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

Percentage Accurate: 98.4% → 98.4%

Time: 35.3s

Alternatives: 20

Speedup: 1.0×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.4% accurate, 1.0× speedup

Math

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

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 98.7%

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

2. Final simplification 98.7%

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

Alternative 2: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -500000000 \lor \neg \left(t + -1 \leq -0.999999999\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -500000000.0) (not (<= (+ t -1.0) -0.999999999)))
   (/ (* 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) <= -500000000.0) || !((t + -1.0) <= -0.999999999)) {
		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)) <= (-500000000.0d0)) .or. (.not. ((t + (-1.0d0)) <= (-0.999999999d0)))) 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) <= -500000000.0) || !((t + -1.0) <= -0.999999999)) {
		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) <= -500000000.0) or not ((t + -1.0) <= -0.999999999):
		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) <= -500000000.0) || !(Float64(t + -1.0) <= -0.999999999))
		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) <= -500000000.0) || ~(((t + -1.0) <= -0.999999999)))
		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], -500000000.0], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.999999999]], $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 1) < -5e8 or -0.999999999000000028 < (-.f64 t 1)

   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. Taylor expanded in y around 0 93.7%

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

   if -5e8 < (-.f64 t 1) < -0.999999999000000028

   1. Initial program 97.2%

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

   2. Taylor expanded in t around 0 97.2%

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

      1. mul-1-neg 97.2%

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

   4. Simplified 97.2%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -500000000 \lor \neg \left(t + -1 \leq -0.999999999\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 80.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+75} \lor \neg \left(t + -1 \leq -5 \cdot 10^{+66}\right) \land \left(t + -1 \leq -500000000 \lor \neg \left(t + -1 \leq -0.5\right)\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -1e+75)
         (and (not (<= (+ t -1.0) -5e+66))
              (or (<= (+ t -1.0) -500000000.0) (not (<= (+ t -1.0) -0.5)))))
   (* x (/ (pow a (+ t -1.0)) 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) <= -1e+75) || (!((t + -1.0) <= -5e+66) && (((t + -1.0) <= -500000000.0) || !((t + -1.0) <= -0.5)))) {
		tmp = x * (pow(a, (t + -1.0)) / 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)) <= (-1d+75)) .or. (.not. ((t + (-1.0d0)) <= (-5d+66))) .and. ((t + (-1.0d0)) <= (-500000000.0d0)) .or. (.not. ((t + (-1.0d0)) <= (-0.5d0)))) then
        tmp = x * ((a ** (t + (-1.0d0))) / 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) <= -1e+75) || (!((t + -1.0) <= -5e+66) && (((t + -1.0) <= -500000000.0) || !((t + -1.0) <= -0.5)))) {
		tmp = x * (Math.pow(a, (t + -1.0)) / 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) <= -1e+75) or (not ((t + -1.0) <= -5e+66) and (((t + -1.0) <= -500000000.0) or not ((t + -1.0) <= -0.5))):
		tmp = x * (math.pow(a, (t + -1.0)) / 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) <= -1e+75) || (!(Float64(t + -1.0) <= -5e+66) && ((Float64(t + -1.0) <= -500000000.0) || !(Float64(t + -1.0) <= -0.5))))
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / 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) <= -1e+75) || (~(((t + -1.0) <= -5e+66)) && (((t + -1.0) <= -500000000.0) || ~(((t + -1.0) <= -0.5)))))
		tmp = x * ((a ^ (t + -1.0)) / 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], -1e+75], And[N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+66]], $MachinePrecision], Or[LessEqual[N[(t + -1.0), $MachinePrecision], -500000000.0], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -0.5]], $MachinePrecision]]]], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $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 1) < -9.99999999999999927e74 or -4.99999999999999991e66 < (-.f64 t 1) < -5e8 or -0.5 < (-.f64 t 1)

   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. Taylor expanded in y around 0 94.1%

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

   3. Taylor expanded in b around 0 87.4%

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

   5. Simplified 87.4%

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

   if -9.99999999999999927e74 < (-.f64 t 1) < -4.99999999999999991e66 or -5e8 < (-.f64 t 1) < -0.5

   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/ 84.8%

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

      2. *-commutative 84.8%

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

      3. +-commutative 84.8%

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

      4. associate--l+ 84.8%

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

      5. exp-sum 80.7%

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

      6. *-commutative 80.7%

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

      7. exp-to-pow 81.3%

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

      8. sub-neg 81.3%

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

      9. metadata-eval 81.3%

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

      10. exp-diff 73.1%

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

      11. *-commutative 73.1%

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

      12. exp-to-pow 73.1%

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

   3. Simplified 73.1%

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

   4. Taylor expanded in t around 0 87.8%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -1 \cdot 10^{+75} \lor \neg \left(t + -1 \leq -5 \cdot 10^{+66}\right) \land \left(t + -1 \leq -500000000 \lor \neg \left(t + -1 \leq -0.5\right)\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 4: 80.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -1.26 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a}}{e^{b} \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq -820000000 \lor \neg \left(t \leq 82\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a (+ t -1.0)) y))))
   (if (<= t -1.26e+75)
     t_1
     (if (<= t -4.8e+66)
       (/ (/ (pow z y) a) (* (exp b) (/ y x)))
       (if (or (<= t -820000000.0) (not (<= t 82.0)))
         t_1
         (/ (* x (pow z y)) (* a (* y (exp b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, (t + -1.0)) / y);
	double tmp;
	if (t <= -1.26e+75) {
		tmp = t_1;
	} else if (t <= -4.8e+66) {
		tmp = (pow(z, y) / a) / (exp(b) * (y / x));
	} else if ((t <= -820000000.0) || !(t <= 82.0)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = x * ((a ** (t + (-1.0d0))) / y)
    if (t <= (-1.26d+75)) then
        tmp = t_1
    else if (t <= (-4.8d+66)) then
        tmp = ((z ** y) / a) / (exp(b) * (y / x))
    else if ((t <= (-820000000.0d0)) .or. (.not. (t <= 82.0d0))) then
        tmp = t_1
    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 t_1 = x * (Math.pow(a, (t + -1.0)) / y);
	double tmp;
	if (t <= -1.26e+75) {
		tmp = t_1;
	} else if (t <= -4.8e+66) {
		tmp = (Math.pow(z, y) / a) / (Math.exp(b) * (y / x));
	} else if ((t <= -820000000.0) || !(t <= 82.0)) {
		tmp = t_1;
	} else {
		tmp = (x * Math.pow(z, y)) / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, (t + -1.0)) / y)
	tmp = 0
	if t <= -1.26e+75:
		tmp = t_1
	elif t <= -4.8e+66:
		tmp = (math.pow(z, y) / a) / (math.exp(b) * (y / x))
	elif (t <= -820000000.0) or not (t <= 82.0):
		tmp = t_1
	else:
		tmp = (x * math.pow(z, y)) / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ Float64(t + -1.0)) / y))
	tmp = 0.0
	if (t <= -1.26e+75)
		tmp = t_1;
	elseif (t <= -4.8e+66)
		tmp = Float64(Float64((z ^ y) / a) / Float64(exp(b) * Float64(y / x)));
	elseif ((t <= -820000000.0) || !(t <= 82.0))
		tmp = t_1;
	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)
	t_1 = x * ((a ^ (t + -1.0)) / y);
	tmp = 0.0;
	if (t <= -1.26e+75)
		tmp = t_1;
	elseif (t <= -4.8e+66)
		tmp = ((z ^ y) / a) / (exp(b) * (y / x));
	elseif ((t <= -820000000.0) || ~((t <= 82.0)))
		tmp = t_1;
	else
		tmp = (x * (z ^ y)) / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.26e+75], t$95$1, If[LessEqual[t, -4.8e+66], N[(N[(N[Power[z, y], $MachinePrecision] / a), $MachinePrecision] / N[(N[Exp[b], $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -820000000.0], N[Not[LessEqual[t, 82.0]], $MachinePrecision]], t$95$1, 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 3 regimes

2. if t < -1.26000000000000003e75 or -4.8000000000000003e66 < t < -8.2e8 or 82 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.8%

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

   3. Taylor expanded in b around 0 88.1%

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

   5. Simplified 88.1%

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

   if -1.26000000000000003e75 < t < -4.8000000000000003e66

   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. *-commutative 100.0%

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

      2. associate-/l* 100.0%

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

      3. exp-diff 50.0%

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

      4. associate-/l/ 50.0%

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

      5. exp-sum 0.0%

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

      6. *-commutative 0.0%

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

      7. exp-to-pow 0.0%

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

      8. *-commutative 0.0%

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

      9. exp-to-pow 0.0%

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

      10. sub-neg 0.0%

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

      11. metadata-eval 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in t around 0 100.0%

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

   if -8.2e8 < t < 82

   1. Initial program 97.3%

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

      1. associate-*l/ 84.1%

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

      2. *-commutative 84.1%

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

      3. +-commutative 84.1%

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

      4. associate--l+ 84.1%

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

      5. exp-sum 84.1%

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

      6. *-commutative 84.1%

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

      7. exp-to-pow 84.7%

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

      8. sub-neg 84.7%

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

      9. metadata-eval 84.7%

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

      10. exp-diff 76.2%

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

      11. *-commutative 76.2%

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

      12. exp-to-pow 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in t around 0 87.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+75}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{{z}^{y}}{a}}{e^{b} \cdot \frac{y}{x}}\\ \mathbf{elif}\;t \leq -820000000 \lor \neg \left(t \leq 82\right):\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 5: 85.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 1.9 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -1.85e-7) (not (<= t 1.9e-39)))
   (/ (* 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 <= -1.85e-7) || !(t <= 1.9e-39)) {
		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 <= (-1.85d-7)) .or. (.not. (t <= 1.9d-39))) 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 <= -1.85e-7) || !(t <= 1.9e-39)) {
		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 <= -1.85e-7) or not (t <= 1.9e-39):
		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 ((t <= -1.85e-7) || !(t <= 1.9e-39))
		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 <= -1.85e-7) || ~((t <= 1.9e-39)))
		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[t, -1.85e-7], N[Not[LessEqual[t, 1.9e-39]], $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 t < -1.85000000000000002e-7 or 1.9000000000000001e-39 < t

