a);
	else
		tmp = (x / (a - (a * t_1))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+191], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -2.4e+130], N[(x / N[(a * N[(y * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e+76], N[(N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, -8.5e-200], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.75e-266], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a - N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.25000000000000005e191

   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 93.0%

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

      1. div-exp 75.1%

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

      2. exp-to-pow 75.1%

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

      3. sub-neg 75.1%

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

      4. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 93.0%

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

   7. Taylor expanded in b around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. associate-/l* 62.2%

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

   9. Simplified 62.2%

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

   10. Taylor expanded in b around inf 69.0%

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

       1. associate-*r/ 69.0%

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

       2. associate-*r* 69.0%

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

       3. neg-mul-1 69.0%

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

       4. associate-*l/ 69.0%

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

       5. neg-mul-1 69.0%

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

       6. associate-*r/ 69.0%

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

       7. *-commutative 69.0%

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

       8. associate-*l* 69.0%

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

       9. mul-1-neg 69.0%

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

   12. Simplified 69.0%

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

   if -1.25000000000000005e191 < b < -2.40000000000000024e130

   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 54.1%

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

      1. div-exp 40.7%

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

      2. exp-to-pow 40.7%

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

      3. sub-neg 40.7%

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

      4. metadata-eval 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in t around 0 40.9%

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

   7. Taylor expanded in b around 0 60.8%

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

   8. Taylor expanded in a around 0 67.3%

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

   if -2.40000000000000024e130 < b < -1.24999999999999998e76

   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 88.4%

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

      1. div-exp 58.9%

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

      2. exp-to-pow 58.9%

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

      3. sub-neg 58.9%

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

      4. metadata-eval 58.9%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around 0 59.5%

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

   7. Taylor expanded in b around 0 32.1%

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

      1. +-commutative 32.1%

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

      2. mul-1-neg 32.1%

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

      3. unsub-neg 32.1%

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

      4. associate-/l* 43.3%

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

   9. Simplified 43.3%

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

   10. Taylor expanded in b around inf 32.1%

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

       1. associate-/l* 43.3%

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

       2. associate-*r* 43.3%

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

       3. neg-mul-1 43.3%

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

       4. *-commutative 43.3%

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

   12. Simplified 43.3%

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

   if -1.24999999999999998e76 < b < -8.50000000000000014e-200

   1. Initial program 98.8%

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

      1. associate-/l* 95.4%

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

      2. associate--l+ 95.4%

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

      3. exp-sum 85.0%

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

      4. associate-/l* 85.0%

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

      5. *-commutative 85.0%

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

      6. exp-to-pow 85.1%

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

      7. exp-diff 76.7%

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

      8. *-commutative 76.7%

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

      9. exp-to-pow 77.2%

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

      10. sub-neg 77.2%

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

      11. metadata-eval 77.2%

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

   3. Simplified 77.2%

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

   5. Taylor expanded in t around 0 63.0%

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

      1. times-frac 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in y around 0 43.1%

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

      1. associate-*r* 43.1%

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

   10. Simplified 43.1%

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

   11. Taylor expanded in b around 0 34.8%

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

       1. clear-num 35.1%

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

       2. inv-pow 35.1%

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

   13. Applied egg-rr 35.1%

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

       1. unpow-1 35.1%

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

       2. associate-/l* 43.0%

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

   15. Simplified 43.0%

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

   if -8.50000000000000014e-200 < b < -2.75000000000000013e-266

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 41.3%

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

      1. div-exp 41.3%

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

      2. exp-to-pow 42.3%

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

      3. sub-neg 42.3%

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

      4. metadata-eval 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in t around 0 23.2%

