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

Percentage Accurate: 98.3% → 98.3%

Time: 23.8s

Alternatives: 20

Speedup: 1.0×

• 47.1% 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 98.8%

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

3. Final simplification 98.8%

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

Alternative 2: 92.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+18} \lor \neg \left(t \leq 11000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5e+18) (not (<= t 11000000000.0)))
   (/ (* 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 <= -5e+18) || !(t <= 11000000000.0)) {
		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 <= (-5d+18)) .or. (.not. (t <= 11000000000.0d0))) 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 <= -5e+18) || !(t <= 11000000000.0)) {
		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 <= -5e+18) or not (t <= 11000000000.0):
		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 ((t <= -5e+18) || !(t <= 11000000000.0))
		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 <= -5e+18) || ~((t <= 11000000000.0)))
		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[t, -5e+18], N[Not[LessEqual[t, 11000000000.0]], $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 t < -5e18 or 1.1e10 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 91.9%

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

   if -5e18 < t < 1.1e10

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0 97.3%

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

      1. +-commutative 97.3%

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

      2. mul-1-neg 97.3%

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

      3. unsub-neg 97.3%

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

   5. Simplified 97.3%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+18} \lor \neg \left(t \leq 11000000000\right):\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z - \log a\right) - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot e^{b}\\ t_2 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a \cdot t\_1}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 10500000000:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{t\_1}}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (exp b))) (t_2 (/ (* x (pow a (+ t -1.0))) y)))
   (if (<= t -7.2e+98)
     t_2
     (if (<= t -5.5e+23)
       (/ x (* a t_1))
       (if (<= t -2.25e-13)
         t_2
         (if (<= t -1.12e-135)
           (/ (/ (* x (pow z y)) a) y)
           (if (<= t 10500000000.0) (/ x (/ a (/ (pow z y) t_1))) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * exp(b);
	double t_2 = (x * pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -7.2e+98) {
		tmp = t_2;
	} else if (t <= -5.5e+23) {
		tmp = x / (a * t_1);
	} else if (t <= -2.25e-13) {
		tmp = t_2;
	} else if (t <= -1.12e-135) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (t <= 10500000000.0) {
		tmp = x / (a / (pow(z, y) / t_1));
	} 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 = y * exp(b)
    t_2 = (x * (a ** (t + (-1.0d0)))) / y
    if (t <= (-7.2d+98)) then
        tmp = t_2
    else if (t <= (-5.5d+23)) then
        tmp = x / (a * t_1)
    else if (t <= (-2.25d-13)) then
        tmp = t_2
    else if (t <= (-1.12d-135)) then
        tmp = ((x * (z ** y)) / a) / y
    else if (t <= 10500000000.0d0) then
        tmp = x / (a / ((z ** y) / t_1))
    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 = y * Math.exp(b);
	double t_2 = (x * Math.pow(a, (t + -1.0))) / y;
	double tmp;
	if (t <= -7.2e+98) {
		tmp = t_2;
	} else if (t <= -5.5e+23) {
		tmp = x / (a * t_1);
	} else if (t <= -2.25e-13) {
		tmp = t_2;
	} else if (t <= -1.12e-135) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (t <= 10500000000.0) {
		tmp = x / (a / (Math.pow(z, y) / t_1));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * math.exp(b)
	t_2 = (x * math.pow(a, (t + -1.0))) / y
	tmp = 0
	if t <= -7.2e+98:
		tmp = t_2
	elif t <= -5.5e+23:
		tmp = x / (a * t_1)
	elif t <= -2.25e-13:
		tmp = t_2
	elif t <= -1.12e-135:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif t <= 10500000000.0:
		tmp = x / (a / (math.pow(z, y) / t_1))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * exp(b))
	t_2 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	tmp = 0.0
	if (t <= -7.2e+98)
		tmp = t_2;
	elseif (t <= -5.5e+23)
		tmp = Float64(x / Float64(a * t_1));
	elseif (t <= -2.25e-13)
		tmp = t_2;
	elseif (t <= -1.12e-135)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (t <= 10500000000.0)
		tmp = Float64(x / Float64(a / Float64((z ^ y) / t_1)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * exp(b);
	t_2 = (x * (a ^ (t + -1.0))) / y;
	tmp = 0.0;
	if (t <= -7.2e+98)
		tmp = t_2;
	elseif (t <= -5.5e+23)
		tmp = x / (a * t_1);
	elseif (t <= -2.25e-13)
		tmp = t_2;
	elseif (t <= -1.12e-135)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (t <= 10500000000.0)
		tmp = x / (a / ((z ^ y) / t_1));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[t, -7.2e+98], t$95$2, If[LessEqual[t, -5.5e+23], N[(x / N[(a * t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.25e-13], t$95$2, If[LessEqual[t, -1.12e-135], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 10500000000.0], N[(x / N[(a / N[(N[Power[z, y], $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.19999999999999962e98 or -5.50000000000000004e23 < t < -2.25e-13 or 1.05e10 < t

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 92.7%

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

   4. Taylor expanded in b around 0 84.7%

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

      1. exp-to-pow 84.7%

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

      2. sub-neg 84.7%

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

      3. metadata-eval 84.7%

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

      4. +-commutative 84.7%

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

   6. Simplified 84.7%

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

   if -7.19999999999999962e98 < t < -5.50000000000000004e23

   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%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 69.2%

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

      4. associate-/r* 69.2%

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

      5. *-commutative 69.2%

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

      6. exp-to-pow 69.2%

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

      7. exp-diff 30.8%

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

      8. *-commutative 30.8%

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

      9. exp-to-pow 30.8%

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

      10. sub-neg 30.8%

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

      11. metadata-eval 30.8%

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

   3. Simplified 30.8%

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

   5. Taylor expanded in t around 0 77.0%

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

      1. associate-/l* 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in y around 0 92.4%

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

   if -2.25e-13 < t < -1.12e-135

   1. Initial program 99.4%

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

   3. Taylor expanded in b around 0 84.2%

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

      1. exp-sum 84.2%

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

      2. *-commutative 84.2%

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

      3. exp-to-pow 84.2%

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

      4. exp-to-pow 84.9%

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

      5. sub-neg 84.9%

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

      6. metadata-eval 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in t around 0 84.9%

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

   if -1.12e-135 < t < 1.05e10

   1. Initial program 96.9%

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

      1. associate-/l* 96.8%

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

      2. associate--l+ 96.8%

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

      3. exp-sum 82.1%

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

      4. associate-/r* 82.1%

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

      5. *-commutative 82.1%

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

      6. exp-to-pow 82.1%

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

      7. exp-diff 82.1%

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

      8. *-commutative 82.1%

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

      9. exp-to-pow 83.2%

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

      10. sub-neg 83.2%

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

      11. metadata-eval 83.2%

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

   3. Simplified 83.2%

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

   5. Taylor expanded in t around 0 83.2%

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

      1. associate-/l* 84.3%

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

   7. Simplified 84.3%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-135}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;t \leq 10500000000:\\ \;\;\;\;\frac{x}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+193} \lor \neg \left(y \leq 5.5 \cdot 10^{+238}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e+193) (not (<= y 5.5e+238)))
   (/ (/ (* 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+193) || !(y <= 5.5e+238)) {
		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+193)) .or. (.not. (y <= 5.5d+238))) 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+193) || !(y <= 5.5e+238)) {
		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+193) or not (y <= 5.5e+238):
		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+193) || !(y <= 5.5e+238))
		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+193) || ~((y <= 5.5e+238)))
		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+193], N[Not[LessEqual[y, 5.5e+238]], $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 < -3e193 or 5.50000000000000012e238 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in b around 0 100.0%

