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

Percentage Accurate: 98.2% → 98.2%

Time: 18.4s

Alternatives: 29

Speedup: 1.0×

• 46.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

3. Final simplification 98.5%

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

Alternative 2: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -4 \cdot 10^{+44} \lor \neg \left(t + -1 \leq 50\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -4e+44) (not (<= (+ t -1.0) 50.0)))
   (/ (* 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 + -1.0) <= -4e+44) || !((t + -1.0) <= 50.0)) {
		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 + (-1.0d0)) <= (-4d+44)) .or. (.not. ((t + (-1.0d0)) <= 50.0d0))) 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 + -1.0) <= -4e+44) || !((t + -1.0) <= 50.0)) {
		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 + -1.0) <= -4e+44) or not ((t + -1.0) <= 50.0):
		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 ((Float64(t + -1.0) <= -4e+44) || !(Float64(t + -1.0) <= 50.0))
		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 + -1.0) <= -4e+44) || ~(((t + -1.0) <= 50.0)))
		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[N[(t + -1.0), $MachinePrecision], -4e+44], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 50.0]], $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 (-.f64 t #s(literal 1 binary64)) < -4.0000000000000004e44 or 50 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 95.0%

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

   if -4.0000000000000004e44 < (-.f64 t #s(literal 1 binary64)) < 50

   1. Initial program 97.1%

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

   3. Taylor expanded in t around 0 97.0%

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

      1. +-commutative 97.0%

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

      2. mul-1-neg 97.0%

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

      3. unsub-neg 97.0%

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

   5. Simplified 97.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -4 \cdot 10^{+44} \lor \neg \left(t + -1 \leq 50\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1.00000000000005 \lor \neg \left(t + -1 \leq 50\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1.00000000000005) (not (<= (+ t -1.0) 50.0)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (pow z y)) (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1.00000000000005) || !((t + -1.0) <= 50.0)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-1.00000000000005d0)) .or. (.not. ((t + (-1.0d0)) <= 50.0d0))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -1.00000000000005) || !((t + -1.0) <= 50.0)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -1.00000000000005) or not ((t + -1.0) <= 50.0):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -1.00000000000005) || !(Float64(t + -1.0) <= 50.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -1.00000000000005) || ~(((t + -1.0) <= 50.0)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -1.00000000000005], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], 50.0]], $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[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.00000000000004996 or 50 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.6%

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

   if -1.00000000000004996 < (-.f64 t #s(literal 1 binary64)) < 50

   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. Step-by-step derivation

      1. associate-/l* 96.9%

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

      2. associate--l+ 96.9%

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

      3. exp-sum 88.2%

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

      4. associate-/l* 85.1%

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

      5. *-commutative 85.1%

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

      6. exp-to-pow 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 85.1%

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

      8. *-commutative 85.1%

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

      9. exp-to-pow 86.5%

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

      10. sub-neg 86.5%

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

      11. metadata-eval 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in t around 0 87.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1.00000000000005 \lor \neg \left(t + -1 \leq 50\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+158}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t + -1 \leq 20000000000:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -2e+158)
   (/ (* x (pow a (+ t -1.0))) y)
   (if (<= (+ t -1.0) 20000000000.0)
     (/ (* x (pow z y)) (* a (* y (exp b))))
     (/ (/ (* x (pow a t)) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -2e+158) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if ((t + -1.0) <= 20000000000.0) {
		tmp = (x * pow(z, y)) / (a * (y * exp(b)));
	} else {
		tmp = ((x * pow(a, t)) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-2d+158)) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if ((t + (-1.0d0)) <= 20000000000.0d0) then
        tmp = (x * (z ** y)) / (a * (y * exp(b)))
    else
        tmp = ((x * (a ** t)) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -2e+158) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if ((t + -1.0) <= 20000000000.0) {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	} else {
		tmp = ((x * Math.pow(a, t)) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -2e+158:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif (t + -1.0) <= 20000000000.0:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	else:
		tmp = ((x * math.pow(a, t)) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -2e+158)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (Float64(t + -1.0) <= 20000000000.0)
		tmp = Float64(Float64(x * (z ^ y)) / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(Float64(x * (a ^ t)) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -2e+158)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif ((t + -1.0) <= 20000000000.0)
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	else
		tmp = ((x * (a ^ t)) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+158], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 20000000000.0], N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.99999999999999991e158

   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 0 100.0%

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

      1. div-exp 71.0%

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

      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 b around 0 93.6%

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

      1. exp-to-pow 93.6%

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

      2. sub-neg 93.6%

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

      3. metadata-eval 93.6%

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

      4. +-commutative 93.6%

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

   8. Simplified 93.6%

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

   if -1.99999999999999991e158 < (-.f64 t #s(literal 1 binary64)) < 2e10

   1. Initial program 97.6%

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

      1. associate-/l* 97.6%

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

      2. associate--l+ 97.6%

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

      3. exp-sum 88.4%

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

      4. associate-/l* 85.9%

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

      5. *-commutative 85.9%

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

      6. exp-to-pow 85.9%

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

      7. exp-diff 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 80.8%

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

      10. sub-neg 80.8%

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

      11. metadata-eval 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in t around 0 84.0%

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

   if 2e10 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

      1. div-exp 75.9%

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

      2. exp-to-pow 75.9%

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

      3. sub-neg 75.9%

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

      4. metadata-eval 75.9%

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

   5. Simplified 75.9%

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

      1. unpow-prod-up 75.9%

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

      2. unpow-1 75.9%

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

   7. Applied egg-rr 75.9%

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

      1. associate-*r/ 75.9%

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

      2. *-rgt-identity 75.9%

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

   9. Simplified 75.9%

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

   10. Taylor expanded in b around 0 84.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+158}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t + -1 \leq 20000000000:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+158}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t + -1 \leq 20000000000:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= (+ t -1.0) -2e+158)
   (/ (* x (pow a (+ t -1.0))) y)
   (if (<= (+ t -1.0) 20000000000.0)
     (* x (/ (pow z y) (* a (* y (exp b)))))
     (/ (/ (* x (pow a t)) a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -2e+158) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else if ((t + -1.0) <= 20000000000.0) {
		tmp = x * (pow(z, y) / (a * (y * exp(b))));
	} else {
		tmp = ((x * pow(a, t)) / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t + (-1.0d0)) <= (-2d+158)) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else if ((t + (-1.0d0)) <= 20000000000.0d0) then
        tmp = x * ((z ** y) / (a * (y * exp(b))))
    else
        tmp = ((x * (a ** t)) / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t + -1.0) <= -2e+158) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else if ((t + -1.0) <= 20000000000.0) {
		tmp = x * (Math.pow(z, y) / (a * (y * Math.exp(b))));
	} else {
		tmp = ((x * Math.pow(a, t)) / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t + -1.0) <= -2e+158:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	elif (t + -1.0) <= 20000000000.0:
		tmp = x * (math.pow(z, y) / (a * (y * math.exp(b))))
	else:
		tmp = ((x * math.pow(a, t)) / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(t + -1.0) <= -2e+158)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	elseif (Float64(t + -1.0) <= 20000000000.0)
		tmp = Float64(x * Float64((z ^ y) / Float64(a * Float64(y * exp(b)))));
	else
		tmp = Float64(Float64(Float64(x * (a ^ t)) / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t + -1.0) <= -2e+158)
		tmp = (x * (a ^ (t + -1.0))) / y;
	elseif ((t + -1.0) <= 20000000000.0)
		tmp = x * ((z ^ y) / (a * (y * exp(b))));
	else
		tmp = ((x * (a ^ t)) / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(t + -1.0), $MachinePrecision], -2e+158], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], 20000000000.0], N[(x * N[(N[Power[z, y], $MachinePrecision] / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t #s(literal 1 binary64)) < -1.99999999999999991e158

   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 0 100.0%

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

      1. div-exp 71.0%

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

      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 b around 0 93.6%

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

      1. exp-to-pow 93.6%

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

      2. sub-neg 93.6%

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

      3. metadata-eval 93.6%

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

      4. +-commutative 93.6%

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

   8. Simplified 93.6%

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

   if -1.99999999999999991e158 < (-.f64 t #s(literal 1 binary64)) < 2e10

   1. Initial program 97.6%

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

      1. associate-/l* 97.6%

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

      2. associate--l+ 97.6%

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

      3. exp-sum 88.4%

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

      4. associate-/l* 85.9%

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

      5. *-commutative 85.9%

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

      6. exp-to-pow 85.9%

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

      7. exp-diff 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 80.8%

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

      10. sub-neg 80.8%

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

      11. metadata-eval 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in t around 0 84.0%

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

   if 2e10 < (-.f64 t #s(literal 1 binary64))

   1. Initial program 100.0%

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

      1. div-exp 75.9%

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

      2. exp-to-pow 75.9%

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

      3. sub-neg 75.9%

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

      4. metadata-eval 75.9%

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

   5. Simplified 75.9%

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

      1. unpow-prod-up 75.9%

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

      2. unpow-1 75.9%

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

   7. Applied egg-rr 75.9%

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

      1. associate-*r/ 75.9%

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

      2. *-rgt-identity 75.9%

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

   9. Simplified 75.9%

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

   10. Taylor expanded in b around 0 84.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -2 \cdot 10^{+158}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t + -1 \leq 20000000000:\\ \;\;\;\;x \cdot \frac{{z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-14} \lor \neg \left(b \leq 2.2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t + -1\right)}\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -2.1e-14) (not (<= b 2.2e-17)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (* (pow z y) (pow a (+ t -1.0)))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e-14) || !(b <= 2.2e-17)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * (pow(z, y) * pow(a, (t + -1.0)))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-2.1d-14)) .or. (.not. (b <= 2.2d-17))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * ((z ** y) * (a ** (t + (-1.0d0))))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.1e-14) || !(b <= 2.2e-17)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * (Math.pow(z, y) * Math.pow(a, (t + -1.0)))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.1e-14) or not (b <= 2.2e-17):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * (math.pow(z, y) * math.pow(a, (t + -1.0)))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.1e-14) || !(b <= 2.2e-17))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * Float64((z ^ y) * (a ^ Float64(t + -1.0)))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -2.1e-14) || ~((b <= 2.2e-17)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * ((z ^ y) * (a ^ (t + -1.0)))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -2.1e-14], N[Not[LessEqual[b, 2.2e-17]], $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[(N[Power[z, y], $MachinePrecision] * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.0999999999999999e-14 or 2.2e-17 < b

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 93.3%

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

   if -2.0999999999999999e-14 < b < 2.2e-17

   1. Initial program 97.0%

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

   3. Taylor expanded in b around 0 97.0%

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

      1. exp-sum 88.6%

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

      2. *-commutative 88.6%

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

      3. exp-to-pow 88.6%

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

      4. exp-to-pow 89.8%

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

      5. sub-neg 89.8%

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

      6. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{-14} \lor \neg \left(b \leq 2.2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left({z}^{y} \cdot {a}^{\left(t + -1\right)}\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-283}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y))) (t_2 (/ x (* a (* y (exp b))))))
   (if (<= b -1.3e-12)
     t_2
     (if (<= b 8.2e-283)
       t_1
       (if (<= b 8e-134)
         (/ (/ (* x (pow a t)) a) y)
         (if (<= b 4.2e-58)
           t_1
           (if (<= b 3.8e-8) (/ (* x (pow a (+ t -1.0))) 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 / (a * (y * exp(b)));
	double tmp;
	if (b <= -1.3e-12) {
		tmp = t_2;
	} else if (b <= 8.2e-283) {
		tmp = t_1;
	} else if (b <= 8e-134) {
		tmp = ((x * pow(a, t)) / a) / y;
	} else if (b <= 4.2e-58) {
		tmp = t_1;
	} else if (b <= 3.8e-8) {
		tmp = (x * pow(a, (t + -1.0))) / 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 = x * (((z ** y) / a) / y)
    t_2 = x / (a * (y * exp(b)))
    if (b <= (-1.3d-12)) then
        tmp = t_2
    else if (b <= 8.2d-283) then
        tmp = t_1
    else if (b <= 8d-134) then
        tmp = ((x * (a ** t)) / a) / y
    else if (b <= 4.2d-58) then
        tmp = t_1
    else if (b <= 3.8d-8) then
        tmp = (x * (a ** (t + (-1.0d0)))) / 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 / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -1.3e-12) {
		tmp = t_2;
	} else if (b <= 8.2e-283) {
		tmp = t_1;
	} else if (b <= 8e-134) {
		tmp = ((x * Math.pow(a, t)) / a) / y;
	} else if (b <= 4.2e-58) {
		tmp = t_1;
	} else if (b <= 3.8e-8) {
		tmp = (x * Math.pow(a, (t + -1.0))) / 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 / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -1.3e-12:
		tmp = t_2
	elif b <= 8.2e-283:
		tmp = t_1
	elif b <= 8e-134:
		tmp = ((x * math.pow(a, t)) / a) / y
	elif b <= 4.2e-58:
		tmp = t_1
	elif b <= 3.8e-8:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -1.3e-12)
		tmp = t_2;
	elseif (b <= 8.2e-283)
		tmp = t_1;
	elseif (b <= 8e-134)
		tmp = Float64(Float64(Float64(x * (a ^ t)) / a) / y);
	elseif (b <= 4.2e-58)
		tmp = t_1;
	elseif (b <= 3.8e-8)
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / 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 * (y * exp(b)));
	tmp = 0.0;
	if (b <= -1.3e-12)
		tmp = t_2;
	elseif (b <= 8.2e-283)
		tmp = t_1;
	elseif (b <= 8e-134)
		tmp = ((x * (a ^ t)) / a) / y;
	elseif (b <= 4.2e-58)
		tmp = t_1;
	elseif (b <= 3.8e-8)
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.3e-12], t$95$2, If[LessEqual[b, 8.2e-283], t$95$1, If[LessEqual[b, 8e-134], N[(N[(N[(x * N[Power[a, t], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.2e-58], t$95$1, If[LessEqual[b, 3.8e-8], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.29999999999999991e-12 or 3.80000000000000028e-8 < b