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

   7. Taylor expanded in b around 0 23.2%

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

      1. +-commutative 23.2%

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

      2. mul-1-neg 23.2%

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

      3. unsub-neg 23.2%

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

      4. associate-/l* 23.2%

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

   9. Simplified 23.2%

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

   10. Taylor expanded in b around inf 56.8%

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

       1. mul-1-neg 56.8%

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

       2. *-commutative 56.8%

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

       3. times-frac 61.6%

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

       4. distribute-rgt-neg-in 61.6%

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

   12. Simplified 61.6%

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

   if -2.75000000000000013e-266 < b

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 81.7%

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

      1. div-exp 71.6%

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

      2. exp-to-pow 72.2%

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

      3. sub-neg 72.2%

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

      4. metadata-eval 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0 58.6%

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

   7. Taylor expanded in b around 0 46.6%

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

   8. Taylor expanded in a around 0 50.7%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+76}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-200}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -2.75 \cdot 10^{-266}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a - a \cdot \left(b \cdot \left(-1 - b \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.7% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ t_2 := b \cdot \left(-1 - b \cdot 0.5\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - t\_2\right)\right)}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-209}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-266}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a - a \cdot t\_2}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- x (* b (+ x (* b (* x -0.5))))) (* y a)))
        (t_2 (* b (- -1.0 (* b 0.5)))))
   (if (<= b -1.25e+191)
     t_1
     (if (<= b -1.6e+123)
       (/ x (* a (* y (- 1.0 t_2))))
       (if (<= b -3.5e+103)
         t_1
         (if (<= b -5.8e-209)
           (/ 1.0 (* a (/ y x)))
           (if (<= b -3.2e-266)
             (* (/ b y) (/ x (- a)))
             (/ (/ x (- a (* a t_2))) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	double t_2 = b * (-1.0 - (b * 0.5));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = t_1;
	} else if (b <= -1.6e+123) {
		tmp = x / (a * (y * (1.0 - t_2)));
	} else if (b <= -3.5e+103) {
		tmp = t_1;
	} else if (b <= -5.8e-209) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -3.2e-266) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a - (a * t_2))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x - (b * (x + (b * (x * (-0.5d0)))))) / (y * a)
    t_2 = b * ((-1.0d0) - (b * 0.5d0))
    if (b <= (-1.25d+191)) then
        tmp = t_1
    else if (b <= (-1.6d+123)) then
        tmp = x / (a * (y * (1.0d0 - t_2)))
    else if (b <= (-3.5d+103)) then
        tmp = t_1
    else if (b <= (-5.8d-209)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-3.2d-266)) then
        tmp = (b / y) * (x / -a)
    else
        tmp = (x / (a - (a * t_2))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	double t_2 = b * (-1.0 - (b * 0.5));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = t_1;
	} else if (b <= -1.6e+123) {
		tmp = x / (a * (y * (1.0 - t_2)));
	} else if (b <= -3.5e+103) {
		tmp = t_1;
	} else if (b <= -5.8e-209) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -3.2e-266) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a - (a * t_2))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x - (b * (x + (b * (x * -0.5))))) / (y * a)
	t_2 = b * (-1.0 - (b * 0.5))
	tmp = 0
	if b <= -1.25e+191:
		tmp = t_1
	elif b <= -1.6e+123:
		tmp = x / (a * (y * (1.0 - t_2)))
	elif b <= -3.5e+103:
		tmp = t_1
	elif b <= -5.8e-209:
		tmp = 1.0 / (a * (y / x))
	elif b <= -3.2e-266:
		tmp = (b / y) * (x / -a)
	else:
		tmp = (x / (a - (a * t_2))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x - Float64(b * Float64(x + Float64(b * Float64(x * -0.5))))) / Float64(y * a))
	t_2 = Float64(b * Float64(-1.0 - Float64(b * 0.5)))
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = t_1;
	elseif (b <= -1.6e+123)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - t_2))));
	elseif (b <= -3.5e+103)
		tmp = t_1;
	elseif (b <= -5.8e-209)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -3.2e-266)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	else
		tmp = Float64(Float64(x / Float64(a - Float64(a * t_2))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x - (b * (x + (b * (x * -0.5))))) / (y * a);
	t_2 = b * (-1.0 - (b * 0.5));
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = t_1;
	elseif (b <= -1.6e+123)
		tmp = x / (a * (y * (1.0 - t_2)));
	elseif (b <= -3.5e+103)
		tmp = t_1;
	elseif (b <= -5.8e-209)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -3.2e-266)
		tmp = (b / y) * (x / -a);
	else
		tmp = (x / (a - (a * t_2))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x - N[(b * N[(x + N[(b * N[(x * -0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+191], t$95$1, If[LessEqual[b, -1.6e+123], N[(x / N[(a * N[(y * N[(1.0 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.5e+103], t$95$1, If[LessEqual[b, -5.8e-209], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.2e-266], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a - N[(a * t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.25000000000000005e191 or -1.60000000000000002e123 < b < -3.5e103

   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 94.0%

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

      1. div-exp 78.8%

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

      2. exp-to-pow 78.8%

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

      3. sub-neg 78.8%

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

      4. metadata-eval 78.8%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in t around 0 94.0%

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

   7. Taylor expanded in b around 0 70.0%

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

   8. Taylor expanded in a around 0 76.1%

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

      1. associate-*r* 76.1%

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

      2. neg-mul-1 76.1%

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

      3. distribute-rgt-out 76.1%

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

      4. metadata-eval 76.1%

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

   10. Simplified 76.1%

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

   if -1.25000000000000005e191 < b < -1.60000000000000002e123

   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 56.9%

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

      1. div-exp 44.4%

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

      2. exp-to-pow 44.4%

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

      3. sub-neg 44.4%

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

      4. metadata-eval 44.4%

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

   5. Simplified 44.4%

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

   6. Taylor expanded in t around 0 44.6%

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

   7. Taylor expanded in b around 0 57.1%

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

   8. Taylor expanded in a around 0 63.2%

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

   if -3.5e103 < b < -5.80000000000000052e-209

   1. Initial program 99.0%

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

      1. associate-/l* 96.3%

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

      2. associate--l+ 96.3%

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

      3. exp-sum 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 82.8%

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

      7. exp-diff 67.5%

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

      8. *-commutative 67.5%

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

      9. exp-to-pow 67.9%

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

      10. sub-neg 67.9%

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

      11. metadata-eval 67.9%

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

   3. Simplified 67.9%

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

   5. Taylor expanded in t around 0 56.5%

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

      1. times-frac 54.9%

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

   7. Simplified 54.9%

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

   8. Taylor expanded in y around 0 42.0%

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

      1. associate-*r* 40.3%

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

   10. Simplified 40.3%

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

   11. Taylor expanded in b around 0 35.5%

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

       1. clear-num 35.7%

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

       2. inv-pow 35.7%

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

   13. Applied egg-rr 35.7%

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

       1. unpow-1 35.7%

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

       2. associate-/l* 42.1%

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

   15. Simplified 42.1%

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

   if -5.80000000000000052e-209 < b < -3.2e-266

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 41.3%

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

      1. div-exp 41.3%

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

      2. exp-to-pow 42.3%

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

      3. sub-neg 42.3%

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

      4. metadata-eval 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in t around 0 23.2%

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

   7. Taylor expanded in b around 0 23.2%

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

      1. +-commutative 23.2%

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

      2. mul-1-neg 23.2%

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

      3. unsub-neg 23.2%

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

      4. associate-/l* 23.2%

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

   9. Simplified 23.2%

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

   10. Taylor expanded in b around inf 56.8%

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

       1. mul-1-neg 56.8%

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

       2. *-commutative 56.8%

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

       3. times-frac 61.6%

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

       4. distribute-rgt-neg-in 61.6%

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

   12. Simplified 61.6%

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

   if -3.2e-266 < b

   1. Initial program 97.3%

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

   3. Taylor expanded in y around 0 81.7%

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

      1. div-exp 71.6%

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

      2. exp-to-pow 72.2%

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

      3. sub-neg 72.2%

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

      4. metadata-eval 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in t around 0 58.6%