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

      1. exp-sum 61.3%

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

      2. *-commutative 61.3%

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

      3. exp-to-pow 61.3%

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

      4. exp-to-pow 61.3%

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

      5. sub-neg 61.3%

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

      6. metadata-eval 61.3%

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

   5. Simplified 61.3%

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

   6. Taylor expanded in t around 0 100.0%

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

   if -3e193 < y < 5.50000000000000012e238

   1. Initial program 98.7%

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

   3. Taylor expanded in y around 0 91.0%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+193} \lor \neg \left(y \leq 5.5 \cdot 10^{+238}\right):\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot e^{\left(t + -1\right) \cdot \log a - b}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.5% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ t_2 := \frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+100}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-261}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-171}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* x (pow a (+ t -1.0))) y)) (t_2 (/ x (* a (* y (exp b))))))
   (if (<= b -7.5e+100)
     t_2
     (if (<= b 1.7e-261)
       t_1
       (if (<= b 9e-171)
         (/ (/ (* x (pow z y)) a) y)
         (if (<= b 5e+33) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * pow(a, (t + -1.0))) / y;
	double t_2 = x / (a * (y * exp(b)));
	double tmp;
	if (b <= -7.5e+100) {
		tmp = t_2;
	} else if (b <= 1.7e-261) {
		tmp = t_1;
	} else if (b <= 9e-171) {
		tmp = ((x * pow(z, y)) / a) / y;
	} else if (b <= 5e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * (a ** (t + (-1.0d0)))) / y
    t_2 = x / (a * (y * exp(b)))
    if (b <= (-7.5d+100)) then
        tmp = t_2
    else if (b <= 1.7d-261) then
        tmp = t_1
    else if (b <= 9d-171) then
        tmp = ((x * (z ** y)) / a) / y
    else if (b <= 5d+33) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x * Math.pow(a, (t + -1.0))) / y;
	double t_2 = x / (a * (y * Math.exp(b)));
	double tmp;
	if (b <= -7.5e+100) {
		tmp = t_2;
	} else if (b <= 1.7e-261) {
		tmp = t_1;
	} else if (b <= 9e-171) {
		tmp = ((x * Math.pow(z, y)) / a) / y;
	} else if (b <= 5e+33) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x * math.pow(a, (t + -1.0))) / y
	t_2 = x / (a * (y * math.exp(b)))
	tmp = 0
	if b <= -7.5e+100:
		tmp = t_2
	elif b <= 1.7e-261:
		tmp = t_1
	elif b <= 9e-171:
		tmp = ((x * math.pow(z, y)) / a) / y
	elif b <= 5e+33:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y)
	t_2 = Float64(x / Float64(a * Float64(y * exp(b))))
	tmp = 0.0
	if (b <= -7.5e+100)
		tmp = t_2;
	elseif (b <= 1.7e-261)
		tmp = t_1;
	elseif (b <= 9e-171)
		tmp = Float64(Float64(Float64(x * (z ^ y)) / a) / y);
	elseif (b <= 5e+33)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x * (a ^ (t + -1.0))) / y;
	t_2 = x / (a * (y * exp(b)));
	tmp = 0.0;
	if (b <= -7.5e+100)
		tmp = t_2;
	elseif (b <= 1.7e-261)
		tmp = t_1;
	elseif (b <= 9e-171)
		tmp = ((x * (z ^ y)) / a) / y;
	elseif (b <= 5e+33)
		tmp = t_1;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.5e+100], t$95$2, If[LessEqual[b, 1.7e-261], t$95$1, If[LessEqual[b, 9e-171], N[(N[(N[(x * N[Power[z, y], $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[b, 5e+33], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.49999999999999983e100 or 4.99999999999999973e33 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 74.4%

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

      4. associate-/r* 74.4%

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

      5. *-commutative 74.4%

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

      6. exp-to-pow 74.4%

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

      7. exp-diff 55.6%

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

      8. *-commutative 55.6%

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

      9. exp-to-pow 55.6%

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

      10. sub-neg 55.6%

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

      11. metadata-eval 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in t around 0 66.8%

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

      1. associate-/l* 66.8%

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

   7. Simplified 66.8%

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

   8. Taylor expanded in y around 0 82.3%

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

   if -7.49999999999999983e100 < b < 1.7e-261 or 9.0000000000000008e-171 < b < 4.99999999999999973e33

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 81.6%

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

   4. Taylor expanded in b around 0 80.3%

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

      1. exp-to-pow 81.1%

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

      2. sub-neg 81.1%

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

      3. metadata-eval 81.1%

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

      4. +-commutative 81.1%

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

   6. Simplified 81.1%

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

   if 1.7e-261 < b < 9.0000000000000008e-171

   1. Initial program 94.5%

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

   3. Taylor expanded in b around 0 94.5%

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

      1. exp-sum 78.7%

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

      2. *-commutative 78.7%

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

      3. exp-to-pow 78.7%

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

      4. exp-to-pow 79.0%

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

      5. sub-neg 79.0%

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

      6. metadata-eval 79.0%

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

   5. Simplified 79.0%

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

   6. Taylor expanded in t around 0 84.6%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+100}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-261}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-171}:\\ \;\;\;\;\frac{\frac{x \cdot {z}^{y}}{a}}{y}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+33}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+112} \lor \neg \left(b \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1e+112) (not (<= b 6.5e+33)))
   (/ x (* a (* y (exp b))))
   (/ (* x (pow a (+ t -1.0))) y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1e+112) || !(b <= 6.5e+33)) {
		tmp = x / (a * (y * exp(b)));
	} else {
		tmp = (x * pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1d+112)) .or. (.not. (b <= 6.5d+33))) then
        tmp = x / (a * (y * exp(b)))
    else
        tmp = (x * (a ** (t + (-1.0d0)))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1e+112) || !(b <= 6.5e+33)) {
		tmp = x / (a * (y * Math.exp(b)));
	} else {
		tmp = (x * Math.pow(a, (t + -1.0))) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1e+112) or not (b <= 6.5e+33):
		tmp = x / (a * (y * math.exp(b)))
	else:
		tmp = (x * math.pow(a, (t + -1.0))) / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1e+112) || !(b <= 6.5e+33))
		tmp = Float64(x / Float64(a * Float64(y * exp(b))));
	else
		tmp = Float64(Float64(x * (a ^ Float64(t + -1.0))) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1e+112) || ~((b <= 6.5e+33)))
		tmp = x / (a * (y * exp(b)));
	else
		tmp = (x * (a ^ (t + -1.0))) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1e+112], N[Not[LessEqual[b, 6.5e+33]], $MachinePrecision]], N[(x / N[(a * N[(y * N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[Power[a, N[(t + -1.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.9999999999999993e111 or 6.49999999999999993e33 < b

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/r* 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. exp-diff 56.0%

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

      8. *-commutative 56.0%

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

      9. exp-to-pow 56.0%

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

      10. sub-neg 56.0%

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

      11. metadata-eval 56.0%

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

   3. Simplified 56.0%

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

   5. Taylor expanded in t around 0 67.4%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

   8. Taylor expanded in y around 0 83.0%

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

   if -9.9999999999999993e111 < b < 6.49999999999999993e33

   1. Initial program 97.8%

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

   3. Taylor expanded in y around 0 75.9%

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

   4. Taylor expanded in b around 0 74.7%

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

      1. exp-to-pow 75.4%

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

      2. sub-neg 75.4%

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

      3. metadata-eval 75.4%

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

      4. +-commutative 75.4%

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

   6. Simplified 75.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+112} \lor \neg \left(b \leq 6.5 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{x}{a \cdot \left(y \cdot e^{b}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot {a}^{\left(t + -1\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.2% 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 98.8%