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 93.4%

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

   if -1.85000000000000002e-7 < t < 1.9000000000000001e-39

   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. Step-by-step derivation

      1. associate-*l/ 83.6%

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

      2. *-commutative 83.6%

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

      3. +-commutative 83.6%

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

      4. associate--l+ 83.6%

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

      5. exp-sum 83.6%

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

      6. *-commutative 83.6%

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

      7. exp-to-pow 84.2%

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

      8. sub-neg 84.2%

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

      9. metadata-eval 84.2%

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

      10. exp-diff 75.9%

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

      11. *-commutative 75.9%

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

      12. exp-to-pow 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in t around 0 87.9%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-7} \lor \neg \left(t \leq 1.9 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {z}^{y}}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 6: 81.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+46} \lor \neg \left(y \leq 3.5 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.6e+46) (not (<= y 3.5e+94)))
   (/ (/ (* x (pow z y)) a) y)
   (* (/ (pow a (+ t -1.0)) y) (/ x (exp b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+46) || !(y <= 3.5e+94)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (pow(a, (t + -1.0)) / y) * (x / exp(b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.6d+46)) .or. (.not. (y <= 3.5d+94))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = ((a ** (t + (-1.0d0))) / y) * (x / exp(b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.6e+46) || !(y <= 3.5e+94)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (Math.pow(a, (t + -1.0)) / y) * (x / Math.exp(b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.6e+46) or not (y <= 3.5e+94):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (math.pow(a, (t + -1.0)) / y) * (x / math.exp(b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.6e+46) || !(y <= 3.5e+94))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64((a ^ Float64(t + -1.0)) / y) * Float64(x / exp(b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.6e+46) || ~((y <= 3.5e+94)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = ((a ^ (t + -1.0)) / y) * (x / exp(b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.6e+46], N[Not[LessEqual[y, 3.5e+94]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision] * N[(x / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5999999999999999e46 or 3.4999999999999997e94 < 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/ 81.6%

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

      2. *-commutative 81.6%

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

      3. +-commutative 81.6%

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

      4. associate--l+ 81.6%

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

      5. exp-sum 60.2%

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

      6. *-commutative 60.2%

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

      7. exp-to-pow 60.2%

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

      8. sub-neg 60.2%

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

      9. metadata-eval 60.2%

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

      10. exp-diff 46.9%

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

      11. *-commutative 46.9%

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

      12. exp-to-pow 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in b around 0 57.2%

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

   5. Taylor expanded in t around 0 79.9%

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

   if -1.5999999999999999e46 < y < 3.4999999999999997e94

   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. Step-by-step derivation

      1. associate-*l/ 90.1%

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

      2. *-commutative 90.1%

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

      3. +-commutative 90.1%

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

      4. associate--l+ 90.1%

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

      5. exp-sum 71.7%

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

      6. *-commutative 71.7%

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

      7. exp-to-pow 72.1%

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

      8. sub-neg 72.1%

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

      9. metadata-eval 72.1%

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

      10. exp-diff 72.1%

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

      11. *-commutative 72.1%

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

      12. exp-to-pow 72.1%

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

   3. Simplified 72.1%

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

   4. Taylor expanded in y around 0 80.0%

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

      1. times-frac 81.8%

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

      2. sub-neg 81.8%

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

      3. metadata-eval 81.8%

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

   6. Simplified 81.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+46} \lor \neg \left(y \leq 3.5 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{{a}^{\left(t + -1\right)}}{y} \cdot \frac{x}{e^{b}}\\ \end{array} \]

Alternative 7: 75.3% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ t_2 := \frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ t_3 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{if}\;b \leq -8.4 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ (pow a (+ t -1.0)) y)))
        (t_2 (/ x (* y (* a (exp b)))))
        (t_3 (/ (/ (* x (pow z y)) a) y)))
   (if (<= b -8.4e+21)
     t_2
     (if (<= b -2.6e-69)
       t_1
       (if (<= b -5.2e-116)
         t_3
         (if (<= b 7e-236) t_1 (if (<= b 6.6e+20) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (pow(a, (t + -1.0)) / y);
	double t_2 = x / (y * (a * exp(b)));
	double t_3 = ((x * pow(z, y)) / a) / y;
	double tmp;
	if (b <= -8.4e+21) {
		tmp = t_2;
	} else if (b <= -2.6e-69) {
		tmp = t_1;
	} else if (b <= -5.2e-116) {
		tmp = t_3;
	} else if (b <= 7e-236) {
		tmp = t_1;
	} else if (b <= 6.6e+20) {
		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 * ((a ** (t + (-1.0d0))) / y)
    t_2 = x / (y * (a * exp(b)))
    t_3 = ((x * (z ** y)) / a) / y
    if (b <= (-8.4d+21)) then
        tmp = t_2
    else if (b <= (-2.6d-69)) then
        tmp = t_1
    else if (b <= (-5.2d-116)) then
        tmp = t_3
    else if (b <= 7d-236) then
        tmp = t_1
    else if (b <= 6.6d+20) 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(a, (t + -1.0)) / y);
	double t_2 = x / (y * (a * Math.exp(b)));
	double t_3 = ((x * Math.pow(z, y)) / a) / y;
	double tmp;
	if (b <= -8.4e+21) {
		tmp = t_2;
	} else if (b <= -2.6e-69) {
		tmp = t_1;
	} else if (b <= -5.2e-116) {
		tmp = t_3;
	} else if (b <= 7e-236) {
		tmp = t_1;
	} else if (b <= 6.6e+20) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (math.pow(a, (t + -1.0)) / y)
	t_2 = x / (y * (a * math.exp(b)))
	t_3 = ((x * math.pow(z, y)) / a) / y
	tmp = 0
	if b <= -8.4e+21:
		tmp = t_2
	elif b <= -2.6e-69:
		tmp = t_1
	elif b <= -5.2e-116:
		tmp = t_3
	elif b <= 7e-236:
		tmp = t_1
	elif b <= 6.6e+20:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64((a ^ Float64(t + -1.0)) / y))
	t_2 = Float64(x / Float64(y * Float64(a * exp(b))))
	t_3 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	tmp = 0.0
	if (b <= -8.4e+21)
		tmp = t_2;
	elseif (b <= -2.6e-69)
		tmp = t_1;
	elseif (b <= -5.2e-116)
		tmp = t_3;
	elseif (b <= 7e-236)
		tmp = t_1;
	elseif (b <= 6.6e+20)
		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 * ((a ^ (t + -1.0)) / y);
	t_2 = x / (y * (a * exp(b)));
	t_3 = ((x * (z ^ y)) / a) / y;
	tmp = 0.0;
	if (b <= -8.4e+21)
		tmp = t_2;
	elseif (b <= -2.6e-69)
		tmp = t_1;
	elseif (b <= -5.2e-116)
		tmp = t_3;
	elseif (b <= 7e-236)
		tmp = t_1;
	elseif (b <= 6.6e+20)
		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[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[b, -8.4e+21], t$95$2, If[LessEqual[b, -2.6e-69], t$95$1, If[LessEqual[b, -5.2e-116], t$95$3, If[LessEqual[b, 7e-236], t$95$1, If[LessEqual[b, 6.6e+20], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -8.4e21 or 6.6e20 < 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/ 83.2%

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

      2. *-commutative 83.2%

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

      3. +-commutative 83.2%

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

      4. associate--l+ 83.2%

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

      5. exp-sum 63.2%

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

      6. *-commutative 63.2%

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

      7. exp-to-pow 63.2%

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

      8. sub-neg 63.2%

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

      9. metadata-eval 63.2%

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

      10. exp-diff 53.6%

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

      11. *-commutative 53.6%

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

      12. exp-to-pow 53.6%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in t around 0 74.5%

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

   5. Taylor expanded in y around 0 84.3%

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

   if -8.4e21 < b < -2.6000000000000002e-69 or -5.2000000000000001e-116 < b < 6.99999999999999988e-236

   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. Taylor expanded in y around 0 77.5%

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

   3. Taylor expanded in b around 0 77.6%

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

   5. Simplified 82.7%

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

   if -2.6000000000000002e-69 < b < -5.2000000000000001e-116 or 6.99999999999999988e-236 < b < 6.6e20

   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/ 85.8%

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

      2. *-commutative 85.8%

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

      3. +-commutative 85.8%

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

      4. associate--l+ 85.8%

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

      5. exp-sum 72.2%

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

      6. *-commutative 72.2%

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

      7. exp-to-pow 72.9%

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

      8. sub-neg 72.9%

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

      9. metadata-eval 72.9%

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

      10. exp-diff 72.9%

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

      11. *-commutative 72.9%

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

      12. exp-to-pow 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in b around 0 74.7%

