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

Percentage Accurate: 98.3% → 98.3%

Time: 23.8s

Alternatives: 21

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

2. Final simplification 98.5%

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

Alternative 2: 92.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t + -1 \leq -4 \cdot 10^{+125} \lor \neg \left(t + -1 \leq -1\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= (+ t -1.0) -4e+125) (not (<= (+ t -1.0) -1.0)))
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)
   (/ (* x (exp (- (- (* y (log z)) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -4e+125) || !((t + -1.0) <= -1.0)) {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	} else {
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (((t + (-1.0d0)) <= (-4d+125)) .or. (.not. ((t + (-1.0d0)) <= (-1.0d0)))) then
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    else
        tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((t + -1.0) <= -4e+125) || !((t + -1.0) <= -1.0)) {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	} else {
		tmp = (x * Math.exp((((y * Math.log(z)) - Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if ((t + -1.0) <= -4e+125) or not ((t + -1.0) <= -1.0):
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	else:
		tmp = (x * math.exp((((y * math.log(z)) - math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((Float64(t + -1.0) <= -4e+125) || !(Float64(t + -1.0) <= -1.0))
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(y * log(z)) - log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (((t + -1.0) <= -4e+125) || ~(((t + -1.0) <= -1.0)))
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	else
		tmp = (x * exp((((y * log(z)) - log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[N[(t + -1.0), $MachinePrecision], -4e+125], N[Not[LessEqual[N[(t + -1.0), $MachinePrecision], -1.0]], $MachinePrecision]], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision] - N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 t 1) < -3.9999999999999997e125 or -1 < (-.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 -3.9999999999999997e125 < (-.f64 t 1) < -1

   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. Taylor expanded in t around 0 96.6%

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

      1. mul-1-neg 96.6%

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

      2. unsub-neg 96.6%

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

   4. Simplified 96.6%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -4 \cdot 10^{+125} \lor \neg \left(t + -1 \leq -1\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]

Alternative 3: 78.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t + -1 \leq -1.0000000000001:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t + -1 \leq -0.99:\\ \;\;\;\;\frac{{z}^{y}}{a \cdot e^{b}} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= (+ t -1.0) -5e+55)
     t_1
     (if (<= (+ t -1.0) -1.0000000000001)
       (/ (/ (* x (pow z y)) a) y)
       (if (<= (+ t -1.0) -0.99)
         (* (/ (pow z y) (* a (exp b))) (/ x y))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = t_1;
	} else if ((t + -1.0) <= -1.0000000000001) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if ((t + -1.0) <= -0.99) {
		tmp = (pow(z, y) / (a * exp(b))) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    if ((t + (-1.0d0)) <= (-5d+55)) then
        tmp = t_1
    else if ((t + (-1.0d0)) <= (-1.0000000000001d0)) then
        tmp = ((x * (z ** y)) / a) / y
    else if ((t + (-1.0d0)) <= (-0.99d0)) then
        tmp = ((z ** y) / (a * exp(b))) * (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if ((t + -1.0) <= -5e+55) {
		tmp = t_1;
	} else if ((t + -1.0) <= -1.0000000000001) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if ((t + -1.0) <= -0.99) {
		tmp = (Math.pow(z, y) / (a * Math.exp(b))) * (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if (t + -1.0) <= -5e+55:
		tmp = t_1
	elif (t + -1.0) <= -1.0000000000001:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif (t + -1.0) <= -0.99:
		tmp = (math.pow(z, y) / (a * math.exp(b))) * (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (Float64(t + -1.0) <= -5e+55)
		tmp = t_1;
	elseif (Float64(t + -1.0) <= -1.0000000000001)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (Float64(t + -1.0) <= -0.99)
		tmp = Float64(Float64((z ^ y) / Float64(a * exp(b))) * Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if ((t + -1.0) <= -5e+55)
		tmp = t_1;
	elseif ((t + -1.0) <= -1.0000000000001)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif ((t + -1.0) <= -0.99)
		tmp = ((z ^ y) / (a * exp(b))) * (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[N[(t + -1.0), $MachinePrecision], -5e+55], t$95$1, If[LessEqual[N[(t + -1.0), $MachinePrecision], -1.0000000000001], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(t + -1.0), $MachinePrecision], -0.99], N[(N[(N[Power[z, y], $MachinePrecision] / N[(a * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 t 1) < -5.00000000000000046e55 or -0.98999999999999999 < (-.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 93.4%

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

   3. Taylor expanded in b around 0 90.2%

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

   if -5.00000000000000046e55 < (-.f64 t 1) < -1.0000000000000999

   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 t around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in b around 0 93.4%

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

      1. *-commutative 93.4%

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

      2. div-exp 93.4%

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

      3. *-commutative 93.4%

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

      4. exp-to-pow 93.4%

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

      5. rem-exp-log 93.4%

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

      6. associate-*r/ 93.4%

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

   7. Simplified 93.4%

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

   if -1.0000000000000999 < (-.f64 t 1) < -0.98999999999999999

   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/ 89.9%

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

      2. *-commutative 89.9%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in t around 0 83.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t + -1 \leq -5 \cdot 10^{+55}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t + -1 \leq -1.0000000000001:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t + -1 \leq -0.99:\\ \;\;\;\;\frac{{z}^{y}}{a \cdot e^{b}} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]

Alternative 4: 88.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+132} \lor \neg \left(y \leq 14600000000\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e+132) (not (<= y 14600000000.0)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (exp (- (* (+ t -1.0) (log a)) b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+132) || !(y <= 14600000000.0)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-3d+132)) .or. (.not. (y <= 14600000000.0d0))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * exp((((t + (-1.0d0)) * log(a)) - b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e+132) || !(y <= 14600000000.0)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * Math.exp((((t + -1.0) * Math.log(a)) - b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3e+132) or not (y <= 14600000000.0):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * math.exp((((t + -1.0) * math.log(a)) - b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3e+132) || !(y <= 14600000000.0))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * exp(Float64(Float64(Float64(t + -1.0) * log(a)) - b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3e+132) || ~((y <= 14600000000.0)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * exp((((t + -1.0) * log(a)) - b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3e+132], N[Not[LessEqual[y, 14600000000.0]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[Exp[N[(N[(N[(t + -1.0), $MachinePrecision] * N[Log[a], $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9999999999999998e132 or 1.46e10 < 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. Taylor expanded in t around 0 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   4. Simplified 92.4%

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

   5. Taylor expanded in b around 0 85.8%

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

      1. *-commutative 85.8%

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

      2. div-exp 85.8%

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

      3. *-commutative 85.8%

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

      4. exp-to-pow 85.8%

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

      5. rem-exp-log 85.8%

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

      6. associate-*r/ 85.8%

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

   7. Simplified 85.8%

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

   if -2.9999999999999998e132 < y < 1.46e10

   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. 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. Recombined 2 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+132} \lor \neg \left(y \leq 14600000000\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]

Alternative 5: 81.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+129} \lor \neg \left(y \leq 28500000\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -8.5e+129) (not (<= y 28500000.0)))
   (/ (/ (* x (pow z y)) a) y)
   (/ (* x (/ (pow a (+ t -1.0)) (exp b))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e+129) || !(y <= 28500000.0)) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else {
		tmp = (x * (pow(a, (t + -1.0)) / exp(b))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-8.5d+129)) .or. (.not. (y <= 28500000.0d0))) then
        tmp = ((x * (z ** y)) / a) / y
    else
        tmp = (x * ((a ** (t + (-1.0d0))) / exp(b))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -8.5e+129) || !(y <= 28500000.0)) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else {
		tmp = (x * (Math.pow(a, (t + -1.0)) / Math.exp(b))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -8.5e+129) or not (y <= 28500000.0):
		tmp = ((x * math.pow(z, y)) / a) / y
	else:
		tmp = (x * (math.pow(a, (t + -1.0)) / math.exp(b))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -8.5e+129) || !(y <= 28500000.0))
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	else
		tmp = Float64(Float64(x * Float64((a ^ Float64(t + -1.0)) / exp(b))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -8.5e+129) || ~((y <= 28500000.0)))
		tmp = ((x * (z ^ y)) / a) / y;
	else
		tmp = (x * ((a ^ (t + -1.0)) / exp(b))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -8.5e+129], N[Not[LessEqual[y, 28500000.0]], $MachinePrecision]], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.5000000000000001e129 or 2.85e7 < 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. Taylor expanded in t around 0 92.4%