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

   1. associate-/l* 98.8%

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

   2. associate--l+ 98.8%

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

   3. exp-sum 76.9%

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

   4. associate-/r* 76.9%

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

   5. *-commutative 76.9%

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

   6. exp-to-pow 76.9%

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

   7. exp-diff 64.8%

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

   8. *-commutative 64.8%

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

   9. exp-to-pow 65.3%

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

   10. sub-neg 65.3%

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

   11. metadata-eval 65.3%

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

3. Simplified 65.3%

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

5. Taylor expanded in t around 0 62.9%

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

   1. associate-/l* 64.9%

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

7. Simplified 64.9%

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

8. Taylor expanded in y around 0 61.1%

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

9. Final simplification 61.1%

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

Alternative 8: 40.6% accurate, 9.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \frac{x}{y}\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq -9000000000:\\ \;\;\;\;\frac{x \cdot a - y \cdot \left(a \cdot t\_1\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-293}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot t\_1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (/ x y))))
   (if (<= b -1.9e+134)
     (/ (- (/ x y) (/ (* x b) y)) a)
     (if (<= b -9000000000.0)
       (/ (- (* x a) (* y (* a t_1))) (* y (* a a)))
       (if (<= b 8.8e-293)
         (/ (- (* a (/ x a)) (* y t_1)) (* y a))
         (/ (/ x (+ y (* y b))) a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x / y);
	double tmp;
	if (b <= -1.9e+134) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= -9000000000.0) {
		tmp = ((x * a) - (y * (a * t_1))) / (y * (a * a));
	} else if (b <= 8.8e-293) {
		tmp = ((a * (x / a)) - (y * t_1)) / (y * a);
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (x / y)
    if (b <= (-1.9d+134)) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else if (b <= (-9000000000.0d0)) then
        tmp = ((x * a) - (y * (a * t_1))) / (y * (a * a))
    else if (b <= 8.8d-293) then
        tmp = ((a * (x / a)) - (y * t_1)) / (y * a)
    else
        tmp = (x / (y + (y * b))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (x / y);
	double tmp;
	if (b <= -1.9e+134) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= -9000000000.0) {
		tmp = ((x * a) - (y * (a * t_1))) / (y * (a * a));
	} else if (b <= 8.8e-293) {
		tmp = ((a * (x / a)) - (y * t_1)) / (y * a);
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (x / y)
	tmp = 0
	if b <= -1.9e+134:
		tmp = ((x / y) - ((x * b) / y)) / a
	elif b <= -9000000000.0:
		tmp = ((x * a) - (y * (a * t_1))) / (y * (a * a))
	elif b <= 8.8e-293:
		tmp = ((a * (x / a)) - (y * t_1)) / (y * a)
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(x / y))
	tmp = 0.0
	if (b <= -1.9e+134)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	elseif (b <= -9000000000.0)
		tmp = Float64(Float64(Float64(x * a) - Float64(y * Float64(a * t_1))) / Float64(y * Float64(a * a)));
	elseif (b <= 8.8e-293)
		tmp = Float64(Float64(Float64(a * Float64(x / a)) - Float64(y * t_1)) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (x / y);
	tmp = 0.0;
	if (b <= -1.9e+134)
		tmp = ((x / y) - ((x * b) / y)) / a;
	elseif (b <= -9000000000.0)
		tmp = ((x * a) - (y * (a * t_1))) / (y * (a * a));
	elseif (b <= 8.8e-293)
		tmp = ((a * (x / a)) - (y * t_1)) / (y * a);
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+134], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, -9000000000.0], N[(N[(N[(x * a), $MachinePrecision] - N[(y * N[(a * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * N[(a * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.8e-293], N[(N[(N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(y * t$95$1), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.89999999999999999e134

   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%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 75.0%

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

      4. associate-/r* 75.0%

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

      5. *-commutative 75.0%

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

      6. exp-to-pow 75.0%

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

      7. exp-diff 54.2%

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

      8. *-commutative 54.2%

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

      9. exp-to-pow 54.2%

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

      10. sub-neg 54.2%

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

      11. metadata-eval 54.2%

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

   3. Simplified 54.2%

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

   5. Taylor expanded in t around 0 64.6%

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

      1. associate-/l* 64.6%

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

   7. Simplified 64.6%

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

      1. *-un-lft-identity 64.6%

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

      2. associate-/r/ 64.6%

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

      3. times-frac 64.6%

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

   9. Applied egg-rr 64.6%

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

       1. associate-*l/ 64.6%

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

       2. *-lft-identity 64.6%

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

   11. Simplified 64.6%

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

   12. Taylor expanded in y around 0 83.6%

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

   13. Taylor expanded in b around 0 55.7%

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

       1. +-commutative 55.7%

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

       2. mul-1-neg 55.7%

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

       3. unsub-neg 55.7%

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

       4. *-commutative 55.7%

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

   15. Simplified 55.7%

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

   if -1.89999999999999999e134 < b < -9e9

   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%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 68.4%

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

      4. associate-/r* 68.4%

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

      5. *-commutative 68.4%

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

      6. exp-to-pow 68.4%

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

      7. exp-diff 42.1%

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

      8. *-commutative 42.1%

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

      9. exp-to-pow 42.1%

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

      10. sub-neg 42.1%

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

      11. metadata-eval 42.1%

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

   3. Simplified 42.1%

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

   5. Taylor expanded in t around 0 58.1%

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

      1. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   8. Taylor expanded in y around 0 63.7%

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

   9. Taylor expanded in b around 0 24.0%

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

       1. +-commutative 24.0%

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

       2. mul-1-neg 24.0%

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

       3. unsub-neg 24.0%

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

       4. *-commutative 24.0%

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

       5. *-commutative 24.0%

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

       6. times-frac 19.1%

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

   11. Simplified 19.1%

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

       1. associate-*r/ 19.1%

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

       2. frac-sub 33.6%

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

       3. *-commutative 33.6%

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

       4. *-commutative 33.6%

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

       5. *-commutative 33.6%

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

   13. Applied egg-rr 33.6%

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

       1. associate-*l* 43.7%

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

       2. associate-*l* 48.6%

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

   15. Simplified 48.6%

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

   if -9e9 < b < 8.8e-293

   1. Initial program 98.8%

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

      1. associate-/l* 97.2%

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

      2. associate--l+ 97.2%

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

      3. exp-sum 87.9%

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

      4. associate-/r* 87.9%

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

      5. *-commutative 87.9%

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

      6. exp-to-pow 87.9%

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

      7. exp-diff 84.1%

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

      8. *-commutative 84.1%

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

      9. exp-to-pow 85.0%

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

      10. sub-neg 85.0%

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

      11. metadata-eval 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in t around 0 55.5%