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

   7. Taylor expanded in b around 0 46.6%

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

   8. Taylor expanded in a around 0 50.7%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{x - b \cdot \left(x + b \cdot \left(x \cdot -0.5\right)\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-209}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-266}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a - a \cdot \left(b \cdot \left(-1 - b \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.0% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(-1 - b \cdot 0.5\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x - x \cdot \left(b \cdot 0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - t\_1\right)\right)}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-269}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a - a \cdot t\_1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- -1.0 (* b 0.5)))))
   (if (<= b -1.25e+191)
     (/ (- (/ x a) (* b (/ (- x (* x (* b 0.5))) a))) y)
     (if (<= b -1.25e+129)
       (/ x (* a (* y (- 1.0 t_1))))
       (if (<= b -2.3e-213)
         (/ 1.0 (* a (/ y x)))
         (if (<= b -1.45e-269)
           (* (/ b y) (/ x (- a)))
           (if (<= b 2.8e-301)
             (/ (* b (- (/ x (* a b)) (/ x a))) y)
             (/ (/ x (- a (* a t_1))) y))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (-1.0 - (b * 0.5));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y;
	} else if (b <= -1.25e+129) {
		tmp = x / (a * (y * (1.0 - t_1)));
	} else if (b <= -2.3e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.45e-269) {
		tmp = (b / y) * (x / -a);
	} else if (b <= 2.8e-301) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a - (a * t_1))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * ((-1.0d0) - (b * 0.5d0))
    if (b <= (-1.25d+191)) then
        tmp = ((x / a) - (b * ((x - (x * (b * 0.5d0))) / a))) / y
    else if (b <= (-1.25d+129)) then
        tmp = x / (a * (y * (1.0d0 - t_1)))
    else if (b <= (-2.3d-213)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-1.45d-269)) then
        tmp = (b / y) * (x / -a)
    else if (b <= 2.8d-301) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a - (a * t_1))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (-1.0 - (b * 0.5));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y;
	} else if (b <= -1.25e+129) {
		tmp = x / (a * (y * (1.0 - t_1)));
	} else if (b <= -2.3e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.45e-269) {
		tmp = (b / y) * (x / -a);
	} else if (b <= 2.8e-301) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a - (a * t_1))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (-1.0 - (b * 0.5))
	tmp = 0
	if b <= -1.25e+191:
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y
	elif b <= -1.25e+129:
		tmp = x / (a * (y * (1.0 - t_1)))
	elif b <= -2.3e-213:
		tmp = 1.0 / (a * (y / x))
	elif b <= -1.45e-269:
		tmp = (b / y) * (x / -a)
	elif b <= 2.8e-301:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a - (a * t_1))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(-1.0 - Float64(b * 0.5)))
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = Float64(Float64(Float64(x / a) - Float64(b * Float64(Float64(x - Float64(x * Float64(b * 0.5))) / a))) / y);
	elseif (b <= -1.25e+129)
		tmp = Float64(x / Float64(a * Float64(y * Float64(1.0 - t_1))));
	elseif (b <= -2.3e-213)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -1.45e-269)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	elseif (b <= 2.8e-301)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a - Float64(a * t_1))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (-1.0 - (b * 0.5));
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = ((x / a) - (b * ((x - (x * (b * 0.5))) / a))) / y;
	elseif (b <= -1.25e+129)
		tmp = x / (a * (y * (1.0 - t_1)));
	elseif (b <= -2.3e-213)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -1.45e-269)
		tmp = (b / y) * (x / -a);
	elseif (b <= 2.8e-301)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a - (a * t_1))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(-1.0 - N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+191], N[(N[(N[(x / a), $MachinePrecision] - N[(b * N[(N[(x - N[(x * N[(b * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.25e+129], N[(x / N[(a * N[(y * N[(1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.3e-213], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e-269], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-301], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a - N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.25000000000000005e191

   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 93.0%

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

      1. div-exp 75.1%

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

      2. exp-to-pow 75.1%

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

      3. sub-neg 75.1%

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

      4. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 93.0%

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

   7. Taylor expanded in b around 0 71.7%

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

   8. Taylor expanded in b around 0 71.7%

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

   10. Simplified 89.6%

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

   if -1.25000000000000005e191 < b < -1.2500000000000001e129

   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 54.1%

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

      1. div-exp 40.7%

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

      2. exp-to-pow 40.7%

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

      3. sub-neg 40.7%

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

      4. metadata-eval 40.7%

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

   5. Simplified 40.7%

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

   6. Taylor expanded in t around 0 40.9%

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

   7. Taylor expanded in b around 0 60.8%

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

   8. Taylor expanded in a around 0 67.3%

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

   if -1.2500000000000001e129 < b < -2.30000000000000003e-213

   1. Initial program 99.1%

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

      1. associate-/l* 96.6%

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

      2. associate--l+ 96.6%

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

      3. exp-sum 82.8%

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

      4. associate-/l* 82.8%

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

      5. *-commutative 82.8%

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

      6. exp-to-pow 82.8%

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

      7. exp-diff 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 69.3%

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

      10. sub-neg 69.3%

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

      11. metadata-eval 69.3%

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

   3. Simplified 69.3%

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

   5. Taylor expanded in t around 0 58.9%

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

      1. times-frac 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in y around 0 47.3%

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

      1. associate-*r* 44.2%

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

   10. Simplified 44.2%

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

   11. Taylor expanded in b around 0 35.4%

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

       1. clear-num 35.6%

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

       2. inv-pow 35.6%

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

   13. Applied egg-rr 35.6%

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

       1. unpow-1 35.6%

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

       2. associate-/l* 40.1%

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

   15. Simplified 40.1%

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

   if -2.30000000000000003e-213 < b < -1.45e-269

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 41.3%

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

      1. div-exp 41.3%

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

      2. exp-to-pow 42.3%

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

      3. sub-neg 42.3%

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

      4. metadata-eval 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in t around 0 23.2%

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

   7. Taylor expanded in b around 0 23.2%

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

      1. +-commutative 23.2%

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

      2. mul-1-neg 23.2%

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

      3. unsub-neg 23.2%

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

      4. associate-/l* 23.2%

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

   9. Simplified 23.2%

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

   10. Taylor expanded in b around inf 56.8%

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

       1. mul-1-neg 56.8%

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

       2. *-commutative 56.8%

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

       3. times-frac 61.6%

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

       4. distribute-rgt-neg-in 61.6%

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

   12. Simplified 61.6%

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

   if -1.45e-269 < b < 2.8000000000000001e-301

   1. Initial program 87.5%

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

   3. Taylor expanded in y around 0 63.8%

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

      1. div-exp 63.8%

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

      2. exp-to-pow 64.1%

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

      3. sub-neg 64.1%

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

      4. metadata-eval 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in t around 0 44.8%

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

   7. Taylor expanded in b around 0 44.8%

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

      1. +-commutative 44.8%

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

      2. mul-1-neg 44.8%

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

      3. unsub-neg 44.8%

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

      4. associate-/l* 44.8%

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

   9. Simplified 44.8%

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

   10. Taylor expanded in b around inf 64.8%

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

   if 2.8000000000000001e-301 < b

   1. Initial program 97.9%

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

   3. Taylor expanded in y around 0 82.8%

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

      1. div-exp 72.1%

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

      2. exp-to-pow 72.7%

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

      3. sub-neg 72.7%

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

      4. metadata-eval 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in t around 0 59.4%