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

      1. mul-1-neg 92.4%

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

      2. unsub-neg 92.4%

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

   4. Simplified 92.4%

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

   5. Taylor expanded in b around 0 85.8%

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

      1. *-commutative 85.8%

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

      2. div-exp 85.8%

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

      3. *-commutative 85.8%

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

      4. exp-to-pow 85.8%

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

      5. rem-exp-log 85.8%

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

      6. associate-*r/ 85.8%

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

   7. Simplified 85.8%

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

   if -8.5000000000000001e129 < y < 2.85e7

   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. Taylor expanded in y around 0 94.8%

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

      1. *-commutative 94.8%

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

      2. exp-diff 87.6%

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

      3. sub-neg 87.6%

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

      4. metadata-eval 87.6%

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

      5. *-commutative 87.6%

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

      6. exp-to-pow 88.3%

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

   4. Simplified 88.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+129} \lor \neg \left(y \leq 28500000\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{{a}^{\left(t + -1\right)}}{e^{b}}}{y}\\ \end{array} \]

Alternative 6: 75.2% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ t_2 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_3 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;t \leq -1.8 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.0145:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ (* x (pow z y)) a) y))
        (t_2 (/ (* x (pow a (+ t -1.0))) y))
        (t_3 (/ x (* a (* y (exp b))))))
   (if (<= t -1.8e+57)
     t_2
     (if (<= t -3.4e-19)
       t_1
       (if (<= t -6.4e-85)
         t_3
         (if (<= t 2.8e-268) t_1 (if (<= t 0.0145) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * pow(z, y)) / a) / y;
	double t_2 = (x * pow(a, (t + -1.0))) / y;
	double t_3 = x / (a * (y * exp(b)));
	double tmp;
	if (t <= -1.8e+57) {
		tmp = t_2;
	} else if (t <= -3.4e-19) {
		tmp = t_1;
	} else if (t <= -6.4e-85) {
		tmp = t_3;
	} else if (t <= 2.8e-268) {
		tmp = t_1;
	} else if (t <= 0.0145) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = ((x * (z ** y)) / a) / y
    t_2 = (x * (a ** (t + (-1.0d0)))) / y
    t_3 = x / (a * (y * exp(b)))
    if (t <= (-1.8d+57)) then
        tmp = t_2
    else if (t <= (-3.4d-19)) then
        tmp = t_1
    else if (t <= (-6.4d-85)) then
        tmp = t_3
    else if (t <= 2.8d-268) then
        tmp = t_1
    else if (t <= 0.0145d0) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x * Math.pow(z, y)) / a) / y;
	double t_2 = (x * Math.pow(a, (t + -1.0))) / y;
	double t_3 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (t <= -1.8e+57) {
		tmp = t_2;
	} else if (t <= -3.4e-19) {
		tmp = t_1;
	} else if (t <= -6.4e-85) {
		tmp = t_3;
	} else if (t <= 2.8e-268) {
		tmp = t_1;
	} else if (t <= 0.0145) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x * math.pow(z, y)) / a) / y
	t_2 = (x * math.pow(a, (t + -1.0))) / y
	t_3 = x / (a * (y * math.exp(b)))
	tmp = 0
	if t <= -1.8e+57:
		tmp = t_2
	elif t <= -3.4e-19:
		tmp = t_1
	elif t <= -6.4e-85:
		tmp = t_3
	elif t <= 2.8e-268:
		tmp = t_1
	elif t <= 0.0145:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x * (z ^ y)) / a) / y)
	t_2 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_3 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (t <= -1.8e+57)
		tmp = t_2;
	elseif (t <= -3.4e-19)
		tmp = t_1;
	elseif (t <= -6.4e-85)
		tmp = t_3;
	elseif (t <= 2.8e-268)
		tmp = t_1;
	elseif (t <= 0.0145)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x * (z ^ y)) / a) / y;
	t_2 = (x * (a ^ (t + -1.0))) / y;
	t_3 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (t <= -1.8e+57)
		tmp = t_2;
	elseif (t <= -3.4e-19)
		tmp = t_1;
	elseif (t <= -6.4e-85)
		tmp = t_3;
	elseif (t <= 2.8e-268)
		tmp = t_1;
	elseif (t <= 0.0145)
		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[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.8e+57], t$95$2, If[LessEqual[t, -3.4e-19], t$95$1, If[LessEqual[t, -6.4e-85], t$95$3, If[LessEqual[t, 2.8e-268], t$95$1, If[LessEqual[t, 0.0145], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.8000000000000001e57 or 0.0145000000000000007 < 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%

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

   3. Taylor expanded in b around 0 90.2%

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

   if -1.8000000000000001e57 < t < -3.4000000000000002e-19 or -6.40000000000000054e-85 < t < 2.80000000000000015e-268

   1. Initial program 97.9%

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

   2. Taylor expanded in t around 0 97.9%

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

      1. mul-1-neg 97.9%

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

      2. unsub-neg 97.9%

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

   4. Simplified 97.9%

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

   5. Taylor expanded in b around 0 80.5%

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

      1. *-commutative 80.5%

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

      2. div-exp 80.5%

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

      3. *-commutative 80.5%

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

      4. exp-to-pow 80.5%

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

      5. rem-exp-log 81.3%

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

      6. associate-*r/ 81.3%

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

   7. Simplified 81.3%

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

   if -3.4000000000000002e-19 < t < -6.40000000000000054e-85 or 2.80000000000000015e-268 < t < 0.0145000000000000007

   1. Initial program 96.2%

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

      1. associate-*l/ 91.0%

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

      2. *-commutative 91.0%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around 0 88.9%

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

   5. Taylor expanded in y around 0 84.5%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.8 \cdot 10^{+57}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-85}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-268}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 0.0145:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]

Alternative 7: 75.5% accurate, 2.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -150 \lor \neg \left(t \leq 0.0145\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -150.0) (not (<= t 0.0145)))
   (/ (* x (pow a (+ t -1.0))) y)
   (/ x (* a (* y (exp b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -150.0) || !(t <= 0.0145)) {
		tmp = (x * pow(a, (t + -1.0))) / y;
	} else {
		tmp = x / (a * (y * exp(b)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((t <= (-150.0d0)) .or. (.not. (t <= 0.0145d0))) then
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    else
        tmp = x / (a * (y * exp(b)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -150.0) || !(t <= 0.0145)) {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	} else {
		tmp = x / (a * (y * Math.exp(b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -150.0) or not (t <= 0.0145):
		tmp = (x * math.pow(a, (t + -1.0))) / y
	else:
		tmp = x / (a * (y * math.exp(b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -150.0) || !(t <= 0.0145))
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -150.0) || ~((t <= 0.0145)))
		tmp = (x * (a ^ (t + -1.0))) / y;
	else
		tmp = x / (a * (y * exp(b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -150.0], N[Not[LessEqual[t, 0.0145]], $MachinePrecision]], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -150 or 0.0145000000000000007 < 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 91.4%

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

   3. Taylor expanded in b around 0 89.1%

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

   if -150 < t < 0.0145000000000000007

   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/ 90.6%

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

      2. *-commutative 90.6%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 82.4%

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

   5. Taylor expanded in y around 0 68.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -150 \lor \neg \left(t \leq 0.0145\right):\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]