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

      1. associate-/l* 61.2%

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

   7. Simplified 61.2%

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

   8. Taylor expanded in y around 0 41.8%

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

   9. Taylor expanded in b around 0 41.6%

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

       1. +-commutative 41.6%

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

       2. mul-1-neg 41.6%

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

       3. unsub-neg 41.6%

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

       4. *-commutative 41.6%

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

       5. *-commutative 41.6%

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

       6. times-frac 36.7%

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

   11. Simplified 36.7%

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

       1. associate-/r* 34.8%

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

       2. div-inv 34.8%

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

       3. associate-*r/ 34.8%

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

       4. frac-sub 43.7%

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

       5. div-inv 43.7%

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

       6. *-commutative 43.7%

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

   13. Applied egg-rr 43.7%

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

   if 8.8e-293 < b

   1. Initial program 98.3%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 74.5%

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

      4. associate-/r* 74.5%

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

      5. *-commutative 74.5%

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

      6. exp-to-pow 74.5%

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

      7. exp-diff 64.2%

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

      8. *-commutative 64.2%

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

      9. exp-to-pow 64.7%

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

      10. sub-neg 64.7%

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

      11. metadata-eval 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

      1. *-un-lft-identity 67.4%

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

      2. associate-/r/ 67.4%

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

      3. times-frac 65.8%

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

   9. Applied egg-rr 65.8%

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

       1. associate-*l/ 65.8%

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

       2. *-lft-identity 65.8%

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

   11. Simplified 65.8%

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

   12. Taylor expanded in y around 0 63.1%

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

   13. Taylor expanded in b around 0 39.5%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+134}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq -9000000000:\\ \;\;\;\;\frac{x \cdot a - y \cdot \left(a \cdot \left(b \cdot \frac{x}{y}\right)\right)}{y \cdot \left(a \cdot a\right)}\\ \mathbf{elif}\;b \leq 8.8 \cdot 10^{-293}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot \left(b \cdot \frac{x}{y}\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.6% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-292}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot \left(b \cdot \frac{x}{y}\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.1e-292)
   (/ (- (* a (/ x a)) (* y (* b (/ x y)))) (* y a))
   (/ (/ x (+ y (* y b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.1e-292) {
		tmp = ((a * (x / a)) - (y * (b * (x / y)))) / (y * a);
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.1d-292) then
        tmp = ((a * (x / a)) - (y * (b * (x / y)))) / (y * a)
    else
        tmp = (x / (y + (y * b))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.1e-292) {
		tmp = ((a * (x / a)) - (y * (b * (x / y)))) / (y * a);
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.1e-292:
		tmp = ((a * (x / a)) - (y * (b * (x / y)))) / (y * a)
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.1e-292)
		tmp = Float64(Float64(Float64(a * Float64(x / a)) - Float64(y * Float64(b * Float64(x / y)))) / Float64(y * a));
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.1e-292)
		tmp = ((a * (x / a)) - (y * (b * (x / y)))) / (y * a);
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.1e-292], N[(N[(N[(a * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(y * N[(b * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.0999999999999999e-292

   1. Initial program 99.5%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 79.6%

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

      4. associate-/r* 79.6%

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

      5. *-commutative 79.6%

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

      6. exp-to-pow 79.6%

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

      7. exp-diff 65.5%

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

      8. *-commutative 65.5%

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

      9. exp-to-pow 65.9%

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

      10. sub-neg 65.9%

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

      11. metadata-eval 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in t around 0 59.6%

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

      1. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in y around 0 62.0%

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

   9. Taylor expanded in b around 0 41.9%

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

       1. +-commutative 41.9%

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

       2. mul-1-neg 41.9%

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

       3. unsub-neg 41.9%

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

       4. *-commutative 41.9%

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

       5. *-commutative 41.9%

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

       6. times-frac 36.7%

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

   11. Simplified 36.7%

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

       1. associate-/r* 36.7%

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

       2. div-inv 36.7%

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

       3. associate-*r/ 37.5%

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

       4. frac-sub 44.4%

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

       5. div-inv 44.4%

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

       6. *-commutative 44.4%

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

   13. Applied egg-rr 44.4%

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

   if 3.0999999999999999e-292 < b

   1. Initial program 98.3%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 74.5%

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

      4. associate-/r* 74.5%

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

      5. *-commutative 74.5%

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

      6. exp-to-pow 74.5%

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

      7. exp-diff 64.2%

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

      8. *-commutative 64.2%

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

      9. exp-to-pow 64.7%

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

      10. sub-neg 64.7%

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

      11. metadata-eval 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

      1. *-un-lft-identity 67.4%

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

      2. associate-/r/ 67.4%

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

      3. times-frac 65.8%

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

   9. Applied egg-rr 65.8%

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

       1. associate-*l/ 65.8%

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

       2. *-lft-identity 65.8%

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

   11. Simplified 65.8%

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

   12. Taylor expanded in y around 0 63.1%

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

   13. Taylor expanded in b around 0 39.5%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.1 \cdot 10^{-292}:\\ \;\;\;\;\frac{a \cdot \frac{x}{a} - y \cdot \left(b \cdot \frac{x}{y}\right)}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 40.3% accurate, 16.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.82 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.82e+84)
   (/ (- (/ x y) (/ (* x b) y)) a)
   (if (<= b 7.4e-284) (* x (/ 1.0 (* y a))) (/ (/ x (+ y (* y b))) a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.82e+84) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 7.4e-284) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.82d+84)) then
        tmp = ((x / y) - ((x * b) / y)) / a
    else if (b <= 7.4d-284) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / (y + (y * b))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.82e+84) {
		tmp = ((x / y) - ((x * b) / y)) / a;
	} else if (b <= 7.4e-284) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.82e+84:
		tmp = ((x / y) - ((x * b) / y)) / a
	elif b <= 7.4e-284:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.82e+84)
		tmp = Float64(Float64(Float64(x / y) - Float64(Float64(x * b) / y)) / a);
	elseif (b <= 7.4e-284)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.82e+84)
		tmp = ((x / y) - ((x * b) / y)) / a;
	elseif (b <= 7.4e-284)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.82e+84], N[(N[(N[(x / y), $MachinePrecision] - N[(N[(x * b), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[b, 7.4e-284], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.8200000000000001e84

   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%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 73.2%

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

      4. associate-/r* 73.2%

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

      5. *-commutative 73.2%

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

      6. exp-to-pow 73.2%

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

      7. exp-diff 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in t around 0 62.6%