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 76.9%

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

      4. associate-/l* 76.9%

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

      5. *-commutative 76.9%

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

      6. exp-to-pow 76.9%

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

      7. exp-diff 56.9%

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

      8. *-commutative 56.9%

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

      9. exp-to-pow 57.0%

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

      10. sub-neg 57.0%

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

      11. metadata-eval 57.0%

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

   3. Simplified 57.0%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. associate-/r* 68.1%

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

      2. exp-to-pow 68.2%

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

      3. sub-neg 68.2%

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

      4. metadata-eval 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in t around 0 84.7%

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

   if -1.29999999999999991e-12 < b < 8.19999999999999973e-283 or 8.00000000000000032e-134 < b < 4.19999999999999975e-58

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in b around 0 80.8%

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

      1. associate-/l* 80.6%

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

      2. div-exp 80.6%

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

      3. *-commutative 80.6%

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

      4. exp-to-pow 80.6%

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

      5. rem-exp-log 82.0%

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

   8. Simplified 82.0%

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

   if 8.19999999999999973e-283 < b < 8.00000000000000032e-134

   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. Add Preprocessing

   3. Taylor expanded in y around 0 91.7%

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

      1. div-exp 91.7%

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

      2. exp-to-pow 92.1%

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

      3. sub-neg 92.1%

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

      4. metadata-eval 92.1%

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

   5. Simplified 92.1%

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

      1. unpow-prod-up 92.2%

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

      2. unpow-1 92.2%

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

   7. Applied egg-rr 92.2%

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

      1. associate-*r/ 92.2%

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

      2. *-rgt-identity 92.2%

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

   9. Simplified 92.2%

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

   10. Taylor expanded in b around 0 92.3%

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

   if 4.19999999999999975e-58 < b < 3.80000000000000028e-8

   1. Initial program 96.1%

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

   3. Taylor expanded in y around 0 79.8%

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

      1. div-exp 79.9%

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

      2. exp-to-pow 83.5%

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

      3. sub-neg 83.5%

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

      4. metadata-eval 83.5%

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

   5. Simplified 83.5%

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

   6. Taylor expanded in b around 0 79.6%

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

      1. exp-to-pow 82.5%

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

      2. sub-neg 82.5%

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

      3. metadata-eval 82.5%

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

      4. +-commutative 82.5%

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

   8. Simplified 82.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{-283}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-134}:\\ \;\;\;\;\frac{\frac{x \cdot {a}^{t}}{a}}{y}\\ \mathbf{elif}\;b \leq 4.2 \cdot 10^{-58}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 3.8 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ t_3 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-135}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (/ (pow z y) a) y)))
        (t_2 (/ x (* a (* y (exp b)))))
        (t_3 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= b -4.2e-12)
     t_2
     (if (<= b 1.2e-282)
       t_1
       (if (<= b 1.25e-135)
         t_3
         (if (<= b 2.4e-56) t_1 (if (<= b 6e-8) t_3 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 / (a * (y * exp(b)));
	double t_3 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (b <= -4.2e-12) {
		tmp = t_2;
	} else if (b <= 1.2e-282) {
		tmp = t_1;
	} else if (b <= 1.25e-135) {
		tmp = t_3;
	} else if (b <= 2.4e-56) {
		tmp = t_1;
	} else if (b <= 6e-8) {
		tmp = t_3;
	} 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 * (y * exp(b)))
    t_3 = (x * (a ** (t + (-1.0d0)))) / y
    if (b <= (-4.2d-12)) then
        tmp = t_2
    else if (b <= 1.2d-282) then
        tmp = t_1
    else if (b <= 1.25d-135) then
        tmp = t_3
    else if (b <= 2.4d-56) then
        tmp = t_1
    else if (b <= 6d-8) then
        tmp = t_3
    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 / (a * (y * Math.exp(b)));
	double t_3 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (b <= -4.2e-12) {
		tmp = t_2;
	} else if (b <= 1.2e-282) {
		tmp = t_1;
	} else if (b <= 1.25e-135) {
		tmp = t_3;
	} else if (b <= 2.4e-56) {
		tmp = t_1;
	} else if (b <= 6e-8) {
		tmp = t_3;
	} 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 / (a * (y * math.exp(b)))
	t_3 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if b <= -4.2e-12:
		tmp = t_2
	elif b <= 1.2e-282:
		tmp = t_1
	elif b <= 1.25e-135:
		tmp = t_3
	elif b <= 2.4e-56:
		tmp = t_1
	elif b <= 6e-8:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(Float64((z ^ y) / a) / y))
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	t_3 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (b <= -4.2e-12)
		tmp = t_2;
	elseif (b <= 1.2e-282)
		tmp = t_1;
	elseif (b <= 1.25e-135)
		tmp = t_3;
	elseif (b <= 2.4e-56)
		tmp = t_1;
	elseif (b <= 6e-8)
		tmp = t_3;
	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 * (y * exp(b)));
	t_3 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (b <= -4.2e-12)
		tmp = t_2;
	elseif (b <= 1.2e-282)
		tmp = t_1;
	elseif (b <= 1.25e-135)
		tmp = t_3;
	elseif (b <= 2.4e-56)
		tmp = t_1;
	elseif (b <= 6e-8)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -4.2e-12], t$95$2, If[LessEqual[b, 1.2e-282], t$95$1, If[LessEqual[b, 1.25e-135], t$95$3, If[LessEqual[b, 2.4e-56], t$95$1, If[LessEqual[b, 6e-8], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.19999999999999988e-12 or 5.99999999999999946e-8 < b

   1. Initial program 99.9%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. 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 76.9%

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

      4. associate-/l* 76.9%

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

      5. *-commutative 76.9%

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

      6. exp-to-pow 76.9%

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

      7. exp-diff 56.9%

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

      8. *-commutative 56.9%

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

      9. exp-to-pow 57.0%

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

      10. sub-neg 57.0%

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

      11. metadata-eval 57.0%

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

   3. Simplified 57.0%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. associate-/r* 68.1%

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

      2. exp-to-pow 68.2%

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

      3. sub-neg 68.2%

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

      4. metadata-eval 68.2%

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

   7. Simplified 68.2%

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

   8. Taylor expanded in t around 0 84.7%

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

   if -4.19999999999999988e-12 < b < 1.19999999999999998e-282 or 1.25000000000000005e-135 < b < 2.40000000000000001e-56

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 80.8%

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

      1. +-commutative 80.8%

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

      2. mul-1-neg 80.8%

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

      3. unsub-neg 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in b around 0 80.8%

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

      1. associate-/l* 80.6%

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

      2. div-exp 80.6%

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

      3. *-commutative 80.6%

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

      4. exp-to-pow 80.6%

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

      5. rem-exp-log 82.0%

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

   8. Simplified 82.0%

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

   if 1.19999999999999998e-282 < b < 1.25000000000000005e-135 or 2.40000000000000001e-56 < b < 5.99999999999999946e-8

   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 87.7%

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

      1. div-exp 87.8%

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

      2. exp-to-pow 89.2%

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

      3. sub-neg 89.2%

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

      4. metadata-eval 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in b around 0 87.7%

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

      1. exp-to-pow 88.9%

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

      2. sub-neg 88.9%

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

      3. metadata-eval 88.9%

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

      4. +-commutative 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-282}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-135}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-56}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-8}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \frac{\frac{{z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a \cdot e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -4.2e-12)
   (/ x (* a (* y (exp b))))
   (if (<= b 2.4e-54) (* x (/ (/ (pow z y) a) y)) (/ (/ x (* a (exp b))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.2e-12) {
		tmp = x / (a * (y * exp(b)));
	} else if (b <= 2.4e-54) {
		tmp = x * ((pow(z, y) / a) / y);
	} else {
		tmp = (x / (a * exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-4.2d-12)) then
        tmp = x / (a * (y * exp(b)))
    else if (b <= 2.4d-54) then
        tmp = x * (((z ** y) / a) / y)
    else
        tmp = (x / (a * exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -4.2e-12) {
		tmp = x / (a * (y * Math.exp(b)));
	} else if (b <= 2.4e-54) {
		tmp = x * ((Math.pow(z, y) / a) / y);
	} else {
		tmp = (x / (a * Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -4.2e-12:
		tmp = x / (a * (y * math.exp(b)))
	elif b <= 2.4e-54:
		tmp = x * ((math.pow(z, y) / a) / y)
	else:
		tmp = (x / (a * math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -4.2e-12)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	elseif (b <= 2.4e-54)
		tmp = Float64(x * Float64(Float64((z ^ y) / a) / y));
	else
		tmp = Float64(Float64(x / Float64(a * exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -4.2e-12)
		tmp = x / (a * (y * exp(b)));
	elseif (b <= 2.4e-54)
		tmp = x * (((z ^ y) / a) / y);
	else
		tmp = (x / (a * exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -4.2e-12], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-54], N[(x * N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.19999999999999988e-12

   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 71.7%

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

      4. associate-/l* 71.7%

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

      5. *-commutative 71.7%

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

      6. exp-to-pow 71.7%

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

      7. exp-diff 51.5%

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

      8. *-commutative 51.5%

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

      9. exp-to-pow 51.5%

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

      10. sub-neg 51.5%

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

      11. metadata-eval 51.5%

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

   3. Simplified 51.5%

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

   5. Taylor expanded in y around 0 70.3%

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

      1. associate-/r* 67.1%

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

      2. exp-to-pow 67.2%

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

      3. sub-neg 67.2%

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

      4. metadata-eval 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in t around 0 81.5%

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

   if -4.19999999999999988e-12 < b < 2.40000000000000013e-54

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in b around 0 75.2%

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

      1. associate-/l* 74.1%

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

      2. div-exp 74.1%

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

      3. *-commutative 74.1%

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

      4. exp-to-pow 74.1%

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

      5. rem-exp-log 75.3%

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

   8. Simplified 75.3%

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

   if 2.40000000000000013e-54 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 93.3%

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

      1. div-exp 73.0%

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

      2. exp-to-pow 73.7%

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

      3. sub-neg 73.7%

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

      4. metadata-eval 73.7%

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

   5. Simplified 73.7%

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

   6. Taylor expanded in t around 0 84.6%

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

Alternative 10: 59.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. associate-/l* 98.5%

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

   2. associate--l+ 98.5%

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

   3. exp-sum 82.4%

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

   4. associate-/l* 80.9%

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

   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 70.3%

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

   8. *-commutative 70.3%

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

   9. exp-to-pow 71.0%

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

   10. sub-neg 71.0%

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

   11. metadata-eval 71.0%

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

3. Simplified 71.0%

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

5. Taylor expanded in y around 0 70.1%

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

   1. associate-/r* 68.5%

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

   2. exp-to-pow 69.1%

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

   3. sub-neg 69.1%

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

   4. metadata-eval 69.1%

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

7. Simplified 69.1%

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

8. Taylor expanded in t around 0 64.2%

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

Alternative 11: 52.2% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-252}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) + \frac{-1}{y}\right)\right)}{a}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 10^{+20}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(y \cdot b\right)\right) + 0.5 \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.02e-252)
   (/
    (*
     x
     (+
      (/ 1.0 y)
      (*
       b
       (+
        (* b (+ (* -0.16666666666666666 (/ b y)) (* 0.5 (/ 1.0 y))))
        (/ -1.0 y)))))
    a)
   (if (<= b 1.7e-290)
     (/ (* x b) (* y (- a)))
     (if (<= b 9e-7)
       (/ (* x (- (/ 1.0 a) (/ b a))) y)
       (if (<= b 1e+20)
         (/
          x
          (+
           (* y a)
           (*
            b
            (+
             (* y a)
             (*
              b
              (+ (* 0.16666666666666666 (* a (* y b))) (* 0.5 (* 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 <= -1.02e-252) {
		tmp = (x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))))) / a;
	} else if (b <= 1.7e-290) {
		tmp = (x * b) / (y * -a);
	} else if (b <= 9e-7) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else if (b <= 1e+20) {
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * (a * (y * b))) + (0.5 * (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 <= (-1.02d-252)) then
        tmp = (x * ((1.0d0 / y) + (b * ((b * (((-0.16666666666666666d0) * (b / y)) + (0.5d0 * (1.0d0 / y)))) + ((-1.0d0) / y))))) / a
    else if (b <= 1.7d-290) then
        tmp = (x * b) / (y * -a)
    else if (b <= 9d-7) then
        tmp = (x * ((1.0d0 / a) - (b / a))) / y
    else if (b <= 1d+20) then
        tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666d0 * (a * (y * b))) + (0.5d0 * (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 <= -1.02e-252) {
		tmp = (x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))))) / a;
	} else if (b <= 1.7e-290) {
		tmp = (x * b) / (y * -a);
	} else if (b <= 9e-7) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else if (b <= 1e+20) {
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * (a * (y * b))) + (0.5 * (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 <= -1.02e-252:
		tmp = (x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))))) / a
	elif b <= 1.7e-290:
		tmp = (x * b) / (y * -a)
	elif b <= 9e-7:
		tmp = (x * ((1.0 / a) - (b / a))) / y
	elif b <= 1e+20:
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * (a * (y * b))) + (0.5 * (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 <= -1.02e-252)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / y) + Float64(b * Float64(Float64(b * Float64(Float64(-0.16666666666666666 * Float64(b / y)) + Float64(0.5 * Float64(1.0 / y)))) + Float64(-1.0 / y))))) / a);
	elseif (b <= 1.7e-290)
		tmp = Float64(Float64(x * b) / Float64(y * Float64(-a)));
	elseif (b <= 9e-7)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) / y);
	elseif (b <= 1e+20)
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * a) + Float64(b * Float64(Float64(0.16666666666666666 * Float64(a * Float64(y * b))) + Float64(0.5 * 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 <= -1.02e-252)
		tmp = (x * ((1.0 / y) + (b * ((b * ((-0.16666666666666666 * (b / y)) + (0.5 * (1.0 / y)))) + (-1.0 / y))))) / a;
	elseif (b <= 1.7e-290)
		tmp = (x * b) / (y * -a);
	elseif (b <= 9e-7)
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	elseif (b <= 1e+20)
		tmp = x / ((y * a) + (b * ((y * a) + (b * ((0.16666666666666666 * (a * (y * b))) + (0.5 * (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, -1.02e-252], N[(N[(x * N[(N[(1.0 / y), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(-0.16666666666666666 * N[(b / y), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 1.7e-290], N[(N[(x * b), $MachinePrecision] / N[(y * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-7], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1e+20], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(0.16666666666666666 * N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $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 5 regimes