Alternative 8: 57.4% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.3 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 3.3e+84) (/ x (* a (* y (exp b)))) (/ (/ (/ x a) (exp b)) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.3e+84) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = ((x / a) / exp(b)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 3.3d+84) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = ((x / a) / exp(b)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 3.3e+84) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = ((x / a) / Math.exp(b)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 3.3e+84:
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = ((x / a) / math.exp(b)) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 3.3e+84)
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(Float64(x / a) / exp(b)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 3.3e+84)
		tmp = x / (a * (y * exp(b)));
	else
		tmp = ((x / a) / exp(b)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 3.3e+84], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / a), $MachinePrecision] / N[Exp[b], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.30000000000000017e84

   1. Initial program 97.9%

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

      1. associate-*l/ 89.3%

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

      2. *-commutative 89.3%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in t around 0 71.0%

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

   5. Taylor expanded in y around 0 63.1%

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

   if 3.30000000000000017e84 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. unsub-neg 78.8%

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

   4. Simplified 78.8%

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

   5. Taylor expanded in y around 0 54.1%

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

      1. exp-neg 54.1%

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

      2. associate-*l/ 54.1%

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

      3. *-lft-identity 54.1%

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

      4. exp-sum 54.1%

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

      5. rem-exp-log 54.4%

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

      6. *-commutative 54.4%

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

      7. associate-/r* 53.1%

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

   7. Simplified 53.1%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.3 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{a}}{e^{b}}}{y}\\ \end{array} \]

Alternative 9: 59.1% accurate, 2.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. associate-*l/ 89.8%

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

   2. *-commutative 89.8%

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

3. Simplified 71.1%

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

4. Taylor expanded in t around 0 68.9%

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

5. Taylor expanded in y around 0 58.2%

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

6. Final simplification 58.2%

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

Alternative 10: 39.6% accurate, 14.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \mathbf{if}\;b \leq -4 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x \cdot \frac{a}{x} - a \cdot b}{y \cdot \left(a \cdot \frac{a}{x}\right)}\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{1 - b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- (/ x y) (/ x (/ y b))) a)))
   (if (<= b -4e+87)
     t_1
     (if (<= b -6.2e-19)
       (/ (- (* x (/ a x)) (* a b)) (* y (* a (/ a x))))
       (if (<= b 1.1e-243)
         t_1
         (if (<= b 9.2e-206)
           (/ x (* y (* a b)))
           (if (<= b 3.9e-97)
             (/ (/ (- 1.0 b) (/ a x)) y)
             (/ x (* y (+ a (* a b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x / y) - (x / (y / b))) / a;
	double tmp;
	if (b <= -4e+87) {
		tmp = t_1;
	} else if (b <= -6.2e-19) {
		tmp = ((x * (a / x)) - (a * b)) / (y * (a * (a / x)));
	} else if (b <= 1.1e-243) {
		tmp = t_1;
	} else if (b <= 9.2e-206) {
		tmp = x / (y * (a * b));
	} else if (b <= 3.9e-97) {
		tmp = ((1.0 - b) / (a / x)) / y;
	} 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) :: tmp
    t_1 = ((x / y) - (x / (y / b))) / a
    if (b <= (-4d+87)) then
        tmp = t_1
    else if (b <= (-6.2d-19)) then
        tmp = ((x * (a / x)) - (a * b)) / (y * (a * (a / x)))
    else if (b <= 1.1d-243) then
        tmp = t_1
    else if (b <= 9.2d-206) then
        tmp = x / (y * (a * b))
    else if (b <= 3.9d-97) then
        tmp = ((1.0d0 - b) / (a / x)) / y
    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 = ((x / y) - (x / (y / b))) / a;
	double tmp;
	if (b <= -4e+87) {
		tmp = t_1;
	} else if (b <= -6.2e-19) {
		tmp = ((x * (a / x)) - (a * b)) / (y * (a * (a / x)));
	} else if (b <= 1.1e-243) {
		tmp = t_1;
	} else if (b <= 9.2e-206) {
		tmp = x / (y * (a * b));
	} else if (b <= 3.9e-97) {
		tmp = ((1.0 - b) / (a / x)) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x / y) - (x / (y / b))) / a
	tmp = 0
	if b <= -4e+87:
		tmp = t_1
	elif b <= -6.2e-19:
		tmp = ((x * (a / x)) - (a * b)) / (y * (a * (a / x)))
	elif b <= 1.1e-243:
		tmp = t_1
	elif b <= 9.2e-206:
		tmp = x / (y * (a * b))
	elif b <= 3.9e-97:
		tmp = ((1.0 - b) / (a / x)) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x / y) - Float64(x / Float64(y / b))) / a)
	tmp = 0.0
	if (b <= -4e+87)
		tmp = t_1;
	elseif (b <= -6.2e-19)
		tmp = Float64(Float64(Float64(x * Float64(a / x)) - Float64(a * b)) / Float64(y * Float64(a * Float64(a / x))));
	elseif (b <= 1.1e-243)
		tmp = t_1;
	elseif (b <= 9.2e-206)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	elseif (b <= 3.9e-97)
		tmp = Float64(Float64(Float64(1.0 - b) / Float64(a / x)) / y);
	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 = ((x / y) - (x / (y / b))) / a;
	tmp = 0.0;
	if (b <= -4e+87)
		tmp = t_1;
	elseif (b <= -6.2e-19)
		tmp = ((x * (a / x)) - (a * b)) / (y * (a * (a / x)));
	elseif (b <= 1.1e-243)
		tmp = t_1;
	elseif (b <= 9.2e-206)
		tmp = x / (y * (a * b));
	elseif (b <= 3.9e-97)
		tmp = ((1.0 - b) / (a / x)) / y;
	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[(N[(N[(x / y), $MachinePrecision] - N[(x / N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[b, -4e+87], t$95$1, If[LessEqual[b, -6.2e-19], N[(N[(N[(x * N[(a / x), $MachinePrecision]), $MachinePrecision] - N[(a * b), $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.1e-243], t$95$1, If[LessEqual[b, 9.2e-206], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.9e-97], N[(N[(N[(1.0 - b), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -3.9999999999999998e87 or -6.1999999999999998e-19 < b < 1.1e-243

   1. Initial program 98.5%

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

      1. associate-*l/ 90.8%

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

      2. *-commutative 90.8%

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

   3. Simplified 72.4%

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

   4. Taylor expanded in t around 0 71.1%

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

   5. Taylor expanded in y around 0 58.0%

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

   6. Taylor expanded in b around 0 42.8%

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

   7. Taylor expanded in a around 0 45.6%

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

      1. +-commutative 45.6%

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

      2. mul-1-neg 45.6%

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

      3. unsub-neg 45.6%

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

      4. *-commutative 45.6%

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

      5. associate-/l* 47.3%

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

   9. Simplified 47.3%

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

   if -3.9999999999999998e87 < b < -6.1999999999999998e-19

   1. Initial program 96.6%

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

      1. associate-*l/ 96.1%

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

      2. *-commutative 96.1%

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

   3. Simplified 71.4%

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

   4. Taylor expanded in t around 0 64.9%

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

   5. Taylor expanded in y around 0 65.4%

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

   6. Taylor expanded in b around 0 17.2%

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

      1. add-sqr-sqrt 1.9%

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

      2. fma-def 1.9%

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

      3. mul-1-neg 1.9%

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

      4. *-un-lft-identity 1.9%

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

      5. times-frac 1.9%

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

      6. *-commutative 1.9%

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

      7. associate-/r* 8.6%

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

      8. times-frac 8.6%

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

      9. clear-num 8.6%

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

      10. div-inv 8.6%

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

      11. *-un-lft-identity 8.6%

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

      12. fma-neg 8.6%

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

      13. add-sqr-sqrt 27.3%

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

      14. associate-/r* 27.2%

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

      15. div-sub 27.2%

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

      16. div-inv 27.2%

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

   8. Applied egg-rr 40.5%

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

      1. *-rgt-identity 40.5%

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

      2. *-commutative 40.5%

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

   10. Simplified 40.5%

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

   if 1.1e-243 < b < 9.2e-206

   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. Simplified 80.0%

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

   4. Taylor expanded in t around 0 51.8%

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

   5. Taylor expanded in y around 0 14.0%

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

   6. Taylor expanded in b around 0 14.0%

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

      1. distribute-lft-out 14.0%

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

      2. *-commutative 14.0%

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

   8. Simplified 14.0%

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

   9. Taylor expanded in b around inf 61.4%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

       3. associate-*r* 70.9%

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

   11. Simplified 70.9%

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

   if 9.2e-206 < b < 3.8999999999999998e-97

   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 t around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in y around 0 41.5%