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

   7. Taylor expanded in b around 0 46.7%

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

   8. Taylor expanded in a around 0 51.1%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{x}{a} - b \cdot \frac{x - x \cdot \left(b \cdot 0.5\right)}{a}}{y}\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+129}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot \left(1 - b \cdot \left(-1 - b \cdot 0.5\right)\right)\right)}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-269}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a - a \cdot \left(b \cdot \left(-1 - b \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.9% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-211}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-265}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (+ y (* y b))))))
   (if (<= b -1.25e+191)
     (/ (* x (/ b (- a))) y)
     (if (<= b -2.3e+158)
       t_1
       (if (<= b -5.2e+75)
         (/ (* b (/ x a)) (- y))
         (if (<= b -6e-211)
           (/ 1.0 (* a (/ y x)))
           (if (<= b -1e-265) (* (/ b y) (/ x (- a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (y * b)));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -2.3e+158) {
		tmp = t_1;
	} else if (b <= -5.2e+75) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -6e-211) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1e-265) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a * (y + (y * b)))
    if (b <= (-1.25d+191)) then
        tmp = (x * (b / -a)) / y
    else if (b <= (-2.3d+158)) then
        tmp = t_1
    else if (b <= (-5.2d+75)) then
        tmp = (b * (x / a)) / -y
    else if (b <= (-6d-211)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-1d-265)) then
        tmp = (b / y) * (x / -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (y * b)));
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -2.3e+158) {
		tmp = t_1;
	} else if (b <= -5.2e+75) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -6e-211) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1e-265) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y + (y * b)))
	tmp = 0
	if b <= -1.25e+191:
		tmp = (x * (b / -a)) / y
	elif b <= -2.3e+158:
		tmp = t_1
	elif b <= -5.2e+75:
		tmp = (b * (x / a)) / -y
	elif b <= -6e-211:
		tmp = 1.0 / (a * (y / x))
	elif b <= -1e-265:
		tmp = (b / y) * (x / -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y + Float64(y * b))))
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= -2.3e+158)
		tmp = t_1;
	elseif (b <= -5.2e+75)
		tmp = Float64(Float64(b * Float64(x / a)) / Float64(-y));
	elseif (b <= -6e-211)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -1e-265)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y + (y * b)));
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = (x * (b / -a)) / y;
	elseif (b <= -2.3e+158)
		tmp = t_1;
	elseif (b <= -5.2e+75)
		tmp = (b * (x / a)) / -y;
	elseif (b <= -6e-211)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -1e-265)
		tmp = (b / y) * (x / -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.25e+191], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -2.3e+158], t$95$1, If[LessEqual[b, -5.2e+75], N[(N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, -6e-211], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1e-265], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.25000000000000005e191

   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 93.0%

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

      1. div-exp 75.1%

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

      2. exp-to-pow 75.1%

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

      3. sub-neg 75.1%

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

      4. metadata-eval 75.1%

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

   5. Simplified 75.1%

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

   6. Taylor expanded in t around 0 93.0%

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

   7. Taylor expanded in b around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. mul-1-neg 69.0%

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

      3. unsub-neg 69.0%

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

      4. associate-/l* 62.2%

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

   9. Simplified 62.2%

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

   10. Taylor expanded in b around inf 69.0%

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

       1. associate-*r/ 69.0%

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

       2. associate-*r* 69.0%

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

       3. neg-mul-1 69.0%

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

       4. associate-*l/ 69.0%

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

       5. neg-mul-1 69.0%

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

       6. associate-*r/ 69.0%

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

       7. *-commutative 69.0%

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

       8. associate-*l* 69.0%

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

       9. mul-1-neg 69.0%

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

   12. Simplified 69.0%

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

   if -1.25000000000000005e191 < b < -2.29999999999999986e158 or -9.99999999999999985e-266 < b

   1. Initial program 97.5%

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

      1. associate-/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 76.6%

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

      4. associate-/l* 76.0%

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

      5. *-commutative 76.0%

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

      6. exp-to-pow 76.0%

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

      7. exp-diff 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 t around 0 59.8%

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

      1. times-frac 53.7%

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

   7. Simplified 53.7%

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

   8. Taylor expanded in y around 0 53.9%

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

      1. associate-*r* 50.5%

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

   10. Simplified 50.5%

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

   11. Taylor expanded in b around 0 34.4%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   12. Step-by-step derivation

       1. distribute-lft-out 36.4%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 36.4%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   13. Simplified 36.4%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   if -2.29999999999999986e158 < b < -5.1999999999999997e75

   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 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 62.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 62.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 62.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 62.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 62.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 62.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 35.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 35.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 35.6%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 35.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 44.7%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 44.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 35.6%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   11. Step-by-step derivation

       1. associate-/l* 44.7%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(b \cdot \frac{x}{a}\right)}}{y} \]

       2. associate-*r* 44.7%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot b\right) \cdot \frac{x}{a}}}{y} \]

       3. neg-mul-1 44.7%

          \[\leadsto \frac{\color{blue}{\left(-b\right)} \cdot \frac{x}{a}}{y} \]

       4. *-commutative 44.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} \cdot \left(-b\right)}}{y} \]

   12. Simplified 44.7%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} \cdot \left(-b\right)}}{y} \]

   if -5.1999999999999997e75 < b < -6.00000000000000009e-211

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 95.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 95.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 85.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.1%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 76.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 76.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 77.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 61.1%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 61.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 43.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 43.1%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 43.1%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 34.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. clear-num 35.1%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 35.1%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   13. Applied egg-rr 35.1%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 35.1%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 43.0%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 43.0%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if -6.00000000000000009e-211 < b < -9.99999999999999985e-266

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 41.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 41.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 42.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 42.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 42.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 42.3%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 23.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 23.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 23.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 23.2%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 23.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 23.2%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 23.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 56.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 56.8%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 56.8%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{a \cdot y} \]

       3. times-frac 61.6%

          \[\leadsto -\color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

       4. distribute-rgt-neg-in 61.6%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