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

      1. associate-/l* 62.6%

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

   7. Simplified 62.6%

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

      1. *-un-lft-identity 62.6%

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

      2. associate-/r/ 62.6%

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

      3. times-frac 62.6%

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

   9. Applied egg-rr 62.6%

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

       1. associate-*l/ 62.6%

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

       2. *-lft-identity 62.6%

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

   11. Simplified 62.6%

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

   12. Taylor expanded in y around 0 78.9%

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

   13. Taylor expanded in b around 0 51.8%

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

       1. +-commutative 51.8%

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

       2. mul-1-neg 51.8%

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

       3. unsub-neg 51.8%

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

       4. *-commutative 51.8%

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

   15. Simplified 51.8%

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

   if -1.8200000000000001e84 < b < 7.4000000000000001e-284

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 82.9%

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

   4. Taylor expanded in b around 0 81.4%

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

      1. exp-to-pow 82.2%

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

      2. sub-neg 82.2%

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

      3. metadata-eval 82.2%

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

      4. +-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in t around 0 39.8%

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

      1. clear-num 39.7%

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

      2. associate-/r/ 39.8%

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

      3. *-commutative 39.8%

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

   9. Applied egg-rr 39.8%

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

   if 7.4000000000000001e-284 < b

   1. Initial program 98.3%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 74.5%

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

      4. associate-/r* 74.5%

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

      5. *-commutative 74.5%

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

      6. exp-to-pow 74.5%

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

      7. exp-diff 64.2%

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

      8. *-commutative 64.2%

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

      9. exp-to-pow 64.7%

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

      10. sub-neg 64.7%

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

      11. metadata-eval 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

      1. *-un-lft-identity 67.4%

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

      2. associate-/r/ 67.4%

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

      3. times-frac 65.8%

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

   9. Applied egg-rr 65.8%

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

       1. associate-*l/ 65.8%

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

       2. *-lft-identity 65.8%

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

   11. Simplified 65.8%

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

   12. Taylor expanded in y around 0 63.1%

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

   13. Taylor expanded in b around 0 39.5%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.82 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{x}{y} - \frac{x \cdot b}{y}}{a}\\ \mathbf{elif}\;b \leq 7.4 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.3% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq 10^{-292}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1e+158)
   (* (/ x y) (/ (- b) a))
   (if (<= b 1e-292) (* x (/ 1.0 (* y a))) (/ 1.0 (* a (/ y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1e+158) {
		tmp = (x / y) * (-b / a);
	} else if (b <= 1e-292) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	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+158)) then
        tmp = (x / y) * (-b / a)
    else if (b <= 1d-292) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = 1.0d0 / (a * (y / x))
    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+158) {
		tmp = (x / y) * (-b / a);
	} else if (b <= 1e-292) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1e+158:
		tmp = (x / y) * (-b / a)
	elif b <= 1e-292:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1e+158)
		tmp = Float64(Float64(x / y) * Float64(Float64(-b) / a));
	elseif (b <= 1e-292)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1e+158)
		tmp = (x / y) * (-b / a);
	elseif (b <= 1e-292)
		tmp = x * (1.0 / (y * a));
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1e+158], N[(N[(x / y), $MachinePrecision] * N[((-b) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e-292], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.99999999999999953e157

   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%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 78.0%

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

      4. associate-/r* 78.0%

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

      5. *-commutative 78.0%

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

      6. exp-to-pow 78.0%

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

      7. exp-diff 53.7%

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

      8. *-commutative 53.7%

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

      9. exp-to-pow 53.7%

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

      10. sub-neg 53.7%

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

      11. metadata-eval 53.7%

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

   3. Simplified 53.7%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 65.9%

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

   7. Simplified 65.9%

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

   8. Taylor expanded in y around 0 83.2%

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

   9. Taylor expanded in b around 0 45.4%

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

       1. +-commutative 45.4%

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

       2. mul-1-neg 45.4%

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

       3. unsub-neg 45.4%

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

       4. *-commutative 45.4%

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

       5. *-commutative 45.4%

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

       6. times-frac 45.9%

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

   11. Simplified 45.9%

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

   12. Taylor expanded in b around inf 45.4%

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

       1. mul-1-neg 45.4%

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

       2. times-frac 45.9%

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

       3. *-commutative 45.9%

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

       4. distribute-rgt-neg-out 45.9%

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

       5. distribute-neg-frac 45.9%

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

   14. Simplified 45.9%

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

   if -9.99999999999999953e157 < b < 1.0000000000000001e-292

   1. Initial program 99.2%

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

   3. Taylor expanded in y around 0 81.2%

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

   4. Taylor expanded in b around 0 72.6%

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

      1. exp-to-pow 73.2%

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

      2. sub-neg 73.2%

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

      3. metadata-eval 73.2%

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

      4. +-commutative 73.2%

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

   6. Simplified 73.2%

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

   7. Taylor expanded in t around 0 38.9%

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

      1. clear-num 38.9%

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

      2. associate-/r/ 39.0%

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

      3. *-commutative 39.0%

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

   9. Applied egg-rr 39.0%

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

   if 1.0000000000000001e-292 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 82.5%

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

   4. Taylor expanded in b around 0 60.1%

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

      1. exp-to-pow 60.4%

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

      2. sub-neg 60.4%

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

      3. metadata-eval 60.4%

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

      4. +-commutative 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in t around 0 27.6%

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

      1. clear-num 28.1%

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

      2. inv-pow 28.1%

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

      3. *-commutative 28.1%

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

   9. Applied egg-rr 28.1%

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

       1. unpow-1 28.1%

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

       2. *-commutative 28.1%

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

       3. associate-*r/ 32.8%

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

   11. Simplified 32.8%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{-b}{a}\\ \mathbf{elif}\;b \leq 10^{-292}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.96 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{-a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.96e+83)
   (* (/ x (- a)) (/ b y))
   (if (<= b 6e-287) (* x (/ 1.0 (* y a))) (/ 1.0 (* a (/ y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.96e+83) {
		tmp = (x / -a) * (b / y);
	} else if (b <= 6e-287) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	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 <= (-1.96d+83)) then
        tmp = (x / -a) * (b / y)
    else if (b <= 6d-287) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = 1.0d0 / (a * (y / x))
    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 <= -1.96e+83) {
		tmp = (x / -a) * (b / y);
	} else if (b <= 6e-287) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.96e+83:
		tmp = (x / -a) * (b / y)
	elif b <= 6e-287:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.96e+83)
		tmp = Float64(Float64(x / Float64(-a)) * Float64(b / y));
	elseif (b <= 6e-287)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.96e+83)
		tmp = (x / -a) * (b / y);
	elseif (b <= 6e-287)
		tmp = x * (1.0 / (y * a));
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.96e+83], N[(N[(x / (-a)), $MachinePrecision] * N[(b / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6e-287], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.96e83

   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%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 73.2%

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

      4. associate-/r* 73.2%

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

      5. *-commutative 73.2%

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

      6. exp-to-pow 73.2%

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

      7. exp-diff 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in t around 0 62.6%

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

      1. associate-/l* 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in y around 0 78.9%

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

   9. Taylor expanded in b around 0 46.4%

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

       1. +-commutative 46.4%

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

       2. mul-1-neg 46.4%

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

       3. unsub-neg 46.4%

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

       4. *-commutative 46.4%

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

       5. *-commutative 46.4%

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

       6. times-frac 40.0%

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

   11. Simplified 40.0%

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

   12. Taylor expanded in b around inf 46.4%

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

       1. associate-*r/ 46.4%

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

       2. *-commutative 46.4%

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

       3. neg-mul-1 46.4%

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

       4. distribute-lft-neg-in 46.4%

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

       5. times-frac 44.8%

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

       6. remove-double-neg 44.8%

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

       7. neg-mul-1 44.8%

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

       8. metadata-eval 44.8%

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

       9. times-frac 44.8%

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

       10. *-lft-identity 44.8%

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

       11. neg-mul-1 44.8%

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

       12. distribute-frac-neg 44.8%

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

       13. remove-double-neg 44.8%

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

   14. Simplified 44.8%

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

   if -1.96e83 < b < 5.99999999999999984e-287

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 82.9%

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

   4. Taylor expanded in b around 0 81.4%

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

      1. exp-to-pow 82.2%

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

      2. sub-neg 82.2%

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

      3. metadata-eval 82.2%

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

      4. +-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in t around 0 39.8%

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

      1. clear-num 39.7%

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

      2. associate-/r/ 39.8%

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

      3. *-commutative 39.8%

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

   9. Applied egg-rr 39.8%

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

   if 5.99999999999999984e-287 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 82.5%

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

   4. Taylor expanded in b around 0 60.1%

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

      1. exp-to-pow 60.4%

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

      2. sub-neg 60.4%

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

      3. metadata-eval 60.4%

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

      4. +-commutative 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in t around 0 27.6%