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

   5. Taylor expanded in t around 0 78.6%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-116}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-236}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8: 74.1% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+21} \lor \neg \left(b \leq 1.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -8.2e+21) (not (<= b 1.6e+88)))
   (/ x (* y (* a (exp b))))
   (* x (/ (pow a (+ t -1.0)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.2e+21) || !(b <= 1.6e+88)) {
		tmp = x / (y * (a * exp(b)));
	} else {
		tmp = x * (pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-8.2d+21)) .or. (.not. (b <= 1.6d+88))) then
        tmp = x / (y * (a * exp(b)))
    else
        tmp = x * ((a ** (t + (-1.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -8.2e+21) || !(b <= 1.6e+88)) {
		tmp = x / (y * (a * Math.exp(b)));
	} else {
		tmp = x * (Math.pow(a, (t + -1.0)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -8.2e+21) or not (b <= 1.6e+88):
		tmp = x / (y * (a * math.exp(b)))
	else:
		tmp = x * (math.pow(a, (t + -1.0)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -8.2e+21) || !(b <= 1.6e+88))
		tmp = Float64(x / Float64(y * Float64(a * exp(b))));
	else
		tmp = Float64(x * Float64((a ^ Float64(t + -1.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -8.2e+21) || ~((b <= 1.6e+88)))
		tmp = x / (y * (a * exp(b)));
	else
		tmp = x * ((a ^ (t + -1.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -8.2e+21], N[Not[LessEqual[b, 1.6e+88]], $MachinePrecision]], N[(x / N[(y * N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -8.2e21 or 1.5999999999999999e88 < 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/ 84.3%

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

      2. *-commutative 84.3%

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

      3. +-commutative 84.3%

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

      4. associate--l+ 84.3%

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

      5. exp-sum 64.8%

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

      6. *-commutative 64.8%

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

      7. exp-to-pow 64.8%

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

      8. sub-neg 64.8%

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

      9. metadata-eval 64.8%

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

      10. exp-diff 54.6%

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

      11. *-commutative 54.6%

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

      12. exp-to-pow 54.6%

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

   3. Simplified 54.6%

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

   4. Taylor expanded in t around 0 76.0%

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

   5. Taylor expanded in y around 0 87.2%

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

   if -8.2e21 < b < 1.5999999999999999e88

   1. Initial program 97.8%

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

   2. Taylor expanded in y around 0 71.7%

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

   3. Taylor expanded in b around 0 70.6%

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

   5. Simplified 72.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.2 \cdot 10^{+21} \lor \neg \left(b \leq 1.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{{a}^{\left(t + -1\right)}}{y}\\ \end{array} \]

Alternative 9: 58.9% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.7%

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

   1. associate-*l/ 86.8%

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

   2. *-commutative 86.8%

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

   3. +-commutative 86.8%

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

   4. associate--l+ 86.8%

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

   5. exp-sum 67.3%

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

   6. *-commutative 67.3%

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

   7. exp-to-pow 67.6%

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

   8. sub-neg 67.6%

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

   9. metadata-eval 67.6%

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

   10. exp-diff 62.5%

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

   11. *-commutative 62.5%

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

   12. exp-to-pow 62.5%

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

3. Simplified 62.5%

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

4. Taylor expanded in t around 0 67.3%

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

5. Taylor expanded in y around 0 58.2%

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

6. Final simplification 58.2%

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

Alternative 10: 38.8% accurate, 9.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(y \cdot y\right)\\ t_2 := \frac{x \cdot y - \left(y \cdot a\right) \cdot \left(x \cdot \frac{b}{a}\right)}{t_1}\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+206}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot \left(1 - b\right)}{y}}{a \cdot a}\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot y}{a} - y \cdot \left(x \cdot b\right)}{t_1}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{y \cdot \frac{x}{y} - a \cdot \left(b \cdot \frac{x}{a}\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-301}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-285}:\\ \;\;\;\;\frac{x \cdot \left(a - \left(y \cdot a\right) \cdot \frac{b}{y}\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (* y y)))
        (t_2 (/ (- (* x y) (* (* y a) (* x (/ b a)))) t_1)))
   (if (<= b -3.4e+206)
     (/ (* a (/ (* x (- 1.0 b)) y)) (* a a))
     (if (<= b -2.6e-17)
       (/ (- (* a (/ (* x y) a)) (* y (* x b))) t_1)
       (if (<= b -1.65e-68)
         t_2
         (if (<= b -4.5e-242)
           (/ (- (* y (/ x y)) (* a (* b (/ x a)))) (* y a))
           (if (<= b 1.1e-301)
             (- (* x (/ b (* y a))))
             (if (<= b 8.8e-285)
               (/ (* x (- a (* (* y a) (/ b y)))) (* y (* a a)))
               (if (<= b 6.2e-232) t_2 (/ x (* y (+ a (* a b)))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (y * y);
	double t_2 = ((x * y) - ((y * a) * (x * (b / a)))) / t_1;
	double tmp;
	if (b <= -3.4e+206) {
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	} else if (b <= -2.6e-17) {
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / t_1;
	} else if (b <= -1.65e-68) {
		tmp = t_2;
	} else if (b <= -4.5e-242) {
		tmp = ((y * (x / y)) - (a * (b * (x / a)))) / (y * a);
	} else if (b <= 1.1e-301) {
		tmp = -(x * (b / (y * a)));
	} else if (b <= 8.8e-285) {
		tmp = (x * (a - ((y * a) * (b / y)))) / (y * (a * a));
	} else if (b <= 6.2e-232) {
		tmp = t_2;
	} else {
		tmp = x / (y * (a + (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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (y * y)
    t_2 = ((x * y) - ((y * a) * (x * (b / a)))) / t_1
    if (b <= (-3.4d+206)) then
        tmp = (a * ((x * (1.0d0 - b)) / y)) / (a * a)
    else if (b <= (-2.6d-17)) then
        tmp = ((a * ((x * y) / a)) - (y * (x * b))) / t_1
    else if (b <= (-1.65d-68)) then
        tmp = t_2
    else if (b <= (-4.5d-242)) then
        tmp = ((y * (x / y)) - (a * (b * (x / a)))) / (y * a)
    else if (b <= 1.1d-301) then
        tmp = -(x * (b / (y * a)))
    else if (b <= 8.8d-285) then
        tmp = (x * (a - ((y * a) * (b / y)))) / (y * (a * a))
    else if (b <= 6.2d-232) then
        tmp = t_2
    else
        tmp = x / (y * (a + (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 t_1 = a * (y * y);
	double t_2 = ((x * y) - ((y * a) * (x * (b / a)))) / t_1;
	double tmp;
	if (b <= -3.4e+206) {
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	} else if (b <= -2.6e-17) {
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / t_1;
	} else if (b <= -1.65e-68) {
		tmp = t_2;
	} else if (b <= -4.5e-242) {
		tmp = ((y * (x / y)) - (a * (b * (x / a)))) / (y * a);
	} else if (b <= 1.1e-301) {
		tmp = -(x * (b / (y * a)));
	} else if (b <= 8.8e-285) {
		tmp = (x * (a - ((y * a) * (b / y)))) / (y * (a * a));
	} else if (b <= 6.2e-232) {
		tmp = t_2;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (y * y)
	t_2 = ((x * y) - ((y * a) * (x * (b / a)))) / t_1
	tmp = 0
	if b <= -3.4e+206:
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a)
	elif b <= -2.6e-17:
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / t_1
	elif b <= -1.65e-68:
		tmp = t_2
	elif b <= -4.5e-242:
		tmp = ((y * (x / y)) - (a * (b * (x / a)))) / (y * a)
	elif b <= 1.1e-301:
		tmp = -(x * (b / (y * a)))
	elif b <= 8.8e-285:
		tmp = (x * (a - ((y * a) * (b / y)))) / (y * (a * a))
	elif b <= 6.2e-232:
		tmp = t_2
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(y * y))
	t_2 = Float64(Float64(Float64(x * y) - Float64(Float64(y * a) * Float64(x * Float64(b / a)))) / t_1)
	tmp = 0.0
	if (b <= -3.4e+206)
		tmp = Float64(Float64(a * Float64(Float64(x * Float64(1.0 - b)) / y)) / Float64(a * a));
	elseif (b <= -2.6e-17)
		tmp = Float64(Float64(Float64(a * Float64(Float64(x * y) / a)) - Float64(y * Float64(x * b))) / t_1);
	elseif (b <= -1.65e-68)
		tmp = t_2;
	elseif (b <= -4.5e-242)
		tmp = Float64(Float64(Float64(y * Float64(x / y)) - Float64(a * Float64(b * Float64(x / a)))) / Float64(y * a));
	elseif (b <= 1.1e-301)
		tmp = Float64(-Float64(x * Float64(b / Float64(y * a))));
	elseif (b <= 8.8e-285)
		tmp = Float64(Float64(x * Float64(a - Float64(Float64(y * a) * Float64(b / y)))) / Float64(y * Float64(a * a)));
	elseif (b <= 6.2e-232)
		tmp = t_2;
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (y * y);
	t_2 = ((x * y) - ((y * a) * (x * (b / a)))) / t_1;
	tmp = 0.0;
	if (b <= -3.4e+206)
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	elseif (b <= -2.6e-17)
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / t_1;
	elseif (b <= -1.65e-68)
		tmp = t_2;
	elseif (b <= -4.5e-242)
		tmp = ((y * (x / y)) - (a * (b * (x / a)))) / (y * a);
	elseif (b <= 1.1e-301)
		tmp = -(x * (b / (y * a)));
	elseif (b <= 8.8e-285)
		tmp = (x * (a - ((y * a) * (b / y)))) / (y * (a * a));
	elseif (b <= 6.2e-232)
		tmp = t_2;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * y), $MachinePrecision] - N[(N[(y * a), $MachinePrecision] * N[(x * N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[b, -3.4e+206], N[(N[(a * N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -2.6e-17], N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[b, -1.65e-68], t$95$2, If[LessEqual[b, -4.5e-242], N[(N[(N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(b * N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-301], (-N[(x * N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[b, 8.8e-285], N[(N[(x * N[(a - N[(N[(y * a), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e-232], t$95$2, N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -3.39999999999999999e206