   12. Simplified 61.6%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+75}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-211}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-265}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 38.3% accurate, 9.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+74}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-200}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-265}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+191)
   (/ (* x (/ b (- a))) y)
   (if (<= b -4.1e+157)
     (/ x (* a (+ y (* y b))))
     (if (<= b -9e+74)
       (/ (* b (/ x a)) (- y))
       (if (<= b -6e-200)
         (/ 1.0 (* a (/ y x)))
         (if (<= b -1.1e-265)
           (* (/ b y) (/ x (- a)))
           (/ (/ x (+ a (* a b))) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -4.1e+157) {
		tmp = x / (a * (y + (y * b)));
	} else if (b <= -9e+74) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -6e-200) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.1e-265) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+191)) then
        tmp = (x * (b / -a)) / y
    else if (b <= (-4.1d+157)) then
        tmp = x / (a * (y + (y * b)))
    else if (b <= (-9d+74)) then
        tmp = (b * (x / a)) / -y
    else if (b <= (-6d-200)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-1.1d-265)) then
        tmp = (b / y) * (x / -a)
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -4.1e+157) {
		tmp = x / (a * (y + (y * b)));
	} else if (b <= -9e+74) {
		tmp = (b * (x / a)) / -y;
	} else if (b <= -6e-200) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.1e-265) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+191:
		tmp = (x * (b / -a)) / y
	elif b <= -4.1e+157:
		tmp = x / (a * (y + (y * b)))
	elif b <= -9e+74:
		tmp = (b * (x / a)) / -y
	elif b <= -6e-200:
		tmp = 1.0 / (a * (y / x))
	elif b <= -1.1e-265:
		tmp = (b / y) * (x / -a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= -4.1e+157)
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	elseif (b <= -9e+74)
		tmp = Float64(Float64(b * Float64(x / a)) / Float64(-y));
	elseif (b <= -6e-200)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -1.1e-265)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = (x * (b / -a)) / y;
	elseif (b <= -4.1e+157)
		tmp = x / (a * (y + (y * b)));
	elseif (b <= -9e+74)
		tmp = (b * (x / a)) / -y;
	elseif (b <= -6e-200)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -1.1e-265)
		tmp = (b / y) * (x / -a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+191], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -4.1e+157], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -9e+74], N[(N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision] / (-y)), $MachinePrecision], If[LessEqual[b, -6e-200], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-265], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.25000000000000005e191

   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 93.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 75.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 75.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 75.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 75.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 75.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 93.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 69.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 69.0%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 62.2%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 62.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 69.0%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   11. Step-by-step derivation

       1. associate-*r/ 69.0%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a}}}{y} \]

       2. associate-*r* 69.0%

          \[\leadsto \frac{\frac{\color{blue}{\left(-1 \cdot b\right) \cdot x}}{a}}{y} \]

       3. neg-mul-1 69.0%

          \[\leadsto \frac{\frac{\color{blue}{\left(-b\right)} \cdot x}{a}}{y} \]

       4. associate-*l/ 69.0%

          \[\leadsto \frac{\color{blue}{\frac{-b}{a} \cdot x}}{y} \]

       5. neg-mul-1 69.0%

          \[\leadsto \frac{\frac{\color{blue}{-1 \cdot b}}{a} \cdot x}{y} \]

       6. associate-*r/ 69.0%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a}\right)} \cdot x}{y} \]

       7. *-commutative 69.0%

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{a} \cdot -1\right)} \cdot x}{y} \]

       8. associate-*l* 69.0%

          \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-1 \cdot x\right)}}{y} \]

       9. mul-1-neg 69.0%

          \[\leadsto \frac{\frac{b}{a} \cdot \color{blue}{\left(-x\right)}}{y} \]

   12. Simplified 69.0%

       \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-x\right)}}{y} \]

   if -1.25000000000000005e191 < b < -4.10000000000000016e157

   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 36.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 36.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 36.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 36.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 27.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 27.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 27.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 27.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 27.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 27.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 27.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 27.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 28.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 18.9%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 18.9%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 45.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   12. Step-by-step derivation

       1. distribute-lft-out 73.1%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 73.1%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   13. Simplified 73.1%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   if -4.10000000000000016e157 < b < -8.9999999999999999e74

   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 85.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 62.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 62.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 62.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 62.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 62.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 62.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 35.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 35.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 35.6%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 35.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 44.7%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 44.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 35.6%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   11. Step-by-step derivation

       1. associate-/l* 44.7%

          \[\leadsto \frac{-1 \cdot \color{blue}{\left(b \cdot \frac{x}{a}\right)}}{y} \]

       2. associate-*r* 44.7%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot b\right) \cdot \frac{x}{a}}}{y} \]

       3. neg-mul-1 44.7%

          \[\leadsto \frac{\color{blue}{\left(-b\right)} \cdot \frac{x}{a}}{y} \]

       4. *-commutative 44.7%

          \[\leadsto \frac{\color{blue}{\frac{x}{a} \cdot \left(-b\right)}}{y} \]

   12. Simplified 44.7%

       \[\leadsto \frac{\color{blue}{\frac{x}{a} \cdot \left(-b\right)}}{y} \]

   if -8.9999999999999999e74 < b < -5.99999999999999989e-200

   1. Initial program 98.8%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 95.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 95.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 85.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 85.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 85.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 85.1%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 76.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 76.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 77.2%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.2%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.2%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 63.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 61.1%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 61.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 43.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 43.1%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 43.1%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 34.8%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. clear-num 35.1%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 35.1%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   13. Applied egg-rr 35.1%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 35.1%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 43.0%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 43.0%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if -5.99999999999999989e-200 < b < -1.10000000000000005e-265

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 41.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 41.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 42.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 42.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 42.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 42.3%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 23.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 23.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 23.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 23.2%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 23.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 23.2%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 23.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 56.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 56.8%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 56.8%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{a \cdot y} \]

       3. times-frac 61.6%

          \[\leadsto -\color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

       4. distribute-rgt-neg-in 61.6%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

   12. Simplified 61.6%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

   if -1.10000000000000005e-265 < b

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 71.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 72.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 72.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 72.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 72.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 58.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 38.4%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 6 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{+157}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq -9 \cdot 10^{+74}:\\ \;\;\;\;\frac{b \cdot \frac{x}{a}}{-y}\\ \mathbf{elif}\;b \leq -6 \cdot 10^{-200}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-265}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.4% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-297}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+191)
   (/ (* x (/ b (- a))) y)
   (if (<= b -4.2e+158)
     (/ x (* a (+ y (* y b))))
     (if (<= b 5.6e-297)
       (/ (* b (- (/ x (* a b)) (/ x a))) y)
       (/ (/ x (+ a (* a b))) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -4.2e+158) {
		tmp = x / (a * (y + (y * b)));
	} else if (b <= 5.6e-297) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.25d+191)) then
        tmp = (x * (b / -a)) / y
    else if (b <= (-4.2d+158)) then
        tmp = x / (a * (y + (y * b)))
    else if (b <= 5.6d-297) then
        tmp = (b * ((x / (a * b)) - (x / a))) / y
    else
        tmp = (x / (a + (a * b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+191) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -4.2e+158) {
		tmp = x / (a * (y + (y * b)));
	} else if (b <= 5.6e-297) {
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+191:
		tmp = (x * (b / -a)) / y
	elif b <= -4.2e+158:
		tmp = x / (a * (y + (y * b)))
	elif b <= 5.6e-297:
		tmp = (b * ((x / (a * b)) - (x / a))) / y
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+191)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= -4.2e+158)
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	elseif (b <= 5.6e-297)
		tmp = Float64(Float64(b * Float64(Float64(x / Float64(a * b)) - Float64(x / a))) / y);
	else
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.25e+191)
		tmp = (x * (b / -a)) / y;
	elseif (b <= -4.2e+158)
		tmp = x / (a * (y + (y * b)));
	elseif (b <= 5.6e-297)
		tmp = (b * ((x / (a * b)) - (x / a))) / y;
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+191], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -4.2e+158], N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.6e-297], N[(N[(b * N[(N[(x / N[(a * b), $MachinePrecision]), $MachinePrecision] - N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.25000000000000005e191