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

      1. clear-num 28.1%

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

      2. inv-pow 28.1%

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

      3. *-commutative 28.1%

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

   9. Applied egg-rr 28.1%

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

       1. unpow-1 28.1%

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

       2. *-commutative 28.1%

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

       3. associate-*r/ 32.8%

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

   11. Simplified 32.8%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.96 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{-a} \cdot \frac{b}{y}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-287}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 34.7% accurate, 18.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.5e+83)
   (/ (* x (- b)) (* y a))
   (if (<= b 9.8e-286) (* x (/ 1.0 (* y a))) (/ 1.0 (* a (/ y x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.5e+83) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 9.8e-286) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	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 <= (-5.5d+83)) then
        tmp = (x * -b) / (y * a)
    else if (b <= 9.8d-286) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = 1.0d0 / (a * (y / x))
    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 <= -5.5e+83) {
		tmp = (x * -b) / (y * a);
	} else if (b <= 9.8e-286) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.5e+83:
		tmp = (x * -b) / (y * a)
	elif b <= 9.8e-286:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.5e+83)
		tmp = Float64(Float64(x * Float64(-b)) / Float64(y * a));
	elseif (b <= 9.8e-286)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.5e+83)
		tmp = (x * -b) / (y * a);
	elseif (b <= 9.8e-286)
		tmp = x * (1.0 / (y * a));
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.5e+83], N[(N[(x * (-b)), $MachinePrecision] / N[(y * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.8e-286], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.4999999999999996e83

   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%

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

      2. associate--l+ 100.0%

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

      3. exp-sum 73.2%

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

      4. associate-/r* 73.2%

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

      5. *-commutative 73.2%

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

      6. exp-to-pow 73.2%

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

      7. exp-diff 50.0%

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

      8. *-commutative 50.0%

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

      9. exp-to-pow 50.0%

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

      10. sub-neg 50.0%

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

      11. metadata-eval 50.0%

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

   3. Simplified 50.0%

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

   5. Taylor expanded in t around 0 62.6%

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

      1. associate-/l* 62.6%

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

   7. Simplified 62.6%

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

   8. Taylor expanded in y around 0 78.9%

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

   9. Taylor expanded in b around 0 46.4%

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

       1. +-commutative 46.4%

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

       2. mul-1-neg 46.4%

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

       3. unsub-neg 46.4%

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

       4. *-commutative 46.4%

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

       5. *-commutative 46.4%

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

       6. times-frac 40.0%

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

   11. Simplified 40.0%

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

   12. Taylor expanded in b around inf 46.4%

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

   if -5.4999999999999996e83 < b < 9.8000000000000002e-286

   1. Initial program 99.0%

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

   3. Taylor expanded in y around 0 82.9%

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

   4. Taylor expanded in b around 0 81.4%

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

      1. exp-to-pow 82.2%

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

      2. sub-neg 82.2%

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

      3. metadata-eval 82.2%

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

      4. +-commutative 82.2%

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

   6. Simplified 82.2%

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

   7. Taylor expanded in t around 0 39.8%

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

      1. clear-num 39.7%

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

      2. associate-/r/ 39.8%

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

      3. *-commutative 39.8%

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

   9. Applied egg-rr 39.8%

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

   if 9.8000000000000002e-286 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 82.5%

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

   4. Taylor expanded in b around 0 60.1%

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

      1. exp-to-pow 60.4%

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

      2. sub-neg 60.4%

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

      3. metadata-eval 60.4%

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

      4. +-commutative 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in t around 0 27.6%

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

      1. clear-num 28.1%

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

      2. inv-pow 28.1%

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

      3. *-commutative 28.1%

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

   9. Applied egg-rr 28.1%

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

       1. unpow-1 28.1%

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

       2. *-commutative 28.1%

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

       3. associate-*r/ 32.8%

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

   11. Simplified 32.8%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{x \cdot \left(-b\right)}{y \cdot a}\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{-286}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 34.4% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.4e-274) (* (/ x (* y a)) (- 1.0 b)) (/ 1.0 (* a (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.4e-274) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	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 <= 3.4d-274) then
        tmp = (x / (y * a)) * (1.0d0 - b)
    else
        tmp = 1.0d0 / (a * (y / x))
    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 <= 3.4e-274) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.4e-274:
		tmp = (x / (y * a)) * (1.0 - b)
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.4e-274)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(1.0 - b));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.4e-274)
		tmp = (x / (y * a)) * (1.0 - b);
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.4e-274], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.39999999999999981e-274

   1. Initial program 99.3%

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

      1. associate-/l* 98.6%

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

      2. associate--l+ 98.6%

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

      3. exp-sum 80.1%

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

      4. associate-/r* 80.1%

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

      5. *-commutative 80.1%

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

      6. exp-to-pow 80.1%

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

      7. exp-diff 66.4%

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

      8. *-commutative 66.4%

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

      9. exp-to-pow 67.0%

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

      10. sub-neg 67.0%

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

      11. metadata-eval 67.0%

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

   3. Simplified 67.0%

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

   5. Taylor expanded in t around 0 60.1%

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

      1. associate-/l* 62.5%

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

   7. Simplified 62.5%

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

      1. *-un-lft-identity 62.5%

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

      2. associate-/r/ 62.5%

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

      3. times-frac 58.7%

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

   9. Applied egg-rr 58.7%

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

       1. associate-*l/ 58.7%

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

       2. *-lft-identity 58.7%

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

   11. Simplified 58.7%

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

   12. Taylor expanded in y around 0 56.3%

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

   13. Taylor expanded in b around 0 42.2%

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

       1. +-commutative 42.2%

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

       2. *-commutative 42.2%

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

       3. mul-1-neg 42.2%

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

       4. times-frac 37.2%

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

       5. *-commutative 37.2%

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

       6. sub-neg 37.2%

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

       7. *-rgt-identity 37.2%

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

       8. times-frac 42.2%

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

       9. associate-*l/ 40.8%

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

       10. distribute-lft-out-- 40.8%

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

       11. *-commutative 40.8%

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

   15. Simplified 40.8%

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

   if 3.39999999999999981e-274 < b

   1. Initial program 98.4%

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

   3. Taylor expanded in y around 0 82.1%

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

   4. Taylor expanded in b around 0 59.0%

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

      1. exp-to-pow 59.2%

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

      2. sub-neg 59.2%

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

      3. metadata-eval 59.2%

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

      4. +-commutative 59.2%

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

   6. Simplified 59.2%

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

   7. Taylor expanded in t around 0 26.9%

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

      1. clear-num 27.4%

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

      2. inv-pow 27.4%

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

      3. *-commutative 27.4%

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

   9. Applied egg-rr 27.4%

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

       1. unpow-1 27.4%

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

       2. *-commutative 27.4%

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

       3. associate-*r/ 32.3%

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

   11. Simplified 32.3%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.4 \cdot 10^{-274}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.1% accurate, 22.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 2 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2e-290) (* (/ x (* y a)) (- 1.0 b)) (/ (/ x (+ y (* y b))) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2e-290) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2d-290) then
        tmp = (x / (y * a)) * (1.0d0 - b)
    else
        tmp = (x / (y + (y * b))) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2e-290) {
		tmp = (x / (y * a)) * (1.0 - b);
	} else {
		tmp = (x / (y + (y * b))) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2e-290:
		tmp = (x / (y * a)) * (1.0 - b)
	else:
		tmp = (x / (y + (y * b))) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2e-290)
		tmp = Float64(Float64(x / Float64(y * a)) * Float64(1.0 - b));
	else
		tmp = Float64(Float64(x / Float64(y + Float64(y * b))) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2e-290)
		tmp = (x / (y * a)) * (1.0 - b);
	else
		tmp = (x / (y + (y * b))) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2e-290], N[(N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision] * N[(1.0 - b), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + N[(y * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.0000000000000001e-290