2. if b < -1.02000000000000002e-252

   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* 99.2%

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

      2. associate--l+ 99.2%

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

      3. exp-sum 80.8%

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

      4. associate-/l* 78.1%

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

      5. *-commutative 78.1%

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

      6. exp-to-pow 78.1%

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

      7. exp-diff 66.8%

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

      8. *-commutative 66.8%

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

      9. exp-to-pow 67.5%

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

      10. sub-neg 67.5%

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

      11. metadata-eval 67.5%

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

   3. Simplified 67.5%

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

   5. Taylor expanded in y around 0 71.0%

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

      1. associate-/r* 69.2%

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

      2. exp-to-pow 69.8%

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

      3. sub-neg 69.8%

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

      4. metadata-eval 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in t around 0 54.7%

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

   9. Taylor expanded in b around 0 50.0%

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

   10. Taylor expanded in a around 0 56.9%

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

   if -1.02000000000000002e-252 < b < 1.69999999999999992e-290

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. associate--l+ 99.0%

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

      3. exp-sum 86.4%

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

      4. associate-/l* 86.4%

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

      5. *-commutative 86.4%

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

      6. exp-to-pow 86.4%

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

      7. exp-diff 86.4%

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

      8. *-commutative 86.4%

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

      9. exp-to-pow 87.4%

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

      10. sub-neg 87.4%

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

      11. metadata-eval 87.4%

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

   3. Simplified 87.4%

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

   5. Taylor expanded in y around 0 49.9%

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

      1. associate-/r* 49.9%

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

      2. exp-to-pow 50.3%

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

      3. sub-neg 50.3%

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

      4. metadata-eval 50.3%

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

   7. Simplified 50.3%

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

   8. Taylor expanded in t around 0 38.4%

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

   9. Taylor expanded in b around 0 38.4%

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

       1. associate-/r* 38.4%

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

       2. +-commutative 38.4%

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

       3. mul-1-neg 38.4%

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

       4. unsub-neg 38.4%

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

       5. associate-/r* 38.4%

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

   11. Simplified 38.4%

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

   12. Taylor expanded in b around inf 57.3%

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

   if 1.69999999999999992e-290 < b < 8.99999999999999959e-7

   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. Step-by-step derivation

      1. associate-/l* 95.1%

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

      2. associate--l+ 95.1%

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

      3. exp-sum 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* 81.1%

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

      5. *-commutative 81.1%

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

      6. exp-to-pow 81.1%

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

      7. exp-diff 81.1%

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

      8. *-commutative 81.1%

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

      9. exp-to-pow 82.2%

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

      10. sub-neg 82.2%

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

      11. metadata-eval 82.2%

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

   3. Simplified 82.2%

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

   5. Taylor expanded in y around 0 71.4%

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

      1. associate-/r* 71.4%

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

      2. exp-to-pow 72.5%

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

      3. sub-neg 72.5%

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

      4. metadata-eval 72.5%

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

   7. Simplified 72.5%

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

   8. Taylor expanded in t around 0 46.6%

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

   9. Taylor expanded in b around 0 35.8%

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

       1. associate-/r* 34.2%

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

       2. +-commutative 34.2%

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

       3. mul-1-neg 34.2%

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

       4. unsub-neg 34.2%

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

       5. associate-/r* 35.8%

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

   11. Simplified 35.8%

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

   12. Taylor expanded in y around 0 50.1%

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

   if 8.99999999999999959e-7 < b < 1e20

   1. Initial program 95.7%

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

      1. associate-/l* 95.7%

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

      2. associate--l+ 95.7%

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

      3. exp-sum 95.7%

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

      4. associate-/l* 95.7%

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

      5. *-commutative 95.7%

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

      6. exp-to-pow 95.7%

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

      7. exp-diff 94.0%

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

      8. *-commutative 94.0%

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

      9. exp-to-pow 100.0%

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

      10. sub-neg 100.0%

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

      11. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 94.0%

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

      1. associate-/r* 94.0%

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

      2. exp-to-pow 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 100.0%

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

   9. Taylor expanded in b around 0 85.2%

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

   if 1e20 < 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 97.1%

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

      1. div-exp 71.7%

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

      2. exp-to-pow 71.7%

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

      3. sub-neg 71.7%

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

      4. metadata-eval 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around 0 88.2%

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

   7. Taylor expanded in b around 0 71.0%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{-252}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} + b \cdot \left(b \cdot \left(-0.16666666666666666 \cdot \frac{b}{y} + 0.5 \cdot \frac{1}{y}\right) + \frac{-1}{y}\right)\right)}{a}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-7}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq 10^{+20}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(y \cdot a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot \left(y \cdot b\right)\right) + 0.5 \cdot \left(y \cdot a\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 42.8% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+158}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x (+ a (* a b))) y)))
   (if (<= b -1.2e+94)
     (/ (- (/ x a) (/ (* x b) a)) y)
     (if (<= b -8e-168)
       (* b (- (/ x (* a (* y b))) (/ x (* y a))))
       (if (<= b -3e-287)
         t_1
         (if (<= b 1.9e-290)
           (* x (/ b (* y (- a))))
           (if (<= b 4.3e+158)
             t_1
             (/ x (* a (+ y (* b (+ y (* 0.5 (* y b))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a + (a * b))) / y;
	double tmp;
	if (b <= -1.2e+94) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -8e-168) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if (b <= -3e-287) {
		tmp = t_1;
	} else if (b <= 1.9e-290) {
		tmp = x * (b / (y * -a));
	} else if (b <= 4.3e+158) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / (a + (a * b))) / y
    if (b <= (-1.2d+94)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= (-8d-168)) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else if (b <= (-3d-287)) then
        tmp = t_1
    else if (b <= 1.9d-290) then
        tmp = x * (b / (y * -a))
    else if (b <= 4.3d+158) then
        tmp = t_1
    else
        tmp = x / (a * (y + (b * (y + (0.5d0 * (y * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / (a + (a * b))) / y;
	double tmp;
	if (b <= -1.2e+94) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -8e-168) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if (b <= -3e-287) {
		tmp = t_1;
	} else if (b <= 1.9e-290) {
		tmp = x * (b / (y * -a));
	} else if (b <= 4.3e+158) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / (a + (a * b))) / y
	tmp = 0
	if b <= -1.2e+94:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= -8e-168:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	elif b <= -3e-287:
		tmp = t_1
	elif b <= 1.9e-290:
		tmp = x * (b / (y * -a))
	elif b <= 4.3e+158:
		tmp = t_1
	else:
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / Float64(a + Float64(a * b))) / y)
	tmp = 0.0
	if (b <= -1.2e+94)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= -8e-168)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	elseif (b <= -3e-287)
		tmp = t_1;
	elseif (b <= 1.9e-290)
		tmp = Float64(x * Float64(b / Float64(y * Float64(-a))));
	elseif (b <= 4.3e+158)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(0.5 * Float64(y * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / (a + (a * b))) / y;
	tmp = 0.0;
	if (b <= -1.2e+94)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= -8e-168)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	elseif (b <= -3e-287)
		tmp = t_1;
	elseif (b <= 1.9e-290)
		tmp = x * (b / (y * -a));
	elseif (b <= 4.3e+158)
		tmp = t_1;
	else
		tmp = x / (a * (y + (b * (y + (0.5 * (y * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -1.2e+94], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -8e-168], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3e-287], t$95$1, If[LessEqual[b, 1.9e-290], N[(x * N[(b / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.3e+158], t$95$1, N[(x / N[(a * N[(y + N[(b * N[(y + N[(0.5 * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.19999999999999991e94

   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 92.8%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 70.8%

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

      3. sub-neg 70.8%

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

      4. metadata-eval 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in t around 0 88.0%

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

   7. Taylor expanded in b around 0 55.2%

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

   if -1.19999999999999991e94 < b < -8.0000000000000004e-168

   1. Initial program 98.2%

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

      1. associate-/l* 99.4%

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

      2. associate--l+ 99.4%

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

      3. exp-sum 86.5%

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

      4. associate-/l* 83.2%

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

      5. *-commutative 83.2%

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

      6. exp-to-pow 83.2%

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

      7. exp-diff 76.8%

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

      8. *-commutative 76.8%

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

      9. exp-to-pow 77.4%

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

      10. sub-neg 77.4%

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

      11. metadata-eval 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. associate-/r* 71.0%

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

      2. exp-to-pow 71.6%

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

      3. sub-neg 71.6%

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

      4. metadata-eval 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in t around 0 45.0%

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

   9. Taylor expanded in b around 0 37.4%

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

       1. associate-/r* 37.4%

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

       2. +-commutative 37.4%

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

       3. mul-1-neg 37.4%

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

       4. unsub-neg 37.4%

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

       5. associate-/r* 37.4%

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

   11. Simplified 37.4%

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

   12. Taylor expanded in b around inf 40.5%

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

       1. mul-1-neg 40.5%

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

       2. +-commutative 40.5%

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

       3. unsub-neg 40.5%

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

       4. *-commutative 40.5%

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

   14. Simplified 40.5%

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

   if -8.0000000000000004e-168 < b < -2.99999999999999992e-287 or 1.89999999999999988e-290 < b < 4.3e158

   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 80.9%

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

      1. div-exp 76.1%

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

      2. exp-to-pow 77.3%

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

      3. sub-neg 77.3%

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

      4. metadata-eval 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in t around 0 60.6%

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

   7. Taylor expanded in b around 0 45.4%

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

   if -2.99999999999999992e-287 < b < 1.89999999999999988e-290

   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 81.8%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 81.8%

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

      10. sub-neg 81.8%

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

      11. metadata-eval 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in y around 0 38.4%

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

      1. associate-/r* 38.4%

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

      2. exp-to-pow 38.4%

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

      3. sub-neg 38.4%

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

      4. metadata-eval 38.4%

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

   7. Simplified 38.4%

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

   8. Taylor expanded in t around 0 38.7%

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

   9. Taylor expanded in b around 0 38.7%

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

       1. associate-/r* 38.7%

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

       2. +-commutative 38.7%

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

       3. mul-1-neg 38.7%

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

       4. unsub-neg 38.7%

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

       5. associate-/r* 38.7%

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

   11. Simplified 38.7%

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

   12. Taylor expanded in b around inf 73.3%

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

       1. neg-mul-1 73.3%

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

       2. distribute-neg-frac2 73.3%

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

       3. distribute-lft-neg-in 73.3%

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

   14. Simplified 73.3%

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

   if 4.3e158 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 81.1%

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

      4. associate-/l* 81.1%

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

      5. *-commutative 81.1%

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

      6. exp-to-pow 81.1%

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

      7. exp-diff 54.1%

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

      8. *-commutative 54.1%

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

      9. exp-to-pow 54.1%

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

      10. sub-neg 54.1%

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

      11. metadata-eval 54.1%

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

   3. Simplified 54.1%

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

   5. Taylor expanded in y around 0 64.9%

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

      1. associate-/r* 64.9%

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

      2. exp-to-pow 64.9%

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

      3. sub-neg 64.9%

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

      4. metadata-eval 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in t around 0 92.0%

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

   9. Taylor expanded in b around 0 81.6%

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

       1. *-commutative 81.6%

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

   11. Simplified 81.6%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-287}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 4.3 \cdot 10^{+158}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + 0.5 \cdot \left(y \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 45.2% accurate, 8.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+168)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 4.4e-215)
     (/ x (+ (* y a) (* b (* (* y b) (* a 0.5)))))
     (if (<= b 2.2e+94)
       (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y)
       (/
        x
        (*
         a
         (+
          y
          (*
           b
           (+ y (* b (+ (* 0.16666666666666666 (* y b)) (* y 0.5))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 4.4e-215) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} else if (b <= 2.2e+94) {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-7.5d+168)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 4.4d-215) then
        tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5d0))))
    else if (b <= 2.2d+94) then
        tmp = (x / (a + (b * (a + (0.5d0 * (a * b)))))) / y
    else
        tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666d0 * (y * b)) + (y * 0.5d0)))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 4.4e-215) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} else if (b <= 2.2e+94) {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	} else {
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.5e+168:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 4.4e-215:
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))))
	elif b <= 2.2e+94:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	else:
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+168)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 4.4e-215)
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * b) * Float64(a * 0.5)))));
	elseif (b <= 2.2e+94)
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(b * Float64(y + Float64(b * Float64(Float64(0.16666666666666666 * Float64(y * b)) + Float64(y * 0.5))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.5e+168)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 4.4e-215)
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	elseif (b <= 2.2e+94)
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	else
		tmp = x / (a * (y + (b * (y + (b * ((0.16666666666666666 * (y * b)) + (y * 0.5)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+168], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 4.4e-215], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e+94], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y + N[(b * N[(y + N[(b * N[(N[(0.16666666666666666 * N[(y * b), $MachinePrecision]), $MachinePrecision] + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.4999999999999999e168