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

      1. exp-neg 41.5%

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

      2. associate-*l/ 41.5%

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

      3. *-lft-identity 41.5%

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

      4. exp-sum 41.5%

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

      5. rem-exp-log 42.4%

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

      6. *-commutative 42.4%

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

      7. associate-/r* 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in b around 0 42.4%

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

      1. +-commutative 42.4%

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

      2. mul-1-neg 42.4%

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

      3. unsub-neg 42.4%

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

      4. associate-/l* 42.3%

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

   10. Simplified 42.3%

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

       1. clear-num 46.7%

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

       2. sub-div 46.7%

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

   12. Applied egg-rr 46.7%

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

   if 3.8999999999999998e-97 < b

   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/ 87.2%

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

      2. *-commutative 87.2%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in t around 0 70.2%

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

   5. Taylor expanded in y around 0 70.7%

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

   6. Taylor expanded in b around 0 35.3%

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

4. Final simplification 43.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4 \cdot 10^{+87}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \mathbf{elif}\;b \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;\frac{x \cdot \frac{a}{x} - a \cdot b}{y \cdot \left(a \cdot \frac{a}{x}\right)}\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-243}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x}{\frac{y}{b}}}{a}\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{-206}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-97}:\\ \;\;\;\;\frac{\frac{1 - b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 11: 42.4% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+53}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a} + \frac{x}{y} \cdot \frac{b \cdot b}{a}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-242}:\\ \;\;\;\;\frac{1 - b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 10^{-95}:\\ \;\;\;\;\frac{\frac{1 - b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.25e+53)
   (+ (/ (- x (* x b)) (* y a)) (* (/ x y) (/ (* b b) a)))
   (if (<= b 1.4e-242)
     (/ (- 1.0 b) (* y (/ a x)))
     (if (<= b 3.7e-209)
       (/ x (* y (* a b)))
       (if (<= b 1e-95)
         (/ (/ (- 1.0 b) (/ a x)) y)
         (/ x (* y (+ a (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.25e+53) {
		tmp = ((x - (x * b)) / (y * a)) + ((x / y) * ((b * b) / a));
	} else if (b <= 1.4e-242) {
		tmp = (1.0 - b) / (y * (a / x));
	} else if (b <= 3.7e-209) {
		tmp = x / (y * (a * b));
	} else if (b <= 1e-95) {
		tmp = ((1.0 - b) / (a / x)) / y;
	} 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 <= (-1.25d+53)) then
        tmp = ((x - (x * b)) / (y * a)) + ((x / y) * ((b * b) / a))
    else if (b <= 1.4d-242) then
        tmp = (1.0d0 - b) / (y * (a / x))
    else if (b <= 3.7d-209) then
        tmp = x / (y * (a * b))
    else if (b <= 1d-95) then
        tmp = ((1.0d0 - b) / (a / x)) / y
    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 <= -1.25e+53) {
		tmp = ((x - (x * b)) / (y * a)) + ((x / y) * ((b * b) / a));
	} else if (b <= 1.4e-242) {
		tmp = (1.0 - b) / (y * (a / x));
	} else if (b <= 3.7e-209) {
		tmp = x / (y * (a * b));
	} else if (b <= 1e-95) {
		tmp = ((1.0 - b) / (a / x)) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.25e+53:
		tmp = ((x - (x * b)) / (y * a)) + ((x / y) * ((b * b) / a))
	elif b <= 1.4e-242:
		tmp = (1.0 - b) / (y * (a / x))
	elif b <= 3.7e-209:
		tmp = x / (y * (a * b))
	elif b <= 1e-95:
		tmp = ((1.0 - b) / (a / x)) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.25e+53)
		tmp = Float64(Float64(Float64(x - Float64(x * b)) / Float64(y * a)) + Float64(Float64(x / y) * Float64(Float64(b * b) / a)));
	elseif (b <= 1.4e-242)
		tmp = Float64(Float64(1.0 - b) / Float64(y * Float64(a / x)));
	elseif (b <= 3.7e-209)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	elseif (b <= 1e-95)
		tmp = Float64(Float64(Float64(1.0 - b) / Float64(a / x)) / y);
	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 <= -1.25e+53)
		tmp = ((x - (x * b)) / (y * a)) + ((x / y) * ((b * b) / a));
	elseif (b <= 1.4e-242)
		tmp = (1.0 - b) / (y * (a / x));
	elseif (b <= 3.7e-209)
		tmp = x / (y * (a * b));
	elseif (b <= 1e-95)
		tmp = ((1.0 - b) / (a / x)) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.25e+53], N[(N[(N[(x - N[(x * b), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * N[(N[(b * b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.4e-242], N[(N[(1.0 - b), $MachinePrecision] / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-209], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-95], N[(N[(N[(1.0 - b), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.2500000000000001e53

   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/ 93.9%

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

      2. *-commutative 93.9%

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

   3. Simplified 65.3%

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

   4. Taylor expanded in t around 0 69.5%

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

   5. Taylor expanded in y around 0 83.9%

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

   6. Taylor expanded in b around 0 7.0%

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

      1. distribute-lft-out 11.2%

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

      2. *-commutative 11.2%

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

   8. Simplified 11.2%

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

   9. Taylor expanded in b around 0 64.2%

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

       1. +-commutative 64.2%

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

       2. *-commutative 64.2%

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

       3. mul-1-neg 64.2%

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

       4. times-frac 63.9%

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

       5. *-commutative 63.9%

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

       6. sub-neg 63.9%

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

       7. *-commutative 63.9%

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

       8. times-frac 64.2%

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

       9. *-commutative 64.2%

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

       10. div-sub 64.2%

           \[\leadsto \color{blue}{\frac{x - x \cdot b}{y \cdot a}} + \frac{{b}^{2} \cdot x}{a \cdot y} \]

       11. times-frac 62.4%

           \[\leadsto \frac{x - x \cdot b}{y \cdot a} + \color{blue}{\frac{{b}^{2}}{a} \cdot \frac{x}{y}} \]