   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/ 85.0%

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

      2. *-commutative 85.0%

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

      3. +-commutative 85.0%

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

      4. associate--l+ 85.0%

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

      5. exp-sum 60.0%

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

      6. *-commutative 60.0%

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

      7. exp-to-pow 60.0%

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

      8. sub-neg 60.0%

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

      9. metadata-eval 60.0%

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

      10. exp-diff 45.0%

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

      11. *-commutative 45.0%

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

      12. exp-to-pow 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in t around 0 70.0%

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

   5. Taylor expanded in y around 0 95.1%

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

   6. Taylor expanded in b around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. times-frac 61.4%

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

   8. Simplified 61.4%

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

      1. unsub-neg 61.4%

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

      2. *-commutative 61.4%

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

      3. associate-/r* 61.4%

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

      4. associate-*r/ 61.4%

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

      5. frac-sub 70.9%

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

   10. Applied egg-rr 70.9%

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

       1. *-commutative 70.9%

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

       2. distribute-lft-out-- 70.9%

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

       3. associate-*l/ 80.4%

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

       4. *-commutative 80.4%

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

       5. div-sub 80.4%

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

       6. *-rgt-identity 80.4%

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

       7. distribute-lft-out-- 80.4%

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

   12. Simplified 80.4%

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

   if -3.39999999999999999e206 < b < -2.60000000000000003e-17

   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/ 92.3%

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

      2. *-commutative 92.3%

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

      3. +-commutative 92.3%

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

      4. associate--l+ 92.3%

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

      5. exp-sum 64.1%

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

      6. *-commutative 64.1%

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

      7. exp-to-pow 64.1%

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

      8. sub-neg 64.1%

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

      9. metadata-eval 64.1%

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

      10. exp-diff 56.4%

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

      11. *-commutative 56.4%

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

      12. exp-to-pow 56.4%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in t around 0 69.4%

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

   5. Taylor expanded in y around 0 77.3%

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

   6. Taylor expanded in b around 0 28.2%

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

      1. mul-1-neg 28.2%

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

      2. times-frac 28.0%

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

   8. Simplified 28.0%

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

      1. unsub-neg 28.0%

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

      2. associate-/r* 28.0%

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

      3. *-commutative 28.0%

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

      4. frac-times 28.2%

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

      5. frac-sub 35.0%

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

      6. *-commutative 35.0%

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

      7. *-commutative 35.0%

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

   10. Applied egg-rr 35.0%

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

       1. associate-*r* 42.7%

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

       2. associate-*l/ 42.7%

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

       3. associate-*r* 49.8%

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

   12. Simplified 49.8%

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

   if -2.60000000000000003e-17 < b < -1.6499999999999999e-68 or 8.7999999999999996e-285 < b < 6.1999999999999998e-232

   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/ 95.8%

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

      2. *-commutative 95.8%

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

      3. +-commutative 95.8%

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

      4. associate--l+ 95.8%

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

      5. exp-sum 66.7%

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

      6. *-commutative 66.7%

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

      7. exp-to-pow 66.7%

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

      8. sub-neg 66.7%

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

      9. metadata-eval 66.7%

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

      10. exp-diff 66.7%

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

      11. *-commutative 66.7%

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

      12. exp-to-pow 66.7%

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

   3. Simplified 66.7%

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

   4. Taylor expanded in t around 0 43.2%

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

   5. Taylor expanded in y around 0 22.5%

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

   6. Taylor expanded in b around 0 22.4%

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

      1. mul-1-neg 22.4%

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

      2. times-frac 22.4%

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

   8. Simplified 22.4%

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

      1. unsub-neg 22.4%

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

      2. associate-*l/ 22.4%

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

      3. frac-sub 25.8%

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

      4. *-commutative 25.8%

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

      5. *-commutative 25.8%

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

   10. Applied egg-rr 25.8%

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

       1. *-commutative 25.8%

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

       2. associate-*r/ 25.8%

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

       3. *-commutative 25.8%

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

       4. associate-*r/ 25.8%

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

       5. *-commutative 25.8%

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

       6. associate-*r* 45.9%

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

   12. Simplified 45.9%

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

   if -1.6499999999999999e-68 < b < -4.4999999999999999e-242

   1. Initial program 96.7%

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

      1. associate-*l/ 82.6%

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

      2. *-commutative 82.6%

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

      3. +-commutative 82.6%

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

      4. associate--l+ 82.6%

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

      5. exp-sum 59.3%

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

      6. *-commutative 59.3%

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

      7. exp-to-pow 59.9%

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

      8. sub-neg 59.9%

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

      9. metadata-eval 59.9%

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

      10. exp-diff 59.9%

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

      11. *-commutative 59.9%

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

      12. exp-to-pow 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in t around 0 54.1%

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

   5. Taylor expanded in y around 0 32.4%

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

   6. Taylor expanded in b around 0 32.4%

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

      1. mul-1-neg 32.4%

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

      2. times-frac 29.4%

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

   8. Simplified 29.4%

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

      1. unsub-neg 29.4%

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

      2. *-commutative 29.4%

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

      3. associate-/r* 26.2%

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

      4. associate-*l/ 26.2%

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

      5. frac-sub 35.5%

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

      6. *-commutative 35.5%

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

   10. Applied egg-rr 35.5%

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

   if -4.4999999999999999e-242 < b < 1.1e-301

   1. Initial program 99.4%

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

   2. Taylor expanded in y around 0 75.6%

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

   3. Taylor expanded in t around 0 31.6%

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

      1. sub-neg 31.6%

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

      2. mul-1-neg 31.6%

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

      3. distribute-neg-in 31.6%

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

      4. +-commutative 31.6%

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

      5. exp-neg 31.6%

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

      6. associate-*l/ 31.6%

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

      7. *-lft-identity 31.6%

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

      8. +-commutative 31.6%

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

      9. exp-sum 31.6%

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

      10. rem-exp-log 32.2%

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

      11. associate-/r* 32.2%

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

   5. Simplified 32.2%

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

   6. Taylor expanded in b around 0 32.2%

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

      1. +-commutative 32.2%

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

      2. mul-1-neg 32.2%

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

      3. unsub-neg 32.2%

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

      4. *-commutative 32.2%

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

   8. Simplified 32.2%

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

   9. Taylor expanded in b around inf 41.5%

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

       1. associate-*r/ 41.5%

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

       2. mul-1-neg 41.5%

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

       3. distribute-lft-neg-out 41.5%

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

       4. *-commutative 41.5%

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

       5. associate-*r/ 43.3%

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

       6. *-commutative 43.3%

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

   11. Simplified 43.3%

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

   if 1.1e-301 < b < 8.7999999999999996e-285

   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%

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

      2. *-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--l+ 100.0%

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

      5. exp-sum 100.0%

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

      6. *-commutative 100.0%

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

      7. exp-to-pow 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. exp-diff 100.0%

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

      11. *-commutative 100.0%

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

      12. exp-to-pow 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around 0 28.8%

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

   5. Taylor expanded in y around 0 28.8%

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

   6. Taylor expanded in b around 0 3.8%

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

      1. mul-1-neg 3.8%

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

      2. times-frac 28.8%

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

   8. Simplified 28.8%

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

      1. unsub-neg 28.8%

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

      2. associate-*r/ 28.8%

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

      3. frac-sub 100.0%

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

      4. *-commutative 100.0%

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

      5. *-commutative 100.0%

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

   10. Applied egg-rr 100.0%

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

       1. *-commutative 100.0%

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

       2. associate-*r* 100.0%

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

       3. distribute-rgt-out-- 100.0%

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

       4. *-commutative 100.0%

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

       5. associate-*l* 100.0%

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

   12. Simplified 100.0%

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

   if 6.1999999999999998e-232 < b

   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/ 82.9%

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

      2. *-commutative 82.9%

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

      3. +-commutative 82.9%

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

      4. associate--l+ 82.9%

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

      5. exp-sum 67.7%

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

      6. *-commutative 67.7%

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

      7. exp-to-pow 68.1%

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

      8. sub-neg 68.1%

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

      9. metadata-eval 68.1%

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

      10. exp-diff 62.2%

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

      11. *-commutative 62.2%

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

      12. exp-to-pow 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in t around 0 76.8%