   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 96.5%

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

      1. div-exp 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 96.5%

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

   7. Taylor expanded in b around 0 68.7%

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

   if -7.4999999999999999e168 < b < 4.39999999999999993e-215

   1. Initial program 97.4%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 84.2%

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

      4. associate-/l* 81.6%

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

      5. *-commutative 81.6%

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

      6. exp-to-pow 81.6%

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

      7. exp-diff 75.6%

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

      8. *-commutative 75.6%

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

      9. exp-to-pow 76.6%

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

      10. sub-neg 76.6%

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

      11. metadata-eval 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/r* 67.9%

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

      2. exp-to-pow 68.7%

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

      3. sub-neg 68.7%

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

      4. metadata-eval 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in t around 0 49.7%

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

   9. Taylor expanded in b around 0 32.7%

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

   10. Taylor expanded in b around inf 40.4%

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

       1. associate-*r* 40.4%

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

       2. *-commutative 40.4%

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

       3. *-commutative 40.4%

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

   12. Simplified 40.4%

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

   if 4.39999999999999993e-215 < b < 2.20000000000000012e94

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 80.8%

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

      1. div-exp 74.1%

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

      2. exp-to-pow 75.3%

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

      3. sub-neg 75.3%

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

      4. metadata-eval 75.3%

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

   5. Simplified 75.3%

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

   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 48.7%

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

   if 2.20000000000000012e94 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 82.7%

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

      4. associate-/l* 82.7%

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

      5. *-commutative 82.7%

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

      6. exp-to-pow 82.7%

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

      7. exp-diff 61.5%

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

      8. *-commutative 61.5%

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

      9. exp-to-pow 61.5%

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

      10. sub-neg 61.5%

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

      11. metadata-eval 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in y around 0 71.2%

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

      1. associate-/r* 67.4%

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

      2. exp-to-pow 67.4%

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

      3. sub-neg 67.4%

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

      4. metadata-eval 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in t around 0 90.5%

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

   9. Taylor expanded in b around 0 79.3%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+94}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + b \cdot \left(y + b \cdot \left(0.16666666666666666 \cdot \left(y \cdot b\right) + y \cdot 0.5\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 43.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2e+99)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b -9.2e-169)
     (* b (- (/ x (* a (* y b))) (/ x (* y a))))
     (if (<= b -1.15e-289)
       (/ (/ x (+ a (* a b))) y)
       (if (<= b 1.7e-290)
         (* x (/ b (* y (- a))))
         (/ x (* y (+ a (* b (+ a (* 0.5 (* a b))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+99) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -9.2e-169) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if (b <= -1.15e-289) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 1.7e-290) {
		tmp = x * (b / (y * -a));
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-2d+99)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= (-9.2d-169)) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else if (b <= (-1.15d-289)) then
        tmp = (x / (a + (a * b))) / y
    else if (b <= 1.7d-290) then
        tmp = x * (b / (y * -a))
    else
        tmp = x / (y * (a + (b * (a + (0.5d0 * (a * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2e+99) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -9.2e-169) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if (b <= -1.15e-289) {
		tmp = (x / (a + (a * b))) / y;
	} else if (b <= 1.7e-290) {
		tmp = x * (b / (y * -a));
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2e+99:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= -9.2e-169:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	elif b <= -1.15e-289:
		tmp = (x / (a + (a * b))) / y
	elif b <= 1.7e-290:
		tmp = x * (b / (y * -a))
	else:
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2e+99)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= -9.2e-169)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	elseif (b <= -1.15e-289)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	elseif (b <= 1.7e-290)
		tmp = Float64(x * Float64(b / Float64(y * Float64(-a))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2e+99)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= -9.2e-169)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	elseif (b <= -1.15e-289)
		tmp = (x / (a + (a * b))) / y;
	elseif (b <= 1.7e-290)
		tmp = x * (b / (y * -a));
	else
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2e+99], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -9.2e-169], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e-289], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.7e-290], N[(x * N[(b / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.9999999999999999e99

   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 92.8%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 70.8%

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

      3. sub-neg 70.8%

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

      4. metadata-eval 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in t around 0 88.0%

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

   7. Taylor expanded in b around 0 55.2%

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

   if -1.9999999999999999e99 < b < -9.2000000000000004e-169

   1. Initial program 98.2%

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

      1. associate-/l* 99.4%

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

      2. associate--l+ 99.4%

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

      3. exp-sum 86.5%

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

      4. associate-/l* 83.2%

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

      5. *-commutative 83.2%

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

      6. exp-to-pow 83.2%

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

      7. exp-diff 76.8%

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

      8. *-commutative 76.8%

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

      9. exp-to-pow 77.4%

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

      10. sub-neg 77.4%

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

      11. metadata-eval 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in y around 0 71.1%

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

      1. associate-/r* 71.0%

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

      2. exp-to-pow 71.6%

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

      3. sub-neg 71.6%

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

      4. metadata-eval 71.6%

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

   7. Simplified 71.6%

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

   8. Taylor expanded in t around 0 45.0%

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

   9. Taylor expanded in b around 0 37.4%

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

       1. associate-/r* 37.4%

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

       2. +-commutative 37.4%

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

       3. mul-1-neg 37.4%

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

       4. unsub-neg 37.4%

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

       5. associate-/r* 37.4%

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

   11. Simplified 37.4%

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

   12. Taylor expanded in b around inf 40.5%

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

       1. mul-1-neg 40.5%

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

       2. +-commutative 40.5%

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

       3. unsub-neg 40.5%

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

       4. *-commutative 40.5%

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

   14. Simplified 40.5%

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

   if -9.2000000000000004e-169 < b < -1.1500000000000001e-289

   1. Initial program 89.5%

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

   3. Taylor expanded in y around 0 72.5%

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

      1. div-exp 72.5%

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

      2. exp-to-pow 74.3%

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

      3. sub-neg 74.3%

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

      4. metadata-eval 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in t around 0 50.1%

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

   7. Taylor expanded in b around 0 50.1%

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

   if -1.1500000000000001e-289 < b < 1.69999999999999992e-290

   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 81.8%

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

      4. associate-/l* 81.8%

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

      5. *-commutative 81.8%

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

      6. exp-to-pow 81.8%

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

      7. exp-diff 81.8%

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

      8. *-commutative 81.8%

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

      9. exp-to-pow 81.8%

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

      10. sub-neg 81.8%

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

      11. metadata-eval 81.8%

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

   3. Simplified 81.8%

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

   5. Taylor expanded in y around 0 38.4%

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

      1. associate-/r* 38.4%

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

      2. exp-to-pow 38.4%

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

      3. sub-neg 38.4%

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

      4. metadata-eval 38.4%

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

   7. Simplified 38.4%

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

   8. Taylor expanded in t around 0 38.7%

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

   9. Taylor expanded in b around 0 38.7%

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

       1. associate-/r* 38.7%

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

       2. +-commutative 38.7%

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

       3. mul-1-neg 38.7%

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

       4. unsub-neg 38.7%

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

       5. associate-/r* 38.7%

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

   11. Simplified 38.7%

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

   12. Taylor expanded in b around inf 73.3%

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

       1. neg-mul-1 73.3%

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

       2. distribute-neg-frac2 73.3%

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

       3. distribute-lft-neg-in 73.3%

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

   14. Simplified 73.3%

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

   if 1.69999999999999992e-290 < b

   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* 97.7%

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

      2. associate--l+ 97.7%

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

      3. exp-sum 83.4%

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

      4. associate-/l* 82.6%

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

      5. *-commutative 82.6%

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

      6. exp-to-pow 82.6%

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

      7. exp-diff 71.5%

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

      8. *-commutative 71.5%

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

      9. exp-to-pow 72.1%

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

      10. sub-neg 72.1%

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

      11. metadata-eval 72.1%

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

   3. Simplified 72.1%

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

   5. Taylor expanded in y around 0 71.9%

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

      1. associate-/r* 70.3%

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

      2. exp-to-pow 70.9%

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

      3. sub-neg 70.9%

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

      4. metadata-eval 70.9%

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

   7. Simplified 70.9%

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

   8. Taylor expanded in t around 0 69.6%

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

   9. Taylor expanded in b around 0 51.5%

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

   10. Taylor expanded in y around 0 57.1%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.7% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+168)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 2.2e-217)
     (/ x (+ (* y a) (* b (* (* y b) (* a 0.5)))))
     (/
      (/
       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 <= -7.5e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2.2e-217) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} 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 <= (-7.5d+168)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 2.2d-217) then
        tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5d0))))
    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 <= -7.5e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 2.2e-217) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} 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 <= -7.5e+168:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 2.2e-217:
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))))
	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 <= -7.5e+168)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 2.2e-217)
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * b) * Float64(a * 0.5)))));
	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 <= -7.5e+168)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 2.2e-217)
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	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, -7.5e+168], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 2.2e-217], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $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 3 regimes

2. if b < -7.4999999999999999e168

   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 96.5%

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

      1. div-exp 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 96.5%

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

   7. Taylor expanded in b around 0 68.7%

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

   if -7.4999999999999999e168 < b < 2.19999999999999982e-217

   1. Initial program 97.4%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 84.2%

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

      4. associate-/l* 81.6%

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

      5. *-commutative 81.6%

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

      6. exp-to-pow 81.6%

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

      7. exp-diff 75.6%

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

      8. *-commutative 75.6%

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

      9. exp-to-pow 76.6%

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

      10. sub-neg 76.6%

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

      11. metadata-eval 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/r* 67.9%

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

      2. exp-to-pow 68.7%

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

      3. sub-neg 68.7%

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

      4. metadata-eval 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in t around 0 49.7%

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

   9. Taylor expanded in b around 0 32.7%

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

   10. Taylor expanded in b around inf 40.4%

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

       1. associate-*r* 40.4%

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

       2. *-commutative 40.4%

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

       3. *-commutative 40.4%

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

   12. Simplified 40.4%

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

   if 2.19999999999999982e-217 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 87.9%

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

      1. div-exp 72.7%

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

      2. exp-to-pow 73.4%

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

      3. sub-neg 73.4%

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

      4. metadata-eval 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in t around 0 73.6%

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

   7. Taylor expanded in b around 0 62.2%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 43.3% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -8.2e+168)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 3.6e-218)
     (/ x (+ (* y a) (* b (* (* y b) (* a 0.5)))))
     (if (<= b 4.5e+81)
       (/ (/ x (+ a (* a b))) y)
       (/ x (* y (+ a (* b (+ a (* 0.5 (* a b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 3.6e-218) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} else if (b <= 4.5e+81) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-8.2d+168)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 3.6d-218) then
        tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5d0))))
    else if (b <= 4.5d+81) then
        tmp = (x / (a + (a * b))) / y
    else
        tmp = x / (y * (a + (b * (a + (0.5d0 * (a * b))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -8.2e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 3.6e-218) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} else if (b <= 4.5e+81) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -8.2e+168:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 3.6e-218:
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))))
	elif b <= 4.5e+81:
		tmp = (x / (a + (a * b))) / y
	else:
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -8.2e+168)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 3.6e-218)
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * b) * Float64(a * 0.5)))));
	elseif (b <= 4.5e+81)
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -8.2e+168)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 3.6e-218)
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	elseif (b <= 4.5e+81)
		tmp = (x / (a + (a * b))) / y;
	else
		tmp = x / (y * (a + (b * (a + (0.5 * (a * b))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -8.2e+168], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.6e-218], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.5e+81], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -8.2000000000000006e168

   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 96.5%

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

      1. div-exp 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 96.5%

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

   7. Taylor expanded in b around 0 68.7%

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

   if -8.2000000000000006e168 < b < 3.60000000000000011e-218

   1. Initial program 97.4%

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

      1. associate-/l* 98.9%

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

      2. associate--l+ 98.9%

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

      3. exp-sum 84.2%

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

      4. associate-/l* 81.6%

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

      5. *-commutative 81.6%

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

      6. exp-to-pow 81.6%

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

      7. exp-diff 75.6%

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

      8. *-commutative 75.6%

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

      9. exp-to-pow 76.6%

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

      10. sub-neg 76.6%

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

      11. metadata-eval 76.6%

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

   3. Simplified 76.6%

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

   5. Taylor expanded in y around 0 67.9%

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

      1. associate-/r* 67.9%

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

      2. exp-to-pow 68.7%

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

      3. sub-neg 68.7%

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

      4. metadata-eval 68.7%

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

   7. Simplified 68.7%

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

   8. Taylor expanded in t around 0 49.7%

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

   9. Taylor expanded in b around 0 32.7%

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

   10. Taylor expanded in b around inf 40.4%

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

       1. associate-*r* 40.4%

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

       2. *-commutative 40.4%

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

       3. *-commutative 40.4%

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

   12. Simplified 40.4%

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

   if 3.60000000000000011e-218 < b < 4.50000000000000017e81

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 80.1%

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

      1. div-exp 74.9%

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

      2. exp-to-pow 76.2%

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

      3. sub-neg 76.2%

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

      4. metadata-eval 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in t around 0 57.6%

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

   7. Taylor expanded in b around 0 48.4%

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

   if 4.50000000000000017e81 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 83.3%

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

      4. associate-/l* 83.3%

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

      5. *-commutative 83.3%

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

      6. exp-to-pow 83.3%

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

      7. exp-diff 61.1%

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

      8. *-commutative 61.1%

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

      9. exp-to-pow 61.1%

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

      10. sub-neg 61.1%

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

      11. metadata-eval 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in y around 0 70.4%