   1. Initial program 99.5%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 79.6%

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

      4. associate-/r* 79.6%

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

      5. *-commutative 79.6%

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

      6. exp-to-pow 79.6%

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

      7. exp-diff 65.5%

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

      8. *-commutative 65.5%

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

      9. exp-to-pow 65.9%

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

      10. sub-neg 65.9%

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

      11. metadata-eval 65.9%

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

   3. Simplified 65.9%

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

   5. Taylor expanded in t around 0 59.6%

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

      1. associate-/l* 62.1%

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

   7. Simplified 62.1%

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

      1. *-un-lft-identity 62.1%

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

      2. associate-/r/ 62.1%

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

      3. times-frac 58.1%

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

   9. Applied egg-rr 58.1%

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

       1. associate-*l/ 58.1%

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

       2. *-lft-identity 58.1%

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

   11. Simplified 58.1%

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

   12. Taylor expanded in y around 0 56.5%

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

   13. Taylor expanded in b around 0 41.9%

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

       1. +-commutative 41.9%

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

       2. *-commutative 41.9%

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

       3. mul-1-neg 41.9%

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

       4. times-frac 36.7%

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

       5. *-commutative 36.7%

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

       6. sub-neg 36.7%

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

       7. *-rgt-identity 36.7%

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

       8. times-frac 41.9%

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

       9. associate-*l/ 40.5%

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

       10. distribute-lft-out-- 40.5%

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

       11. *-commutative 40.5%

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

   15. Simplified 40.5%

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

   if 2.0000000000000001e-290 < b

   1. Initial program 98.3%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 74.5%

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

      4. associate-/r* 74.5%

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

      5. *-commutative 74.5%

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

      6. exp-to-pow 74.5%

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

      7. exp-diff 64.2%

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

      8. *-commutative 64.2%

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

      9. exp-to-pow 64.7%

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

      10. sub-neg 64.7%

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

      11. metadata-eval 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

      1. *-un-lft-identity 67.4%

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

      2. associate-/r/ 67.4%

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

      3. times-frac 65.8%

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

   9. Applied egg-rr 65.8%

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

       1. associate-*l/ 65.8%

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

       2. *-lft-identity 65.8%

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

   11. Simplified 65.8%

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

   12. Taylor expanded in y around 0 63.1%

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

   13. Taylor expanded in b around 0 39.5%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2 \cdot 10^{-290}:\\ \;\;\;\;\frac{x}{y \cdot a} \cdot \left(1 - b\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + y \cdot b}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 31.1% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.8 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.8e-289) (* x (/ 1.0 (* y a))) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.8e-289) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7.8d-289) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.8e-289) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.8e-289:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.8e-289)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7.8e-289)
		tmp = x * (1.0 / (y * a));
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.8e-289], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.7999999999999997e-289

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 86.8%

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

   4. Taylor expanded in b around 0 68.1%

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

      1. exp-to-pow 68.5%

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

      2. sub-neg 68.5%

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

      3. metadata-eval 68.5%

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

      4. +-commutative 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in t around 0 32.4%

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

      1. clear-num 32.4%

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

      2. associate-/r/ 32.4%

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

      3. *-commutative 32.4%

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

   9. Applied egg-rr 32.4%

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

   if 7.7999999999999997e-289 < b

   1. Initial program 98.3%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 74.5%

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

      4. associate-/r* 74.5%

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

      5. *-commutative 74.5%

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

      6. exp-to-pow 74.5%

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

      7. exp-diff 64.2%

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

      8. *-commutative 64.2%

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

      9. exp-to-pow 64.7%

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

      10. sub-neg 64.7%

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

      11. metadata-eval 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

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

      1. *-un-lft-identity 67.4%

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

      2. associate-/r/ 67.4%

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

      3. times-frac 65.8%

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

   9. Applied egg-rr 65.8%

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

       1. associate-*l/ 65.8%

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

       2. *-lft-identity 65.8%

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

   11. Simplified 65.8%

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

   12. Taylor expanded in y around 0 63.1%

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

   13. Taylor expanded in b around 0 31.2%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.8 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 31.4% accurate, 26.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 7.8 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 7.8e-284) (* x (/ 1.0 (* y a))) (/ 1.0 (* a (/ y x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.8e-284) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 7.8d-284) then
        tmp = x * (1.0d0 / (y * a))
    else
        tmp = 1.0d0 / (a * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 7.8e-284) {
		tmp = x * (1.0 / (y * a));
	} else {
		tmp = 1.0 / (a * (y / x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 7.8e-284:
		tmp = x * (1.0 / (y * a))
	else:
		tmp = 1.0 / (a * (y / x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 7.8e-284)
		tmp = Float64(x * Float64(1.0 / Float64(y * a)));
	else
		tmp = Float64(1.0 / Float64(a * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 7.8e-284)
		tmp = x * (1.0 / (y * a));
	else
		tmp = 1.0 / (a * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 7.8e-284], N[(x * N[(1.0 / N[(y * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(a * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 7.7999999999999994e-284

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 86.8%

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

   4. Taylor expanded in b around 0 68.1%

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

      1. exp-to-pow 68.5%

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

      2. sub-neg 68.5%

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

      3. metadata-eval 68.5%

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

      4. +-commutative 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in t around 0 32.4%

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

      1. clear-num 32.4%

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

      2. associate-/r/ 32.4%

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

      3. *-commutative 32.4%

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

   9. Applied egg-rr 32.4%

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

   if 7.7999999999999994e-284 < b

   1. Initial program 98.3%

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

   3. Taylor expanded in y around 0 82.5%

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

   4. Taylor expanded in b around 0 60.1%

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

      1. exp-to-pow 60.4%

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

      2. sub-neg 60.4%

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

      3. metadata-eval 60.4%

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

      4. +-commutative 60.4%

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

   6. Simplified 60.4%

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

   7. Taylor expanded in t around 0 27.6%

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

      1. clear-num 28.1%

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

      2. inv-pow 28.1%

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

      3. *-commutative 28.1%

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

   9. Applied egg-rr 28.1%

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

       1. unpow-1 28.1%

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

       2. *-commutative 28.1%

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

       3. associate-*r/ 32.8%

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

   11. Simplified 32.8%

       \[\leadsto \color{blue}{\frac{1}{a \cdot \frac{y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 7.8 \cdot 10^{-284}:\\ \;\;\;\;x \cdot \frac{1}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{a \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 32.4% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq 1.45 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a 1.45e-153) (/ (/ x a) y) (/ x (* y a))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.45e-153) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (a <= 1.45d-153) then
        tmp = (x / a) / y
    else
        tmp = x / (y * a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= 1.45e-153) {
		tmp = (x / a) / y;
	} else {
		tmp = x / (y * a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= 1.45e-153:
		tmp = (x / a) / y
	else:
		tmp = x / (y * a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= 1.45e-153)
		tmp = Float64(Float64(x / a) / y);
	else
		tmp = Float64(x / Float64(y * a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (a <= 1.45e-153)
		tmp = (x / a) / y;
	else
		tmp = x / (y * a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, 1.45e-153], N[(N[(x / a), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.45000000000000001e-153

   1. Initial program 99.4%

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

   3. Taylor expanded in y around 0 80.6%

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

   4. Taylor expanded in b around 0 64.1%

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

      1. exp-to-pow 64.5%

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

      2. sub-neg 64.5%

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

      3. metadata-eval 64.5%

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

      4. +-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in t around 0 33.2%

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

   if 1.45000000000000001e-153 < a

   1. Initial program 98.6%

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

   3. Taylor expanded in y around 0 86.0%

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

   4. Taylor expanded in b around 0 63.7%

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

      1. exp-to-pow 64.1%

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

      2. sub-neg 64.1%

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

      3. metadata-eval 64.1%

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

      4. +-commutative 64.1%

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

   6. Simplified 64.1%

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

   7. Taylor expanded in t around 0 31.0%

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

4. Final simplification 31.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.45 \cdot 10^{-153}:\\ \;\;\;\;\frac{\frac{x}{a}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 31.0% accurate, 31.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 3.5 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 3.5e-283) (/ x (* y a)) (/ (/ x y) a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.5e-283) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 3.5d-283) then
        tmp = x / (y * a)
    else
        tmp = (x / y) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 3.5e-283) {
		tmp = x / (y * a);
	} else {
		tmp = (x / y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 3.5e-283:
		tmp = x / (y * a)
	else:
		tmp = (x / y) / a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 3.5e-283)
		tmp = Float64(x / Float64(y * a));
	else
		tmp = Float64(Float64(x / y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 3.5e-283)
		tmp = x / (y * a);
	else
		tmp = (x / y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 3.5e-283], N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 3.4999999999999999e-283