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

   5. Taylor expanded in y around 0 64.8%

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

   6. Taylor expanded in b around 0 41.2%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+206}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot \left(1 - b\right)}{y}}{a \cdot a}\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot y}{a} - y \cdot \left(x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-68}:\\ \;\;\;\;\frac{x \cdot y - \left(y \cdot a\right) \cdot \left(x \cdot \frac{b}{a}\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{y \cdot \frac{x}{y} - a \cdot \left(b \cdot \frac{x}{a}\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-301}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-285}:\\ \;\;\;\;\frac{x \cdot \left(a - \left(y \cdot a\right) \cdot \frac{b}{y}\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{x \cdot y - \left(y \cdot a\right) \cdot \left(x \cdot \frac{b}{a}\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 11: 36.5% accurate, 12.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+205}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot \left(1 - b\right)}{y}}{a \cdot a}\\ \mathbf{elif}\;b \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot y}{a} - y \cdot \left(x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;b \leq -1.18 \cdot 10^{-147}:\\ \;\;\;\;\frac{\frac{\frac{x \cdot a}{x \cdot b} - a}{\frac{a \cdot a}{x \cdot b}}}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -6.6e+205)
   (/ (* a (/ (* x (- 1.0 b)) y)) (* a a))
   (if (<= b -3.65e+22)
     (/ (- (* a (/ (* x y) a)) (* y (* x b))) (* a (* y y)))
     (if (<= b -1.18e-147)
       (/ (/ (- (/ (* x a) (* x b)) a) (/ (* a a) (* x b))) y)
       (if (<= b 6.2e-232)
         (- (* x (/ b (* y a))))
         (if (<= b 6.6e-173)
           (/ x (* y (* a b)))
           (/ x (* y (+ a (* a b))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -6.6e+205) {
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	} else if (b <= -3.65e+22) {
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / (a * (y * y));
	} else if (b <= -1.18e-147) {
		tmp = ((((x * a) / (x * b)) - a) / ((a * a) / (x * b))) / y;
	} else if (b <= 6.2e-232) {
		tmp = -(x * (b / (y * a)));
	} else if (b <= 6.6e-173) {
		tmp = x / (y * (a * b));
	} else {
		tmp = x / (y * (a + (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 <= (-6.6d+205)) then
        tmp = (a * ((x * (1.0d0 - b)) / y)) / (a * a)
    else if (b <= (-3.65d+22)) then
        tmp = ((a * ((x * y) / a)) - (y * (x * b))) / (a * (y * y))
    else if (b <= (-1.18d-147)) then
        tmp = ((((x * a) / (x * b)) - a) / ((a * a) / (x * b))) / y
    else if (b <= 6.2d-232) then
        tmp = -(x * (b / (y * a)))
    else if (b <= 6.6d-173) then
        tmp = x / (y * (a * b))
    else
        tmp = x / (y * (a + (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 <= -6.6e+205) {
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	} else if (b <= -3.65e+22) {
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / (a * (y * y));
	} else if (b <= -1.18e-147) {
		tmp = ((((x * a) / (x * b)) - a) / ((a * a) / (x * b))) / y;
	} else if (b <= 6.2e-232) {
		tmp = -(x * (b / (y * a)));
	} else if (b <= 6.6e-173) {
		tmp = x / (y * (a * b));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -6.6e+205:
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a)
	elif b <= -3.65e+22:
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / (a * (y * y))
	elif b <= -1.18e-147:
		tmp = ((((x * a) / (x * b)) - a) / ((a * a) / (x * b))) / y
	elif b <= 6.2e-232:
		tmp = -(x * (b / (y * a)))
	elif b <= 6.6e-173:
		tmp = x / (y * (a * b))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -6.6e+205)
		tmp = Float64(Float64(a * Float64(Float64(x * Float64(1.0 - b)) / y)) / Float64(a * a));
	elseif (b <= -3.65e+22)
		tmp = Float64(Float64(Float64(a * Float64(Float64(x * y) / a)) - Float64(y * Float64(x * b))) / Float64(a * Float64(y * y)));
	elseif (b <= -1.18e-147)
		tmp = Float64(Float64(Float64(Float64(Float64(x * a) / Float64(x * b)) - a) / Float64(Float64(a * a) / Float64(x * b))) / y);
	elseif (b <= 6.2e-232)
		tmp = Float64(-Float64(x * Float64(b / Float64(y * a))));
	elseif (b <= 6.6e-173)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -6.6e+205)
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	elseif (b <= -3.65e+22)
		tmp = ((a * ((x * y) / a)) - (y * (x * b))) / (a * (y * y));
	elseif (b <= -1.18e-147)
		tmp = ((((x * a) / (x * b)) - a) / ((a * a) / (x * b))) / y;
	elseif (b <= 6.2e-232)
		tmp = -(x * (b / (y * a)));
	elseif (b <= 6.6e-173)
		tmp = x / (y * (a * b));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -6.6e+205], N[(N[(a * N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.65e+22], N[(N[(N[(a * N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.18e-147], N[(N[(N[(N[(N[(x * a), $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / N[(N[(a * a), $MachinePrecision] / N[(x * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.2e-232], (-N[(x * N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[b, 6.6e-173], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -6.6000000000000004e205

   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/ 85.0%

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

      2. *-commutative 85.0%

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

      3. +-commutative 85.0%

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

      4. associate--l+ 85.0%

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

      5. exp-sum 60.0%

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

      6. *-commutative 60.0%

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

      7. exp-to-pow 60.0%

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

      8. sub-neg 60.0%

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

      9. metadata-eval 60.0%

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

      10. exp-diff 45.0%

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

      11. *-commutative 45.0%

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

      12. exp-to-pow 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in t around 0 70.0%

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

   5. Taylor expanded in y around 0 95.1%

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

   6. Taylor expanded in b around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. times-frac 61.4%

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

   8. Simplified 61.4%

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

      1. unsub-neg 61.4%

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

      2. *-commutative 61.4%

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

      3. associate-/r* 61.4%

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

      4. associate-*r/ 61.4%

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

      5. frac-sub 70.9%

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

   10. Applied egg-rr 70.9%

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

       1. *-commutative 70.9%

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

       2. distribute-lft-out-- 70.9%

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

       3. associate-*l/ 80.4%

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

       4. *-commutative 80.4%

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

       5. div-sub 80.4%

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

       6. *-rgt-identity 80.4%

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

       7. distribute-lft-out-- 80.4%

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

   12. Simplified 80.4%

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

   if -6.6000000000000004e205 < b < -3.6499999999999999e22

   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/ 90.9%

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

      2. *-commutative 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. exp-sum 66.7%

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

      6. *-commutative 66.7%

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

      7. exp-to-pow 66.7%

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

      8. sub-neg 66.7%

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

      9. metadata-eval 66.7%

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

      10. exp-diff 60.6%

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

      11. *-commutative 60.6%

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

      12. exp-to-pow 60.6%

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

   3. Simplified 60.6%

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

   4. Taylor expanded in t around 0 75.9%

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

   5. Taylor expanded in y around 0 82.1%

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

   6. Taylor expanded in b around 0 26.8%

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

      1. mul-1-neg 26.8%

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

      2. times-frac 26.5%

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

   8. Simplified 26.5%

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

      1. unsub-neg 26.5%

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

      2. associate-/r* 26.4%

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

      3. *-commutative 26.4%

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

      4. frac-times 26.8%

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

      5. frac-sub 37.8%

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

      6. *-commutative 37.8%

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

      7. *-commutative 37.8%

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

   10. Applied egg-rr 37.8%

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

       1. associate-*r* 43.9%

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

       2. associate-*l/ 43.9%

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

       3. associate-*r* 52.3%

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

   12. Simplified 52.3%

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

   if -3.6499999999999999e22 < b < -1.18000000000000003e-147

   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. Taylor expanded in y around 0 65.3%

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

   3. Taylor expanded in t around 0 20.4%

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

      1. sub-neg 20.4%

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

      2. mul-1-neg 20.4%

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

      3. distribute-neg-in 20.4%

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

      4. +-commutative 20.4%

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

      5. exp-neg 20.4%

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

      6. associate-*l/ 20.4%

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

      7. *-lft-identity 20.4%

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

      8. +-commutative 20.4%

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

      9. exp-sum 20.4%

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

      10. rem-exp-log 20.4%

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

      11. associate-/r* 20.4%

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

   5. Simplified 20.4%

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

   6. Taylor expanded in b around 0 17.3%

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

      1. +-commutative 17.3%

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

      2. mul-1-neg 17.3%

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

      3. unsub-neg 17.3%

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

      4. *-commutative 17.3%

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

   8. Simplified 17.3%

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

      1. clear-num 17.3%

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

      2. frac-sub 19.9%

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

   10. Applied egg-rr 19.9%

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

       1. associate-*r/ 26.5%

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

       2. *-rgt-identity 26.5%

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

       3. associate-*r/ 30.1%

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

   12. Simplified 30.1%

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

   if -1.18000000000000003e-147 < b < 6.1999999999999998e-232

   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. Taylor expanded in y around 0 77.9%