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

      1. associate-/r* 66.7%

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

      2. exp-to-pow 66.7%

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

      3. sub-neg 66.7%

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

      4. metadata-eval 66.7%

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

   7. Simplified 66.7%

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

   8. Taylor expanded in t around 0 90.9%

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

   9. Taylor expanded in b around 0 59.9%

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

   10. Taylor expanded in y around 0 72.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 51.6% accurate, 10.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 10^{-218}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} + b \cdot \left(b \cdot \left(\frac{b}{a} \cdot \frac{-0.16666666666666666}{y}\right) + \frac{-1}{y \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1e-218)
   (*
    x
    (+
     (/ 1.0 (* y a))
     (* b (+ (* b (* (/ b a) (/ -0.16666666666666666 y))) (/ -1.0 (* 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 <= 1e-218) {
		tmp = x * ((1.0 / (y * a)) + (b * ((b * ((b / a) * (-0.16666666666666666 / y))) + (-1.0 / (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 <= 1d-218) then
        tmp = x * ((1.0d0 / (y * a)) + (b * ((b * ((b / a) * ((-0.16666666666666666d0) / y))) + ((-1.0d0) / (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 <= 1e-218) {
		tmp = x * ((1.0 / (y * a)) + (b * ((b * ((b / a) * (-0.16666666666666666 / y))) + (-1.0 / (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 <= 1e-218:
		tmp = x * ((1.0 / (y * a)) + (b * ((b * ((b / a) * (-0.16666666666666666 / y))) + (-1.0 / (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 <= 1e-218)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) + Float64(b * Float64(Float64(b * Float64(Float64(b / a) * Float64(-0.16666666666666666 / y))) + Float64(-1.0 / 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 <= 1e-218)
		tmp = x * ((1.0 / (y * a)) + (b * ((b * ((b / a) * (-0.16666666666666666 / y))) + (-1.0 / (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, 1e-218], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(b * N[(N[(b / a), $MachinePrecision] * N[(-0.16666666666666666 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $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 2 regimes

2. if b < 1e-218

   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* 99.1%

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

      2. associate--l+ 99.1%

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

      3. exp-sum 81.7%

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

      4. associate-/l* 79.7%

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

      5. *-commutative 79.7%

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

      6. exp-to-pow 79.7%

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

      7. exp-diff 70.6%

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

      8. *-commutative 70.6%

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

      9. exp-to-pow 71.5%

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

      10. sub-neg 71.5%

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

      11. metadata-eval 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in y around 0 69.3%

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

      1. associate-/r* 67.9%

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

      2. exp-to-pow 68.5%

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

      3. sub-neg 68.5%

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

      4. metadata-eval 68.5%

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

   7. Simplified 68.5%

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

   8. Taylor expanded in t around 0 53.2%

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

   9. Taylor expanded in b around 0 49.4%

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

   10. Taylor expanded in b around inf 49.4%

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

       1. associate-*r/ 49.4%

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

       2. *-commutative 49.4%

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

       3. times-frac 51.5%

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

   12. Simplified 51.5%

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

   if 1e-218 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 87.9%

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

      1. div-exp 72.7%

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

      2. exp-to-pow 73.4%

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

      3. sub-neg 73.4%

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

      4. metadata-eval 73.4%

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

   5. Simplified 73.4%

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

   6. Taylor expanded in t around 0 73.6%

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

   7. Taylor expanded in b around 0 62.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 10^{-218}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} + b \cdot \left(b \cdot \left(\frac{b}{a} \cdot \frac{-0.16666666666666666}{y}\right) + \frac{-1}{y \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 39.7% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-287} \lor \neg \left(b \leq 1.7 \cdot 10^{-290}\right):\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -2.4e+95)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b -1.45e-169)
     (* b (- (/ x (* a (* y b))) (/ x (* y a))))
     (if (or (<= b -3.5e-287) (not (<= b 1.7e-290)))
       (/ (/ x (+ a (* a b))) y)
       (* x (/ b (* y (- a))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -2.4e+95) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -1.45e-169) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if ((b <= -3.5e-287) || !(b <= 1.7e-290)) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = x * (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 (b <= (-2.4d+95)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= (-1.45d-169)) then
        tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
    else if ((b <= (-3.5d-287)) .or. (.not. (b <= 1.7d-290))) then
        tmp = (x / (a + (a * b))) / y
    else
        tmp = x * (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 (b <= -2.4e+95) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= -1.45e-169) {
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	} else if ((b <= -3.5e-287) || !(b <= 1.7e-290)) {
		tmp = (x / (a + (a * b))) / y;
	} else {
		tmp = x * (b / (y * -a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -2.4e+95:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= -1.45e-169:
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)))
	elif (b <= -3.5e-287) or not (b <= 1.7e-290):
		tmp = (x / (a + (a * b))) / y
	else:
		tmp = x * (b / (y * -a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -2.4e+95)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= -1.45e-169)
		tmp = Float64(b * Float64(Float64(x / Float64(a * Float64(y * b))) - Float64(x / Float64(y * a))));
	elseif ((b <= -3.5e-287) || !(b <= 1.7e-290))
		tmp = Float64(Float64(x / Float64(a + Float64(a * b))) / y);
	else
		tmp = Float64(x * Float64(b / Float64(y * Float64(-a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -2.4e+95)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= -1.45e-169)
		tmp = b * ((x / (a * (y * b))) - (x / (y * a)));
	elseif ((b <= -3.5e-287) || ~((b <= 1.7e-290)))
		tmp = (x / (a + (a * b))) / y;
	else
		tmp = x * (b / (y * -a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -2.4e+95], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -1.45e-169], N[(b * N[(N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -3.5e-287], N[Not[LessEqual[b, 1.7e-290]], $MachinePrecision]], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(b / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.4e95

   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 92.8%

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

      1. div-exp 70.8%

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

      2. exp-to-pow 70.8%

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

      3. sub-neg 70.8%

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

      4. metadata-eval 70.8%

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

   5. Simplified 70.8%

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

   6. Taylor expanded in t around 0 88.0%

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

   7. Taylor expanded in b around 0 55.2%

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

   if -2.4e95 < b < -1.4500000000000001e-169

   1. Initial program 98.2%

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

      1. associate-/l* 99.4%

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

      2. associate--l+ 99.4%

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

      3. exp-sum 86.5%

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

      4. associate-/l* 83.2%

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

      5. *-commutative 83.2%

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

      6. exp-to-pow 83.2%

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

      7. exp-diff 76.8%

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

      8. *-commutative 76.8%

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

      9. exp-to-pow 77.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 71.0%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 71.6%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 71.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 71.6%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 71.6%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 45.0%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 37.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 37.4%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 37.4%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 37.4%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 37.4%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 37.4%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 37.4%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 40.5%

       \[\leadsto \color{blue}{b \cdot \left(-1 \cdot \frac{x}{a \cdot y} + \frac{x}{a \cdot \left(b \cdot y\right)}\right)} \]
   13. Step-by-step derivation

       1. mul-1-neg 40.5%

          \[\leadsto b \cdot \left(\color{blue}{\left(-\frac{x}{a \cdot y}\right)} + \frac{x}{a \cdot \left(b \cdot y\right)}\right) \]

       2. +-commutative 40.5%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{a \cdot \left(b \cdot y\right)} + \left(-\frac{x}{a \cdot y}\right)\right)} \]

       3. unsub-neg 40.5%

          \[\leadsto b \cdot \color{blue}{\left(\frac{x}{a \cdot \left(b \cdot y\right)} - \frac{x}{a \cdot y}\right)} \]

       4. *-commutative 40.5%

          \[\leadsto b \cdot \left(\frac{x}{a \cdot \color{blue}{\left(y \cdot b\right)}} - \frac{x}{a \cdot y}\right) \]

   14. Simplified 40.5%

       \[\leadsto \color{blue}{b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{a \cdot y}\right)} \]

   if -1.4500000000000001e-169 < b < -3.5e-287 or 1.69999999999999992e-290 < 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 85.2%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 73.2%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 74.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 74.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 68.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.8%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]

   if -3.5e-287 < b < 1.69999999999999992e-290

   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 81.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 38.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 38.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 38.7%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 38.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 38.7%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 38.7%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 38.7%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 38.7%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 73.3%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y}\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 73.3%

          \[\leadsto x \cdot \color{blue}{\left(-\frac{b}{a \cdot y}\right)} \]

       2. distribute-neg-frac2 73.3%

          \[\leadsto x \cdot \color{blue}{\frac{b}{-a \cdot y}} \]

       3. distribute-lft-neg-in 73.3%

          \[\leadsto x \cdot \frac{b}{\color{blue}{\left(-a\right) \cdot y}} \]

   14. Simplified 73.3%

       \[\leadsto x \cdot \color{blue}{\frac{b}{\left(-a\right) \cdot y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-169}:\\ \;\;\;\;b \cdot \left(\frac{x}{a \cdot \left(y \cdot b\right)} - \frac{x}{y \cdot a}\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-287} \lor \neg \left(b \leq 1.7 \cdot 10^{-290}\right):\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 40.0% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ t_2 := \frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{if}\;b \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{-171}:\\ \;\;\;\;t\_1 - b \cdot t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))) (t_2 (/ (- (/ x a) (/ (* x b) a)) y)))
   (if (<= b -3.5e+96)
     t_2
     (if (<= b -3.25e-171)
       (- t_1 (* b t_1))
       (if (<= b -4.2e-287)
         t_2
         (if (<= b 2.6e-290)
           (* x (/ b (* y (- a))))
           (/ (/ x (+ a (* a b))) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double t_2 = ((x / a) - ((x * b) / a)) / y;
	double tmp;
	if (b <= -3.5e+96) {
		tmp = t_2;
	} else if (b <= -3.25e-171) {
		tmp = t_1 - (b * t_1);
	} else if (b <= -4.2e-287) {
		tmp = t_2;
	} else if (b <= 2.6e-290) {
		tmp = x * (b / (y * -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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x / (y * a)
    t_2 = ((x / a) - ((x * b) / a)) / y
    if (b <= (-3.5d+96)) then
        tmp = t_2
    else if (b <= (-3.25d-171)) then
        tmp = t_1 - (b * t_1)
    else if (b <= (-4.2d-287)) then
        tmp = t_2
    else if (b <= 2.6d-290) then
        tmp = x * (b / (y * -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 t_1 = x / (y * a);
	double t_2 = ((x / a) - ((x * b) / a)) / y;
	double tmp;
	if (b <= -3.5e+96) {
		tmp = t_2;
	} else if (b <= -3.25e-171) {
		tmp = t_1 - (b * t_1);
	} else if (b <= -4.2e-287) {
		tmp = t_2;
	} else if (b <= 2.6e-290) {
		tmp = x * (b / (y * -a));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	t_2 = ((x / a) - ((x * b) / a)) / y
	tmp = 0
	if b <= -3.5e+96:
		tmp = t_2
	elif b <= -3.25e-171:
		tmp = t_1 - (b * t_1)
	elif b <= -4.2e-287:
		tmp = t_2
	elif b <= 2.6e-290:
		tmp = x * (b / (y * -a))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	t_2 = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y)
	tmp = 0.0
	if (b <= -3.5e+96)
		tmp = t_2;
	elseif (b <= -3.25e-171)
		tmp = Float64(t_1 - Float64(b * t_1));
	elseif (b <= -4.2e-287)
		tmp = t_2;
	elseif (b <= 2.6e-290)
		tmp = Float64(x * Float64(b / Float64(y * 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)
	t_1 = x / (y * a);
	t_2 = ((x / a) - ((x * b) / a)) / y;
	tmp = 0.0;
	if (b <= -3.5e+96)
		tmp = t_2;
	elseif (b <= -3.25e-171)
		tmp = t_1 - (b * t_1);
	elseif (b <= -4.2e-287)
		tmp = t_2;
	elseif (b <= 2.6e-290)
		tmp = x * (b / (y * -a));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -3.5e+96], t$95$2, If[LessEqual[b, -3.25e-171], N[(t$95$1 - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.2e-287], t$95$2, If[LessEqual[b, 2.6e-290], N[(x * N[(b / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.4999999999999999e96 or -3.2500000000000002e-171 < b < -4.1999999999999998e-287

   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 88.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 72.4%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 72.9%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 72.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 72.9%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 72.9%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 78.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 54.6%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   if -3.4999999999999999e96 < b < -3.2500000000000002e-171

   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* 99.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 77.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 77.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 77.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.3%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 71.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 72.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 72.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 72.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 72.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 47.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 38.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. +-commutative 38.4%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

       2. mul-1-neg 38.4%

          \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

       3. unsub-neg 38.4%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

       4. associate-/l* 38.4%

          \[\leadsto \frac{x}{a \cdot y} - \color{blue}{b \cdot \frac{x}{a \cdot y}} \]

   11. Simplified 38.4%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y} - b \cdot \frac{x}{a \cdot y}} \]

   if -4.1999999999999998e-287 < b < 2.60000000000000001e-290

   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 81.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 38.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 38.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 38.7%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 38.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 38.7%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 38.7%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 38.7%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 38.7%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 73.3%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y}\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 73.3%

          \[\leadsto x \cdot \color{blue}{\left(-\frac{b}{a \cdot y}\right)} \]

       2. distribute-neg-frac2 73.3%

          \[\leadsto x \cdot \color{blue}{\frac{b}{-a \cdot y}} \]

       3. distribute-lft-neg-in 73.3%

          \[\leadsto x \cdot \frac{b}{\color{blue}{\left(-a\right) \cdot y}} \]