   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 93.0%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 75.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 75.1%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 75.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 75.1%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 75.1%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 93.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 69.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 69.0%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 69.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 62.2%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 62.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 69.0%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   11. Step-by-step derivation

       1. associate-*r/ 69.0%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a}}}{y} \]

       2. associate-*r* 69.0%

          \[\leadsto \frac{\frac{\color{blue}{\left(-1 \cdot b\right) \cdot x}}{a}}{y} \]

       3. neg-mul-1 69.0%

          \[\leadsto \frac{\frac{\color{blue}{\left(-b\right)} \cdot x}{a}}{y} \]

       4. associate-*l/ 69.0%

          \[\leadsto \frac{\color{blue}{\frac{-b}{a} \cdot x}}{y} \]

       5. neg-mul-1 69.0%

          \[\leadsto \frac{\frac{\color{blue}{-1 \cdot b}}{a} \cdot x}{y} \]

       6. associate-*r/ 69.0%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a}\right)} \cdot x}{y} \]

       7. *-commutative 69.0%

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{a} \cdot -1\right)} \cdot x}{y} \]

       8. associate-*l* 69.0%

          \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-1 \cdot x\right)}}{y} \]

       9. mul-1-neg 69.0%

          \[\leadsto \frac{\frac{b}{a} \cdot \color{blue}{\left(-x\right)}}{y} \]

   12. Simplified 69.0%

       \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-x\right)}}{y} \]

   if -1.25000000000000005e191 < b < -4.1999999999999998e158

   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 36.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 36.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 36.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 36.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 27.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 27.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 27.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 27.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 27.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 27.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 27.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 27.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 27.4%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 28.4%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 18.9%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 18.9%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 45.7%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   12. Step-by-step derivation

       1. distribute-lft-out 73.1%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 73.1%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   13. Simplified 73.1%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   if -4.1999999999999998e158 < b < 5.59999999999999968e-297

   1. Initial program 98.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 64.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 64.8%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 64.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 64.8%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 64.8%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 46.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 34.8%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 34.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 34.8%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 34.8%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 36.9%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 36.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 40.6%

       \[\leadsto \frac{\color{blue}{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}}{y} \]

   if 5.59999999999999968e-297 < b

   1. Initial program 97.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 72.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 72.7%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 72.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 72.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 72.7%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 59.4%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 38.0%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 43.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+191}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-297}:\\ \;\;\;\;\frac{b \cdot \left(\frac{x}{a \cdot b} - \frac{x}{a}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 35.2% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 370000000000:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* a (+ y (* y b))))))
   (if (<= y -3.6e-13)
     t_1
     (if (<= y 370000000000.0)
       (/ (- x (* x b)) (* y a))
       (if (<= y 4.7e+94) (/ (* x (/ b (- a))) y) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (y * b)));
	double tmp;
	if (y <= -3.6e-13) {
		tmp = t_1;
	} else if (y <= 370000000000.0) {
		tmp = (x - (x * b)) / (y * a);
	} else if (y <= 4.7e+94) {
		tmp = (x * (b / -a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (a * (y + (y * b)))
    if (y <= (-3.6d-13)) then
        tmp = t_1
    else if (y <= 370000000000.0d0) then
        tmp = (x - (x * b)) / (y * a)
    else if (y <= 4.7d+94) then
        tmp = (x * (b / -a)) / y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (a * (y + (y * b)));
	double tmp;
	if (y <= -3.6e-13) {
		tmp = t_1;
	} else if (y <= 370000000000.0) {
		tmp = (x - (x * b)) / (y * a);
	} else if (y <= 4.7e+94) {
		tmp = (x * (b / -a)) / y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (a * (y + (y * b)))
	tmp = 0
	if y <= -3.6e-13:
		tmp = t_1
	elif y <= 370000000000.0:
		tmp = (x - (x * b)) / (y * a)
	elif y <= 4.7e+94:
		tmp = (x * (b / -a)) / y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(a * Float64(y + Float64(y * b))))
	tmp = 0.0
	if (y <= -3.6e-13)
		tmp = t_1;
	elseif (y <= 370000000000.0)
		tmp = Float64(Float64(x - Float64(x * b)) / Float64(y * a));
	elseif (y <= 4.7e+94)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (a * (y + (y * b)));
	tmp = 0.0;
	if (y <= -3.6e-13)
		tmp = t_1;
	elseif (y <= 370000000000.0)
		tmp = (x - (x * b)) / (y * a);
	elseif (y <= 4.7e+94)
		tmp = (x * (b / -a)) / y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.6e-13], t$95$1, If[LessEqual[y, 370000000000.0], N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.7e+94], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5999999999999998e-13 or 4.70000000000000017e94 < y

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 58.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 57.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 57.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 57.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 48.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 48.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 49.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 49.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 49.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 49.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 54.0%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 49.1%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 49.1%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 44.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 37.9%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 37.9%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 33.4%

       \[\leadsto \frac{x}{\color{blue}{a \cdot y + a \cdot \left(b \cdot y\right)}} \]
   12. Step-by-step derivation

       1. distribute-lft-out 39.2%

          \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + b \cdot y\right)}} \]

       2. *-commutative 39.2%

          \[\leadsto \frac{x}{a \cdot \left(y + \color{blue}{y \cdot b}\right)} \]