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

   3. Taylor expanded in t around 0 30.7%

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

      1. sub-neg 30.7%

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

      2. mul-1-neg 30.7%

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

      3. distribute-neg-in 30.7%

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

      4. +-commutative 30.7%

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

      5. exp-neg 30.7%

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

      6. associate-*l/ 30.7%

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

      7. *-lft-identity 30.7%

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

      8. +-commutative 30.7%

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

      9. exp-sum 30.7%

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

      10. rem-exp-log 30.9%

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

      11. associate-/r* 30.9%

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

   5. Simplified 30.9%

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

   6. Taylor expanded in b around 0 30.9%

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

      1. +-commutative 30.9%

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

      2. mul-1-neg 30.9%

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

      3. unsub-neg 30.9%

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

      4. *-commutative 30.9%

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

   8. Simplified 30.9%

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

   9. Taylor expanded in b around inf 40.8%

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

       1. associate-*r/ 40.8%

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

       2. mul-1-neg 40.8%

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

       3. distribute-lft-neg-out 40.8%

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

       4. *-commutative 40.8%

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

       5. associate-*r/ 41.5%

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

       6. *-commutative 41.5%

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

   11. Simplified 41.5%

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

   if 6.1999999999999998e-232 < b < 6.6000000000000006e-173

   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/ 83.6%

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

      2. *-commutative 83.6%

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

      3. +-commutative 83.6%

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

      4. associate--l+ 83.6%

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

      5. exp-sum 68.3%

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

      6. *-commutative 68.3%

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

      7. exp-to-pow 69.2%

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

      8. sub-neg 69.2%

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

      9. metadata-eval 69.2%

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

      10. exp-diff 69.2%

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

      11. *-commutative 69.2%

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

      12. exp-to-pow 69.2%

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

   3. Simplified 69.2%

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

   4. Taylor expanded in t around 0 77.5%

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

   5. Taylor expanded in y around 0 24.8%

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

   6. Taylor expanded in b around 0 24.8%

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

   7. Taylor expanded in b around inf 39.9%

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

   if 6.6000000000000006e-173 < b

   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/ 82.8%

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

      2. *-commutative 82.8%

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

      3. +-commutative 82.8%

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

      4. associate--l+ 82.8%

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

      5. exp-sum 67.7%

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

      6. *-commutative 67.7%

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

      7. exp-to-pow 67.9%

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

      8. sub-neg 67.9%

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

      9. metadata-eval 67.9%

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

      10. exp-diff 61.3%

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

      11. *-commutative 61.3%

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

      12. exp-to-pow 61.3%

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

   3. Simplified 61.3%

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

   4. Taylor expanded in t around 0 76.7%

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

   5. Taylor expanded in y around 0 69.6%

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

   6. Taylor expanded in b around 0 43.2%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+205}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot \left(1 - b\right)}{y}}{a \cdot a}\\ \mathbf{elif}\;b \leq -3.65 \cdot 10^{+22}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot y}{a} - y \cdot \left(x \cdot b\right)}{a \cdot \left(y \cdot y\right)}\\ \mathbf{elif}\;b \leq -1.18 \cdot 10^{-147}:\\ \;\;\;\;\frac{\frac{\frac{x \cdot a}{x \cdot b} - a}{\frac{a \cdot a}{x \cdot b}}}{y}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-232}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-173}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 12: 42.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -320000000000:\\ \;\;\;\;\frac{b \cdot b}{y \cdot \frac{a}{x}} + \frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -320000000000.0)
   (+ (/ (* b b) (* y (/ a x))) (/ (- x (* x b)) (* y a)))
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -320000000000.0) {
		tmp = ((b * b) / (y * (a / x))) + ((x - (x * b)) / (y * a));
	} else {
		tmp = x / (y * (a + (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 <= (-320000000000.0d0)) then
        tmp = ((b * b) / (y * (a / x))) + ((x - (x * b)) / (y * a))
    else
        tmp = x / (y * (a + (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 <= -320000000000.0) {
		tmp = ((b * b) / (y * (a / x))) + ((x - (x * b)) / (y * a));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -320000000000.0:
		tmp = ((b * b) / (y * (a / x))) + ((x - (x * b)) / (y * a))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -320000000000.0)
		tmp = Float64(Float64(Float64(b * b) / Float64(y * Float64(a / x))) + Float64(Float64(x - Float64(x * b)) / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -320000000000.0)
		tmp = ((b * b) / (y * (a / x))) + ((x - (x * b)) / (y * a));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -320000000000.0], N[(N[(N[(b * b), $MachinePrecision] / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.2e11

   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/ 89.1%

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

      2. *-commutative 89.1%

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

      3. +-commutative 89.1%

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

      4. associate--l+ 89.1%

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

      5. exp-sum 65.5%

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

      6. *-commutative 65.5%

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

      7. exp-to-pow 65.5%

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

      8. sub-neg 65.5%

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

      9. metadata-eval 65.5%

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

      10. exp-diff 56.4%

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

      11. *-commutative 56.4%

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

      12. exp-to-pow 56.4%

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

   3. Simplified 56.4%

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

   4. Taylor expanded in t around 0 74.6%

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

   5. Taylor expanded in y around 0 87.5%

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

   6. Taylor expanded in b around 0 6.5%

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

   7. Taylor expanded in b around 0 62.7%

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

      1. *-commutative 62.7%

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

      2. associate-/l* 59.1%

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

      3. unpow2 59.1%

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

      4. associate-*r/ 55.4%

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

      5. *-commutative 55.4%

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

      6. mul-1-neg 55.4%

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

      7. times-frac 55.4%

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

      8. distribute-lft-neg-in 55.4%

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

      9. cancel-sign-sub-inv 55.4%

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

      10. associate-/r* 55.4%

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

      11. times-frac 55.4%

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

      12. associate-/r* 57.2%

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

      13. div-sub 57.2%

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

      14. *-commutative 57.2%

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

      15. div-sub 57.2%

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

      16. associate-/r* 55.4%

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

      17. *-commutative 55.4%

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

   9. Simplified 55.4%

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

   if -3.2e11 < b

   1. Initial program 98.4%

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

      1. associate-*l/ 86.2%

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

      2. *-commutative 86.2%

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

      3. +-commutative 86.2%

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

      4. associate--l+ 86.2%

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

      5. exp-sum 67.8%

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

      6. *-commutative 67.8%

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

      7. exp-to-pow 68.1%

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

      8. sub-neg 68.1%

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

      9. metadata-eval 68.1%

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

      10. exp-diff 64.2%

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

      11. *-commutative 64.2%

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

      12. exp-to-pow 64.2%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in t around 0 65.3%

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

   5. Taylor expanded in y around 0 50.1%

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

   6. Taylor expanded in b around 0 36.2%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -320000000000:\\ \;\;\;\;\frac{b \cdot b}{y \cdot \frac{a}{x}} + \frac{x - x \cdot b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 13: 39.2% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot \left(1 - b\right)}{y}}{a \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.6e-61)
   (/ (* a (/ (* x (- 1.0 b)) y)) (* a a))
   (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.6e-61) {
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	} else {
		tmp = x / (y * (a + (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 <= (-1.6d-61)) then
        tmp = (a * ((x * (1.0d0 - b)) / y)) / (a * a)
    else
        tmp = x / (y * (a + (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 <= -1.6e-61) {
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.6e-61:
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a)
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.6e-61)
		tmp = Float64(Float64(a * Float64(Float64(x * Float64(1.0 - b)) / y)) / Float64(a * a));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.6e-61)
		tmp = (a * ((x * (1.0 - b)) / y)) / (a * a);
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.6e-61], N[(N[(a * N[(N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.6000000000000001e-61

   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/ 91.2%

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

      2. *-commutative 91.2%

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

      3. +-commutative 91.2%

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

      4. associate--l+ 91.2%

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

      5. exp-sum 63.2%

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

      6. *-commutative 63.2%

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

      7. exp-to-pow 63.2%

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

      8. sub-neg 63.2%

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

      9. metadata-eval 63.2%

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

      10. exp-diff 54.4%

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

      11. *-commutative 54.4%

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

      12. exp-to-pow 54.4%

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

   3. Simplified 54.4%

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

   4. Taylor expanded in t around 0 66.5%

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

   5. Taylor expanded in y around 0 72.8%

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

   6. Taylor expanded in b around 0 36.1%

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

      1. mul-1-neg 36.1%

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

      2. times-frac 34.7%

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

   8. Simplified 34.7%

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

      1. unsub-neg 34.7%

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

      2. *-commutative 34.7%

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

      3. associate-/r* 37.3%

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

      4. associate-*r/ 43.2%

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

      5. frac-sub 43.7%

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

   10. Applied egg-rr 43.7%

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

       1. *-commutative 43.7%

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

       2. distribute-lft-out-- 43.7%

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

       3. associate-*l/ 45.1%

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

       4. *-commutative 45.1%

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

       5. div-sub 45.1%

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

       6. *-rgt-identity 45.1%

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

       7. distribute-lft-out-- 45.1%

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

   12. Simplified 45.1%

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

   if -1.6000000000000001e-61 < b

   1. Initial program 98.3%

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

      1. associate-*l/ 85.3%

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

      2. *-commutative 85.3%

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

      3. +-commutative 85.3%

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

      4. associate--l+ 85.3%

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

      5. exp-sum 68.8%

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

      6. *-commutative 68.8%

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

      7. exp-to-pow 69.1%

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

      8. sub-neg 69.1%

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

      9. metadata-eval 69.1%

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

      10. exp-diff 65.4%

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

      11. *-commutative 65.4%

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

      12. exp-to-pow 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in t around 0 67.6%

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

   5. Taylor expanded in y around 0 52.8%

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

   6. Taylor expanded in b around 0 37.9%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{-61}:\\ \;\;\;\;\frac{a \cdot \frac{x \cdot \left(1 - b\right)}{y}}{a \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 14: 36.3% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+145}:\\ \;\;\;\;\frac{\frac{a \cdot \left(x \cdot \left(1 - b\right)\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-232}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.05e+145)
   (/ (/ (* a (* x (- 1.0 b))) (* a a)) y)
   (if (<= b 6.6e-232) (- (* x (/ b (* y a)))) (/ x (* y (+ a (* a b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.05e+145) {
		tmp = ((a * (x * (1.0 - b))) / (a * a)) / y;
	} else if (b <= 6.6e-232) {
		tmp = -(x * (b / (y * a)));
	} else {
		tmp = x / (y * (a + (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 <= (-1.05d+145)) then
        tmp = ((a * (x * (1.0d0 - b))) / (a * a)) / y
    else if (b <= 6.6d-232) then
        tmp = -(x * (b / (y * a)))
    else
        tmp = x / (y * (a + (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 <= -1.05e+145) {
		tmp = ((a * (x * (1.0 - b))) / (a * a)) / y;
	} else if (b <= 6.6e-232) {
		tmp = -(x * (b / (y * a)));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.05e+145:
		tmp = ((a * (x * (1.0 - b))) / (a * a)) / y
	elif b <= 6.6e-232:
		tmp = -(x * (b / (y * a)))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.05e+145)
		tmp = Float64(Float64(Float64(a * Float64(x * Float64(1.0 - b))) / Float64(a * a)) / y);
	elseif (b <= 6.6e-232)
		tmp = Float64(-Float64(x * Float64(b / Float64(y * a))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.05e+145)
		tmp = ((a * (x * (1.0 - b))) / (a * a)) / y;
	elseif (b <= 6.6e-232)
		tmp = -(x * (b / (y * a)));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.05e+145], N[(N[(N[(a * N[(x * N[(1.0 - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 6.6e-232], (-N[(x * N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.04999999999999995e145