   14. Simplified 73.3%

       \[\leadsto x \cdot \color{blue}{\frac{b}{\left(-a\right) \cdot y}} \]

   if 2.60000000000000001e-290 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 74.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 74.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 71.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq -3.25 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{y \cdot a} - b \cdot \frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-287}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 39.8% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y \cdot a}\\ \mathbf{if}\;b \leq -7 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)}{a}\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-71}:\\ \;\;\;\;t\_1 - b \cdot t\_1\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-251}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (* y a))))
   (if (<= b -7e+166)
     (/ (* x (- (/ 1.0 y) (/ b y))) a)
     (if (<= b -2.9e-71)
       (- t_1 (* b t_1))
       (if (<= b -4.8e-251)
         (/ 1.0 (* a (/ y x)))
         (if (<= b 3.1e-290)
           (/ (* x b) (* y (- a)))
           (/ (/ x (+ a (* a b))) y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (y * a);
	double tmp;
	if (b <= -7e+166) {
		tmp = (x * ((1.0 / y) - (b / y))) / a;
	} else if (b <= -2.9e-71) {
		tmp = t_1 - (b * t_1);
	} else if (b <= -4.8e-251) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 3.1e-290) {
		tmp = (x * b) / (y * -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) :: t_1
    real(8) :: tmp
    t_1 = x / (y * a)
    if (b <= (-7d+166)) then
        tmp = (x * ((1.0d0 / y) - (b / y))) / a
    else if (b <= (-2.9d-71)) then
        tmp = t_1 - (b * t_1)
    else if (b <= (-4.8d-251)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 3.1d-290) then
        tmp = (x * b) / (y * -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 t_1 = x / (y * a);
	double tmp;
	if (b <= -7e+166) {
		tmp = (x * ((1.0 / y) - (b / y))) / a;
	} else if (b <= -2.9e-71) {
		tmp = t_1 - (b * t_1);
	} else if (b <= -4.8e-251) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 3.1e-290) {
		tmp = (x * b) / (y * -a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (y * a)
	tmp = 0
	if b <= -7e+166:
		tmp = (x * ((1.0 / y) - (b / y))) / a
	elif b <= -2.9e-71:
		tmp = t_1 - (b * t_1)
	elif b <= -4.8e-251:
		tmp = 1.0 / (a * (y / x))
	elif b <= 3.1e-290:
		tmp = (x * b) / (y * -a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(y * a))
	tmp = 0.0
	if (b <= -7e+166)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / y) - Float64(b / y))) / a);
	elseif (b <= -2.9e-71)
		tmp = Float64(t_1 - Float64(b * t_1));
	elseif (b <= -4.8e-251)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 3.1e-290)
		tmp = Float64(Float64(x * b) / Float64(y * 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)
	t_1 = x / (y * a);
	tmp = 0.0;
	if (b <= -7e+166)
		tmp = (x * ((1.0 / y) - (b / y))) / a;
	elseif (b <= -2.9e-71)
		tmp = t_1 - (b * t_1);
	elseif (b <= -4.8e-251)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 3.1e-290)
		tmp = (x * b) / (y * -a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7e+166], N[(N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -2.9e-71], N[(t$95$1 - N[(b * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.8e-251], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.1e-290], N[(N[(x * b), $MachinePrecision] / N[(y * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.9999999999999997e166

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 70.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 70.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 70.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 70.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 46.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 46.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 46.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 46.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 46.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 46.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 63.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 63.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 63.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 63.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 63.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 70.1%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 29.5%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 29.5%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 29.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 29.5%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 29.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 29.5%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 29.5%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in a around 0 55.0%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)}{a}} \]

   if -6.9999999999999997e166 < b < -2.8999999999999999e-71

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.5%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 71.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 71.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 71.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 71.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 71.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 71.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 71.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 71.7%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 71.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 71.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 71.7%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 60.0%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 41.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y} + \frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. +-commutative 41.1%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} + -1 \cdot \frac{b \cdot x}{a \cdot y}} \]

       2. mul-1-neg 41.1%

          \[\leadsto \frac{x}{a \cdot y} + \color{blue}{\left(-\frac{b \cdot x}{a \cdot y}\right)} \]

       3. unsub-neg 41.1%

          \[\leadsto \color{blue}{\frac{x}{a \cdot y} - \frac{b \cdot x}{a \cdot y}} \]

       4. associate-/l* 41.1%

          \[\leadsto \frac{x}{a \cdot y} - \color{blue}{b \cdot \frac{x}{a \cdot y}} \]

   11. Simplified 41.1%

       \[\leadsto \color{blue}{\frac{x}{a \cdot y} - b \cdot \frac{x}{a \cdot y}} \]

   if -2.8999999999999999e-71 < b < -4.79999999999999992e-251

   1. Initial program 94.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 97.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 97.7%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 87.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.9%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.9%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.9%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 79.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 79.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 82.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 82.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 82.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 82.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.3%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 71.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 73.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 73.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 73.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 73.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 31.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 31.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. clear-num 31.5%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 31.5%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   11. Applied egg-rr 31.5%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 31.5%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 38.3%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   13. Simplified 38.3%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if -4.79999999999999992e-251 < b < 3.0999999999999999e-290

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 86.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 86.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 86.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 86.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 86.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 87.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 87.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 87.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 49.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 49.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 50.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 50.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 50.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 50.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 38.4%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 38.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 38.4%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 38.4%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 38.4%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 38.4%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 38.4%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 38.4%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 57.3%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if 3.0999999999999999e-290 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 74.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 74.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 71.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)}{a}\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-71}:\\ \;\;\;\;\frac{x}{y \cdot a} - b \cdot \frac{x}{y \cdot a}\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-251}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 39.9% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)}{a}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{1 - b}{y \cdot a}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-250}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.4e+166)
   (/ (* x (- (/ 1.0 y) (/ b y))) a)
   (if (<= b -1.7e-59)
     (* x (/ (- 1.0 b) (* y a)))
     (if (<= b -2.5e-250)
       (/ 1.0 (* a (/ y x)))
       (if (<= b 2.25e-290)
         (/ (* x b) (* y (- 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 <= -7.4e+166) {
		tmp = (x * ((1.0 / y) - (b / y))) / a;
	} else if (b <= -1.7e-59) {
		tmp = x * ((1.0 - b) / (y * a));
	} else if (b <= -2.5e-250) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.25e-290) {
		tmp = (x * b) / (y * -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 <= (-7.4d+166)) then
        tmp = (x * ((1.0d0 / y) - (b / y))) / a
    else if (b <= (-1.7d-59)) then
        tmp = x * ((1.0d0 - b) / (y * a))
    else if (b <= (-2.5d-250)) then
        tmp = 1.0d0 / (a * (y / x))
    else if (b <= 2.25d-290) then
        tmp = (x * b) / (y * -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 <= -7.4e+166) {
		tmp = (x * ((1.0 / y) - (b / y))) / a;
	} else if (b <= -1.7e-59) {
		tmp = x * ((1.0 - b) / (y * a));
	} else if (b <= -2.5e-250) {
		tmp = 1.0 / (a * (y / x));
	} else if (b <= 2.25e-290) {
		tmp = (x * b) / (y * -a);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.4e+166:
		tmp = (x * ((1.0 / y) - (b / y))) / a
	elif b <= -1.7e-59:
		tmp = x * ((1.0 - b) / (y * a))
	elif b <= -2.5e-250:
		tmp = 1.0 / (a * (y / x))
	elif b <= 2.25e-290:
		tmp = (x * b) / (y * -a)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.4e+166)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / y) - Float64(b / y))) / a);
	elseif (b <= -1.7e-59)
		tmp = Float64(x * Float64(Float64(1.0 - b) / Float64(y * a)));
	elseif (b <= -2.5e-250)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	elseif (b <= 2.25e-290)
		tmp = Float64(Float64(x * b) / Float64(y * 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 <= -7.4e+166)
		tmp = (x * ((1.0 / y) - (b / y))) / a;
	elseif (b <= -1.7e-59)
		tmp = x * ((1.0 - b) / (y * a));
	elseif (b <= -2.5e-250)
		tmp = 1.0 / (a * (y / x));
	elseif (b <= 2.25e-290)
		tmp = (x * b) / (y * -a);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.4e+166], N[(N[(x * N[(N[(1.0 / y), $MachinePrecision] - N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -1.7e-59], N[(x * N[(N[(1.0 - b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.5e-250], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e-290], N[(N[(x * b), $MachinePrecision] / N[(y * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -7.40000000000000044e166

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 70.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 70.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 70.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 70.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 46.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 46.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 46.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 46.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 46.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 46.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 63.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 63.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 63.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 63.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 63.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 70.1%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 29.5%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 29.5%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 29.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 29.5%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 29.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 29.5%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 29.5%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in a around 0 55.0%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)}{a}} \]

   if -7.40000000000000044e166 < b < -1.70000000000000009e-59

   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. Step-by-step derivation

      1. associate-/l* 99.4%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.4%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 68.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 68.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 68.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 68.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 68.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 68.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 70.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 70.8%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 70.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 70.8%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 70.8%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 59.6%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 41.0%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 41.0%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 41.0%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 41.0%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 41.0%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 41.0%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 41.0%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in y around 0 32.5%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]
   13. Step-by-step derivation

       1. associate-/l* 37.4%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}} \]

       2. div-sub 37.5%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{1 - b}{a}}}{y} \]

       3. associate-/r* 41.0%

          \[\leadsto x \cdot \color{blue}{\frac{1 - b}{a \cdot y}} \]

   14. Simplified 41.0%

       \[\leadsto \color{blue}{x \cdot \frac{1 - b}{a \cdot y}} \]

   if -1.70000000000000009e-59 < b < -2.50000000000000013e-250

   1. Initial program 95.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      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 89.0%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 83.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 83.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 84.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 84.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 84.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 84.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 72.7%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 72.7%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 74.2%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 74.2%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 74.2%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 74.2%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 33.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 33.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. clear-num 33.1%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 33.1%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   11. Applied egg-rr 33.1%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 33.1%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 38.9%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   13. Simplified 38.9%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if -2.50000000000000013e-250 < b < 2.25e-290

   1. Initial program 99.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 86.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 86.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 86.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 86.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 86.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 86.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 87.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 87.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 87.4%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 87.4%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 49.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 49.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 50.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 50.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 50.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 50.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 38.4%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 38.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 38.4%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 38.4%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 38.4%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 38.4%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 38.4%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 38.4%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 57.3%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if 2.25e-290 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 74.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 74.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 71.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.4 \cdot 10^{+166}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{y} - \frac{b}{y}\right)}{a}\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-59}:\\ \;\;\;\;x \cdot \frac{1 - b}{y \cdot a}\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-250}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-290}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 37.3% accurate, 10.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{a}}{y}\\ t_2 := y \cdot \left(-a\right)\\ \mathbf{if}\;b \leq -3.8 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot b}{t\_2}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{t\_2}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+78}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ x a) y)) (t_2 (* y (- a))))
   (if (<= b -3.8e-156)
     (/ (* x b) t_2)
     (if (<= b -1.15e-289)
       t_1
       (if (<= b 2.5e-290)
         (* x (/ b t_2))
         (if (<= b 4.6e+78) t_1 (/ x (* a (+ y (* y b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double t_2 = y * -a;
	double tmp;
	if (b <= -3.8e-156) {
		tmp = (x * b) / t_2;
	} else if (b <= -1.15e-289) {
		tmp = t_1;
	} else if (b <= 2.5e-290) {
		tmp = x * (b / t_2);
	} else if (b <= 4.6e+78) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x / a) / y
    t_2 = y * -a
    if (b <= (-3.8d-156)) then
        tmp = (x * b) / t_2
    else if (b <= (-1.15d-289)) then
        tmp = t_1
    else if (b <= 2.5d-290) then
        tmp = x * (b / t_2)
    else if (b <= 4.6d+78) then
        tmp = t_1
    else
        tmp = x / (a * (y + (y * b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x / a) / y;
	double t_2 = y * -a;
	double tmp;
	if (b <= -3.8e-156) {
		tmp = (x * b) / t_2;
	} else if (b <= -1.15e-289) {
		tmp = t_1;
	} else if (b <= 2.5e-290) {
		tmp = x * (b / t_2);
	} else if (b <= 4.6e+78) {
		tmp = t_1;
	} else {
		tmp = x / (a * (y + (y * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x / a) / y
	t_2 = y * -a
	tmp = 0
	if b <= -3.8e-156:
		tmp = (x * b) / t_2
	elif b <= -1.15e-289:
		tmp = t_1
	elif b <= 2.5e-290:
		tmp = x * (b / t_2)
	elif b <= 4.6e+78:
		tmp = t_1
	else:
		tmp = x / (a * (y + (y * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x / a) / y)
	t_2 = Float64(y * Float64(-a))
	tmp = 0.0
	if (b <= -3.8e-156)
		tmp = Float64(Float64(x * b) / t_2);
	elseif (b <= -1.15e-289)
		tmp = t_1;
	elseif (b <= 2.5e-290)
		tmp = Float64(x * Float64(b / t_2));
	elseif (b <= 4.6e+78)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a * Float64(y + Float64(y * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x / a) / y;
	t_2 = y * -a;
	tmp = 0.0;
	if (b <= -3.8e-156)
		tmp = (x * b) / t_2;
	elseif (b <= -1.15e-289)
		tmp = t_1;
	elseif (b <= 2.5e-290)
		tmp = x * (b / t_2);
	elseif (b <= 4.6e+78)
		tmp = t_1;
	else
		tmp = x / (a * (y + (y * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(y * (-a)), $MachinePrecision]}, If[LessEqual[b, -3.8e-156], N[(N[(x * b), $MachinePrecision] / t$95$2), $MachinePrecision], If[LessEqual[b, -1.15e-289], t$95$1, If[LessEqual[b, 2.5e-290], N[(x * N[(b / t$95$2), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.6e+78], t$95$1, N[(x / N[(a * N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -3.80000000000000008e-156

   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* 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.7%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 65.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 65.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 65.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 69.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 69.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 56.4%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 34.5%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 34.5%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 34.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 34.5%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 34.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 34.5%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 34.5%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 39.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -3.80000000000000008e-156 < b < -1.1500000000000001e-289 or 2.5e-290 < b < 4.6000000000000004e78

   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 77.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 74.5%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 76.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 76.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 76.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 76.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 53.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 47.4%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if -1.1500000000000001e-289 < b < 2.5e-290