       12. unpow2 62.4%

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

   11. Simplified 62.4%

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

   if -1.2500000000000001e53 < b < 1.39999999999999992e-242

   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 73.6%

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

      1. mul-1-neg 73.6%

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

      2. unsub-neg 73.6%

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

   4. Simplified 73.6%

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

   5. Taylor expanded in y around 0 47.0%

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

      1. exp-neg 47.0%

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

      2. associate-*l/ 47.0%

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

      3. *-lft-identity 47.0%

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

      4. exp-sum 47.0%

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

      5. rem-exp-log 47.8%

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

      6. *-commutative 47.8%

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

      7. associate-/r* 47.8%

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

   7. Simplified 47.8%

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

   8. Taylor expanded in b around 0 40.6%

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

      1. +-commutative 40.6%

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

      2. mul-1-neg 40.6%

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

      3. unsub-neg 40.6%

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

      4. associate-/l* 39.5%

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

   10. Simplified 39.5%

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

   11. Taylor expanded in x around 0 40.6%

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

       1. div-sub 40.6%

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

       2. associate-/r/ 40.6%

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

       3. associate-/l/ 40.7%

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

   13. Simplified 40.7%

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

   if 1.39999999999999992e-242 < b < 3.6999999999999998e-209

   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. Simplified 80.0%

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

   4. Taylor expanded in t around 0 51.8%

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

   5. Taylor expanded in y around 0 14.0%

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

   6. Taylor expanded in b around 0 14.0%

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

      1. distribute-lft-out 14.0%

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

      2. *-commutative 14.0%

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

   8. Simplified 14.0%

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

   9. Taylor expanded in b around inf 61.4%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

       3. associate-*r* 70.9%

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

   11. Simplified 70.9%

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

   if 3.6999999999999998e-209 < b < 9.99999999999999989e-96

   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 t around 0 68.2%

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

      1. mul-1-neg 68.2%

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

      2. unsub-neg 68.2%

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

   4. Simplified 68.2%

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

   5. Taylor expanded in y around 0 41.5%

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

      1. exp-neg 41.5%

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

      2. associate-*l/ 41.5%

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

      3. *-lft-identity 41.5%

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

      4. exp-sum 41.5%

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

      5. rem-exp-log 42.4%

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

      6. *-commutative 42.4%

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

      7. associate-/r* 42.4%

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

   7. Simplified 42.4%

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

   8. Taylor expanded in b around 0 42.4%

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

      1. +-commutative 42.4%

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

      2. mul-1-neg 42.4%

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

      3. unsub-neg 42.4%

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

      4. associate-/l* 42.3%

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

   10. Simplified 42.3%

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

       1. clear-num 46.7%

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

       2. sub-div 46.7%

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

   12. Applied egg-rr 46.7%

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

   if 9.99999999999999989e-96 < b

   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/ 87.2%

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

      2. *-commutative 87.2%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in t around 0 70.2%

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

   5. Taylor expanded in y around 0 70.7%

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

   6. Taylor expanded in b around 0 35.3%

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

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+53}:\\ \;\;\;\;\frac{x - x \cdot b}{y \cdot a} + \frac{x}{y} \cdot \frac{b \cdot b}{a}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-242}:\\ \;\;\;\;\frac{1 - b}{y \cdot \frac{a}{x}}\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-209}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 10^{-95}:\\ \;\;\;\;\frac{\frac{1 - b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 12: 37.7% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e-47)
   (* (/ x a) (/ (- b) y))
   (if (<= b 8.5e-242)
     (* (/ x y) (/ 1.0 a))
     (if (<= b 9.5e-208)
       (/ x (* y (* a b)))
       (if (<= b 2.4e-102) (/ (/ x a) y) (/ x (* y (+ a (* a b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-47) {
		tmp = (x / a) * (-b / y);
	} else if (b <= 8.5e-242) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 9.5e-208) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.4e-102) {
		tmp = (x / a) / y;
	} 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 <= (-1d-47)) then
        tmp = (x / a) * (-b / y)
    else if (b <= 8.5d-242) then
        tmp = (x / y) * (1.0d0 / a)
    else if (b <= 9.5d-208) then
        tmp = x / (y * (a * b))
    else if (b <= 2.4d-102) then
        tmp = (x / a) / y
    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 <= -1e-47) {
		tmp = (x / a) * (-b / y);
	} else if (b <= 8.5e-242) {
		tmp = (x / y) * (1.0 / a);
	} else if (b <= 9.5e-208) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.4e-102) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e-47:
		tmp = (x / a) * (-b / y)
	elif b <= 8.5e-242:
		tmp = (x / y) * (1.0 / a)
	elif b <= 9.5e-208:
		tmp = x / (y * (a * b))
	elif b <= 2.4e-102:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e-47)
		tmp = Float64(Float64(x / a) * Float64(Float64(-b) / y));
	elseif (b <= 8.5e-242)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif (b <= 9.5e-208)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	elseif (b <= 2.4e-102)
		tmp = Float64(Float64(x / a) / y);
	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 <= -1e-47)
		tmp = (x / a) * (-b / y);
	elseif (b <= 8.5e-242)
		tmp = (x / y) * (1.0 / a);
	elseif (b <= 9.5e-208)
		tmp = x / (y * (a * b));
	elseif (b <= 2.4e-102)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e-47], N[(N[(x / a), $MachinePrecision] * N[((-b) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.5e-242], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e-208], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e-102], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -9.9999999999999997e-48

   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 t around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in y around 0 74.0%

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

      1. exp-neg 74.0%

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

      2. associate-*l/ 74.0%

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

      3. *-lft-identity 74.0%

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

      4. exp-sum 74.0%

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

      5. rem-exp-log 74.0%

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

      6. *-commutative 74.0%

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

      7. associate-/r* 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in b around 0 37.9%

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

      1. +-commutative 37.9%

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

      2. mul-1-neg 37.9%

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

      3. unsub-neg 37.9%

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

      4. associate-/l* 37.9%

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

   10. Simplified 37.9%

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

   11. Taylor expanded in b around inf 34.2%

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

       1. mul-1-neg 34.2%

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

       2. times-frac 39.1%

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

       3. *-commutative 39.1%

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

       4. distribute-rgt-neg-in 39.1%

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

   13. Simplified 39.1%

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

   if -9.9999999999999997e-48 < b < 8.4999999999999997e-242

   1. Initial program 97.5%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in t around 0 68.6%

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

   5. Taylor expanded in y around 0 43.5%

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

   6. Taylor expanded in b around 0 43.5%

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

      1. *-commutative 43.5%

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

   8. Simplified 43.5%

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

      1. *-un-lft-identity 43.5%

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

      2. *-commutative 43.5%

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

      3. times-frac 45.0%

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

   10. Applied egg-rr 45.0%

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

   if 8.4999999999999997e-242 < b < 9.5000000000000001e-208

   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. Simplified 80.0%

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

   4. Taylor expanded in t around 0 51.8%

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

   5. Taylor expanded in y around 0 14.0%

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

   6. Taylor expanded in b around 0 14.0%

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

      1. distribute-lft-out 14.0%

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

      2. *-commutative 14.0%

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

   8. Simplified 14.0%

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

   9. Taylor expanded in b around inf 61.4%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

       3. associate-*r* 70.9%

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

   11. Simplified 70.9%

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

   if 9.5000000000000001e-208 < b < 2.4e-102

   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/ 84.7%

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

      2. *-commutative 84.7%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 40.2%

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

   5. Taylor expanded in y around 0 26.4%

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

   6. Taylor expanded in b around 0 26.4%

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

      1. associate-/r* 44.3%

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

   8. Simplified 44.3%

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

   if 2.4e-102 < b

   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/ 86.1%

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

      2. *-commutative 86.1%

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

   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 69.3%

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

   5. Taylor expanded in y around 0 69.9%

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

   6. Taylor expanded in b around 0 34.9%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 13: 36.9% accurate, 20.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-207} \lor \neg \left(b \leq 8.5 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e-47)
   (* (/ x a) (/ (- b) y))
   (if (<= b 2.8e-243)
     (* (/ x y) (/ 1.0 a))
     (if (or (<= b 4.1e-207) (not (<= b 8.5e-55)))
       (/ x (* y (* a b)))
       (/ (/ x a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-47) {
		tmp = (x / a) * (-b / y);
	} else if (b <= 2.8e-243) {
		tmp = (x / y) * (1.0 / a);
	} else if ((b <= 4.1e-207) || !(b <= 8.5e-55)) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1d-47)) then
        tmp = (x / a) * (-b / y)
    else if (b <= 2.8d-243) then
        tmp = (x / y) * (1.0d0 / a)
    else if ((b <= 4.1d-207) .or. (.not. (b <= 8.5d-55))) then
        tmp = x / (y * (a * b))
    else
        tmp = (x / a) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e-47) {
		tmp = (x / a) * (-b / y);
	} else if (b <= 2.8e-243) {
		tmp = (x / y) * (1.0 / a);
	} else if ((b <= 4.1e-207) || !(b <= 8.5e-55)) {
		tmp = x / (y * (a * b));
	} else {
		tmp = (x / a) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e-47:
		tmp = (x / a) * (-b / y)
	elif b <= 2.8e-243:
		tmp = (x / y) * (1.0 / a)
	elif (b <= 4.1e-207) or not (b <= 8.5e-55):
		tmp = x / (y * (a * b))
	else:
		tmp = (x / a) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e-47)
		tmp = Float64(Float64(x / a) * Float64(Float64(-b) / y));
	elseif (b <= 2.8e-243)
		tmp = Float64(Float64(x / y) * Float64(1.0 / a));
	elseif ((b <= 4.1e-207) || !(b <= 8.5e-55))
		tmp = Float64(x / Float64(y * Float64(a * b)));
	else
		tmp = Float64(Float64(x / a) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1e-47)
		tmp = (x / a) * (-b / y);
	elseif (b <= 2.8e-243)
		tmp = (x / y) * (1.0 / a);
	elseif ((b <= 4.1e-207) || ~((b <= 8.5e-55)))
		tmp = x / (y * (a * b));
	else
		tmp = (x / a) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e-47], N[(N[(x / a), $MachinePrecision] * N[((-b) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-243], N[(N[(x / y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 4.1e-207], N[Not[LessEqual[b, 8.5e-55]], $MachinePrecision]], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -9.9999999999999997e-48