   13. Simplified 39.2%

       \[\leadsto \frac{x}{\color{blue}{a \cdot \left(y + y \cdot b\right)}} \]

   if -3.5999999999999998e-13 < y < 3.7e11

   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 95.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 83.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 84.6%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 84.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 84.6%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 84.6%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 68.1%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 45.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 45.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 45.0%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 45.0%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 45.7%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 45.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in a around 0 43.7%

       \[\leadsto \color{blue}{\frac{x - b \cdot x}{a \cdot y}} \]

   if 3.7e11 < y < 4.70000000000000017e94

   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 58.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 44.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 44.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 44.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 44.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 44.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 35.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 7.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 7.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 7.7%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 7.7%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 7.7%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 7.7%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 30.6%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   11. Step-by-step derivation

       1. associate-*r/ 30.6%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a}}}{y} \]

       2. associate-*r* 30.6%

          \[\leadsto \frac{\frac{\color{blue}{\left(-1 \cdot b\right) \cdot x}}{a}}{y} \]

       3. neg-mul-1 30.6%

          \[\leadsto \frac{\frac{\color{blue}{\left(-b\right)} \cdot x}{a}}{y} \]

       4. associate-*l/ 31.0%

          \[\leadsto \frac{\color{blue}{\frac{-b}{a} \cdot x}}{y} \]

       5. neg-mul-1 31.0%

          \[\leadsto \frac{\frac{\color{blue}{-1 \cdot b}}{a} \cdot x}{y} \]

       6. associate-*r/ 31.0%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a}\right)} \cdot x}{y} \]

       7. *-commutative 31.0%

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{a} \cdot -1\right)} \cdot x}{y} \]

       8. associate-*l* 31.0%

          \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-1 \cdot x\right)}}{y} \]

       9. mul-1-neg 31.0%

          \[\leadsto \frac{\frac{b}{a} \cdot \color{blue}{\left(-x\right)}}{y} \]

   12. Simplified 31.0%

       \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-x\right)}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \mathbf{elif}\;y \leq 370000000000:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 33.7% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{if}\;b \leq -3.1 \cdot 10^{+191}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-265}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (/ b y) (/ x (- a)))))
   (if (<= b -3.1e+191)
     t_1
     (if (<= b -8e-213)
       (/ 1.0 (* a (/ y x)))
       (if (<= b -1.1e-265) t_1 (/ (/ x a) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b / y) * (x / -a);
	double tmp;
	if (b <= -3.1e+191) {
		tmp = t_1;
	} else if (b <= -8e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.1e-265) {
		tmp = t_1;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (b / y) * (x / -a)
    if (b <= (-3.1d+191)) then
        tmp = t_1
    else if (b <= (-8d-213)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-1.1d-265)) then
        tmp = t_1
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (b / y) * (x / -a);
	double tmp;
	if (b <= -3.1e+191) {
		tmp = t_1;
	} else if (b <= -8e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.1e-265) {
		tmp = t_1;
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (b / y) * (x / -a)
	tmp = 0
	if b <= -3.1e+191:
		tmp = t_1
	elif b <= -8e-213:
		tmp = 1.0 / (a * (y / x))
	elif b <= -1.1e-265:
		tmp = t_1
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(b / y) * Float64(x / Float64(-a)))
	tmp = 0.0
	if (b <= -3.1e+191)
		tmp = t_1;
	elseif (b <= -8e-213)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -1.1e-265)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (b / y) * (x / -a);
	tmp = 0.0;
	if (b <= -3.1e+191)
		tmp = t_1;
	elseif (b <= -8e-213)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -1.1e-265)
		tmp = t_1;
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.1e+191], t$95$1, If[LessEqual[b, -8e-213], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.1e-265], t$95$1, N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.09999999999999999e191 or -7.9999999999999996e-213 < b < -1.10000000000000005e-265

   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 79.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 66.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 66.4%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 66.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 66.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 66.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 74.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 56.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 56.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 56.9%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 56.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 51.9%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 51.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 60.5%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 60.5%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 60.5%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{a \cdot y} \]

       3. times-frac 62.0%

          \[\leadsto -\color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

       4. distribute-rgt-neg-in 62.0%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

   12. Simplified 62.0%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

   if -3.09999999999999999e191 < b < -7.9999999999999996e-213

   1. Initial program 99.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 76.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 76.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 76.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 76.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 63.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 63.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 63.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 63.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 63.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 55.4%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 53.0%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 53.0%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 46.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 42.3%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 42.3%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 36.7%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. clear-num 36.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 36.9%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   13. Applied egg-rr 36.9%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 36.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 40.5%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 40.5%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if -1.10000000000000005e-265 < b

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 71.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 72.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 72.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 72.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 72.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 58.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 30.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.1 \cdot 10^{+191}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-265}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 34.8% accurate, 13.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-269}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.5e+103)
   (/ (* x (/ b (- a))) y)
   (if (<= b -2.3e-213)
     (/ 1.0 (* a (/ y x)))
     (if (<= b -1.45e-269) (* (/ b y) (/ x (- a))) (/ (/ x a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+103) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -2.3e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.45e-269) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-6.5d+103)) then
        tmp = (x * (b / -a)) / y
    else if (b <= (-2.3d-213)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= (-1.45d-269)) then
        tmp = (b / y) * (x / -a)
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.5e+103) {
		tmp = (x * (b / -a)) / y;
	} else if (b <= -2.3e-213) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= -1.45e-269) {
		tmp = (b / y) * (x / -a);
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.5e+103:
		tmp = (x * (b / -a)) / y
	elif b <= -2.3e-213:
		tmp = 1.0 / (a * (y / x))
	elif b <= -1.45e-269:
		tmp = (b / y) * (x / -a)
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.5e+103)
		tmp = Float64(Float64(x * Float64(b / Float64(-a))) / y);
	elseif (b <= -2.3e-213)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= -1.45e-269)
		tmp = Float64(Float64(b / y) * Float64(x / Float64(-a)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.5e+103)
		tmp = (x * (b / -a)) / y;
	elseif (b <= -2.3e-213)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= -1.45e-269)
		tmp = (b / y) * (x / -a);
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.5e+103], N[(N[(x * N[(b / (-a)), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -2.3e-213], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e-269], N[(N[(b / y), $MachinePrecision] * N[(x / (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -6.50000000000000001e103

   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 81.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 67.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      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%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 77.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 54.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 54.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 54.6%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 54.6%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 50.8%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 50.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 54.6%

       \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a}}}{y} \]
   11. Step-by-step derivation

       1. associate-*r/ 54.6%

          \[\leadsto \frac{\color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{a}}}{y} \]