   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 81.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 38.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 38.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 38.7%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 38.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 38.7%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 38.7%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 38.7%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 38.7%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 73.3%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y}\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 73.3%

          \[\leadsto x \cdot \color{blue}{\left(-\frac{b}{a \cdot y}\right)} \]

       2. distribute-neg-frac2 73.3%

          \[\leadsto x \cdot \color{blue}{\frac{b}{-a \cdot y}} \]

       3. distribute-lft-neg-in 73.3%

          \[\leadsto x \cdot \frac{b}{\color{blue}{\left(-a\right) \cdot y}} \]

   14. Simplified 73.3%

       \[\leadsto x \cdot \color{blue}{\frac{b}{\left(-a\right) \cdot y}} \]

   if 4.6000000000000004e78 < b

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.6%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 61.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 61.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 61.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 61.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 61.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 61.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.0%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 67.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 67.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 67.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 91.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 43.5%

      \[\leadsto \frac{x}{a \cdot \color{blue}{\left(y + b \cdot y\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{-156}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-289}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y + y \cdot b\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 49.7% accurate, 11.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} + b \cdot \left(0.5 \cdot \frac{b}{y \cdot a} + \frac{-1}{y \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.3e-217)
   (* x (+ (/ 1.0 (* y a)) (* b (+ (* 0.5 (/ b (* y a))) (/ -1.0 (* 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 <= 2.3e-217) {
		tmp = x * ((1.0 / (y * a)) + (b * ((0.5 * (b / (y * a))) + (-1.0 / (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 <= 2.3d-217) then
        tmp = x * ((1.0d0 / (y * a)) + (b * ((0.5d0 * (b / (y * a))) + ((-1.0d0) / (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 <= 2.3e-217) {
		tmp = x * ((1.0 / (y * a)) + (b * ((0.5 * (b / (y * a))) + (-1.0 / (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 <= 2.3e-217:
		tmp = x * ((1.0 / (y * a)) + (b * ((0.5 * (b / (y * a))) + (-1.0 / (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 <= 2.3e-217)
		tmp = Float64(x * Float64(Float64(1.0 / Float64(y * a)) + Float64(b * Float64(Float64(0.5 * Float64(b / Float64(y * a))) + Float64(-1.0 / 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 <= 2.3e-217)
		tmp = x * ((1.0 / (y * a)) + (b * ((0.5 * (b / (y * a))) + (-1.0 / (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, 2.3e-217], N[(x * N[(N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(0.5 * N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $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 2 regimes

2. if b < 2.30000000000000005e-217

   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* 99.1%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.1%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 81.7%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 79.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 79.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 79.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 71.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 71.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 71.5%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.3%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 68.5%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 68.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 68.5%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 68.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 53.2%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 46.8%

      \[\leadsto x \cdot \color{blue}{\left(b \cdot \left(0.5 \cdot \frac{b}{a \cdot y} - \frac{1}{a \cdot y}\right) + \frac{1}{a \cdot y}\right)} \]

   if 2.30000000000000005e-217 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 87.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 72.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 73.4%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 73.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 73.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 73.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 73.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 62.2%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + 0.5 \cdot a\right)\right)}}}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.3 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(\frac{1}{y \cdot a} + b \cdot \left(0.5 \cdot \frac{b}{y \cdot a} + \frac{-1}{y \cdot a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + b \cdot \left(0.16666666666666666 \cdot \left(a \cdot b\right) + a \cdot 0.5\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 43.6% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -7.5e+168)
   (/ (- (/ x a) (/ (* x b) a)) y)
   (if (<= b 1.3e-215)
     (/ x (+ (* y a) (* b (* (* y b) (* a 0.5)))))
     (/ (/ x (+ a (* b (+ a (* 0.5 (* a b)))))) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -7.5e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.3e-215) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (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 <= (-7.5d+168)) then
        tmp = ((x / a) - ((x * b) / a)) / y
    else if (b <= 1.3d-215) then
        tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5d0))))
    else
        tmp = (x / (a + (b * (a + (0.5d0 * (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 <= -7.5e+168) {
		tmp = ((x / a) - ((x * b) / a)) / y;
	} else if (b <= 1.3e-215) {
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	} else {
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -7.5e+168:
		tmp = ((x / a) - ((x * b) / a)) / y
	elif b <= 1.3e-215:
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))))
	else:
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -7.5e+168)
		tmp = Float64(Float64(Float64(x / a) - Float64(Float64(x * b) / a)) / y);
	elseif (b <= 1.3e-215)
		tmp = Float64(x / Float64(Float64(y * a) + Float64(b * Float64(Float64(y * b) * Float64(a * 0.5)))));
	else
		tmp = Float64(Float64(x / Float64(a + Float64(b * Float64(a + Float64(0.5 * Float64(a * b)))))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -7.5e+168)
		tmp = ((x / a) - ((x * b) / a)) / y;
	elseif (b <= 1.3e-215)
		tmp = x / ((y * a) + (b * ((y * b) * (a * 0.5))));
	else
		tmp = (x / (a + (b * (a + (0.5 * (a * b)))))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -7.5e+168], N[(N[(N[(x / a), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.3e-215], N[(x / N[(N[(y * a), $MachinePrecision] + N[(b * N[(N[(y * b), $MachinePrecision] * N[(a * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(b * N[(a + N[(0.5 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.4999999999999999e168

   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 96.5%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 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 96.5%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 68.7%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]

   if -7.4999999999999999e168 < b < 1.3e-215

   1. Initial program 97.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.9%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.9%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 84.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.6%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.6%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.6%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 75.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 75.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 76.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 76.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 76.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 76.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 67.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 67.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 68.7%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 68.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 68.7%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 68.7%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 49.7%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 32.7%

      \[\leadsto \frac{x}{\color{blue}{a \cdot y + b \cdot \left(0.5 \cdot \left(a \cdot \left(b \cdot y\right)\right) + a \cdot y\right)}} \]

   10. Taylor expanded in b around inf 40.4%

       \[\leadsto \frac{x}{a \cdot y + b \cdot \color{blue}{\left(0.5 \cdot \left(a \cdot \left(b \cdot y\right)\right)\right)}} \]
   11. Step-by-step derivation

       1. associate-*r* 40.4%

          \[\leadsto \frac{x}{a \cdot y + b \cdot \color{blue}{\left(\left(0.5 \cdot a\right) \cdot \left(b \cdot y\right)\right)}} \]

       2. *-commutative 40.4%

          \[\leadsto \frac{x}{a \cdot y + b \cdot \left(\color{blue}{\left(a \cdot 0.5\right)} \cdot \left(b \cdot y\right)\right)} \]

       3. *-commutative 40.4%

          \[\leadsto \frac{x}{a \cdot y + b \cdot \left(\left(a \cdot 0.5\right) \cdot \color{blue}{\left(y \cdot b\right)}\right)} \]

   12. Simplified 40.4%

       \[\leadsto \frac{x}{a \cdot y + b \cdot \color{blue}{\left(\left(a \cdot 0.5\right) \cdot \left(y \cdot b\right)\right)}} \]

   if 1.3e-215 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 87.9%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 72.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 73.4%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 73.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 73.4%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 73.4%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 73.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 60.3%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}}{y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+168}:\\ \;\;\;\;\frac{\frac{x}{a} - \frac{x \cdot b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-215}:\\ \;\;\;\;\frac{x}{y \cdot a + b \cdot \left(\left(y \cdot b\right) \cdot \left(a \cdot 0.5\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + b \cdot \left(a + 0.5 \cdot \left(a \cdot b\right)\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 40.1% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \frac{1 - b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e+93)
   (/ (* x (- (/ 1.0 a) (/ b a))) y)
   (if (<= b -5.1e-281)
     (* x (/ (- 1.0 b) (* y a)))
     (if (<= b 3.3e-290) (* x (/ b (* y (- 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 <= -1.05e+93) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else if (b <= -5.1e-281) {
		tmp = x * ((1.0 - b) / (y * a));
	} else if (b <= 3.3e-290) {
		tmp = x * (b / (y * -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 <= (-1.05d+93)) then
        tmp = (x * ((1.0d0 / a) - (b / a))) / y
    else if (b <= (-5.1d-281)) then
        tmp = x * ((1.0d0 - b) / (y * a))
    else if (b <= 3.3d-290) then
        tmp = x * (b / (y * -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 <= -1.05e+93) {
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	} else if (b <= -5.1e-281) {
		tmp = x * ((1.0 - b) / (y * a));
	} else if (b <= 3.3e-290) {
		tmp = x * (b / (y * -a));
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e+93:
		tmp = (x * ((1.0 / a) - (b / a))) / y
	elif b <= -5.1e-281:
		tmp = x * ((1.0 - b) / (y * a))
	elif b <= 3.3e-290:
		tmp = x * (b / (y * -a))
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e+93)
		tmp = Float64(Float64(x * Float64(Float64(1.0 / a) - Float64(b / a))) / y);
	elseif (b <= -5.1e-281)
		tmp = Float64(x * Float64(Float64(1.0 - b) / Float64(y * a)));
	elseif (b <= 3.3e-290)
		tmp = Float64(x * Float64(b / Float64(y * 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 <= -1.05e+93)
		tmp = (x * ((1.0 / a) - (b / a))) / y;
	elseif (b <= -5.1e-281)
		tmp = x * ((1.0 - b) / (y * a));
	elseif (b <= 3.3e-290)
		tmp = x * (b / (y * -a));
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e+93], N[(N[(x * N[(N[(1.0 / a), $MachinePrecision] - N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, -5.1e-281], N[(x * N[(N[(1.0 - b), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e-290], N[(x * N[(b / N[(y * (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.0499999999999999e93

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 73.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 73.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 73.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 73.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 50.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 50.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 50.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 50.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 50.0%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 50.0%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.1%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 64.3%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 64.3%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 64.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 64.3%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 64.3%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 69.2%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 28.9%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 28.9%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 28.9%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 28.9%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 28.9%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 28.9%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 28.9%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in y around 0 42.6%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]

   if -1.0499999999999999e93 < b < -5.10000000000000025e-281

   1. Initial program 96.4%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.6%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.6%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 85.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 77.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 77.5%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 78.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 78.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 78.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 78.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 73.2%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 73.2%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 74.2%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 74.2%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 74.2%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 74.2%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 46.3%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 40.1%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 40.1%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 40.1%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 40.1%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 40.1%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 40.1%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 40.1%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in y around 0 33.9%

       \[\leadsto \color{blue}{\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}} \]
   13. Step-by-step derivation

       1. associate-/l* 38.8%

          \[\leadsto \color{blue}{x \cdot \frac{\frac{1}{a} - \frac{b}{a}}{y}} \]

       2. div-sub 38.8%

          \[\leadsto x \cdot \frac{\color{blue}{\frac{1 - b}{a}}}{y} \]

       3. associate-/r* 40.1%

          \[\leadsto x \cdot \color{blue}{\frac{1 - b}{a \cdot y}} \]

   14. Simplified 40.1%

       \[\leadsto \color{blue}{x \cdot \frac{1 - b}{a \cdot y}} \]

   if -5.10000000000000025e-281 < b < 3.29999999999999986e-290

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 100.0%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 83.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 83.3%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 83.3%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 83.3%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 83.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 83.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 83.3%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 83.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 83.3%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 83.3%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 35.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 35.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 35.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 35.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 35.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 35.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 35.7%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 35.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 35.7%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 35.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 35.7%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 35.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 35.7%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 35.7%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 67.3%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y}\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 67.3%

          \[\leadsto x \cdot \color{blue}{\left(-\frac{b}{a \cdot y}\right)} \]

       2. distribute-neg-frac2 67.3%

          \[\leadsto x \cdot \color{blue}{\frac{b}{-a \cdot y}} \]

       3. distribute-lft-neg-in 67.3%

          \[\leadsto x \cdot \frac{b}{\color{blue}{\left(-a\right) \cdot y}} \]

   14. Simplified 67.3%

       \[\leadsto x \cdot \color{blue}{\frac{b}{\left(-a\right) \cdot y}} \]

   if 3.29999999999999986e-290 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 74.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 74.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 71.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+93}:\\ \;\;\;\;\frac{x \cdot \left(\frac{1}{a} - \frac{b}{a}\right)}{y}\\ \mathbf{elif}\;b \leq -5.1 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \frac{1 - b}{y \cdot a}\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 37.6% accurate, 13.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-a\right)\\ \mathbf{if}\;b \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;\frac{x \cdot b}{t\_1}\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- a))))
   (if (<= b -4.5e-154)
     (/ (* x b) t_1)
     (if (<= b -5.6e-285)
       (/ (/ x a) y)
       (if (<= b 3.1e-290) (* x (/ b t_1)) (/ (/ x (+ a (* a b))) y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -a;
	double tmp;
	if (b <= -4.5e-154) {
		tmp = (x * b) / t_1;
	} else if (b <= -5.6e-285) {
		tmp = (x / a) / y;
	} else if (b <= 3.1e-290) {
		tmp = x * (b / t_1);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * -a
    if (b <= (-4.5d-154)) then
        tmp = (x * b) / t_1
    else if (b <= (-5.6d-285)) then
        tmp = (x / a) / y
    else if (b <= 3.1d-290) then
        tmp = x * (b / t_1)
    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 t_1 = y * -a;
	double tmp;
	if (b <= -4.5e-154) {
		tmp = (x * b) / t_1;
	} else if (b <= -5.6e-285) {
		tmp = (x / a) / y;
	} else if (b <= 3.1e-290) {
		tmp = x * (b / t_1);
	} else {
		tmp = (x / (a + (a * b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -a
	tmp = 0
	if b <= -4.5e-154:
		tmp = (x * b) / t_1
	elif b <= -5.6e-285:
		tmp = (x / a) / y
	elif b <= 3.1e-290:
		tmp = x * (b / t_1)
	else:
		tmp = (x / (a + (a * b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-a))
	tmp = 0.0
	if (b <= -4.5e-154)
		tmp = Float64(Float64(x * b) / t_1);
	elseif (b <= -5.6e-285)
		tmp = Float64(Float64(x / a) / y);
	elseif (b <= 3.1e-290)
		tmp = Float64(x * Float64(b / t_1));
	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)
	t_1 = y * -a;
	tmp = 0.0;
	if (b <= -4.5e-154)
		tmp = (x * b) / t_1;
	elseif (b <= -5.6e-285)
		tmp = (x / a) / y;
	elseif (b <= 3.1e-290)
		tmp = x * (b / t_1);
	else
		tmp = (x / (a + (a * b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-a)), $MachinePrecision]}, If[LessEqual[b, -4.5e-154], N[(N[(x * b), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[b, -5.6e-285], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 3.1e-290], N[(x * N[(b / t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.4999999999999997e-154