   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 t around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

   4. Simplified 84.4%

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

   5. Taylor expanded in y around 0 74.0%

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

      1. exp-neg 74.0%

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

      2. associate-*l/ 74.0%

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

      3. *-lft-identity 74.0%

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

      4. exp-sum 74.0%

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

      5. rem-exp-log 74.0%

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

      6. *-commutative 74.0%

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

      7. associate-/r* 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in b around 0 37.9%

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

      1. +-commutative 37.9%

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

      2. mul-1-neg 37.9%

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

      3. unsub-neg 37.9%

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

      4. associate-/l* 37.9%

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

   10. Simplified 37.9%

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

   11. Taylor expanded in b around inf 34.2%

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

       1. mul-1-neg 34.2%

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

       2. times-frac 39.1%

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

       3. *-commutative 39.1%

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

       4. distribute-rgt-neg-in 39.1%

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

   13. Simplified 39.1%

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

   if -9.9999999999999997e-48 < b < 2.79999999999999994e-243

   1. Initial program 97.5%

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

      1. associate-*l/ 88.8%

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

      2. *-commutative 88.8%

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

   3. Simplified 76.9%

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

   4. Taylor expanded in t around 0 68.6%

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

   5. Taylor expanded in y around 0 43.5%

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

   6. Taylor expanded in b around 0 43.5%

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

      1. *-commutative 43.5%

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

   8. Simplified 43.5%

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

      1. *-un-lft-identity 43.5%

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

      2. *-commutative 43.5%

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

      3. times-frac 45.0%

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

   10. Applied egg-rr 45.0%

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

   if 2.79999999999999994e-243 < b < 4.0999999999999999e-207 or 8.49999999999999968e-55 < b

   1. Initial program 99.9%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

   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 72.0%

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

   5. Taylor expanded in y around 0 65.2%

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

   6. Taylor expanded in b around 0 28.2%

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

      1. distribute-lft-out 28.2%

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

      2. *-commutative 28.2%

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

   8. Simplified 28.2%

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

   9. Taylor expanded in b around inf 35.2%

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

       1. associate-*r* 33.9%

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

       2. *-commutative 33.9%

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

       3. associate-*r* 38.4%

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

   11. Simplified 38.4%

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

   if 4.0999999999999999e-207 < b < 8.49999999999999968e-55

   1. Initial program 96.2%

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

      1. associate-*l/ 86.0%

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

      2. *-commutative 86.0%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in t around 0 59.5%

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

   5. Taylor expanded in y around 0 34.5%

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

   6. Taylor expanded in b around 0 34.5%

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

      1. associate-/r* 43.6%

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

   8. Simplified 43.6%

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

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{-b}{y}\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-243}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{1}{a}\\ \mathbf{elif}\;b \leq 4.1 \cdot 10^{-207} \lor \neg \left(b \leq 8.5 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \end{array} \]

Alternative 14: 39.2% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.4 \cdot 10^{-239}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.4e-239)
   (/ (* x (/ (- 1.0 b) a)) y)
   (if (<= b 1.2e-208)
     (/ x (* y (* a b)))
     (if (<= b 2.5e-102) (/ (/ x a) y) (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.4e-239) {
		tmp = (x * ((1.0 - b) / a)) / y;
	} else if (b <= 1.2e-208) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.5e-102) {
		tmp = (x / a) / y;
	} 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 <= 1.4d-239) then
        tmp = (x * ((1.0d0 - b) / a)) / y
    else if (b <= 1.2d-208) then
        tmp = x / (y * (a * b))
    else if (b <= 2.5d-102) then
        tmp = (x / a) / y
    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 <= 1.4e-239) {
		tmp = (x * ((1.0 - b) / a)) / y;
	} else if (b <= 1.2e-208) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.5e-102) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.4e-239:
		tmp = (x * ((1.0 - b) / a)) / y
	elif b <= 1.2e-208:
		tmp = x / (y * (a * b))
	elif b <= 2.5e-102:
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.4e-239)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / a)) / y);
	elseif (b <= 1.2e-208)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	elseif (b <= 2.5e-102)
		tmp = Float64(Float64(x / a) / y);
	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 <= 1.4e-239)
		tmp = (x * ((1.0 - b) / a)) / y;
	elseif (b <= 1.2e-208)
		tmp = x / (y * (a * b));
	elseif (b <= 2.5e-102)
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.4e-239], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.2e-208], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e-102], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < 1.40000000000000006e-239

   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. Taylor expanded in t around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 59.5%

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

      1. exp-neg 59.5%

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

      2. associate-*l/ 59.5%

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

      3. *-lft-identity 59.5%

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

      4. exp-sum 59.5%

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

      5. rem-exp-log 60.1%

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

      6. *-commutative 60.1%

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

      7. associate-/r* 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in b around 0 41.3%

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

      1. +-commutative 41.3%

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

      2. mul-1-neg 41.3%

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

      3. unsub-neg 41.3%

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

      4. associate-/l* 40.5%

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

   10. Simplified 40.5%

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

   11. Taylor expanded in x around 0 42.0%

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

       1. *-commutative 42.0%

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

       2. div-sub 42.0%

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

   13. Simplified 42.0%

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

   if 1.40000000000000006e-239 < b < 1.1999999999999999e-208

   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. Simplified 80.0%

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

   4. Taylor expanded in t around 0 51.8%

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

   5. Taylor expanded in y around 0 14.0%

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

   6. Taylor expanded in b around 0 14.0%

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

      1. distribute-lft-out 14.0%

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

      2. *-commutative 14.0%

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

   8. Simplified 14.0%

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

   9. Taylor expanded in b around inf 61.4%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

       3. associate-*r* 70.9%

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

   11. Simplified 70.9%

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

   if 1.1999999999999999e-208 < b < 2.50000000000000013e-102

   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/ 84.7%

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

      2. *-commutative 84.7%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in t around 0 40.2%