   1. Initial program 99.5%

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

   3. Taylor expanded in y around 0 86.8%

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

   4. Taylor expanded in b around 0 68.1%

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

      1. exp-to-pow 68.5%

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

      2. sub-neg 68.5%

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

      3. metadata-eval 68.5%

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

      4. +-commutative 68.5%

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

   6. Simplified 68.5%

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

   7. Taylor expanded in t around 0 32.4%

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

   if 3.4999999999999999e-283 < b

   1. Initial program 98.3%

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

      1. associate-/l* 98.8%

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

      2. associate--l+ 98.8%

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

      3. exp-sum 74.5%

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

      4. associate-/r* 74.5%

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

      5. *-commutative 74.5%

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

      6. exp-to-pow 74.5%

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

      7. exp-diff 64.2%

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

      8. *-commutative 64.2%

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

      9. exp-to-pow 64.7%

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

      10. sub-neg 64.7%

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

      11. metadata-eval 64.7%

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

   3. Simplified 64.7%

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

   5. Taylor expanded in t around 0 65.9%

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

      1. associate-/l* 67.4%

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

   7. Simplified 67.4%

      \[\leadsto \frac{x}{\color{blue}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 67.4%

         \[\leadsto \frac{\color{blue}{1 \cdot x}}{\frac{a}{\frac{{z}^{y}}{y \cdot e^{b}}}} \]

      2. associate-/r/ 67.4%

         \[\leadsto \frac{1 \cdot x}{\color{blue}{\frac{a}{{z}^{y}} \cdot \left(y \cdot e^{b}\right)}} \]

      3. times-frac 65.8%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{{z}^{y}}} \cdot \frac{x}{y \cdot e^{b}}} \]

   9. Applied egg-rr 65.8%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{{z}^{y}}} \cdot \frac{x}{y \cdot e^{b}}} \]
   10. Step-by-step derivation

       1. associate-*l/ 65.8%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{x}{y \cdot e^{b}}}{\frac{a}{{z}^{y}}}} \]

       2. *-lft-identity 65.8%

          \[\leadsto \frac{\color{blue}{\frac{x}{y \cdot e^{b}}}}{\frac{a}{{z}^{y}}} \]

   11. Simplified 65.8%

       \[\leadsto \color{blue}{\frac{\frac{x}{y \cdot e^{b}}}{\frac{a}{{z}^{y}}}} \]

   12. Taylor expanded in y around 0 63.1%

       \[\leadsto \frac{\frac{x}{y \cdot e^{b}}}{\color{blue}{a}} \]

   13. Taylor expanded in b around 0 31.2%

       \[\leadsto \frac{\frac{x}{\color{blue}{y}}}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 3.5 \cdot 10^{-283}:\\ \;\;\;\;\frac{x}{y \cdot a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.3% accurate, 63.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y \cdot a} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ x (* y a)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = x / (y * a)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x / (y * a);
}

Python

def code(x, y, z, t, a, b):
	return x / (y * a)

Julia

function code(x, y, z, t, a, b)
	return Float64(x / Float64(y * a))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x / (y * a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x / N[(y * a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 84.5%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right) - b}}}{y} \]

4. Taylor expanded in b around 0 63.8%

   \[\leadsto \frac{x \cdot \color{blue}{e^{\log a \cdot \left(t - 1\right)}}}{y} \]
5. Step-by-step derivation

   1. exp-to-pow 64.2%

      \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(t - 1\right)}}}{y} \]

   2. sub-neg 64.2%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(t + \left(-1\right)\right)}}}{y} \]

   3. metadata-eval 64.2%

      \[\leadsto \frac{x \cdot {a}^{\left(t + \color{blue}{-1}\right)}}{y} \]

   4. +-commutative 64.2%

      \[\leadsto \frac{x \cdot {a}^{\color{blue}{\left(-1 + t\right)}}}{y} \]

6. Simplified 64.2%

   \[\leadsto \frac{x \cdot \color{blue}{{a}^{\left(-1 + t\right)}}}{y} \]

7. Taylor expanded in t around 0 29.8%

   \[\leadsto \color{blue}{\frac{x}{a \cdot y}} \]

8. Final simplification 29.8%

   \[\leadsto \frac{x}{y \cdot a} \]
9. Add Preprocessing

Developer target: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := {a}^{\left(t - 1\right)}\\ t_2 := \frac{x \cdot \frac{t\_1}{y}}{\left(b + 1\right) - y \cdot \log z}\\ \mathbf{if}\;t < -0.8845848504127471:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t < 852031.2288374073:\\ \;\;\;\;\frac{\frac{x}{y} \cdot t\_1}{e^{b - \log z \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (pow a (- t 1.0)))
        (t_2 (/ (* x (/ t_1 y)) (- (+ b 1.0) (* y (log z))))))
   (if (< t -0.8845848504127471)
     t_2
     (if (< t 852031.2288374073)
       (/ (* (/ x y) t_1) (exp (- b (* (log z) y))))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a ** (t - 1.0d0)
    t_2 = (x * (t_1 / y)) / ((b + 1.0d0) - (y * log(z)))
    if (t < (-0.8845848504127471d0)) then
        tmp = t_2
    else if (t < 852031.2288374073d0) then
        tmp = ((x / y) * t_1) / exp((b - (log(z) * y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = Math.pow(a, (t - 1.0));
	double t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * Math.log(z)));
	double tmp;
	if (t < -0.8845848504127471) {
		tmp = t_2;
	} else if (t < 852031.2288374073) {
		tmp = ((x / y) * t_1) / Math.exp((b - (Math.log(z) * y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.pow(a, (t - 1.0))
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * math.log(z)))
	tmp = 0
	if t < -0.8845848504127471:
		tmp = t_2
	elif t < 852031.2288374073:
		tmp = ((x / y) * t_1) / math.exp((b - (math.log(z) * y)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = a ^ Float64(t - 1.0)
	t_2 = Float64(Float64(x * Float64(t_1 / y)) / Float64(Float64(b + 1.0) - Float64(y * log(z))))
	tmp = 0.0
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = Float64(Float64(Float64(x / y) * t_1) / exp(Float64(b - Float64(log(z) * y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a ^ (t - 1.0);
	t_2 = (x * (t_1 / y)) / ((b + 1.0) - (y * log(z)));
	tmp = 0.0;
	if (t < -0.8845848504127471)
		tmp = t_2;
	elseif (t < 852031.2288374073)
		tmp = ((x / y) * t_1) / exp((b - (log(z) * y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[a, N[(t - 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] / N[(N[(b + 1.0), $MachinePrecision] - N[(y * N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -0.8845848504127471], t$95$2, If[Less[t, 852031.2288374073], N[(N[(N[(x / y), $MachinePrecision] * t$95$1), $MachinePrecision] / N[Exp[N[(b - N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024031 
(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))