   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* 99.7%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.7%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 80.5%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 78.5%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 78.5%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 78.5%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 65.4%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 65.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 65.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 65.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 65.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 70.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 69.0%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 69.0%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 69.0%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 56.4%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 34.5%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 34.5%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 34.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 34.5%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 34.5%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 34.5%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 34.5%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 39.4%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -4.4999999999999997e-154 < b < -5.59999999999999982e-285

   1. Initial program 91.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.7%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 72.7%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 74.5%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 74.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 74.5%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 74.5%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 45.6%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 45.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if -5.59999999999999982e-285 < b < 3.0999999999999999e-290

   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 81.8%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 81.8%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 81.8%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 81.8%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 81.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 81.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 81.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 38.4%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 38.4%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 38.4%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 38.4%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 38.7%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 38.7%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 38.7%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 38.7%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 38.7%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 38.7%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 38.7%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 73.3%

       \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y}\right)} \]
   13. Step-by-step derivation

       1. neg-mul-1 73.3%

          \[\leadsto x \cdot \color{blue}{\left(-\frac{b}{a \cdot y}\right)} \]

       2. distribute-neg-frac2 73.3%

          \[\leadsto x \cdot \color{blue}{\frac{b}{-a \cdot y}} \]

       3. distribute-lft-neg-in 73.3%

          \[\leadsto x \cdot \frac{b}{\color{blue}{\left(-a\right) \cdot y}} \]

   14. Simplified 73.3%

       \[\leadsto x \cdot \color{blue}{\frac{b}{\left(-a\right) \cdot y}} \]

   if 3.0999999999999999e-290 < b

   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. Add Preprocessing

   3. Taylor expanded in y around 0 86.8%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 73.3%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 74.0%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 74.0%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 74.0%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 71.2%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 48.6%

      \[\leadsto \frac{\frac{x}{\color{blue}{a + a \cdot b}}}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;b \leq -5.6 \cdot 10^{-285}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-290}:\\ \;\;\;\;x \cdot \frac{b}{y \cdot \left(-a\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a + a \cdot b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 31.8% accurate, 17.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-a\right)\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot b}{t\_1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{x}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- a))))
   (if (<= y -4.5e-50)
     (/ (* x b) t_1)
     (if (<= y 2.3e+37) (/ (/ x a) y) (* b (/ x t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -a;
	double tmp;
	if (y <= -4.5e-50) {
		tmp = (x * b) / t_1;
	} else if (y <= 2.3e+37) {
		tmp = (x / a) / y;
	} else {
		tmp = b * (x / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * -a
    if (y <= (-4.5d-50)) then
        tmp = (x * b) / t_1
    else if (y <= 2.3d+37) then
        tmp = (x / a) / y
    else
        tmp = b * (x / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -a;
	double tmp;
	if (y <= -4.5e-50) {
		tmp = (x * b) / t_1;
	} else if (y <= 2.3e+37) {
		tmp = (x / a) / y;
	} else {
		tmp = b * (x / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -a
	tmp = 0
	if y <= -4.5e-50:
		tmp = (x * b) / t_1
	elif y <= 2.3e+37:
		tmp = (x / a) / y
	else:
		tmp = b * (x / t_1)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-a))
	tmp = 0.0
	if (y <= -4.5e-50)
		tmp = Float64(Float64(x * b) / t_1);
	elseif (y <= 2.3e+37)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(b * Float64(x / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -a;
	tmp = 0.0;
	if (y <= -4.5e-50)
		tmp = (x * b) / t_1;
	elseif (y <= 2.3e+37)
		tmp = (x / a) / y;
	else
		tmp = b * (x / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-a)), $MachinePrecision]}, If[LessEqual[y, -4.5e-50], N[(N[(x * b), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[y, 2.3e+37], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(b * N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.49999999999999962e-50

   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 74.2%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 69.7%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 69.7%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 69.7%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 60.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 60.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 60.6%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 60.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 60.6%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 60.6%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 59.6%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 58.1%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 58.1%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 58.1%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 58.1%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 58.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 55.5%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 25.2%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 25.2%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 25.2%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 25.2%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 25.2%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 25.2%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 25.2%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 38.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]

   if -4.49999999999999962e-50 < y < 2.30000000000000002e37

   1. Initial program 97.1%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 95.4%

      \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]
   4. Step-by-step derivation

      1. div-exp 82.1%

         \[\leadsto \frac{x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{e^{b}}}}{y} \]

      2. exp-to-pow 83.3%

         \[\leadsto \frac{x \cdot \frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y} \]

      3. sub-neg 83.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y} \]

      4. metadata-eval 83.3%

         \[\leadsto \frac{x \cdot \frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y} \]

   5. Simplified 83.3%

      \[\leadsto \frac{x \cdot \color{blue}{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}}{y} \]

   6. Taylor expanded in t around 0 77.8%

      \[\leadsto \frac{\color{blue}{\frac{x}{a \cdot e^{b}}}}{y} \]

   7. Taylor expanded in b around 0 42.0%

      \[\leadsto \frac{\frac{x}{\color{blue}{a}}}{y} \]

   if 2.30000000000000002e37 < y

   1. Initial program 100.0%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/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 59.3%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 57.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 57.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 57.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 51.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 51.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 51.9%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 51.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 51.9%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 51.9%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 52.8%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 50.9%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 50.9%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 50.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 50.9%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 50.9%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 29.3%

      \[\leadsto x \cdot \frac{\color{blue}{\frac{1}{a \cdot y}}}{e^{b}} \]

   9. Taylor expanded in b around 0 22.4%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b}{a \cdot y} + \frac{1}{a \cdot y}\right)} \]
   10. Step-by-step derivation

       1. associate-/r* 18.8%

          \[\leadsto x \cdot \left(-1 \cdot \frac{b}{a \cdot y} + \color{blue}{\frac{\frac{1}{a}}{y}}\right) \]

       2. +-commutative 18.8%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} + -1 \cdot \frac{b}{a \cdot y}\right)} \]

       3. mul-1-neg 18.8%

          \[\leadsto x \cdot \left(\frac{\frac{1}{a}}{y} + \color{blue}{\left(-\frac{b}{a \cdot y}\right)}\right) \]

       4. unsub-neg 18.8%

          \[\leadsto x \cdot \color{blue}{\left(\frac{\frac{1}{a}}{y} - \frac{b}{a \cdot y}\right)} \]

       5. associate-/r* 22.4%

          \[\leadsto x \cdot \left(\color{blue}{\frac{1}{a \cdot y}} - \frac{b}{a \cdot y}\right) \]

   11. Simplified 22.4%

       \[\leadsto x \cdot \color{blue}{\left(\frac{1}{a \cdot y} - \frac{b}{a \cdot y}\right)} \]

   12. Taylor expanded in b around inf 29.1%

       \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{a \cdot y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 29.1%

          \[\leadsto \color{blue}{-\frac{b \cdot x}{a \cdot y}} \]

       2. associate-/l* 29.4%

          \[\leadsto -\color{blue}{b \cdot \frac{x}{a \cdot y}} \]

       3. distribute-rgt-neg-in 29.4%

          \[\leadsto \color{blue}{b \cdot \left(-\frac{x}{a \cdot y}\right)} \]

       4. distribute-neg-frac2 29.4%

          \[\leadsto b \cdot \color{blue}{\frac{x}{-a \cdot y}} \]

       5. *-commutative 29.4%

          \[\leadsto b \cdot \frac{x}{-\color{blue}{y \cdot a}} \]

       6. distribute-rgt-neg-in 29.4%

          \[\leadsto b \cdot \frac{x}{\color{blue}{y \cdot \left(-a\right)}} \]

   14. Simplified 29.4%

       \[\leadsto \color{blue}{b \cdot \frac{x}{y \cdot \left(-a\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-50}:\\ \;\;\;\;\frac{x \cdot b}{y \cdot \left(-a\right)}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+37}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{x}{y \cdot \left(-a\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 31.5% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x 1.8e-96) (/ 1.0 (* a (/ y x))) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.8e-96) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= 1.8d-96) then
        tmp = 1.0d0 / (a * (y / x))
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= 1.8e-96) {
		tmp = 1.0 / (a * (y / x));
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= 1.8e-96:
		tmp = 1.0 / (a * (y / x))
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= 1.8e-96)
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	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 (x <= 1.8e-96)
		tmp = 1.0 / (a * (y / x));
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, 1.8e-96], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.80000000000000004e-96

   1. Initial program 98.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 98.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 84.1%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 82.0%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 82.0%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 82.0%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 70.1%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 70.7%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 70.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 70.7%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 70.7%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 69.5%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.5%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 69.1%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 69.1%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 69.1%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 69.1%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 63.8%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 34.5%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
   10. Step-by-step derivation

       1. clear-num 34.2%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. inv-pow 34.2%

          \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]

   11. Applied egg-rr 34.2%

       \[\leadsto \color{blue}{{\left(\frac{a \cdot y}{x}\right)}^{-1}} \]
   12. Step-by-step derivation

       1. unpow-1 34.2%

          \[\leadsto \color{blue}{\frac{1}{\frac{a \cdot y}{x}}} \]

       2. associate-/l* 32.5%

          \[\leadsto \frac{1}{\color{blue}{a \cdot \frac{y}{x}}} \]

   13. Simplified 32.5%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]

   if 1.80000000000000004e-96 < x

   1. Initial program 99.2%

      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.2%

         \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

      2. associate--l+ 99.2%

         \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

      3. exp-sum 77.4%

         \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

      4. associate-/l* 77.4%

         \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

      5. *-commutative 77.4%

         \[\leadsto x \cdot \left(e^{\color{blue}{\log z \cdot y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      6. exp-to-pow 77.4%

         \[\leadsto x \cdot \left(\color{blue}{{z}^{y}} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right) \]

      7. exp-diff 71.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

      8. *-commutative 71.0%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      9. exp-to-pow 71.8%

         \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

      10. sub-neg 71.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

      11. metadata-eval 71.8%

          \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

   3. Simplified 71.8%

      \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 71.9%

      \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
   6. Step-by-step derivation

      1. associate-/r* 68.8%

         \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

      2. exp-to-pow 69.2%

         \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

      3. sub-neg 69.2%

         \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

      4. metadata-eval 69.2%

         \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

   7. Simplified 69.2%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

   8. Taylor expanded in t around 0 65.2%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   9. Taylor expanded in b around 0 29.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 31.3% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-/l* 98.5%

      \[\leadsto \color{blue}{x \cdot \frac{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}} \]

   2. associate--l+ 98.5%

      \[\leadsto x \cdot \frac{e^{\color{blue}{y \cdot \log z + \left(\left(t - 1\right) \cdot \log a - b\right)}}}{y} \]

   3. exp-sum 82.4%

      \[\leadsto x \cdot \frac{\color{blue}{e^{y \cdot \log z} \cdot e^{\left(t - 1\right) \cdot \log a - b}}}{y} \]

   4. associate-/l* 80.9%

      \[\leadsto x \cdot \color{blue}{\left(e^{y \cdot \log z} \cdot \frac{e^{\left(t - 1\right) \cdot \log a - b}}{y}\right)} \]

   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 70.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a}}{e^{b}}}}{y}\right) \]

   8. *-commutative 70.3%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{e^{\color{blue}{\log a \cdot \left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   9. exp-to-pow 71.0%

      \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{e^{b}}}{y}\right) \]

   10. sub-neg 71.0%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{e^{b}}}{y}\right) \]

   11. metadata-eval 71.0%

       \[\leadsto x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{e^{b}}}{y}\right) \]

3. Simplified 71.0%

   \[\leadsto \color{blue}{x \cdot \left({z}^{y} \cdot \frac{\frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 70.1%

   \[\leadsto x \cdot \color{blue}{\frac{e^{\log a \cdot \left(t - 1\right)}}{y \cdot e^{b}}} \]
6. Step-by-step derivation

   1. associate-/r* 68.5%

      \[\leadsto x \cdot \color{blue}{\frac{\frac{e^{\log a \cdot \left(t - 1\right)}}{y}}{e^{b}}} \]

   2. exp-to-pow 69.1%

      \[\leadsto x \cdot \frac{\frac{\color{blue}{{a}^{\left(t - 1\right)}}}{y}}{e^{b}} \]

   3. sub-neg 69.1%

      \[\leadsto x \cdot \frac{\frac{{a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y}}{e^{b}} \]

   4. metadata-eval 69.1%

      \[\leadsto x \cdot \frac{\frac{{a}^{\left(t + \color{blue}{-1}\right)}}{y}}{e^{b}} \]

7. Simplified 69.1%

   \[\leadsto x \cdot \color{blue}{\frac{\frac{{a}^{\left(t + -1\right)}}{y}}{e^{b}}} \]

8. Taylor expanded in t around 0 64.2%

   \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot e^{b}\right)}} \]

9. Taylor expanded in b around 0 33.1%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

10. Final simplification 33.1%

    \[\leadsto \frac{x}{y \cdot a} \]
11. Add Preprocessing

Developer target: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024101 
(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))