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

   5. Taylor expanded in y around 0 26.4%

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

   6. Taylor expanded in b around 0 26.4%

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

      1. associate-/r* 44.3%

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

   8. Simplified 44.3%

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

   if 2.50000000000000013e-102 < b

   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/ 86.1%

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

      2. *-commutative 86.1%

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

   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 69.3%

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

   5. Taylor expanded in y around 0 69.9%

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

   6. Taylor expanded in b around 0 34.9%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.4 \cdot 10^{-239}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 15: 39.0% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{1 - b}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 6e-243)
   (/ (* x (/ (- 1.0 b) a)) y)
   (if (<= b 1.08e-203)
     (/ x (* y (* a b)))
     (if (<= b 2.3e-102)
       (/ (- 1.0 b) (* y (/ a x)))
       (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 6e-243) {
		tmp = (x * ((1.0 - b) / a)) / y;
	} else if (b <= 1.08e-203) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.3e-102) {
		tmp = (1.0 - b) / (y * (a / x));
	} 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 <= 6d-243) then
        tmp = (x * ((1.0d0 - b) / a)) / y
    else if (b <= 1.08d-203) then
        tmp = x / (y * (a * b))
    else if (b <= 2.3d-102) then
        tmp = (1.0d0 - b) / (y * (a / x))
    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 <= 6e-243) {
		tmp = (x * ((1.0 - b) / a)) / y;
	} else if (b <= 1.08e-203) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.3e-102) {
		tmp = (1.0 - b) / (y * (a / x));
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 6e-243:
		tmp = (x * ((1.0 - b) / a)) / y
	elif b <= 1.08e-203:
		tmp = x / (y * (a * b))
	elif b <= 2.3e-102:
		tmp = (1.0 - b) / (y * (a / x))
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 6e-243)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / a)) / y);
	elseif (b <= 1.08e-203)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	elseif (b <= 2.3e-102)
		tmp = Float64(Float64(1.0 - b) / Float64(y * Float64(a / x)));
	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 <= 6e-243)
		tmp = (x * ((1.0 - b) / a)) / y;
	elseif (b <= 1.08e-203)
		tmp = x / (y * (a * b));
	elseif (b <= 2.3e-102)
		tmp = (1.0 - b) / (y * (a / x));
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 6e-243], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 1.08e-203], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-102], N[(N[(1.0 - b), $MachinePrecision] / N[(y * N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < 6.0000000000000002e-243

   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. Taylor expanded in t around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 59.5%

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

      1. exp-neg 59.5%

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

      2. associate-*l/ 59.5%

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

      3. *-lft-identity 59.5%

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

      4. exp-sum 59.5%

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

      5. rem-exp-log 60.1%

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

      6. *-commutative 60.1%

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

      7. associate-/r* 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in b around 0 41.3%

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

      1. +-commutative 41.3%

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

      2. mul-1-neg 41.3%

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

      3. unsub-neg 41.3%

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

      4. associate-/l* 40.5%

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

   10. Simplified 40.5%

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

   11. Taylor expanded in x around 0 42.0%

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

       1. *-commutative 42.0%

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

       2. div-sub 42.0%

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

   13. Simplified 42.0%

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

   if 6.0000000000000002e-243 < b < 1.07999999999999997e-203

   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. Simplified 80.0%

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

   4. Taylor expanded in t around 0 51.8%

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

   5. Taylor expanded in y around 0 14.0%

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

   6. Taylor expanded in b around 0 14.0%

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

      1. distribute-lft-out 14.0%

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

      2. *-commutative 14.0%

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

   8. Simplified 14.0%

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

   9. Taylor expanded in b around inf 61.4%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

       3. associate-*r* 70.9%

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

   11. Simplified 70.9%

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

   if 1.07999999999999997e-203 < b < 2.29999999999999987e-102

   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 t around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in y around 0 43.3%

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

      1. exp-neg 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-lft-identity 43.3%

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

      4. exp-sum 43.3%

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

      5. rem-exp-log 44.3%

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

      6. *-commutative 44.3%

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

      7. associate-/r* 44.3%

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

   7. Simplified 44.3%

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

   8. Taylor expanded in b around 0 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

      4. associate-/l* 44.3%

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

   10. Simplified 44.3%

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

   11. Taylor expanded in x around 0 44.3%

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

       1. div-sub 44.3%

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

       2. associate-/r/ 48.9%

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

       3. associate-/l/ 48.7%

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

   13. Simplified 48.7%

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

   if 2.29999999999999987e-102 < b

   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/ 86.1%

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

      2. *-commutative 86.1%

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

   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 69.3%

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

   5. Taylor expanded in y around 0 69.9%

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

   6. Taylor expanded in b around 0 34.9%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 6 \cdot 10^{-243}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{a}}{y}\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{1 - b}{y \cdot \frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 16: 39.2% accurate, 20.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.9 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{a}}{y}\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{1 - b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 1.9e-240)
   (/ (* x (/ (- 1.0 b) a)) y)
   (if (<= b 9.4e-210)
     (/ x (* y (* a b)))
     (if (<= b 2.3e-102)
       (/ (/ (- 1.0 b) (/ a x)) y)
       (/ x (* y (+ a (* a b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 1.9e-240) {
		tmp = (x * ((1.0 - b) / a)) / y;
	} else if (b <= 9.4e-210) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.3e-102) {
		tmp = ((1.0 - b) / (a / x)) / y;
	} 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 <= 1.9d-240) then
        tmp = (x * ((1.0d0 - b) / a)) / y
    else if (b <= 9.4d-210) then
        tmp = x / (y * (a * b))
    else if (b <= 2.3d-102) then
        tmp = ((1.0d0 - b) / (a / x)) / y
    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 <= 1.9e-240) {
		tmp = (x * ((1.0 - b) / a)) / y;
	} else if (b <= 9.4e-210) {
		tmp = x / (y * (a * b));
	} else if (b <= 2.3e-102) {
		tmp = ((1.0 - b) / (a / x)) / y;
	} else {
		tmp = x / (y * (a + (a * b)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 1.9e-240:
		tmp = (x * ((1.0 - b) / a)) / y
	elif b <= 9.4e-210:
		tmp = x / (y * (a * b))
	elif b <= 2.3e-102:
		tmp = ((1.0 - b) / (a / x)) / y
	else:
		tmp = x / (y * (a + (a * b)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 1.9e-240)
		tmp = Float64(Float64(x * Float64(Float64(1.0 - b) / a)) / y);
	elseif (b <= 9.4e-210)
		tmp = Float64(x / Float64(y * Float64(a * b)));
	elseif (b <= 2.3e-102)
		tmp = Float64(Float64(Float64(1.0 - b) / Float64(a / x)) / y);
	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 <= 1.9e-240)
		tmp = (x * ((1.0 - b) / a)) / y;
	elseif (b <= 9.4e-210)
		tmp = x / (y * (a * b));
	elseif (b <= 2.3e-102)
		tmp = ((1.0 - b) / (a / x)) / y;
	else
		tmp = x / (y * (a + (a * b)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 1.9e-240], N[(N[(x * N[(N[(1.0 - b), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 9.4e-210], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-102], N[(N[(N[(1.0 - b), $MachinePrecision] / N[(a / x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a + N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < 1.89999999999999994e-240

   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. Taylor expanded in t around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   4. Simplified 78.5%