   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. Taylor expanded in y around 0 96.6%

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

   3. Taylor expanded in t around 0 93.2%

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

      1. sub-neg 93.2%

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

      2. mul-1-neg 93.2%

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

      3. distribute-neg-in 93.2%

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

      4. +-commutative 93.2%

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

      5. exp-neg 93.2%

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

      6. associate-*l/ 93.2%

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

      7. *-lft-identity 93.2%

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

      8. +-commutative 93.2%

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

      9. exp-sum 93.2%

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

      10. rem-exp-log 93.2%

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

      11. associate-/r* 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in b around 0 60.0%

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

      1. +-commutative 60.0%

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

      2. mul-1-neg 60.0%

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

      3. unsub-neg 60.0%

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

      4. *-commutative 60.0%

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

   8. Simplified 60.0%

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

      1. frac-sub 69.3%

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

      2. div-inv 69.3%

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

   10. Applied egg-rr 69.3%

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

       1. associate-*r/ 69.3%

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

       2. *-rgt-identity 69.3%

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

       3. *-commutative 69.3%

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

       4. distribute-rgt-out-- 69.3%

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

       5. *-rgt-identity 69.3%

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

       6. distribute-lft-out-- 69.3%

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

   12. Simplified 69.3%

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

   if -1.04999999999999995e145 < b < 6.5999999999999997e-232

   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. Taylor expanded in y around 0 75.9%

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

   3. Taylor expanded in t around 0 38.9%

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

      1. sub-neg 38.9%

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

      2. mul-1-neg 38.9%

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

      3. distribute-neg-in 38.9%

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

      4. +-commutative 38.9%

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

      5. exp-neg 38.9%

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

      6. associate-*l/ 38.9%

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

      7. *-lft-identity 38.9%

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

      8. +-commutative 38.9%

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

      9. exp-sum 38.9%

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

      10. rem-exp-log 39.0%

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

      11. associate-/r* 35.2%

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

   5. Simplified 35.2%

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

   6. Taylor expanded in b around 0 25.7%

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

      1. +-commutative 25.7%

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

      2. mul-1-neg 25.7%

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

      3. unsub-neg 25.7%

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

      4. *-commutative 25.7%

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

   8. Simplified 25.7%

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

   9. Taylor expanded in b around inf 30.8%

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

       1. associate-*r/ 30.8%

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

       2. mul-1-neg 30.8%

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

       3. distribute-lft-neg-out 30.8%

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

       4. *-commutative 30.8%

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

       5. associate-*r/ 34.7%

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

       6. *-commutative 34.7%

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

   11. Simplified 34.7%

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

   if 6.5999999999999997e-232 < b

   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/ 82.9%

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

      2. *-commutative 82.9%

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

      3. +-commutative 82.9%

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

      4. associate--l+ 82.9%

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

      5. exp-sum 67.7%

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

      6. *-commutative 67.7%

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

      7. exp-to-pow 68.1%

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

      8. sub-neg 68.1%

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

      9. metadata-eval 68.1%

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

      10. exp-diff 62.2%

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

      11. *-commutative 62.2%

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

      12. exp-to-pow 62.2%

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

   3. Simplified 62.2%

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

   4. Taylor expanded in t around 0 76.8%

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

   5. Taylor expanded in y around 0 64.8%

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

   6. Taylor expanded in b around 0 41.2%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+145}:\\ \;\;\;\;\frac{\frac{a \cdot \left(x \cdot \left(1 - b\right)\right)}{a \cdot a}}{y}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{-232}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 15: 36.4% accurate, 28.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-231}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.6e-231)
   (- (* x (/ b (* y a))))
   (if (<= b 2.1e-10) (/ x (* y a)) (/ x (* y (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.6e-231) {
		tmp = -(x * (b / (y * a)));
	} else if (b <= 2.1e-10) {
		tmp = x / (y * a);
	} else {
		tmp = x / (y * (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 <= 2.6d-231) then
        tmp = -(x * (b / (y * a)))
    else if (b <= 2.1d-10) then
        tmp = x / (y * a)
    else
        tmp = x / (y * (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 <= 2.6e-231) {
		tmp = -(x * (b / (y * a)));
	} else if (b <= 2.1e-10) {
		tmp = x / (y * a);
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.6e-231:
		tmp = -(x * (b / (y * a)))
	elif b <= 2.1e-10:
		tmp = x / (y * a)
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.6e-231)
		tmp = Float64(-Float64(x * Float64(b / Float64(y * a))));
	elseif (b <= 2.1e-10)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.6e-231)
		tmp = -(x * (b / (y * a)));
	elseif (b <= 2.1e-10)
		tmp = x / (y * a);
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.6e-231], (-N[(x * N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), If[LessEqual[b, 2.1e-10], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < 2.60000000000000003e-231

   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. Taylor expanded in y around 0 80.3%

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

   3. Taylor expanded in t around 0 50.4%

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

      1. sub-neg 50.4%

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

      2. mul-1-neg 50.4%

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

      3. distribute-neg-in 50.4%

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

      4. +-commutative 50.4%

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

      5. exp-neg 50.4%

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

      6. associate-*l/ 50.4%

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

      7. *-lft-identity 50.4%

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

      8. +-commutative 50.4%

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

      9. exp-sum 50.4%

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

      10. rem-exp-log 50.4%

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

      11. associate-/r* 43.1%

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

   5. Simplified 43.1%

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

   6. Taylor expanded in b around 0 32.9%

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

      1. +-commutative 32.9%

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

      2. mul-1-neg 32.9%

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

      3. unsub-neg 32.9%

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

      4. *-commutative 32.9%

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

   8. Simplified 32.9%

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

   9. Taylor expanded in b around inf 36.2%

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

       1. associate-*r/ 36.2%

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

       2. mul-1-neg 36.2%

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

       3. distribute-lft-neg-out 36.2%

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

       4. *-commutative 36.2%

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

       5. associate-*r/ 38.6%

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

       6. *-commutative 38.6%

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

   11. Simplified 38.6%

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

   if 2.60000000000000003e-231 < b < 2.1e-10

   1. Initial program 95.2%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

      3. +-commutative 90.0%

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

      4. associate--l+ 90.0%

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

      5. exp-sum 76.4%

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

      6. *-commutative 76.4%

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

      7. exp-to-pow 77.3%

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

      8. sub-neg 77.3%

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

      9. metadata-eval 77.3%

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

      10. exp-diff 77.3%

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

      11. *-commutative 77.3%

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

      12. exp-to-pow 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in t around 0 80.0%

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

   5. Taylor expanded in y around 0 38.1%

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

   6. Taylor expanded in b around 0 37.4%

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

   if 2.1e-10 < 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/ 78.7%

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

      2. *-commutative 78.7%

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

      3. +-commutative 78.7%

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

      4. associate--l+ 78.7%

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

      5. exp-sum 62.7%

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

      6. *-commutative 62.7%

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

      7. exp-to-pow 62.7%

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

      8. sub-neg 62.7%

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

      9. metadata-eval 62.7%

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

      10. exp-diff 53.3%

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

      11. *-commutative 53.3%

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

      12. exp-to-pow 53.3%

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

   3. Simplified 53.3%

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

   4. Taylor expanded in t around 0 74.8%

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

   5. Taylor expanded in y around 0 80.4%

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

   6. Taylor expanded in b around 0 43.0%

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

   7. Taylor expanded in b around inf 43.0%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.6 \cdot 10^{-231}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 16: 36.5% accurate, 28.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.22 \cdot 10^{-231}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.22e-231) (- (* x (/ b (* y a)))) (/ x (* y (+ a (* a b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.22e-231) {
		tmp = -(x * (b / (y * a)));
	} else {
		tmp = x / (y * (a + (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 <= 1.22d-231) then
        tmp = -(x * (b / (y * a)))
    else
        tmp = x / (y * (a + (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 <= 1.22e-231) {
		tmp = -(x * (b / (y * a)));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.22e-231:
		tmp = -(x * (b / (y * a)))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.22e-231)
		tmp = Float64(-Float64(x * Float64(b / Float64(y * a))));
	else
		tmp = Float64(x / Float64(y * Float64(a + Float64(a * b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.22e-231)
		tmp = -(x * (b / (y * a)));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.22e-231], (-N[(x * N[(b / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.22e-231

   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. Taylor expanded in y around 0 80.3%

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

   3. Taylor expanded in t around 0 50.4%

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

      1. sub-neg 50.4%

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

      2. mul-1-neg 50.4%

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

      3. distribute-neg-in 50.4%

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

      4. +-commutative 50.4%

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

      5. exp-neg 50.4%

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

      6. associate-*l/ 50.4%

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

      7. *-lft-identity 50.4%

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

      8. +-commutative 50.4%

         \[\leadsto \frac{\frac{x}{e^{\color{blue}{\log a + b}}}}{y} \]

      9. exp-sum 50.4%

         \[\leadsto \frac{\frac{x}{\color{blue}{e^{\log a} \cdot e^{b}}}}{y} \]

      10. rem-exp-log 50.4%

          \[\leadsto \frac{\frac{x}{\color{blue}{a} \cdot e^{b}}}{y} \]