       2. associate-*r* 54.6%

          \[\leadsto \frac{\frac{\color{blue}{\left(-1 \cdot b\right) \cdot x}}{a}}{y} \]

       3. neg-mul-1 54.6%

          \[\leadsto \frac{\frac{\color{blue}{\left(-b\right)} \cdot x}{a}}{y} \]

       4. associate-*l/ 56.6%

          \[\leadsto \frac{\color{blue}{\frac{-b}{a} \cdot x}}{y} \]

       5. neg-mul-1 56.6%

          \[\leadsto \frac{\frac{\color{blue}{-1 \cdot b}}{a} \cdot x}{y} \]

       6. associate-*r/ 56.6%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \frac{b}{a}\right)} \cdot x}{y} \]

       7. *-commutative 56.6%

          \[\leadsto \frac{\color{blue}{\left(\frac{b}{a} \cdot -1\right)} \cdot x}{y} \]

       8. associate-*l* 56.6%

          \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-1 \cdot x\right)}}{y} \]

       9. mul-1-neg 56.6%

          \[\leadsto \frac{\frac{b}{a} \cdot \color{blue}{\left(-x\right)}}{y} \]

   12. Simplified 56.6%

       \[\leadsto \frac{\color{blue}{\frac{b}{a} \cdot \left(-x\right)}}{y} \]

   if -6.50000000000000001e103 < b < -2.30000000000000003e-213

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 96.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 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 82.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 67.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 67.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 67.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 67.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 67.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 67.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 56.5%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 54.9%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 54.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 42.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 40.3%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 40.3%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 35.5%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. clear-num 35.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 35.7%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   13. Applied egg-rr 35.7%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 35.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 42.1%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 42.1%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if -2.30000000000000003e-213 < b < -1.45e-269

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 41.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 41.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 42.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 42.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 42.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 42.3%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 23.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 23.2%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   8. Step-by-step derivation

      1. +-commutative 23.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 23.2%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 23.2%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. associate-/l* 23.2%

         \[\leadsto \frac{\frac{x}{a} - \color{blue}{b \cdot \frac{x}{a}}}{y} \]

   9. Simplified 23.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - b \cdot \frac{x}{a}}}{y} \]

   10. Taylor expanded in b around inf 56.8%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   11. Step-by-step derivation

       1. mul-1-neg 56.8%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. *-commutative 56.8%

          \[\leadsto -\frac{\color{blue}{x \cdot b}}{a \cdot y} \]

       3. times-frac 61.6%

          \[\leadsto -\color{blue}{\frac{x}{a} \cdot \frac{b}{y}} \]

       4. distribute-rgt-neg-in 61.6%

          \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

   12. Simplified 61.6%

       \[\leadsto \color{blue}{\frac{x}{a} \cdot \left(-\frac{b}{y}\right)} \]

   if -1.45e-269 < b

   1. Initial program 97.3%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 71.6%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 72.2%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 72.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 72.2%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 72.2%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 58.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 30.5%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.5 \cdot 10^{+103}:\\ \;\;\;\;\frac{x \cdot \frac{b}{-a}}{y}\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-213}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-269}:\\ \;\;\;\;\frac{b}{y} \cdot \frac{x}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 31.3% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-274}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e-274) (/ 1.0 (* a (/ y x))) (/ (/ x a) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e-274) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-3.5d-274)) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -3.5e-274) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -3.5e-274:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -3.5e-274)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e-274)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -3.5e-274], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.49999999999999982e-274

   1. Initial program 98.7%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 75.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 75.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 75.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 75.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 64.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 64.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 64.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 64.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 64.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 64.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 61.7%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 59.2%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 59.2%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 56.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 50.6%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 50.6%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 36.4%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   12. Step-by-step derivation

       1. clear-num 36.5%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 36.5%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   13. Applied egg-rr 36.5%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   14. Step-by-step derivation

       1. unpow-1 36.5%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 38.2%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   15. Simplified 38.2%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if -3.49999999999999982e-274 < b

   1. Initial program 98.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 82.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 72.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 72.7%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 72.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 72.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 72.7%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 59.0%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 30.7%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{-274}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 31.9% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{-117}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.95e-117) (/ (/ 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 <= 1.95e-117) {
		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 <= 1.95d-117) 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 <= 1.95e-117) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.95e-117:
		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 <= 1.95e-117)
		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 <= 1.95e-117)
		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, 1.95e-117], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.94999999999999996e-117

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.3%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 70.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 70.7%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 70.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 70.7%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 70.7%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 62.3%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 38.8%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 1.94999999999999996e-117 < a

   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* 99.3%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.3%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 78.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 77.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 77.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 77.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 66.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 66.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 66.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 66.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 66.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 59.1%

      \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
   6. Step-by-step derivation

      1. times-frac 55.8%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   7. Simplified 55.8%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

   8. Taylor expanded in y around 0 56.9%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
   9. Step-by-step derivation

      1. associate-*r* 52.3%

         \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

   10. Simplified 52.3%

       \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

   11. Taylor expanded in b around 0 31.9%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.95 \cdot 10^{-117}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.6% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.3%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.0%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.0%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 77.7%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 77.3%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   5. *-commutative 77.3%

      \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   6. exp-to-pow 77.3%

      \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

   7. exp-diff 67.1%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 67.1%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 67.6%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 67.6%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 67.6%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 67.6%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in t around 0 61.9%

   \[\leadsto \color{blue}{\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}} \]
6. Step-by-step derivation

   1. times-frac 57.6%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

7. Simplified 57.6%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot \frac{{z}^{y}}{y \cdot e^{b}}} \]

8. Taylor expanded in y around 0 56.0%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]
9. Step-by-step derivation

   1. associate-*r* 51.7%

      \[\leadsto \frac{x}{\color{blue}{\left(a \cdot y\right) \cdot e^{b}}} \]

10. Simplified 51.7%

    \[\leadsto \color{blue}{\frac{x}{\left(a \cdot y\right) \cdot e^{b}}} \]

11. Taylor expanded in b around 0 31.5%

    \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

12. Final simplification 31.5%

    \[\leadsto \frac{x}{y \cdot a} \]
13. Add Preprocessing

Developer target: 72.4% 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 2024084 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (if (< t -0.8845848504127471) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z)))) (if (< t 852031.2288374073) (/ (* (/ x y) (pow a (- t 1.0))) (exp (- b (* (log z) y)))) (/ (* x (/ (pow a (- t 1.0)) y)) (- (+ b 1.0) (* y (log z))))))

  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))