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

   5. Taylor expanded in y around 0 59.5%

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

      1. exp-neg 59.5%

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

      2. associate-*l/ 59.5%

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

      3. *-lft-identity 59.5%

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

      4. exp-sum 59.5%

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

      5. rem-exp-log 60.1%

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

      6. *-commutative 60.1%

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

      7. associate-/r* 55.9%

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

   7. Simplified 55.9%

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

   8. Taylor expanded in b around 0 41.3%

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

      1. +-commutative 41.3%

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

      2. mul-1-neg 41.3%

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

      3. unsub-neg 41.3%

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

      4. associate-/l* 40.5%

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

   10. Simplified 40.5%

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

   11. Taylor expanded in x around 0 42.0%

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

       1. *-commutative 42.0%

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

       2. div-sub 42.0%

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

   13. Simplified 42.0%

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

   if 1.89999999999999994e-240 < b < 9.39999999999999933e-210

   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. Simplified 80.0%

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

   4. Taylor expanded in t around 0 51.8%

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

   5. Taylor expanded in y around 0 14.0%

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

   6. Taylor expanded in b around 0 14.0%

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

      1. distribute-lft-out 14.0%

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

      2. *-commutative 14.0%

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

   8. Simplified 14.0%

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

   9. Taylor expanded in b around inf 61.4%

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

       1. associate-*r* 61.2%

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

       2. *-commutative 61.2%

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

       3. associate-*r* 70.9%

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

   11. Simplified 70.9%

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

   if 9.39999999999999933e-210 < b < 2.29999999999999987e-102

   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 t around 0 66.7%

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

      1. mul-1-neg 66.7%

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

      2. unsub-neg 66.7%

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

   4. Simplified 66.7%

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

   5. Taylor expanded in y around 0 43.3%

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

      1. exp-neg 43.3%

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

      2. associate-*l/ 43.3%

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

      3. *-lft-identity 43.3%

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

      4. exp-sum 43.3%

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

      5. rem-exp-log 44.3%

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

      6. *-commutative 44.3%

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

      7. associate-/r* 44.3%

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

   7. Simplified 44.3%

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

   8. Taylor expanded in b around 0 44.3%

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

      1. +-commutative 44.3%

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

      2. mul-1-neg 44.3%

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

      3. unsub-neg 44.3%

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

      4. associate-/l* 44.3%

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

   10. Simplified 44.3%

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

       1. clear-num 48.8%

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

       2. sub-div 48.9%

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

   12. Applied egg-rr 48.9%

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

   if 2.29999999999999987e-102 < b

   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/ 86.1%

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

      2. *-commutative 86.1%

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

   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 69.3%

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

   5. Taylor expanded in y around 0 69.9%

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

   6. Taylor expanded in b around 0 34.9%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.9 \cdot 10^{-240}:\\ \;\;\;\;\frac{x \cdot \frac{1 - b}{a}}{y}\\ \mathbf{elif}\;b \leq 9.4 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-102}:\\ \;\;\;\;\frac{\frac{1 - b}{\frac{a}{x}}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a + a \cdot b\right)}\\ \end{array} \]

Alternative 17: 33.9% accurate, 23.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-247} \lor \neg \left(b \leq 1.35 \cdot 10^{-209}\right) \land b \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b 3.1e-247) (and (not (<= b 1.35e-209)) (<= b 5e-55)))
   (/ (/ x a) y)
   (/ x (* y (* a b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= 3.1e-247) || (!(b <= 1.35e-209) && (b <= 5e-55))) {
		tmp = (x / a) / y;
	} 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 <= 3.1d-247) .or. (.not. (b <= 1.35d-209)) .and. (b <= 5d-55)) then
        tmp = (x / a) / y
    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 <= 3.1e-247) || (!(b <= 1.35e-209) && (b <= 5e-55))) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * (a * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= 3.1e-247) or (not (b <= 1.35e-209) and (b <= 5e-55)):
		tmp = (x / a) / y
	else:
		tmp = x / (y * (a * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= 3.1e-247) || (!(b <= 1.35e-209) && (b <= 5e-55)))
		tmp = Float64(Float64(x / a) / y);
	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 <= 3.1e-247) || (~((b <= 1.35e-209)) && (b <= 5e-55)))
		tmp = (x / a) / y;
	else
		tmp = x / (y * (a * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, 3.1e-247], And[N[Not[LessEqual[b, 1.35e-209]], $MachinePrecision], LessEqual[b, 5e-55]]], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.10000000000000015e-247 or 1.34999999999999999e-209 < b < 5.0000000000000002e-55

   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. Step-by-step derivation

      1. associate-*l/ 90.8%

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

      2. *-commutative 90.8%

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

   3. Simplified 74.3%

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

   4. Taylor expanded in t around 0 67.4%

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

   5. Taylor expanded in y around 0 55.0%

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

   6. Taylor expanded in b around 0 33.0%

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

      1. associate-/r* 37.3%

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

   8. Simplified 37.3%

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

   if 3.10000000000000015e-247 < b < 1.34999999999999999e-209 or 5.0000000000000002e-55 < b

   1. Initial program 99.9%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

   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 72.0%

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

   5. Taylor expanded in y around 0 65.2%

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

   6. Taylor expanded in b around 0 28.2%

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

      1. distribute-lft-out 28.2%

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

      2. *-commutative 28.2%

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

   8. Simplified 28.2%

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

   9. Taylor expanded in b around inf 35.2%

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

       1. associate-*r* 33.9%

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

       2. *-commutative 33.9%

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

       3. associate-*r* 38.4%

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

   11. Simplified 38.4%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-247} \lor \neg \left(b \leq 1.35 \cdot 10^{-209}\right) \land b \leq 5 \cdot 10^{-55}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(a \cdot b\right)}\\ \end{array} \]

Alternative 18: 34.1% accurate, 34.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 4.9 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.9e-54) (/ (/ x a) y) (/ x (* a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.9e-54) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 4.9d-54) then
        tmp = (x / a) / y
    else
        tmp = x / (a * (y * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.9e-54) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (a * (y * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.9e-54:
		tmp = (x / a) / y
	else:
		tmp = x / (a * (y * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.9e-54)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(a * Float64(y * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 4.9e-54)
		tmp = (x / a) / y;
	else
		tmp = x / (a * (y * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 4.9e-54], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(a * N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.90000000000000021e-54

   1. Initial program 97.9%

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

      1. associate-*l/ 91.3%

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

      2. *-commutative 91.3%

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

   3. Simplified 74.6%

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

   4. Taylor expanded in t around 0 66.6%

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

   5. Taylor expanded in y around 0 52.8%

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

   6. Taylor expanded in b around 0 32.0%

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

      1. associate-/r* 36.5%

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

   8. Simplified 36.5%

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

   if 4.90000000000000021e-54 < b

   1. Initial program 99.9%

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

      1. associate-*l/ 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. Simplified 62.0%

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

   4. Taylor expanded in t around 0 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 72.4%

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

   6. Taylor expanded in b around 0 30.2%

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

      1. distribute-lft-out 30.2%

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

      2. *-commutative 30.2%

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

   8. Simplified 30.2%

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

   9. Taylor expanded in b around inf 31.5%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.9 \cdot 10^{-54}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot b\right)}\\ \end{array} \]

Alternative 19: 30.8% accurate, 45.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{y}{\frac{x}{a}}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ 1.0 (/ y (/ x a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / (x / 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 = 1.0d0 / (y / (x / a))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return 1.0 / (y / (x / a));
}

Python

def code(x, y, z, t, a, b):
	return 1.0 / (y / (x / a))

Julia

function code(x, y, z, t, a, b)
	return Float64(1.0 / Float64(y / Float64(x / a)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = 1.0 / (y / (x / a));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(1.0 / N[(y / N[(x / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

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

   1. associate-*l/ 89.8%

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

   2. *-commutative 89.8%

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

3. Simplified 71.1%

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

4. Taylor expanded in t around 0 68.9%

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

5. Taylor expanded in y around 0 58.2%

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

6. Taylor expanded in b around 0 26.8%

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

   1. *-commutative 26.8%

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

8. Simplified 26.8%

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

   1. clear-num 27.0%

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

   2. inv-pow 27.0%

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

10. Applied egg-rr 27.0%

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

    1. unpow-1 27.0%

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

    2. associate-/l* 31.4%

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

12. Simplified 31.4%

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

13. Final simplification 31.4%

    \[\leadsto \frac{1}{\frac{y}{\frac{x}{a}}} \]

Alternative 20: 30.7% 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 98.5%

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

   1. associate-*l/ 89.8%

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

   2. *-commutative 89.8%

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

3. Simplified 71.1%

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

4. Taylor expanded in t around 0 68.9%

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

5. Taylor expanded in y around 0 58.2%

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

6. Taylor expanded in b around 0 26.8%

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

   1. *-commutative 26.8%

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

8. Simplified 26.8%

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

9. Final simplification 26.8%

   \[\leadsto \frac{x}{y \cdot a} \]

Alternative 21: 30.6% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{a}}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	return (x / a) / y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.5%

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

   1. associate-*l/ 89.8%

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

   2. *-commutative 89.8%

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

3. Simplified 71.1%

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

4. Taylor expanded in t around 0 68.9%

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

5. Taylor expanded in y around 0 58.2%

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

6. Taylor expanded in b around 0 26.8%

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

   1. associate-/r* 31.2%

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

8. Simplified 31.2%

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

9. Final simplification 31.2%

   \[\leadsto \frac{\frac{x}{a}}{y} \]

Developer target: 72.3% 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 2023230 
(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))