      11. associate-/r* 43.1%

          \[\leadsto \frac{\color{blue}{\frac{\frac{x}{a}}{e^{b}}}}{y} \]

   5. Simplified 43.1%

      \[\leadsto \color{blue}{\frac{\frac{\frac{x}{a}}{e^{b}}}{y}} \]

   6. Taylor expanded in b around 0 32.9%

      \[\leadsto \frac{\color{blue}{-1 \cdot \frac{b \cdot x}{a} + \frac{x}{a}}}{y} \]
   7. Step-by-step derivation

      1. +-commutative 32.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} + -1 \cdot \frac{b \cdot x}{a}}}{y} \]

      2. mul-1-neg 32.9%

         \[\leadsto \frac{\frac{x}{a} + \color{blue}{\left(-\frac{b \cdot x}{a}\right)}}{y} \]

      3. unsub-neg 32.9%

         \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{b \cdot x}{a}}}{y} \]

      4. *-commutative 32.9%

         \[\leadsto \frac{\frac{x}{a} - \frac{\color{blue}{x \cdot b}}{a}}{y} \]

   8. Simplified 32.9%

      \[\leadsto \frac{\color{blue}{\frac{x}{a} - \frac{x \cdot b}{a}}}{y} \]

   9. Taylor expanded in b around inf 36.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{b \cdot x}{y \cdot a}} \]
   10. Step-by-step derivation

       1. associate-*r/ 36.2%

          \[\leadsto \color{blue}{\frac{-1 \cdot \left(b \cdot x\right)}{y \cdot a}} \]

       2. mul-1-neg 36.2%

          \[\leadsto \frac{\color{blue}{-b \cdot x}}{y \cdot a} \]

       3. distribute-lft-neg-out 36.2%

          \[\leadsto \frac{\color{blue}{\left(-b\right) \cdot x}}{y \cdot a} \]

       4. *-commutative 36.2%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-b\right)}}{y \cdot a} \]

       5. associate-*r/ 38.6%

          \[\leadsto \color{blue}{x \cdot \frac{-b}{y \cdot a}} \]

       6. *-commutative 38.6%

          \[\leadsto x \cdot \frac{-b}{\color{blue}{a \cdot y}} \]

   11. Simplified 38.6%

       \[\leadsto \color{blue}{x \cdot \frac{-b}{a \cdot y}} \]

   if 1.22e-231 < b

   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/ 82.9%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 82.9%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 82.9%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 82.9%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 67.7%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 67.7%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 68.1%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 68.1%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 68.1%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 62.2%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 62.2%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 62.2%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 62.2%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 76.8%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 64.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 41.2%

      \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot b + a\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.22 \cdot 10^{-231}:\\ \;\;\;\;-x \cdot \frac{b}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 17: 35.6% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.15 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.15e+92) (* x (/ 1.0 (* y a))) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.15e+92) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.15d+92) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.15e+92) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.15e+92:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.15e+92)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.15e+92)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.15e+92], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.14999999999999999e92

   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. Taylor expanded in y around 0 76.9%

      \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}{y}} \]

   3. Taylor expanded in b around 0 64.0%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)} \cdot x}{y}} \]

   5. Simplified 65.2%

      \[\leadsto \color{blue}{\frac{{a}^{\left(-1 + t\right)}}{y} \cdot x} \]

   6. Taylor expanded in t around 0 31.6%

      \[\leadsto \color{blue}{\frac{1}{a \cdot y}} \cdot x \]

   if 1.14999999999999999e92 < 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/ 79.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 79.6%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 79.6%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 79.6%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 64.8%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 64.8%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 64.8%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 64.8%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 64.8%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 53.7%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 53.7%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 53.7%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 53.7%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 77.9%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 87.2%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 44.3%

      \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot b + a\right)}} \]

   7. Taylor expanded in b around inf 39.1%

      \[\leadsto \color{blue}{\frac{x}{a \cdot \left(y \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.15 \cdot 10^{+92}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 18: 35.9% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.3e-9) (* x (/ 1.0 (* y a))) (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.3e-9) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (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 <= 1.3d-9) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = x / (y * (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 <= 1.3e-9) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.3e-9:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.3e-9)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(x / Float64(y * Float64(a * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 1.3e-9)
		tmp = x * (1.0 / (y * a));
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.3e-9], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.3000000000000001e-9

   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. Taylor expanded in y around 0 75.8%

      \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}{y}} \]

   3. Taylor expanded in b around 0 62.5%

      \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)} \cdot x}{y}} \]

   5. Simplified 64.9%

      \[\leadsto \color{blue}{\frac{{a}^{\left(-1 + t\right)}}{y} \cdot x} \]

   6. Taylor expanded in t around 0 31.7%

      \[\leadsto \color{blue}{\frac{1}{a \cdot y}} \cdot x \]

   if 1.3000000000000001e-9 < 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/ 78.7%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

      2. *-commutative 78.7%

         \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

      3. +-commutative 78.7%

         \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

      4. associate--l+ 78.7%

         \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

      5. exp-sum 62.7%

         \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

      6. *-commutative 62.7%

         \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      7. exp-to-pow 62.7%

         \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      8. sub-neg 62.7%

         \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      9. metadata-eval 62.7%

         \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

      10. exp-diff 53.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

      11. *-commutative 53.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

      12. exp-to-pow 53.3%

          \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   3. Simplified 53.3%

      \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

   4. Taylor expanded in t around 0 74.8%

      \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

   5. Taylor expanded in y around 0 80.4%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

   6. Taylor expanded in b around 0 43.0%

      \[\leadsto \frac{x}{y \cdot \color{blue}{\left(a \cdot b + a\right)}} \]

   7. Taylor expanded in b around inf 43.0%

      \[\leadsto \frac{x}{\color{blue}{y \cdot \left(a \cdot b\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.3 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 19: 31.9% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \frac{1}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* x (/ 1.0 (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 / (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 * (1.0d0 / (y * a))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * (1.0 / (y * a));
}

Python

def code(x, y, z, t, a, b):
	return x * (1.0 / (y * a))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * Float64(1.0 / Float64(y * a)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * (1.0 / (y * a));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]

2. Taylor expanded in y around 0 81.0%

   \[\leadsto \color{blue}{\frac{e^{\left(t - 1\right) \cdot \log a - b} \cdot x}{y}} \]

3. Taylor expanded in b around 0 59.8%

   \[\leadsto \color{blue}{\frac{{a}^{\left(t - 1\right)} \cdot x}{y}} \]

5. Simplified 60.8%

   \[\leadsto \color{blue}{\frac{{a}^{\left(-1 + t\right)}}{y} \cdot x} \]

6. Taylor expanded in t around 0 29.2%

   \[\leadsto \color{blue}{\frac{1}{a \cdot y}} \cdot x \]

7. Final simplification 29.2%

   \[\leadsto x \cdot \frac{1}{y \cdot a} \]

Alternative 20: 31.7% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.7%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Step-by-step derivation

   1. associate-*l/ 86.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}} \]

   2. *-commutative 86.8%

      \[\leadsto \color{blue}{e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b} \cdot \frac{x}{y}} \]

   3. +-commutative 86.8%

      \[\leadsto e^{\color{blue}{\left(\left(t - 1\right) \cdot \log a + y \cdot \log z\right)} - b} \cdot \frac{x}{y} \]

   4. associate--l+ 86.8%

      \[\leadsto e^{\color{blue}{\left(t - 1\right) \cdot \log a + \left(y \cdot \log z - b\right)}} \cdot \frac{x}{y} \]

   5. exp-sum 67.3%

      \[\leadsto \color{blue}{\left(e^{\left(t - 1\right) \cdot \log a} \cdot e^{y \cdot \log z - b}\right)} \cdot \frac{x}{y} \]

   6. *-commutative 67.3%

      \[\leadsto \left(e^{\color{blue}{\log a \cdot \left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   7. exp-to-pow 67.6%

      \[\leadsto \left(\color{blue}{{a}^{\left(t - 1\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   8. sub-neg 67.6%

      \[\leadsto \left({a}^{\color{blue}{\left(t + \left(-1\right)\right)}} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   9. metadata-eval 67.6%

      \[\leadsto \left({a}^{\left(t + \color{blue}{-1}\right)} \cdot e^{y \cdot \log z - b}\right) \cdot \frac{x}{y} \]

   10. exp-diff 62.5%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \color{blue}{\frac{e^{y \cdot \log z}}{e^{b}}}\right) \cdot \frac{x}{y} \]

   11. *-commutative 62.5%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{e^{\color{blue}{\log z \cdot y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

   12. exp-to-pow 62.5%

       \[\leadsto \left({a}^{\left(t + -1\right)} \cdot \frac{\color{blue}{{z}^{y}}}{e^{b}}\right) \cdot \frac{x}{y} \]

3. Simplified 62.5%

   \[\leadsto \color{blue}{\left({a}^{\left(t + -1\right)} \cdot \frac{{z}^{y}}{e^{b}}\right) \cdot \frac{x}{y}} \]

4. Taylor expanded in t around 0 67.3%

   \[\leadsto \color{blue}{\frac{{z}^{y} \cdot x}{a \cdot \left(y \cdot e^{b}\right)}} \]

5. Taylor expanded in y around 0 58.2%

   \[\leadsto \color{blue}{\frac{x}{y \cdot \left(a \cdot e^{b}\right)}} \]

6. Taylor expanded in b around 0 28.9%

   \[\leadsto \color{blue}{\frac{x}{y \cdot a}} \]

7. Final simplification 28.9%

   \[\leadsto \frac{x}{y \cdot a} \]

Developer target: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (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))